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2023-05-26 | Sphaleron rate from a modified Backus-Gilbert inversion method | We compute the sphaleron rate in quenched QCD for a temperature $T \simeq
1.24~T_c$ from the inversion of the Euclidean lattice time correlator of the
topological charge density. We explore and compare two different strategies:
one follows a new approach proposed in this study and consists in extracting
the rate from finite lattice spacing correlators, and then in taking the
continuum limit at fixed smoothing radius followed by a zero-smoothing
extrapolation; the other follows the traditional approach of extracting the
rate after performing such double extrapolation directly on the correlator. In
both cases the rate is obtained from a recently-proposed modification of the
standard Backus-Gilbert procedure. The two strategies lead to compatible
estimates within errors, which are then compared to previous results in the
literature at the same or similar temperatures; the new strategy permits to
obtain improved results, in terms of statistical and systematic uncertainties. | 2305.17120v2 |
2023-07-21 | Visibility graph-based covariance functions for scalable spatial analysis in nonconvex domains | We present a new method for constructing valid covariance functions of
Gaussian processes over irregular nonconvex spatial domains such as water
bodies, where the geodesic distance agrees with the Euclidean distance only for
some pairs of points. Standard covariance functions based on geodesic distances
are not positive definite on such domains. Using a visibility graph on the
domain, we use the graphical method of "covariance selection" to propose a
class of covariance functions that preserve Euclidean-based covariances between
points that are connected through the domain. The proposed method preserves the
partially Euclidean nature of the intrinsic geometry on the domain while
maintaining validity (positive definiteness) and marginal stationarity over the
entire parameter space, properties which are not always fulfilled by existing
approaches to construct covariance functions on nonconvex domains. We provide
useful approximations to improve computational efficiency, resulting in a
scalable algorithm. We evaluate the performance of competing state-of-the-art
methods using simulation studies on a contrived nonconvex domain. The method is
applied to data regarding acidity levels in the Chesapeake Bay, showing its
potential for ecological monitoring in real-world spatial applications on
irregular domains. | 2307.11941v2 |
2023-08-23 | Consistency of common spatial estimators under spatial confounding | This paper addresses the asymptotic performance of popular spatial regression
estimators on the task of estimating the effect of an exposure on an outcome in
the presence of an unmeasured spatially-structured confounder. This setting is
often referred to as "spatial confounding." We consider spline models, Gaussian
processes (GP), generalized least squares (GLS), and restricted spatial
regression (RSR) under two data generation processes: one where the confounder
is a fixed effect and one where it is a random effect. The literature on
spatial confounding is confusing and contradictory, and our results correct and
clarify several misunderstandings. We first show that, like an unadjusted OLS
estimator, RSR is asymptotically biased under any spatial confounding scenario.
We then prove a novel result on the consistency of the GLS estimator under
spatial confounding. We finally prove that estimators like GLS, GP, and
splines, that are consistent under confounding by a fixed effect will also be
consistent under confounding by a random effect. We conclude that, contrary to
much of the recent literature on spatial confounding, traditional estimators
based on partially linear models are amenable to estimating effects in the
presence of spatial confounding. We support our theoretical arguments with
simulation studies. | 2308.12181v1 |
2023-09-19 | Stochastic control of the Landau-Lifshitz-Gilbert equation | We consider the stochastic Landau-Lifshitz-Gilbert equation in dimension 1. A
control process is added to the effective field. We show the existence of a
weak martingale solution for the resulting controlled equation. The proof uses
the classical Faedo-Galerkin approximation, along with the Jakubowski version
of the Skorohod Theorem. We then show pathwise uniqueness for the obtained
solution, which is then coupled with the theory of Yamada and Watanabe to give
the existence of a unique strong solution. We then show, using some semigroup
techniques that the obtained solution satisfies the maximum regularity. We then
show the existence of an optimal control. A main ingredient of the proof is
using the compact embedding of a space into itself, albeit with the weak
topology. | 2309.10260v1 |
2023-10-18 | Parallel-in-Time Integration of the Landau-Lifshitz-Gilbert Equation with the Parallel Full Approximation Scheme in Space and Time | Speeding up computationally expensive problems, such as numerical simulations
of large micromagnetic systems, requires efficient use of parallel computing
infrastructures. While parallelism across space is commonly exploited in
micromagnetics, this strategy performs poorly once a minimum number of degrees
of freedom per core is reached. We use magnum.pi, a finite-element
micromagnetic simulation software, to investigate the Parallel Full
Approximation Scheme in Space and Time (PFASST) as a space- and time-parallel
solver for the Landau-Lifshitz-Gilbert equation (LLG). Numerical experiments
show that PFASST enables efficient parallel-in-time integration of the LLG,
significantly improving the speedup gained from using a given number of cores
as well as allowing the code to scale beyond spatial limits. | 2310.11819v1 |
2023-12-29 | Chebyshev and Backus-Gilbert reconstruction for inclusive semileptonic $B_{(s)}$-meson decays from Lattice QCD | We present a study on the nonperturbative calculation of observables for
inclusive semileptonic decays of $B_{(s)}$ mesons using lattice QCD. We focus
on the comparison of two different methods to analyse the lattice data of
Euclidean correlation functions, specifically Chebyshev and Backus-Gilbert
approaches. This type of computation may eventually provide new insight into
the long-standing tension between the inclusive and exclusive determinations of
the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|V_{cb}|$ and $|V_{ub}|$.
We report the results from a pilot lattice computation for the decay $B_s
\rightarrow X_c \, l\nu_l$, where the valence quark masses are approximately
tuned to their physical values using the relativistic-heavy quark action for
the $b$ quark and the domain-wall formalism for the other valence quarks. We
address the computation of the total decay rate as well as leptonic and
hadronic moments, discussing similarities and differences between the two
analysis techniques. | 2312.17401v1 |
2024-02-22 | Gilbert-Varshamov Bound for Codes in $L_1$ Metric using Multivariate Analytic Combinatorics | Analytic combinatorics in several variables refers to a suite of tools that
provide sharp asymptotic estimates for certain combinatorial quantities. In
this paper, we apply these tools to determine the Gilbert--Varshamov lower
bound on the rate of optimal codes in $L_1$ metric. Several different code
spaces are analyzed, including the simplex and the hypercube in $\mathbb{Z^n}$,
all of which are inspired by concrete data storage and transmission models such
as the sticky insertion channel, the permutation channel, the adjacent
transposition (bit-shift) channel, the multilevel flash memory channel, etc. | 2402.14712v1 |
2024-02-28 | Embodied Supervision: Haptic Display of Automation Command to Improve Supervisory Performance | A human operator using a manual control interface has ready access to their
own command signal, both by efference copy and proprioception. In contrast, a
human supervisor typically relies on visual information alone. We propose
supplying a supervisor with a copy of the operators command signal,
hypothesizing improved performance, especially when that copy is provided
through haptic display. We experimentally compared haptic with visual access to
the command signal, quantifying the performance of N equals 10 participants
attempting to determine which of three reference signals was being tracked by
an operator. Results indicate an improved accuracy in identifying the tracked
target when haptic display was available relative to visual display alone. We
conjecture the benefit follows from the relationship of haptics to the
supervisor's own experience, perhaps muscle memory, as an operator. | 2402.18707v1 |
2024-03-14 | Quantum analog of Landau-Lifshitz-Gilbert dynamics | The Landau-Lifshitz-Gilbert (LLG) and Landau-Lifshitz (LL) equations play an
essential role for describing the dynamics of magnetization in solids. While a
quantum analog of the LL dynamics has been proposed in [Phys. Rev. Lett. 110,
147201 (2013)], the corresponding quantum version of LLG remains unknown. Here,
we propose such a quantum LLG equation that inherently conserves purity of the
quantum state. We examine the quantum LLG dynamics of a dimer consisting of two
interacting spin-1/2 particles. Our analysis reveals that, in the case of
ferromagnetic coupling, the evolution of initially uncorrelated spins mirrors
the classical LLG dynamics. However, in the antiferromagnetic scenario, we
observe pronounced deviations from classical behavior, underscoring the unique
dynamics of becoming a spinless state, which is non-locally correlated.
Moreover, when considering spins that are initially correlated, our study
uncovers an unusual form of transient quantum correlation dynamics, which
differ significantly from what is typically seen in open quantum systems. | 2403.09255v1 |
2024-03-15 | Identification and estimation of mediational effects of longitudinal modified treatment policies | We demonstrate a comprehensive semiparametric approach to causal mediation
analysis, addressing the complexities inherent in settings with longitudinal
and continuous treatments, confounders, and mediators. Our methodology utilizes
a nonparametric structural equation model and a cross-fitted sequential
regression technique based on doubly robust pseudo-outcomes, yielding an
efficient, asymptotically normal estimator without relying on restrictive
parametric modeling assumptions. We are motivated by a recent scientific
controversy regarding the effects of invasive mechanical ventilation (IMV) on
the survival of COVID-19 patients, considering acute kidney injury (AKI) as a
mediating factor. We highlight the possibility of "inconsistent mediation," in
which the direct and indirect effects of the exposure operate in opposite
directions. We discuss the significance of mediation analysis for scientific
understanding and its potential utility in treatment decisions. | 2403.09928v1 |
2024-03-22 | Two-scale Analysis for Multiscale Landau-Lifshitz-Gilbert Equation: Theory and Numerical Methods | This paper discusses the theory and numerical method of two-scale analysis
for the multiscale Landau-Lifshitz-Gilbert equation in composite ferromagnetic
materials. The novelty of this work can be summarized in three aspects:
Firstly, the more realistic and complex model is considered, including the
effects of the exchange field, anisotropy field, stray field, and external
magnetic field. The explicit convergence orders in the $H^1$ norm between the
classical solution and the two-scale solution are obtained. Secondly, we
propose a robust numerical framework, which is employed in several
comprehensive experiments to validate the convergence results for the Periodic
and Neumann problems. Thirdly, we design an improved implicit numerical scheme
to reduce the required number of iterations and relaxes the constraints on the
time step size, which can significantly improve computational efficiency.
Specifically, the projection and the expansion methods are given to overcome
the inherent non-consistency in the initial data between the multiscale problem
and homogenized problem. | 2403.14957v1 |
2020-11-30 | Role of Compressive Viscosity and Thermal Conductivity on the Damping of Slow Waves in the Coronal Loops With and Without Heating-Cooling Imbalance | In the present paper, we derive a new dispersion relation for slow
magnetoacoustic waves invoking the effect of thermal conductivity, compressive
viscosity, radiation and unknown heating term along with the consideration of
heating cooling imbalance from linearized MHD equations. We solve the general
dispersion relation to understand role of compressive viscosity and thermal
conductivity in damping of the slow waves in coronal loops with and without
heating cooling imbalance. We have analyzed wave damping for the range of loop
length $L$=50-500 Mm, temperature $T$=5-30 MK, and density
$\rho$=10$^{-11}$-10$^{-9}$ kg m$^{-3}$. It was found that inclusion of
compressive viscosity along with thermal conductivity significantly enhances
the damping of fundamental mode oscillations in shorter (e.g., $L$=50 Mm) and
super-hot ($T>$10 MK) loops. However, role of the viscosity in damping is
insignificant in longer (e.g., $L$=500 Mm) and hot loops (T$\leq$10 MK) where,
instead, thermal conductivity along with the presence of heating cooling
imbalance plays a dominant role. For the shorter loops at the super-hot regime
of the temperature, increment in loop density substantially enhances damping of
the fundamental modes due to thermal conductivity when the viscosity is absent,
however, when the compressive viscosity is added the increase in density
substantially weakens damping. Thermal conductivity alone is found to play a
dominant role in longer loops at lower temperatures (T$\leq$10 MK), while
compressive viscosity dominates in damping at super-hot temperatures ($T>$10
MK) in shorter loops. The predicted scaling law between damping time ($\tau$)
and wave period ($P$) is found to better match to observed SUMER oscillations
when heating cooling imbalance is taken into account in addition to thermal
conductivity and compressive viscosity for the damping of the fundamental slow
mode oscillations. | 2011.14519v2 |
1999-08-20 | The ac-Driven Motion of Dislocations in a Weakly Damped Frenkel-Kontorova Lattice | By means of numerical simulations, we demonstrate that ac field can support
stably moving collective nonlinear excitations in the form of dislocations
(topological solitons, or kinks) in the Frenkel-Kontorova (FK) lattice with
weak friction, which was qualitatively predicted by Bonilla and Malomed [Phys.
Rev. B{\bf 43}, 11539 (1991)]. Direct generation of the moving dislocations
turns out to be virtually impossible; however, they can be generated initially
in the lattice subject to an auxiliary spatial modulation of the on-site
potential strength. Gradually relaxing the modulation, we are able to get the
stable moving dislocations in the uniform FK lattice with the periodic boundary
conditions, provided that the driving frequency is close to the gap frequency
of the linear excitations in the uniform lattice. The excitations have a large
and noninteger index of commensurability with the lattice (suggesting that its
actual value is irrational). The simulations reveal two different types of the
moving dislocations: broad ones, that extend, roughly, to half the full length
of the periodic lattice (in that sense, they cannot be called solitons), and
localized soliton-like dislocations, that can be found in an excited state,
demonstrating strong persistent internal vibrations. The minimum (threshold)
amplitude of the driving force necessary to support the traveling excitation is
found as a function of the friction coefficient. Its extrapolation suggests
that the threshold does not vanish at the zero friction, which may be explained
by radiation losses. The moving dislocation can be observed experimentally in
an array of coupled small Josephson junctions in the form of an {\it inverse
Josephson effect}, i.e., a dc-voltage response to the uniformly applied ac bias
current. | 9908292v1 |
2003-06-19 | Quantum model of phonon transport and heat conductivity in carbon nanoclusters and nanotubes | A complex approach phonon quantum discrete model (PQDM) was developed to
describe dynamics, kinetics and statistics of phonons in carbon nanostructures
with zero-chirality of both zig-zag and armchair geometry. The model allows
include into the pure phonon problem existing interaction with others
subsystems: electrons, photons, impurities and defects. We predict that planar
C- structures are geometrically stable and may bridge interelectrode space in
strong external electric field. The exact solution of generalized thermal
conductivity (TC) equation was obtained for nanotubes. Temperature distribution
along the tube was derived analytically. The diagonalization procedure for the
case ofstrong ph-ph interaction was proposed. It was shown the quadratic
increasing of heat conductivity with the growth of the phonon mean free path
(PMFP). Heat capacitance and the entropy of carbon linear tubes were calculated
as the function of temperature. Our theoretical approach explains the nature of
good TC in carbon and carbon-like materials by existing of the soft vibration
branch (low frequency radial breathing mode phonons with high density of states
at thermal energies) accompanied by structure hardness (high frequency $\phi$-
and z-branches) providing big PMFP. TC coefficient for high conducting channel
in surrounding medium was calculated. The mechanism of heat conductivity
temperature damping was analyzed. Two competitive tendencies produce TC maximum
at intermediate temperatures (100-300)K. It was shown the strongly non-linear
increasing of effective heat conductivity with the growth nanotubes
concentration. It was shown that insertion of armchair nanotube inside a medium
or its coating by polyacetilene molecule considerably changes the structure of
radial breathing phonons. | 0306503v1 |
2005-02-11 | A Weakly Nonlinear Analysis of Impulsively-Forced Faraday Waves | Parametrically-excited surface waves, forced by a periodic sequence of
delta-function impulses, are considered within the framework of the
Zhang-Vi\~nals model (J. Fluid Mech. 1997). The exact impulsive-forcing
results, in the linear and weakly nonlinear regimes, are compared with
numerical results for sinusoidal and multifrequency forcing. We find
surprisingly good agreement between impulsive forcing results and those
obtained using a two-term truncated Fourier series representation of the
impulsive forcing function. As noted previously by Bechhoefer and Johnson (Am.
J. Phys. 1996), in the case of two equally-spaced impulses per period there are
only subharmonic modes of instability. The familiar situation of alternating
subharmonic and harmonic resonance tongues emerges for unequally-spaced
impulses. We extend the linear analysis for two impulses per period to the
weakly nonlinear regime for one-dimensional waves. Specifically, we derive an
analytic expression for the cubic Landau coefficient in the bifurcation
equation as a function of the dimensionless fluid parameters and spacing
between the two impulses. As the capillary parameter is varied, one finds a
parameter region of wave amplitude suppression, which is due to a familiar 1:2
spatio-temporal resonance between the subharmonic mode of instability and a
damped harmonic mode. This resonance occurs for impulsive forcing even when
harmonic resonance tongues are absent from the neutral stability curve. The
strength of this resonance feature can be tuned by varying the spacing between
the impulses. This finding is interpreted in terms of a recent symmetry-based
analysis of multifrequency forced Faraday waves by Porter, Topaz and Silber
(Phys. Rev. Lett. 2004, Phys. Rev. E 2004). | 0502025v1 |
2007-06-25 | Toward faithful templates for non-spinning binary black holes using the effective-one-body approach | We present an accurate approximation of the full gravitational radiation
waveforms generated in the merger of non-eccentric systems of two non-spinning
black holes. Utilizing information from recent numerical relativity simulations
and the natural flexibility of the effective-one-body (EOB) model, we extend
the latter so that it can successfully match the numerical relativity waveforms
during the last stages of inspiral, merger and ringdown. By ``successfully''
here, we mean with phase differences < 8% of a gravitational-wave cycle
accumulated by the end of the ringdown phase, maximizing only over time of
arrival and initial phase. We obtain this result by simply adding a
4-post-Newtonian order correction in the EOB radial potential and determining
the (constant) coefficient by imposing high-matching performances with
numerical waveforms of mass ratios m1/m2 = 1, 3/2, 2 and 4, m1 and m2 being the
individual black-hole masses. The final black-hole mass and spin predicted by
the numerical simulations are used to determine the ringdown frequency and
decay time of three quasi-normal-mode damped sinusoids that are attached to the
EOB inspiral-(plunge) waveform at the EOB light-ring. The EOB waveforms might
be tested and further improved in the future by comparison with extremely long
and accurate inspiral numerical-relativity waveforms. They may already be
employed for coherent searches and parameter estimation of gravitational waves
emitted by non-spinning coalescing binary black holes with ground-based
laser-interferometer detectors. | 0706.3732v3 |
2011-08-21 | Time-Dependent Behavior of Lyman$α$ Photon Transfer in High Redshift Optically Thick Medium | With Monte Carlo simulation method, we investigate the time dependent
behavior of Ly$\alpha$ photon transfer in optically thick medium of the
concordance $\Lambda$CDM universe. At high redshift, the Ly$\alpha$ photon
escaping from optically thick medium has a time scale as long as the age of the
luminous object, or even comparable to the age of the universe. In this case,
time-independent, or stationary solutions of the Ly$\alpha$ photon transfer
with resonant scattering will overlook important features of the escaped
Ly$\alpha$ photons in physical and frequency spaces. More seriously, the
expansion of the universe leads to that the time-independent solutions of the
Ly$\alpha$ photon transfer may not exist. We show that time-dependent solutions
sometimes are essential for understanding the Ly$\alpha$ emission and
absorption at high redshifts. For Ly\alpha photons from sources at redshift
1+z=10 and being surrounded by neutral hydrogen IGM of the $\Lambda$CDM
universe, the escape coefficient is found to be always less, or much less than
one, regardless of the age or life time of the sources. Under such environment,
we also find that even when the Ly$\alpha$ photon luminosity of the sources is
stable, the mean surface brightness is gradually increasing in the first 10^6
years, and then decreasing with a power law of time, but never approaches a
stable, time-independent state. That is, all 1+z=10 sources in a neutral Hubble
expanding IGM with Ly$\alpha$ luminosity L have their maximum of mean surface
brightness ~ 10^{-21}(L/(10^{43}erg/s)) erg s^{-1} cm^{-2} arcsec^{-2} at the
age of about 10^6 years. The time-dependent effects on the red damping wing
profile are also addressed. | 1108.4162v1 |
2011-09-03 | Magnetic Fields Effects on the Electronic Conduction Properties of Molecular Ring Structures | While mesoscopic conducting loops are sensitive to external magnetic fields,
as seen by observations of the Aharonov-Bohm (AB) effect in such structures,
the field needed to observe the AB periodicity in small molecular rings is
unrealistically large. The present study aims to identify conditions under
which magnetic field dependence can be observed in electronic conduction
through such molecules. We consider molecular ring structures modeled both
within the tight-binding (H\"uckel) model and as continuous rings. In fact,
much of the observed qualitative behavior can be rationalized in terms of a
much simpler two-state model. Dephasing in these models is affected by two
common tools: the B\"uttiker probe method and coherence damping within a
density matrix formulation. We show that current through a benzene ring can be
controlled by moderate fields provided that (a) conduction must be dominated by
degenerate (in the free molecule) molecular electronic resonances, associated
with multiple pathways as is often the case with ring molecules; (b)
molecular-leads electronic coupling must is weak so as to affect relatively
distinct conduction resonances; (c) molecular binding to the leads must be
asymmetric (e.g., for benzene, connection in the meta or ortho, but not para,
configurations) and, (d) dephasing has to be small. Under these conditions,
considerable sensitivity to an imposed magnetic field normal to the molecular
ring plane is found in benzene and other aromatic molecules. Interestingly, in
symmetric junctions (e.g. para connected benzene) a large sensitivity of the
transmission coefficient to magnetic field is not reflected in the
current-voltage characteristic. Although sensitivity to magnetic field is
suppressed by dephasing, quantitative estimates indicate that magnetic field
control can be observed under realistic condition. | 1109.0619v1 |
2012-04-01 | Resonance Broadening and Heating of Charged Particles in Magnetohydrodynamic Turbulence | The heating, acceleration, and pitch-angle scattering of charged particles by
MHD turbulence are important in a wide range of astrophysical environments,
including the solar wind, accreting black holes, and galaxy clusters. We
simulate the interaction of high-gyrofrequency test particles with fully
dynamical simulations of subsonic MHD turbulence, focusing on the parameter
regime with beta ~ 1, where beta is the ratio of gas to magnetic pressure. We
use the simulation results to calibrate analytical expressions for test
particle velocity-space diffusion coefficients and provide simple fits that can
be used in other work.
The test particle velocity diffusion in our simulations is due to a
combination of two processes: interactions between particles and magnetic
compressions in the turbulence (as in linear transit-time damping; TTD) and
what we refer to as Fermi Type-B (FTB) interactions, in which charged particles
moving on field lines may be thought of as beads spiralling around moving
wires. We show that test particle heating rates are consistent with a TTD
resonance which is broadened according to a decorrelation prescription that is
Gaussian in time. TTD dominates the heating for v_s >> v_A (e.g. electrons),
where v_s is the thermal speed of species s and v_A is the Alfven speed, while
FTB dominates for v_s << v_A (e.g. minor ions). Proton heating rates for beta ~
1 are comparable to the turbulent cascade rate. Finally, we show that velocity
diffusion of collisionless, large gyrofrequency particles due to large-scale
MHD turbulence does not produce a power-law distribution function. | 1204.0155v2 |
2012-07-18 | Quasinormal-mode spectrum of Kerr black holes and its geometric interpretation | There is a well-known, intuitive geometric correspondence between
high-frequency QNMs of Schwarzschild black holes and null geodesics that reside
on the light-ring : the real part of the mode's frequency relates to the
geodesic's orbital frequency, and the imaginary part of the frequency
corresponds to the Lyapunov exponent of the orbit. For slowly rotating black
holes, the QNM real frequency is a linear combination of a the orbit's
precessional and orbital frequencies, but the correspondence is otherwise
unchanged. In this paper, we find a relationship between the QNM frequencies of
Kerr black holes of arbitrary (astrophysical) spins and general spherical
photon orbits, which is analogous to the relationship for slowly rotating
holes. To derive this result, we first use the WKB approximation to compute
accurate algebraic expressions for large-l QNM frequencies. Comparing our WKB
calculation to the leading-order, geometric-optics approximation to scalar-wave
propagation in the Kerr spacetime, we then draw a correspondence between the
real parts of the parameters of a QNM and the conserved quantities of spherical
photon orbits. At next-to-leading order in this comparison, we relate the
imaginary parts of the QNM parameters to coefficients that modify the amplitude
of the scalar wave. With this correspondence, we find a geometric
interpretation to two features of the QNM spectrum of Kerr black holes: First,
for Kerr holes rotating near the maximal rate, a large number of modes have
nearly zero damping; we connect this characteristic to the fact that a large
number of spherical photon orbits approach the horizon in this limit. Second,
for black holes of any spins, the frequencies of specific sets of modes are
degenerate; we find that this feature arises when the spherical photon orbits
corresponding to these modes form closed (as opposed to ergodically winding)
curves. | 1207.4253v1 |
2013-03-18 | Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach | We apply adjoint-based sensitivity analysis to a time-delayed thermo-acoustic
system: a Rijke tube containing a hot wire. We calculate how the growth rate
and frequency of small oscillations about a base state are affected either by a
generic passive control element in the system (the structural sensitivity
analysis) or by a generic change to its base state (the base-state sensitivity
analysis). We illustrate the structural sensitivity by calculating the effect
of a second hot wire with a small heat release parameter. In a single
calculation, this shows how the second hot wire changes the growth rate and
frequency of the small oscillations, as a function of its position in the tube.
We then examine the components of the structural sensitivity in order to
determine the passive control mechanism that has the strongest influence on the
growth rate. We find that a force applied to the acoustic momentum equation in
the opposite direction to the instantaneous velocity is the most stabilizing
feedback mechanism. We also find that its effect is maximized when it is placed
at the downstream end of the tube. This feedback mechanism could be supplied,
for example, by an adiabatic mesh. We illustrate the base-state sensitivity by
calculating the effects of small variations in the damping factor, the
heat-release time-delay coefficient, the heat-release parameter, and the hot
wire location. The successful application of sensitivity analysis to
thermo-acoustics opens up new possibilities for the passive control of
thermo-acoustic oscillations by providing gradient information that can be
combined with constrained optimization algorithms in order to reduce linear
growth rates. | 1303.4267v2 |
2013-07-12 | Detection of Lyβauto-correlations and Lyα-Lyβ cross-correlations in BOSS Data Release 9 | The Lyman-$\beta$ forest refers to a region in the spectra of distant quasars
that lies between the rest-frame Lyman-$\beta$ and Lyman-$\gamma$ emissions.
The forest in this region is dominated by a combination of absorption due to
resonant Ly$\alpha$ and Ly$\beta$ scattering. When considering the 1D Ly$\beta$
forest in addition to the 1D Ly$\alpha$ forest, the full statistical
description of the data requires four 1D power spectra: Ly$\alpha$ and
Ly$\beta$ auto-power spectra and the Ly$\alpha$-Ly$\beta$ real and imaginary
cross-power spectra. We describe how these can be measured using an optimal
quadratic estimator that naturally disentangles Ly$\alpha$ and Ly$\beta$
contributions. Using a sample of approximately 60,000 quasar sight-lines from
the BOSS Data Release 9, we make the measurement of the one-dimensional power
spectrum of fluctuations due to the Ly$\beta$ resonant scattering. While we
have not corrected our measurements for resolution damping of the power and
other systematic effects carefully enough to use them for cosmological
constraints, we can robustly conclude the following: i) Ly$\beta$ power
spectrum and Ly$\alpha$-Ly$\beta$ cross spectra are detected with high
statistical significance; ii) the cross-correlation coefficient is $\approx 1$
on large scales; iii) the Ly$\beta$ measurements are contaminated by the
associated OVI absorption, which is analogous to the SiIII contamination of the
Ly$\alpha$ forest. Measurements of the Ly$\beta$ forest will allow extension of
the usable path-length for the Ly$\alpha$ measurements while allowing a better
understanding of the physics of intergalactic medium and thus more robust
cosmological constraints. | 1307.3403v4 |
2013-12-20 | Stability Boundaries for Resonant Migrating Planet Pairs | Convergent migration allows pairs of planet to become trapped into mean
motion resonances. Once in resonance, the planets' eccentricities grow to an
equilibrium value that depends on the ratio of migration time scale to the
eccentricity damping timescale, $K=\tau_a/\tau_e$, with higher values of
equilibrium eccentricity for lower values of $K$. For low equilibrium
eccentricities, $e_{eq}\propto K^{-1/2}$. The stability of a planet pair
depends on eccentricity so the system can become unstable before it reaches its
equilibrium eccentricity. Using a resonant overlap criterion that takes into
account the role of first and second order resonances and depends on
eccentricity, we find a function $K_{min}(\mu_p, j)$ that defines the lowest
value for $K$, as a function of the ratio of total planet mass to stellar mass
($\mu_p$) and the period ratio of the resonance defined as $P_1/P_2=j/(j+k)$,
that allows two convergently migrating planets to remain stable in resonance at
their equilibrium eccentricities. We scaled the functions $K_{min}$ for each
resonance of the same order into a single function $K_c$. The function $K_{c}$
for planet pairs in first order resonances is linear with increasing planet
mass and quadratic for pairs in second order resonances with a coefficient
depending on the relative migration rate and strongly on the planet to planet
mass ratio. The linear relation continues until the mass approaches a critical
mass defined by the 2/7 resonance overlap instability law and $K_c \to \infty$.
We compared our analytic boundary with an observed sample of resonant two
planet systems. All but one of the first order resonant planet pair systems
found by radial velocity measurements are well inside the stability region
estimated by this model. We calculated $K_c$ for Kepler systems without
well-constrained eccentricities and found only weak constraints on $K$. | 1312.6099v1 |
2014-04-10 | Electromagnetic effects in the pion dispersion relation at finite temperature | We investigate the charged-neutral pion self-energy difference at finite
temperature. Within Chiral Perturbation Theory we extend previous analysis in
the chiral and soft pion limits. Our analysis with physical masses leads to
additional contributions for temperatures typical of a meson gas, including a
momentum-dependent function for the self energy. In addition, a nonzero
imaginary part arises, which we define consistently in the Coulomb gauge and
comes from an infrared enhanced contribution due to thermal bath photons. For
distributions typical of a heavy-ion meson gas, the charged and neutral pion
masses and their difference depend on temperature through slowly increasing
functions. Chiral symmetry restoration is ultimately responsible for keeping
the corrections smooth and compatible with observed pion spectra. We study
phenomenological effects related to the electromagnetic damping leading to
corrections for transport coefficients and neutral-charged mean free times
differences. An important aspect is the connection with chiral symmetry
restoration through the relation of the pion mass difference with the
vector-axial spectral function difference, which holds at $T=0$ due to a sum
rule in the chiral and soft pion limits. We analyze the modifications of that
sum rule including nonzero pion masses and temperature, up to order $T^2$ and
$M_\pi^2$. Both effects produce terms making the pion mass difference grow
against chiral-restoring decreasing contributions. Finally, we analyze the
corrections to the previous ChPT and sum rule results within the resonance
saturation framework at finite temperature, including explicitly $\rho$ and
$a_1$ exchanges. Our results show that the ChPT result is robust at low and
intermediate temperatures, the leading corrections being of order $T^2
M_\pi^2/M_R^2$ with $M_R$ the involved resonance masses. | 1404.2746v3 |
2014-11-10 | Nonlinear Dynamics of Particles Excited by an Electric Curtain | The use of the electric curtain (EC) has been proposed for manipulation and
control of particles in various applications. The EC studied in this paper is
called the 2-phase EC, which consists of a series of long parallel electrodes
embedded in a thin dielectric surface. The EC is driven by an oscillating
electric potential of a sinusoidal form where the phase difference of the
electric potential between neighboring electrodes is 180 degrees. We
investigate the one- and two-dimensional nonlinear dynamics of a particle in an
EC field. The form of the dimensionless equations of motion is codimension two,
where the dimensionless control parameters are the interaction amplitude ($A$)
and damping coefficient ($\beta$). Our focus on the one-dimensional EC is
primarily on a case of fixed $\beta$ and relatively small $A$, which is
characteristic of typical experimental conditions. We study the nonlinear
behaviors of the one-dimensional EC through the analysis of bifurcations of
fixed points. We analyze these bifurcations by using Floquet theory to
determine the stability of the limit cycles associated with the fixed points in
the Poincar\'e sections. Some of the bifurcations lead to chaotic trajectories
where we then determine the strength of chaos in phase space by calculating the
largest Lyapunov exponent. In the study of the two-dimensional EC we
independently look at bifurcation diagrams of variations in $A$ with fixed
$\beta$ and variations in $\beta$ with fixed $A$. Under certain values of
$\beta$ and $A$, we find that no stable trajectories above the surface exists;
such chaotic trajectories are described by a chaotic attractor, for which the
the largest Lyapunov exponent is found. We show the well-known stable
oscillations between two electrodes come into existence for variations in $A$
and the transitions between several distinct regimes of stable motion for
variations in $\beta$. | 1411.2492v1 |
2015-04-20 | On the Riesz basis property of root vectors system for $2 \times 2$ Dirac type operators | The paper is concerned with the Riesz basis property of a boundary value
problem associated in $L^2[0,1] \otimes \mathbb{C}^2$ with the following $2
\times 2$ Dirac type equation $$ L y = -i B^{-1} y' + Q(x) y = \lambda y, \quad
B = \begin{pmatrix} b_1 & 0 \\ 0 & b_2 \end{pmatrix}, \quad y = \begin{pmatrix}
y_1 \\ y_2 \end{pmatrix}, \quad (1) $$ with a summable potential matrix $Q \in
L^1[0,1] \otimes \mathbb{C}^{2 \times 2}$ and $b_1 < 0 < b_2$. If $b_2 = -b_1
=1$ this equation is equivalent to one dimensional Dirac equation. It is proved
that the system of root functions of a linear boundary value problem
constitutes a Riesz basis in $L^2[0,1] \otimes \mathbb{C}^2$ provided that the
boundary conditions are strictly regular.
By analogy with the case of ordinary differential equations, boundary
conditions are called strictly regular if the eigenvalues of the corresponding
unperturbed $(Q=0)$ operator are asymptotically simple and separated. As
distinguished from the Dirac case there is no simple algebraic criterion of the
strict regularity whenever $b_1 + b_2 \not = 0$. However under certain
restrictions on coefficients of the boundary linear forms we present certain
algebraic criteria of the strict regularity in the latter case. In particular,
it is shown that regular separated boundary conditions are always strictly
regular while periodic (antiperiodic) boundary conditions are strictly regular
if and only if $b_1 + b_2 \not = 0.$
The proof of the main result is based on existence of triangular
transformation operators for system (1). Their existence is also established
here in the case of a summable $Q$. In the case of regular (but not strictly
regular) boundary conditions we prove the Riesz basis property with
parentheses. The main results are applied to establish the Riesz basis property
of the dynamic generator of spatially non-homogenous damped Timoshenko beam
model. | 1504.04954v2 |
2015-10-14 | Fermi surface versus Fermi sea contributions to intrinsic anomalous and spin Hall effects of multiorbital metals in the presence of Coulomb interaction and spin-Coulomb drag | Anomalous Hall effect (AHE) and spin Hall effect (SHE) are fundamental
phenomena, and their potential for application is great. However, we understand
the interaction effects unsatisfactorily, and should have clarified issues
about the roles of the Fermi sea term and Fermi surface term of the
conductivity of the intrinsic AHE or SHE of an interacting multiorbital metal
and about the effects of spin-Coulomb drag on the intrinsic SHE. Here we
resolve the first issue and provide the first step about the second issue by
developing a general formalism in the linear response theory with appropriate
approximations and using analytic arguments. The most striking result is that
even without impurities the Fermi surface term, a non-Berry-curvature term,
plays dominant roles at high or slightly low temperatures. In particular, this
Fermi surface term causes the temperature dependence of the dc anomalous Hall
or spin Hall conductivity due to the interaction-induced quasiparticle damping
and the correction of the dc spin Hall conductivity due to the spin-Coulomb
drag. Those results revise our understanding of the intrinsic AHE and SHE. We
also find that the differences between the dc anomalous Hall and longitudinal
conductivities arise from the difference in the dominant multiband excitations.
This not only explains why the Fermi sea term such as the Berry-curvature term
becomes important in clean and low-temperature case only for interband
transports but also provides the useful principles on treating the
electron-electron interaction in an interacting multiorbital metal for general
formalism of transport coefficients. Several correspondences between our
results and experiments are finally discussed. | 1510.03988v5 |
2016-05-02 | Cosmic Galaxy-IGM HI Relation at ${\it{z}}\sim 2-3$ Probed in the COSMOS/UltraVISTA $1.6$ deg$^2$ Field | We present spatial correlations of galaxies and IGM HI in the
COSMOS/UltraVISTA 1.62 deg$^2$ field. Our data consist of 13,415 photo-$z$
galaxies at $z\sim2-3$ with $K_s<23.4$ and the Ly$\alpha$ forest absorptions in
the background quasar spectra selected from SDSS data with no signature of
damped Ly$\alpha$ system contamination. We estimate a galaxy overdensity
$\delta_{gal}$ in an impact parameter of 2.5 pMpc, and calculate the Ly$\alpha$
forest fluctuations $\delta_{\langle F\rangle}$ whose negative values
correspond to the strong Ly$\alpha$ forest absorptions. We identify weak
evidence of an anti-correlation between $\delta_{gal}$ and $\delta_{\langle
F\rangle}$ with a Spearman's rank correlation coefficient of $-0.39$ suggesting
that the galaxy overdensities and the Ly$\alpha$ forest absorptions positively
correlate in space at the $\sim90\%$ confidence level. This positive
correlation indicates that high-$z$ galaxies exist around an excess of HI gas
in the Ly$\alpha$ forest. We find four cosmic volumes, dubbed
$A_{obs}$-$D_{obs}$, that have extremely large (small) values of $\delta_{gal}
\simeq0.8$ ($-1$) and $\delta_{\langle F\rangle}$ $\simeq0.1$ ($-0.4$), three
out of which, $B_{obs}$-$D_{obs}$, significantly depart from the correlation,
and weaken the correlation signal. We perform cosmological hydrodynamical
simulations, and compare with our observational results. Our simulations
reproduce the correlation, agreeing with the observational results. Moreover,
our simulations have model counterparts of $A_{obs}$-$D_{obs}$, and suggest
that the observations pinpoint, by chance, a galaxy overdensity like a
proto-cluster, gas filaments lying on the sightline, a large void, and
orthogonal low-density filaments. Our simulations indicate that the significant
departures of $B_{obs}$-$D_{obs}$ are produced by the filamentary large-scale
structures and the observation sightline effects. | 1605.00379v3 |
2016-10-19 | New scenario of turbulence theory and wall-bounded turbulence: Theoretical significance | General scenario of turbulence theory is proposed and applied to streaky
wall-bounded turbulence. This scenario introduces a new field of transverse
waves. Significance of the theory rests on a mathematical theorem associated
with the conservation law of current flux, expressed in a form of 4d physical
space-time representation, which predicts a system of Maxwell-type equation and
supports transverse waves traveling with a phase speed c_t. In regard to the
streaky wall flows, there exist both dynamical mechanism and energy channel
which excite transverse waves and exchange energy between flow field and wave
field. Energy is supplied from the flow field to the wave field if wavelengths
are sufficiently large. The waves are accompanied with a new mechanism of
energy dissipation, an internal friction analogous to the Ohm's effect. Some
part of the energy is dissipated into heat. Thus, there exists a sustaining
mechanism, which implies that the streaky structure of wall-bounded turbulence
is a dissipative structure.
The predictions are consistent with experimental observations of wall
turbulence: (i) Existence of traveling waves: The waves are characterized by
two scales of wavelength and a damping-length d. (ii) Existence of two large
scales (LSM and VLSM) observed in turbulent shear flows: Those are interpreted
by the waves amplified with the transient growth mechanism and maintained by
interaction with the new transverse wave field. The waves are robust since they
have their own energy and momentum. (iii) Enhanced energy dissipation in wavy
turbulence. Its bulk rate of energy dissipation takes a form resembling the
models of eddy-viscosity, and its coefficient \nu_D is estimated to be of the
order of c_t d and much larger than the molecular viscosity.
No self-contradiction is incurred by the new field introduced. | 1610.05975v2 |
2016-11-22 | The cross-correlation between 21cm intensity mapping maps and the Lyman-alpha forest in the post-reionization era | We investigate the cross-correlation signal between 21cm intensity mapping
maps and the Lyman-alpha forest in the fully non-linear regime using
state-of-the-art hydrodynamic simulations. The cross-correlation signal between
these fields can provide a coherent and comprehensive picture of the neutral
hydrogen (HI) content of our Universe in the post-reionization era, probing
both its mass content and volume distribution. We compute the auto-power
spectra of both fields together with their cross-power spectrum at z = 2.4 and
find that on large scales the fields are completely anti-correlated. This
anti-correlation arises because regions with high (low) 21cm emission, such as
those with a large (low) concentration of damped Lyman-alpha systems, will show
up as regions with low (high) transmitted flux. We find that on scales smaller
than k = 0.2 h/Mpc the cross-correlation coefficient departs from -1, at a
scale where non-linearities show up. We use the anisotropy of the power spectra
in redshift-space to determine the values of the bias and of the redshift-space
distortion parameters of both fields; we find that the errors on the value of
these parameters could decrease by 30% when adding data from the cross-power
spectrum in a conservative analysis. Our results point out that linear theory
is capable of reproducing the shape and amplitude of the cross-power up to
rather non-linear scales. Finally, we find that the 21cm-Lya cross-power
spectrum can be detected by combining data from a BOSS-like survey together
with 21cm intensity mapping observations by SKA1-MID with a S/N ratio higher
than 3 in the range 0.06< k <1 h/Mpc. We emphasize that while the shape and
amplitude of the 21cm auto-power spectrum can be severely affected by residual
foreground contamination, cross-power spectra will be less sensitive to that
and therefore can be used to identify systematics in the 21cm maps. | 1611.07527v2 |
2017-02-02 | Bouncing on Titan: Motion of the Huygens Probe in the Seconds After Landing | While landing on Titan, several instruments onboard Huygens acquired
measurements that indicate the probe did not immediately come to rest. Detailed
knowledge of the probe's motion can provide insight into the nature of Titan's
surface. Combining accelerometer data from the Huygens Atmospheric Structure
Instrument (HASI) and the Surface Science Package (SSP) with photometry data
from the Descent Imager/Spectral Radiometer (DISR) we develop a quantitative
model to describe motion of the probe, and its interaction with the surface.
The most likely scenario is the following. Upon impact, Huygens created a 12 cm
deep hole in the surface of Titan. It bounced back, out of the hole onto the
flat surface, after which it commenced a 30-40 cm long slide in the southward
direction. The slide ended with the probe out of balance, tilted in the
direction of DISR by around 10 degrees. The probe then wobbled back and forth
five times in the north-south direction, during which it probably encountered a
1-2 cm sized pebble. The SSP provides evidence for movement up to 10 s after
impact. This scenario puts the following constraints on the physical properties
of the surface. For the slide over the surface we determine a friction
coefficient of 0.4. While this value is not necessarily representative for the
surface itself due to the presence of protruding structures on the bottom of
the probe, the dynamics appear to be consistent with a surface consistency of
damp sand. Additionally, we find that spectral changes observed in the first
four seconds after landing are consistent with a transient dust cloud, created
by the impact of the turbulent wake behind the probe on the surface. The
optical properties of the dust particles are consistent with those of Titan
aerosols from Tomasko et al. (P&SS 56, 669). We suggest that the surface at the
landing site was covered by a dust layer, possibly the 7 mm layer of... | 1702.00667v1 |
2017-06-26 | Parsing spatiotemporal dynamical stability in ECoG during seizure onset, propagation, and termination | Understanding brain dynamics in epilepsy is critical for establishing
rigorous control objectives that enable new therapeutic methods to mitigate
seizure occurrence. In multichannel electrocorticography (ECoG) recordings
acquired in 21 subjects during a total of 94 seizures, we apply dynamical
systems stability analysis to assess the balance versus imbalance of seizure
dynamics across different timescales and brain regions. Specifically, we
consider a sliding time window multivariate autoregressive linear approximation
of the data captured by the ECoG channels, where eigendecomposition of the
estimated matrix of coefficients describes the contribution of different
regions to the spatiotemporal process (eigenvectors) associated with a
particular timescale (eigenvalues). Interestingly, we observe a pattern of
eigenvalue evolution and slowly changing (or approximately time-invariant)
eigenvectors across both seizures and subjects. The seizure-onset is marked by
an increase in high frequency spatial information to which a few regions
contribute for a long period. By contrast, the seizure termination is
characterized by a sudden, small time period change in dynamics to which many
regions contribute. As the seizure terminates, the relatively stable ictal
dynamics rapidly transition into the post-ictal regime, marked by relatively
fast-damping oscillations. Our methodology offers a subject-specific
characterization of the spatiotemporal behavior of the seizure, providing new
insights into the dynamic patterns and functional interactions between brain
regions that occur over different timescales. More generally, our approach
informs the development of engineering objectives that can be used to deploy
new control strategies to prevent seizure evolution or to hasten seizure
termination. | 1706.08202v1 |
2017-10-05 | Cross section alignment of polycyclic aromatic hydrocarbons by anisotropic radiation | We study the effect of anisotropic radiation illumination on the alignment of
polycyclic aromatic hydrocarbons (PAHs) and report that cross-sectional
mechanism of alignment earlier considered in terms of gas-grain interactions
can also be efficient for the photon-grain interaction. We demonstrate this by
first calculating the angle-dependence rotational damping and excitation
coefficients by photon absorption followed by infrared emission. We then
calculate the degree of PAH alignment for the different environments and
physical parameters, including the illumination direction, ionization fraction,
and magnetic field strength. For the reflection nebula (RN) conditions with
unidirectional radiation field, we find that the degree of alignment tends to
increase with increasing the angle $\psi$ between the illumination direction
and the magnetic field, as a result of the decrease of the cross-section of
photon absorption with $\psi$. We calculate the polarization of spinning PAH
emission using the obtained degree of alignment for the different physical
parameters, assuming constant grain temperatures. We find that the polarization
of spinning PAH emission from RN can be large, between $5-20~\%$ at frequencies
$\nu > 20$ GHz, whereas the polarization is less than $3~\%$ for
photodissociation regions (PDRs). In realistic conditions, the polarization is
expected to be lower due to grain temperature fluctuations and magnetic field
geometry. The polarization for the diffuse cold neutral medium (CNM) is rather
low, below $1~\%$ at $\nu>20$ GHz, consistent with observations by WMAP and
Planck. Our results demonstrate that the RNe are the favored environment to
observe the polarization of spinning dust emission as well as polarized mid-IR
emission from PAHs. | 1710.01835v2 |
2018-06-01 | Kinetic Model for Stochastic Heating in the INCA Discharge | A novel electron heating mechanism based on periodically structured vortex
fields induced in a plane was first proposed in 2014 [U. Czarnetzki and Kh.
Tarnev, Physics of Plasmas 21, 123508 (2014)]. This theoretical concept has now
been realized in an experiment which confirms efficient collisionless heating
in such array structures [Ph. Ahr, T.V. Tsankov, J. Kuhfeld, U. Czarnetzki,
submitted to Plasma Sources Science and Technology, arXiv:1806.02043v1 (2018)].
The new concept is called "Inductively Coupled Array": INCA. Here, the physical
mechanism behind the collisionless (stochastic) heating is investigated by two
analytical models. Firstly, the electron heating rate in an array field
structure with an exponential spatial decay of the field in the direction
perpendicular to the plane is investigated by stochastically averaging single
electron trajectories. The approach is similar to the Lieberman model for the
classical stochastic heating in standard inductively coupled plasmas. This
analysis shows that classical stochastic heating by thermal motion along the
vertical direction makes a negligible contribution. However, there is a strong
collisonless non-local heating effect in the plane. In conclusion, heating is
non-local in the plane but local in the vertical direction. This insight allows
a straightforward solution of the collisionless Boltzmann equation which not
only confirms the results of the Lieberman model but provides also explicit
expressions for the complex conductivity. Based on the conductivity an
effective stochastic collision frequency, the complex damping coefficient and
the related field penetration of the field into the plasma is calculated.
Finally, elastic collisions with neutral background atoms are included in the
model and a condition for dominance of stochastic heating over Ohmic heating is
derived. | 1806.00505v2 |
2019-01-09 | Wave heating in gravitationally stratified coronal loops in the presence of resistivity and viscosity | In recent years, coronal loops have been the focus of studies related to the
damping of different magnetohydrodynamic (MHD) surface waves and their
connection with coronal seismology and wave heating. For a better understanding
of wave heating, we need to take into account the effects of different
dissipation coefficients such as resistivity and viscosity, the importance of
the loop physical characteristics, and the ways gravity can factor into the
evolution of these phenomena. We aim to map the sites of energy dissipation
from transverse waves in coronal loops in the presence and absence of
gravitational stratification and to compare ideal, resistive, and viscous MHD.
Using the PLUTO code, we performed 3D MHD simulations of kink waves in single,
straight, density-enhanced coronal flux tubes of multiple temperatures. We see
the creation of spatially expanded Kelvin-Helmholtz eddies along the loop,
which deform the initial monolithic loop profile. For the case of driven
oscillations, the Kelvin-Helmholtz instability develops despite physical
dissipation, unless very high values of shear viscosity are used. Energy
dissipation gets its highest values near the apex, but is present all along the
loop. We observe an increased efficiency of wave heating once the kinetic
energy saturates at the later stages of the simulation and a turbulent density
profile has developed. The inclusion of gravity greatly alters the dynamic
evolution of our systems and should not be ignored in future studies. Stronger
physical dissipation leads to stronger wave heating in our set-ups. Finally,
once the kinetic energy of the oscillating loop starts saturating, all the
excess input energy turns into internal energy, resulting in more efficient
wave heating. | 1901.02676v2 |
2019-01-31 | Analysis and active control of geometrically nonlinear responses of smart FG porous plates with graphene nanoplatelets reinforcement based on Bézier extraction of NURBS | In this paper, we propose an effective computational approach to analyze and
active control of geometrically nonlinear responses of functionally graded (FG)
porous plates with graphene nanoplatelets (GPLs) reinforcement integrated with
piezoelectric layers. The key concept behind this work is to utilize
isogeometric analysis (IGA) based on B\'ezier extraction technique and
$C^0$-type higher-order shear deformation theory ($C^0$-HSDT). By applying
B\'ezier extraction, the original Non-Uniform Rational B-Spline (NURBS) control
meshes can be transformed into B\'ezier elements which allow us to inherit the
standard numerical procedure like the standard finite element method (FEM). In
this scenario, the approximation of mechanical displacement field is calculated
via $C^0$-HSDT whilst the electric potential field is considered as a linear
function across the thickness of each piezoelectric sublayer. The FG plate
includes internal pores and GPLs dispersed into metal matrix either uniformly
or non-uniformly along plate's thickness. To control responses of structures,
the top and bottom surfaces of FG plate are firmly bonded with piezoelectric
layers which are considered as sensor and actuator layers. The geometrically
nonlinear equations are solved by Newton-Raphson iterative procedure and
Newmark's integration. The influence of porosity coefficient, weight fraction
of GPLs as well as external electrical voltage on geometrically nonlinear
behaviors of plate structures with various distributions of porosity and GPLs
are thoroughly investigated. A constant displacement and velocity feedback
control approaches are then adopted to actively control geometrically nonlinear
static and dynamic responses, where structural damping effect is taken into
account, based on a closed-loop control with sensor and actuator layers. | 1902.10806v2 |
2019-04-18 | Cosmic-ray transport from AMS-02 B/C data: benchmark models and interpretation | This article aims at establishing new benchmark scenarios for Galactic
cosmic-ray propagation in the GV-TV rigidity range, based on fits to the AMS-02
B/C data with the USINE v3.5 propagation code. We employ a new fitting
procedure, cautiously taking into account data systematic error correlations in
different rigidity bins and considering Solar modulation potential and leading
nuclear cross-section as nuisance parameters. We delineate specific low,
intermediate, and high-rigidity ranges that can be related to both features in
the data and peculiar microphysics mechanisms resulting in spectral breaks. We
single out a scenario which yields excellent fits to the data and includes all
the presumably relevant complexity, the BIG model. This model has two limiting
regimes: (i) the SLIM model, a minimal diffusion-only setup, and (ii) the
QUAINT model, a convection-reacceleration model where transport is tuned by
non-relativistic effects. All models lead to robust predictions in the
high-energy regime ($\gtrsim10$GV), i.e. independent of the propagation
scenario: at $1\sigma$, the diffusion slope $\delta$ is $[0.43-0.53]$, whereas
$K_{10}$, the diffusion coefficient at 10GV, is $[0.26-0.36]$kpc$^2$Myr$^{-1}$;
we confirm the robustness of the high-energy break, with a typical value
$\Delta_h\sim 0.2$. We also find a hint for a similar (reversed) feature at low
rigidity around the B/C peak ($\sim 4$GV) which might be related to some
effective damping scale in the magnetic turbulence. | 1904.08917v2 |
2019-05-06 | Formation and decay of eddy currents generated by crossed surface waves | The mass-transport induced by crossed surface waves consists of the Stokes
and Euler contributions which are very different in nature. The first
contribution is a generalization of Stokes drift for a plane wave in ideal
fluid and the second contribution arises due to the fluid viscosity and it is
excited by a force applied in the viscous sublayer near the fluid surface. We
study the formation and decay of the induced mass-transport theoretically and
experimentally and demonstrate that both contributions have different time
scales for typical experimental conditions. The evolution of the Euler
contribution is described by a diffusion equation, where the fluid kinematic
viscosity plays the role of the diffusion coefficient, while the Stokes
contribution evolves faster, feeling the additional damping near the system
boundaries. The difference becomes more pronounced if the fluid surface is
contaminated. We model the effect of contamination by a thin insoluble liquid
film presented on the fluid surface with the compression modulus being the only
non-zero rheological parameter of the film. Then the Euler contribution into
the mass-transport becomes parametrically larger and the evolution of the
Stokes contribution becomes parametrically faster. The parameter is the same in
both cases and it is equal to the quality factor of surfaces waves, which is
modified by the presence of a surface film. We infer the value of the
compression modulus of the film by fitting the results of transient
measurements of eddy currents and demonstrate that the obtained value leads to
the correct ratio of amplitudes of horizontal and vertical velocities of the
wave motion and is in reasonable agreement with the measured dissipation rate
of surface waves. | 1905.01875v2 |
2019-10-30 | A priori bounds for the $Φ^4$ equation in the full sub-critical regime | We derive a priori bounds for the $\Phi^4$ equation in the full sub-critical
regime using Hairer's theory of regularity structures. The equation is formally
given by \begin{equation} \label{e}(\partial_t-\Delta)\phi = -\phi^3 + \infty
\phi +\xi, \tag{$\star$} \end{equation} where the term $+\infty \phi$
represents infinite terms that have to be removed in a renormalisation
procedure. We emulate fractional dimensions $d<4$ by adjusting the regularity
of the noise term $\xi$, choosing $\xi \in C^{-3+\delta}$. Our main result
states that if $\phi$ satisfies this equation on a space-time cylinder $P=
(0,1) \times \{ |x| \leq 1 \}$, then away from the boundary $\partial P$ the
solution $\phi$ can be bounded in terms of a finite number of explicit
polynomial expressions in $\xi$, and this bound holds uniformly over all
possible choices of boundary data for $\phi$. The derivation of this bound
makes full use of the super-linear damping effect of the non-linear term
$-\phi^3$. A key part of our analysis consists of an appropriate re-formulation
of the theory of regularity structures in the specific context of \eqref{e},
which allows to couple the small scale control one obtains from this theory
with a suitable large scale argument. Along the way we make several new
observations and simplifications. Instead of a model $(\Pi_x)_x$ and the family
of translation operators $(\Gamma_{x,y})_{x,y}$ we work with just a single
object $(\mathbb{X}_{x, y})$ which acts on itself for translations, very much
in the spirit of Gubinelli's theory of branched rough paths. Furthermore, we
show that in the specific context of \eqref{e} the hierarchy of continuity
conditions which constitute Hairer's definition of a \emph{modelled
distribution} can be reduced to the single continuity condition on the
"coefficient on the constant level". | 1910.13854v2 |
2019-11-18 | Wave measurements from ship mounted sensors in the Arctic marginal ice zone | Increased research interest and economic activity in the Arctic raise the
need for new observations of sea ice dynamics. Remote sensing as well as
mathematical and numerical models of wave propagation in sea ice would benefit
from more in situ data for validation. This study presents wave measurements in
the marginal ice zone (MIZ) obtained from ship mounted sensors. The system
combines altimeter readings from the ship bow with ship motion correction data
to provide estimated single point ocean surface elevation. Significant wave
height and mean wave period, as well as one-dimensional wave spectra are
derived from the combined measurements. The results are compared with
integrated parameters from a spectral wave model over a period of eight days in
the open ocean, and with spectra and integrated parameters derived from motion
detecting instruments placed on ice floes inside the MIZ. Mean absolute errors
of the integrated parameters are in the range 15.0-18.9% when comparing with
the spectral wave model and 1.0-9.6% when comparing with valid motion detecting
instruments. The spatial wave damping coefficient is estimated by looking at
the change in spectral wave amplitude found at discrete frequency values as the
ship was moving along the longitudinal direction of the MIZ within time
intervals where the wave field is found to be approximately constant in time.
As expected from theory, high frequency waves are effectively dampened by the
presence of sea ice. The observed wave attenuation rates compare favourably
with a two-layer dissipation model. Our methodology can be regarded as a simple
and reliable way to collect more waves-in-ice data as it can be easily added to
any ship participating to ice expeditions, at little extra cost. | 1911.07612v2 |
2020-08-02 | Phase Diagram, Stability and Magnetic Properties of Nonlinear Excitations in Spinor Bose-Einstein Condensates | We present the phase diagram, the underlying stability and magnetic
properties as well as the dynamics of nonlinear solitary wave excitations
arising in the distinct phases of a harmonically confined spinor $F=1$
Bose-Einstein condensate. Particularly, it is found that nonlinear excitations
in the form of dark-dark-bright solitons exist in the antiferromagnetic and in
the easy-axis phase of a spinor gas, being generally unstable in the former
while possessing stability intervals in the latter phase. Dark-bright-bright
solitons can be realized in the polar and the easy-plane phases as unstable and
stable configurations respectively; the latter phase can also feature stable
dark-dark-dark solitons. Importantly, the persistence of these types of states
upon transitioning, by means of tuning the quadratic Zeeman coefficient from
one phase to the other is unravelled. Additionally, the spin-mixing dynamics of
stable and unstable matter waves is analyzed, revealing among others the
coherent evolution of magnetic dark-bright, nematic dark-bright-bright and
dark-dark-dark solitons. Moreover, for the unstable cases unmagnetized or
magnetic droplet-like configurations and spin-waves consisting of regular and
magnetic solitons are seen to dynamically emerge remaining thereafter robust
while propagating for extremely large evolution times. Interestingly, exposing
spinorial solitons to finite temperatures, their anti-damping in trap
oscillation is showcased. It is found that the latter is suppressed for
stronger bright soliton component "fillings". Our investigations pave the wave
for a systematic production and analysis involving spin transfer processes of
such waveforms which have been recently realized in ultracold experiments. | 2008.00475v3 |
2021-02-18 | On stochastic heating and its phase-space signatures in low-$β$ kinetic turbulence | We revisit the theory of stochastic heating of ions and investigate its
phase-space signatures in kinetic turbulence of relevance to low-$\beta$
portions of the solar wind. We retain a full scale-dependent approach in our
treatment, and consider the case in which electric-field fluctuations can be
described by a generalized Ohm's law that includes Hall and thermo-electric
effects. These two electric-field terms provide the dominant contributions to
stochastic ion heating when the ion-Larmor scale is much smaller than the ion
skin depth, $\rho_{\mathrm{i}}\ll d_{\mathrm{i}}$, which is the case at
$\beta{\ll}1$. Employing well-known spectral scaling laws for Alfv\'en-wave and
kinetic-Alfv\'en-wave turbulent fluctuations, we obtain scaling relations
characterizing the field-perpendicular particle-energization rate and energy
diffusion coefficient associated with stochastic heating in these two regimes.
Phase-space signatures of ion heating are then investigated using 3D
hybrid-kinetic simulations of continuously driven Alfv\'enic turbulence at low
$\beta$. In these simulations, energization of ions parallel to the magnetic
field is sub-dominant compared to its perpendicular counterpart
($Q_{\parallel,\mathrm{i}}\ll Q_{\perp,\mathrm{i}}$), and the fraction of
turbulent energy that goes into ion heating is ${\approx}75$\% at
$\beta_{\mathrm{i}}=0.3$ and ${\approx}40$\% at
$\beta_{\mathrm{i}}{\simeq}0.1$. The phase-space signatures of ion energization
are consistent with Landau-resonant collisionless damping and a
($\beta$-dependent) combination of ion-cyclotron and stochastic heating. We
demonstrate good agreement between our theory and various signatures associated
with the stochastic portion of the heating. We discuss the effect of
intermittency on stochastic heating and the implications of our work for the
interpretation of stochastic heating in solar-wind spacecraft data. | 2102.09654v2 |
2021-06-16 | Accurate and efficient hydrodynamic analysis of structures with sharp edges by the Extended Finite Element Method (XFEM): 2D studies | Achieving accurate numerical results of hydrodynamic loads based on the
potential-flow theory is very challenging for structures with sharp edges, due
to the singular behavior of the local-flow velocities. In this paper, we
introduce the Extended Finite Element Method (XFEM) to solve fluid-structure
interaction problems involving sharp edges on structures. Four different FEM
solvers, including conventional linear and quadratic FEMs as well as their
corresponding XFEM versions with local enrichment by singular basis functions
at sharp edges, are implemented and compared. To demonstrate the accuracy and
efficiency of the XFEMs, a thin flat plate in an infinite fluid domain and a
forced heaving rectangle at the free surface, both in two dimensions, will be
studied. For the flat plate, the mesh convergence studies are carried out for
both the velocity potential in the fluid domain and the added mass, and the
XFEMs show apparent advantages thanks to their local enhancement at the sharp
edges. Three different enrichment strategies are also compared, and suggestions
will be made for the practical implementation of the XFEM. For the forced
heaving rectangle, the linear and 2nd order mean wave loads are studied. Our
results confirm the previous conclusion in the literature that it is not
difficult for a conventional numerical model to obtain convergent results for
added mass and damping coefficients. However, when the 2nd order mean wave
loads requiring the computation of velocity components are calculated via
direct pressure integration, it takes a tremendously large number of elements
for the conventional FEMs to get convergent results. On the contrary, the
numerical results of XFEMs converge rapidly even with very coarse meshes,
especially for the quadratic XFEM. | 2106.08620v2 |
2021-06-25 | Validity of point-mass model in off-resonance dynamic atomic force microscopy | The quantitative measurement of viscoelasticity of nano-scaleentities is an
important goal of nanotechnology research and there is considerable progress
with advent of dynamic Atomic Force Microscopy. The hydrodynamics of
cantilever, the force sensor in AFM measurements, plays a pivotal role in
quantitative estimates of nano-scale viscoelasticity. The point-mass
model,wherein the AFM cantilever is approximated as a point mass with mass-less
spring is widely used in dynamic AFM analysis and its validity, particularly in
liquid environments, is debated. It is suggested that the cantilever must be
treated as a continuous rectangular beam to obtain accurate estimates of
nano-scale viscoelasticity of materials it is probing. Here, we derived
equations, which relate stiffness and damping coefficient of the material under
investigation to measured parameters, by approximating cantilever as a point
mass and also considering the full geometric details. These equations are
derived for both tip-excited as well as base excited cantilevers. We have
performed off-resonance dynamic atomic force spectroscopy on a single protein
molecule to investigate the validity of widely used point-mass model. We
performed measurements with AFMs equipped with different cantilever excitation
methods as well as detection schemes to measure cantilever response. The data
was analyzed using both, continuous-beam model and the point-mass model. We
found that both models yield same results when the experiments are performed in
truly off-resonance regime with small amplitudes and the cantilever stiffness
is much higher than the interaction stiffness. Our findings suggest that a
simple point-mass approximation based model is adequate to describe the
dynamics, provided care is taken while performing experiments so that the
approximations used in these models are valid. | 2106.13631v1 |
2021-11-20 | Current noise and Keldysh vertex function of an Anderson impurity in the Fermi liquid regime | We present a complete microscopic Fermi-liquid description for
next-to-leading order transport through an Anderson impurity under a finite
bias voltage $V$. It is applicable to multilevel quantum dots without
particle-hole or time-reversal symmetry, and is constructed based on the
nonequilibrium Keldysh formalism, taking into account the current conservation
between electrons in the impurity levels and the conduction bands.
Specifically, we derive the formula for the current noise generated in the
steady flow up to terms of order $(eV)^3$ at zero temperature $T=0$. To this
end, we calculate the Keldysh vertex functions
$\Gamma_{\sigma\sigma';\sigma'\sigma}^{ \nu_1\nu_2;\nu_3\nu_4} (\omega,\omega';
\omega',\omega)$, which depend on branches $\nu_1, \nu_2, \nu_3$ and $\nu_4$ of
the time-loop contour and on spin degrees of freedom $\sigma$ and $\sigma'$, up
to linear-order terms with respect to $eV$, $T$, and frequencies $\omega$ and
$\omega'$. The coefficients of these linear-order terms are determined by a set
of the parameters, defined with respect to the equilibrium ground state: the
phase shift, static susceptibilities, and nonlinear three-body susceptibilities
of the impurity electrons. The low-energy expressions of the vertex components
are shown to satisfy the Ward identities with the Keldysh Green's functions
expanded up to terms of order $\omega^2$, $(eV)^2$, and $T^2$. We also find
that the imaginary part of the Ward identities can be described in terms of the
$eV$-dependent collision integrals for a single-quasiparticle excitation and
that for a single quasiparticle-quasihole pair excitation. These collision
integrals ensure the current conservation of the next-to-leading order
Fermi-liquid transport due to the quasiparticles with a finite damping rate. | 2111.10483v2 |
2021-12-01 | Numerical Study of Cosmic Ray Confinement through Dust Resonant Drag Instabilities | We investigate the possibility of cosmic ray (CR) confinement by charged dust
grains through resonant drag instabilities (RDIs). We perform
magnetohydrodynamic particle-in-cell simulations of magnetized gas mixed with
charged dust and cosmic rays, with the gyro-radii of dust and GeV CRs on
$\sim\mathrm{AU}$ scales fully resolved. As a first study, we focus on one type
of RDI wherein charged grains drift super-Alfv{\'e}nically, with Lorentz forces
strongly dominating over drag forces. Dust grains are unstable to the RDIs and
form concentrated columns and sheets, whose scale grows until saturating at the
simulation box size. Initially perfectly-streaming CRs are strongly scattered
by RDI-excited Alfv{\'e}n waves, with the growth rate of the CR perpendicular
velocity components equaling the growth rate of magnetic field perturbations.
These rates are well-predicted by analytic linear theory. CRs finally become
isotropized and drift at least at $\sim v_\mathrm{A}$ by unidirectional
Alfv\'{e}n waves excited by the RDIs, with a uniform distribution of the pitch
angle cosine $\mu$ and a flat profile of the CR pitch angle diffusion
coefficient $D_{\mu\mu}$ around $\mu = 0$, without the "$90$ degree pitch angle
problem." With CR feedback on the gas included, $D_{\mu\mu}$ decreases by a
factor of a few, indicating a lower CR scattering rate, because the
backreaction on the RDI from the CR pressure adds extra wave damping, leading
to lower quasi-steady-state scattering rates. Our study demonstrates that the
dust-induced CR confinement can be very important under certain conditions,
e.g., the dusty circumgalactic medium around quasars or superluminous galaxies. | 2112.00752v2 |
2022-03-09 | A comparison of variational upwinding schemes for geophysical fluids, and their application to potential enstrophy conserving discretisations | Methods for upwinding the potential vorticity in a compatible finite element
discretisation of the rotating shallow water equations are studied. These
include the well-known anticipated potential vorticity method (APVM),
streamwise upwind Petrov-Galerkin (SUPG) method, and a recent approach where
the trial functions are evaluated downstream within the reference element. In
all cases the upwinding scheme conserves both potential vorticity and energy,
since the antisymmetric structure of the equations is preserved. The APVM leads
to a symmetric definite correction to the potential enstrophy that is
dissipative and inconsistent, resulting in a turbulent state where the
potential enstrophy is more strongly damped than for the other schemes. While
the SUPG scheme is widely known to be consistent, since it modifies the test
functions only, the downwinded trial function formulation results in the
advection of downwind corrections. Results of the SUPG and downwinded trial
function schemes are very similar in terms of both potential enstrophy
conservation and turbulent spectra. The main difference between these schemes
is in the energy conservation and residual errors. If just two nonlinear
iterations are applied then the energy conservation errors are improved for the
downwinded trial function formulation, reflecting a smaller residual error than
for the SUPG scheme.
We also present formulations by which potential enstrophy is exactly
integrated at each time level. Results using these formulations are observed to
be stable in the absence of dissipation, despite the uncontrolled aliasing of
grid scale turbulence. Using such a formulation and the APVM with a coefficient
$\mathcal{O}(100)$ times smaller that its regular value leads to turbulent
spectra that are greatly improved at the grid scale over the SUPG and
downwinded trial function formulations with unstable potential enstrophy
errors. | 2203.04629v3 |
2022-03-26 | Ion Alfvén velocity fluctuations and implications for the diffusion of streaming cosmic rays | The interstellar medium (ISM) of star-forming galaxies is magnetized and
turbulent. Cosmic rays (CRs) propagate through it, and those with energies from
$\sim\,\rm{GeV} - \rm{TeV}$ are likely subject to the streaming instability,
whereby the wave damping processes balances excitation of resonant ionic
Alfv\'en waves by the CRs, reaching an equilibrium in which the propagation
speed of the CRs is very close to the local ion Alfv\'en velocity. The
transport of streaming CRs is therefore sensitive to ionic Alfv\'en velocity
fluctuations. In this paper we systematically study these fluctuations using a
large ensemble of compressible MHD turbulence simulations. We show that for
sub-Alfv\'enic turbulence, as applies for a strongly magnetized ISM, the ionic
Alfv\'en velocity probability density function (PDF) is determined solely by
the density fluctuations from shocked gas forming parallel to the magnetic
field, and we develop analytical models for the ionic Alfv\'en velocity PDF up
to second moments. For super-Alfv\'enic turbulence, magnetic and density
fluctuations are correlated in complex ways, and these correlations as well as
contributions from the magnetic fluctuations sets the ionic Alfv\'en velocity
PDF. We discuss the implications of these findings for underlying "macroscopic"
diffusion mechanisms in CRs undergoing the streaming instability, including
modeling the macroscopic diffusion coefficient for the parallel transport in
sub-Alfv\'enic plasmas. We also describe how, for highly-magnetized turbulent
gas, the gas density PDF, and hence column density PDF, can be used to access
information about ionic Alfv\'en velocity structure from observations of the
magnetized ISM. | 2203.13952v3 |
2022-06-24 | Data-driven reduced order models using invariant foliations, manifolds and autoencoders | This paper explores how to identify a reduced order model (ROM) from a
physical system. A ROM captures an invariant subset of the observed dynamics.
We find that there are four ways a physical system can be related to a
mathematical model: invariant foliations, invariant manifolds, autoencoders and
equation-free models. Identification of invariant manifolds and equation-free
models require closed-loop manipulation of the system. Invariant foliations and
autoencoders can also use off-line data. Only invariant foliations and
invariant manifolds can identify ROMs, the rest identify complete models.
Therefore, the common case of identifying a ROM from existing data can only be
achieved using invariant foliations.
Finding an invariant foliation requires approximating high-dimensional
functions. For function approximation, we use polynomials with compressed
tensor coefficients, whose complexity increases linearly with increasing
dimensions. An invariant manifold can also be found as the fixed leaf of a
foliation. This only requires us to resolve the foliation in a small
neighbourhood of the invariant manifold, which greatly simplifies the process.
Combining an invariant foliation with the corresponding invariant manifold
provides an accurate ROM. We analyse the ROM in case of a focus type
equilibrium, typical in mechanical systems. The nonlinear coordinate system
defined by the invariant foliation or the invariant manifold distorts
instantaneous frequencies and damping ratios, which we correct. Through
examples we illustrate the calculation of invariant foliations and manifolds,
and at the same time show that Koopman eigenfunctions and autoencoders fail to
capture accurate ROMs under the same conditions. | 2206.12269v3 |
2022-10-23 | Tidally excited gravity waves in the cores of solar-type stars: resonances and critical-layer formation | We simulate the propagation and dissipation of tidally induced nonlinear
gravity waves in the cores of solar-type stars. We perform hydrodynamical
simulations of a previously developed Boussinesq model using a spectral-element
code to study the stellar core as a wave cavity that is periodically forced at
the outer boundary with a given azimuthal wavenumber and an adjustable
frequency. For low-amplitude forcing, the system exhibits resonances with
standing g-modes at particular frequencies, corresponding to a situation in
which the tidal torque is highly frequency-dependent. For high-amplitude
forcing, the excited waves break promptly near the centre and spin up the core
so that subsequent waves are absorbed in an expanding critical layer, as found
in previous work, leading to a tidal torque with a smooth frequency-dependence.
For intermediate-amplitude forcing, we find that linear damping of the waves
gradually spins up the core such that the resonance condition can be altered
drastically. The system can evolve towards or away from g-mode resonances,
depending on the difference between the forcing frequency and the closest
eigenfrequency. Eventually, a critical layer forms and absorbs the incoming
waves, leading to a situation similar to the high-amplitude case in which the
waves break promptly. We study the dependence of this process on the forcing
amplitude and frequency, as well as on the diffusion coefficients. We emphasize
that the small Prandtl number in the centre of solar-like stars facilitates the
development of a differentially rotating core owing to the nonlinear feedback
of waves. Our simulations and analysis reveal that this important mechanism may
drastically change the phase of gravity waves and thus the classical picture of
resonance locking in solar-type stars needs to be revised. | 2210.12880v2 |
1993-06-22 | Weakly Damped Modes in Star Clusters and Galaxies | A perturber may excite a coherent mode in a star cluster or galaxy. If the
stellar system is stable, it is commonly assumed that such a mode will be
strongly damped and therefore of little practical consequence other than
redistributing momentum and energy deposited by the perturber. This paper
demonstrates that this assumption is false; weakly damped modes exist and may
persist long enough to have observable consequences. To do this, a method for
investigating the dispersion relation for spherical stellar systems and for
locating weakly damped modes in particular is developed and applied to King
models of varying concentration. This leads to the following remarkable result:
King models exhibit {\it very} weakly damped $m=1$ modes over a wide range of
concentration ($0.67\le c\le1.5$ have been examined). The predicted damping
time is tens to hundreds of crossing times. This mode causes the peak density
to shift from and slowly revolve about the initial center. The existence of the
mode is supported by n-body simulation. Higher order modes and possible
astronomical consequences are discussed. Weakly damped modes, for example, may
provide a natural explanation for observed discrepancies between density and
kinematic centers in galaxies, the location of velocity cusps due to massive
black holes, and $m=1$ disturbances of disks embedded in massive halos.
Gravitational shocking may excite the $m=1$ mode in globular clusters, which
could modify their subsequent evolution and displace the positions of exotic
remnants. | 9306020v1 |
1997-12-03 | On the Evolution of Damped Lyman Alpha Systems to Galactic Disks | The mean metallicity of the thick disk of the Galaxy is 0.5 dex higher than
that of the damped Lyman alpha systems. This has been interpreted to argue that
stars in the former do not arise out of gas in the latter. Using new
metallicity and H I column-density data we show the metal-rich damped systems
do contain sufficient baryons at the thick-disk metallicity to account for the
stellar masses of thick disks. Comparing our kinematic data with the
metallicities we show that damped Lyman alpha systems exhibiting the largest
profile velocity widths span a narrow range of high metallicities, while
systems with small velocity widths span a wider range of metallicities. This is
naturally explained by passage of the damped Lyman alpha sightlines through
rapidly rotating disks with negative radial gradients in metallicity. The
systematically lower N(H I) of systems with high velocity widths indicates (a)
the gaseous disks have centrally located holes, and (b) an apparent
inconsistency with the protogalactic clump model for damped Lyman alpha
systems. The higher metallicity of systems with low N(H I) further implies that
stars rather than gas dominate the baryonic content of the most metal-rich
damped systems. | 9712050v1 |
1998-10-23 | Chemical Abundances of the Damped Lya Systems at z>1.5 | We present chemical abundance measurements for 19 damped lya systems observed
with HIRES on the 10m W.M. Keck Telescope. Our principal goal is to investigate
the abundance patterns of the damped systems and thereby determine the
underlying physical processes which dominate their chemical evolution. We place
particular emphasis on gauging the relative importance of two complementary
effects often invoked to explain the damped lya abundances: (1) nucleosynthetic
enrichment from Type II supernovae and (2) an ISM-like dust depletion pattern.
Similar to the principal results of Lu et al. (1996), our observations lend
support both for dust depletion and Type II SN enrichment. Specifically, the
observed overabundance of Zn/Fe and underabundance of Ni/Fe relative to solar
abundances suggest significant dust depletion within the damped lya systems.
Meanwhile, the relative abundances of Al, Si, and Cr vs. Fe are consistent with
both dust depletion and Type II supernova enrichment. Our measurements of Ti/Fe
and the Mn/Fe measurements from Lu et al. (1996), however, cannot be explained
by dust depletion and indicate an underlying Type II SN pattern. Finally, the
observed values of [S/Fe] are inconsistent with the combined effects of dust
depletion and the nucleosynthetic yields expected for Type II supernovae. This
last result emphasizes the need for another physical process to explain the
damped lya abundance patterns.
We also examine the metallicity of the damped lya systems both with respect
to Zn/H and Fe/H. Our results confirm previous surveys by Pettini and
collaborators, i.e., [<Zn/H>] = -1.15 +/- 0.15 dex. [abridged] | 9810381v1 |
2002-04-03 | The role of damped Alfven waves on magnetospheric accretion models of young stars | We examine the role of Alfven wave damping in heating the plasma in the
magnetic funnels of magnetospheric accretion models of young stars. We study
four different damping mechanisms of the Alfven waves: nonlinear, turbulent,
viscous-resistive and collisional. Two different possible origins for the
Alfven waves are discussed: 1) Alfven waves generated at the surface of the
star by the shock produced by the infalling matter; and 2) Alfven waves
generated locally in the funnel by the Kelvin-Helmholtz instability. We find
that, in general, the damping lengths are smaller than the tube length. Since
thermal conduction in the tube is not efficient, Alfven waves generated only at
the star's surface cannot heat the tube to the temperatures necessary to fit
the observations. Only for very low frequency Alfven waves ~10^{-5} the ion
cyclotron frequency, is the viscous-resistive damping length greater than the
tube length. In this case, the Alfven waves produced at the surface of the star
are able to heat the whole tube. Otherwise, local production of Alfven waves is
required to explain the observations. The turbulence level is calculated for
different frequencies for optically thin and thick media. We find that
turbulent velocities varies greatly for different damping mechanisms, reaching
\~100 km s^{-1} for the collisional damping of small frequency waves. | 0204056v1 |
2009-09-19 | Resonantly Damped Kink Magnetohydrodynamic Waves in a Partially Ionized Filament Thread | Transverse oscillations of solar filament and prominence threads have been
frequently reported. These oscillations have the common features of being of
short period (2-10 min) and being damped after a few periods. Kink
magnetohydrodynamic (MHD) wave modes have been proposed as responsible for the
observed oscillations, whereas resonant absorption in the Alfven continuum and
ion-neutral collisions are the best candidates to be the damping mechanisms.
Here, we study both analytically and numerically the time damping of kink MHD
waves in a cylindrical, partially ionized filament thread embedded in a coronal
environment. The thread model is composed of a straight and thin, homogeneous
filament plasma, with a transverse inhomogeneous transitional layer where the
plasma physical properties vary continuously from filament to coronal
conditions. The magnetic field is homogeneous and parallel to the thread axis.
We find that the kink mode is efficiently damped by resonant absorption for
typical wavelengths of filament oscillations, the damping times being
compatible with the observations. Partial ionization does not affect the
process of resonant absorption, and the filament plasma ionization degree is
only important for the damping for wavelengths much shorter than those
observed. To our knowledge, this is the first time that the phenomenon of
resonant absorption is studied in a partially ionized plasma. | 0909.3599v1 |
2009-10-15 | Time damping of non-adiabatic magnetohydrodynamic waves in a partially ionized prominence plasma: Effect of helium | Prominences are partially ionized, magnetized plasmas embedded in the solar
corona. Damped oscillations and propagating waves are commonly observed. These
oscillations have been interpreted in terms of magnetohydrodynamic (MHD) waves.
Ion-neutral collisions and non-adiabatic effects (radiation losses and thermal
conduction) have been proposed as damping mechanisms. We study the effect of
the presence of helium on the time damping of non-adiabatic MHD waves in a
plasma composed by electrons, protons, neutral hydrogen, neutral helium (He I),
and singly ionized helium (He II) in the single-fluid approximation. The
dispersion relation of linear non-adiabatic MHD waves in a homogeneous,
unbounded, and partially ionized prominence medium is derived. The period and
the damping time of Alfven, slow, fast, and thermal waves are computed. A
parametric study of the ratio of the damping time to the period with respect to
the helium abundance is performed. The efficiency of ion-neutral collisions as
well as thermal conduction is increased by the presence of helium. However, if
realistic abundances of helium in prominences (~10%) are considered, this
effect has a minor influence on the wave damping. The presence of helium can be
safely neglected in studies of MHD waves in partially ionized prominence
plasmas. | 0910.2883v1 |
2009-12-21 | The effect of longitudinal flow on resonantly damped kink oscillations | The most promising mechanism acting towards damping the kink oscillations of
coronal loops is resonant absorption. In this context most of previous studies
neglected the effect of the obvious equilibrium flow along magnetic field
lines. The flows are in general sub-Alfv\'enic and hence comparatively slow.
Here we investigate the effect of an equilibrium flow on the resonant
absorption of linear kink MHD waves in a cylindrical magnetic flux tube with
the aim of determining the changes in the frequency of the forward and backward
propagating waves and in the modification of the damping times due to the flow.
A loop model with both the density and the longitudinal flow changing in the
radial direction is considered. We use the thin tube thin boundary (TTTB)
approximation in order to calculate the damping rates. The full resistive
eigenvalue problem is also solved without assuming the TTTB approximation.
Using the small ratio of flow and Alfv\'en speeds we derive simple analytical
expressions to the damping rate. The analytical expressions are in good
agreement with the resistive eigenmode calculations. Under typical coronal
conditions the effect of the flow on the damped kink oscillations is small when
the characteristic scale of the density layer is similar or smaller than the
characteristic width of the velocity layer. However, in the opposite situation
the damping rates can be significantly altered, specially for the backward
propagating wave which is undamped while the forward wave is overdamped. | 0912.4136v1 |
2010-07-12 | Seismology of Standing Kink Oscillations of Solar Prominence Fine Structures | We investigate standing kink magnetohydrodynamic (MHD) oscillations in a
prominence fine structure modeled as a straight and cylindrical magnetic tube
only partially filled with the prominence material, and with its ends fixed at
two rigid walls representing the solar photosphere. The prominence plasma is
partially ionized and a transverse inhomogeneous transitional layer is included
between the prominence thread and the coronal medium. Thus, ion-neutral
collisions and resonant absorption are the considered damping mechanisms.
Approximate analytical expressions of the period, the damping time, and their
ratio are derived for the fundamental mode in the thin tube and thin boundary
approximations. We find that the dominant damping mechanism is resonant
absorption, which provides damping ratios in agreement with the observations,
whereas ion-neutral collisions are irrelevant for the damping. The values of
the damping ratio are independent of both the prominence thread length and its
position within the magnetic tube, and coincide with the values for a tube
fully filled with the prominence plasma. The implications of our results in the
context of the MHD seismology technique are discussed, pointing out that the
reported short-period (2 - 10 min) and short-wavelength (700 - 8,000 km) thread
oscillations may not be consistent with a standing mode interpretation and
could be related to propagating waves. Finally, we show that the inversion of
some prominence physical parameters, e.g., Alfv\'en speed, magnetic field
strength, transverse inhomogeneity length-scale, etc., is possible using
observationally determined values of the period and damping time of the
oscillations along with the analytical approximations of these quantities. | 1007.1959v2 |
2012-10-30 | Mode- and size-dependent Landau-Lifshitz damping in magnetic nanostructures: Evidence for non-local damping | We demonstrate a strong dependence of the effective damping on the nanomagnet
size and the particular spin-wave mode that can be explained by the theory of
intralayer transverse-spin-pumping. The effective Landau-Lifshitz damping is
measured optically in individual, isolated nanomagnets as small as 100 nm. The
measurements are accomplished by use of a novel heterodyne magneto-optical
microwave microscope with unprecedented sensitivity. Experimental data reveal
multiple standing spin-wave modes that we identify by use of micromagnetic
modeling as having either localized or delocalized character, described
generically as end- and center-modes. The damping parameter of the two modes
depends on both the size of the nanomagnet as well as the particular spin-wave
mode that is excited, with values that are enhanced by as much as 40% relative
to that measured for an extended film. Contrary to expectations based on the ad
hoc consideration of lithography-induced edge damage, the damping for the
end-mode decreases as the size of the nanomagnet decreases. The data agree with
the theory for damping caused by the flow of intralayer transverse
spin-currents driven by the magnetization curvature. These results have serious
implications for the performance of nanoscale spintronic devices such as
spin-torque-transfer magnetic random access memory. | 1210.8118v3 |
2012-11-21 | Kinetic theory of surface plasmon polariton in semiconductor nanowires | Based on the semiclassical model Hamiltonian of the surface plasmon polariton
and the nonequilibrium Green-function approach, we present a microscopic
kinetic theory to study the influence of the electron scattering on the
dynamics of the surface plasmon polariton in semiconductor nanowires. The
damping of the surface plasmon polariton originates from the resonant
absorption by the electrons (Landau damping), and the corresponding damping
exhibits size-dependent oscillations and distinct temperature dependence
without any scattering. The scattering influences the damping by introducing a
broadening and a shifting to the resonance. To demonstrate this, we investigate
the damping of the surface plasmon polariton in InAs nanowires in the presence
of the electron-impurity, electron-phonon and electron-electron Coulomb
scatterings. The main effect of the electron-impurity and electron-phonon
scatterings is to introduce a broadening, whereas the electron-electron Coulomb
scattering can not only cause a broadening, but also introduce a shifting to
the resonance. For InAs nanowires under investigation, the broadening due to
the electron-phonon scattering dominates. As a result, the scattering has a
pronounced influence on the damping of the surface plasmon polariton: The
size-dependent oscillations are smeared out and the temperature dependence is
also suppressed in the presence of the scattering. These results demonstrate
the the important role of the scattering on the surface plasmon polariton
damping in semiconductor nanowires. | 1211.5055v2 |
2013-11-12 | Damping filter method for obtaining spatially localized solutions | Spatially localized structures are key components of turbulence and other
spatio-temporally chaotic systems. From a dynamical systems viewpoint, it is
desirable to obtain corresponding exact solutions, though their existence is
not guaranteed. A damping filter method is introduced to obtain variously
localized solutions, and adopted into two typical cases. This method introduces
a spatially selective damping effect to make a good guess at the exact
solution, and we can obtain an exact solution through a continuation with the
damping amplitude. First target is a steady solution to Swift-Hohenberg
equation, which is a representative of bi-stable systems in which localized
solutions coexist, and a model for span-wisely localized cases. Not only
solutions belonging to the well-known snaking branches but also those belonging
to an isolated branch known as "isolas" are found with a continuation paths
between them in phase space extended with the damping amplitude. This indicates
that this spatially selective excitation mechanism has an advantage in
searching spatially localized solutions. Second target is a spatially localized
traveling-wave solution to Kuramoto-Sivashinsky equation, which is a model for
stream-wisely localized cases. Since the spatially selective damping effect
breaks Galilean and translational invariances, the propagation velocity cannot
be determined uniquely while the damping is active, and a singularity arises
when these invariances are recovered. We demonstrate that this singularity can
be avoided by imposing a simple condition, and a localized traveling-wave
solution is obtained with a specific propagation speed. | 1311.2792v2 |
2014-09-19 | Highly confined low-loss plasmons in graphene-boron nitride heterostructures | Graphene plasmons were predicted to possess ultra-strong field confinement
and very low damping at the same time, enabling new classes of devices for deep
subwavelength metamaterials, single-photon nonlinearities, extraordinarily
strong light-matter interactions and nano-optoelectronic switches. While all of
these great prospects require low damping, thus far strong plasmon damping was
observed, with both impurity scattering and many-body effects in graphene
proposed as possible explanations. With the advent of van der Waals
heterostructures, new methods have been developed to integrate graphene with
other atomically flat materials. In this letter we exploit near-field
microscopy to image propagating plasmons in high quality graphene encapsulated
between two films of hexagonal boron nitride (h-BN). We determine dispersion
and particularly plasmon damping in real space. We find unprecedented low
plasmon damping combined with strong field confinement, and identify the main
damping channels as intrinsic thermal phonons in the graphene and dielectric
losses in the h-BN. The observation and in-depth understanding of low plasmon
damping is the key for the development of graphene nano-photonic and
nano-optoelectronic devices. | 1409.5674v1 |
2015-09-02 | Energy Dependence of Synchrotron X-Ray Rims in Tycho's Supernova Remnant | Several young supernova remnants exhibit thin X-ray bright rims of
synchrotron radiation at their forward shocks. Thin rims require strong
magnetic field amplification beyond simple shock compression if rim widths are
only limited by electron energy losses. But, magnetic field damping behind the
shock could produce similarly thin rims with less extreme field amplification.
Variation of rim width with energy may thus discriminate between competing
influences on rim widths. We measured rim widths around Tycho's supernova
remnant in 5 energy bands using an archival 750 ks Chandra observation. Rims
narrow with increasing energy and are well described by either loss-limited or
damped scenarios, so X-ray rim width-energy dependence does not uniquely
specify a model. But, radio counterparts to thin rims are not loss-limited and
better reflect magnetic field structure. Joint radio and X-ray modeling favors
magnetic damping in Tycho's SNR with damping lengths ~1--5% of remnant radius
and magnetic field strengths ~50--400 $\mu$G assuming Bohm diffusion. X-ray rim
widths are ~1% of remnant radius, somewhat smaller than inferred damping
lengths. Electron energy losses are important in all models of X-ray rims,
suggesting that the distinction between loss-limited and damped models is
blurred in soft X-rays. All loss-limited and damping models require magnetic
fields $\gtrsim$ 20 $\mu$G, affirming the necessity of magnetic field
amplification beyond simple compression. | 1509.00877v1 |
2016-02-02 | Forward Modelling of Propagating Slow Waves in Coronal Loops and Their Frequency-Dependent Damping | Propagating slow waves in coronal loops exhibit a damping which depends upon
the frequency of the waves. In this study we aim to investigate the
relationship of the damping length (L$_d$) with the frequency of the
propagating wave. We present a 3-D coronal loop model with uniform density and
temperature and investigate the frequency dependent damping mechanism for the
four chosen wave periods. We include the thermal conduction to damp the waves
as they propagate through the loop. The numerical model output has been forward
modelled to generate synthetic images of SDO/AIA 171 \r{A} and 193 \r{A}
channels. The use of forward modelling, which incorporates the atomic emission
properties into the intensity images, allows us to directly compare our results
with the real observations. The results show that the damping lengths vary
linearly with the periods. We also measure the contributions of the emission
properties on the damping lengths by using density values from the simulation.
In addition to that} we have also calculated the theoretical dependence of
L$_d$ with wave periods and showed that it is consistent with the results we
obtained from the numerical modelling and earlier observations. | 1602.00787v1 |
2016-05-11 | Damping of prominence longitudinal oscillations due to mass accretion | We study the damping of longitudinal oscillations of a prominence thread
caused by the mass accretion. In this model we considered a thin curved
magnetic tube filled with the plasma. The parts of the tube at the two sides of
the thread are filled with hot rarefied plasma. We assume that there are flows
of rarefied plasma toward the thread caused by the plasma evaporation at the
magnetic tube footpoints. Our main assumption is that the hot plasma is
instantaneously accommodated by the thread when it arrives at the thread, and
its temperature and density become equal to those of the thread. Then we derive
the system of ordinary differential equations describing the thread dynamics.
We consider linear and nonlinear oscillation. The nonlinearity reduces the
damping time, however this reduction is small. The damping time is inversely
proportional to the accretion rate. We also obtain that the oscillation periods
decrease with time. However even for the largest initial oscillation amplitude
considered in our article the period reduction does not exceed 20%. We conclude
that the mass accretion can damp the motion of the threads rapidly. Thus, this
mechanism can explain the observed strong damping of large-amplitude
longitudinal oscillations. In addition, the damping time can be used to
determine the mass accretion rate and indirectly the coronal heating. | 1605.03376v1 |
2016-11-17 | Inductive detection of field-like and damping-like AC inverse spin-orbit torques in ferromagnet/normal metal bilayers | Functional spintronic devices rely on spin-charge interconversion effects,
such as the reciprocal processes of electric field-driven spin torque and
magnetization dynamics-driven spin and charge flow. Both damping-like and
field-like spin-orbit torques have been observed in the forward process of
current-driven spin torque and damping-like inverse spin-orbit torque has been
well-studied via spin pumping into heavy metal layers. Here we demonstrate that
established microwave transmission spectroscopy of ferromagnet/normal metal
bilayers under ferromagnetic resonance can be used to inductively detect the AC
charge currents driven by the inverse spin-charge conversion processes. This
technique relies on vector network analyzer ferromagnetic resonance (VNA-FMR)
measurements. We show that in addition to the commonly-extracted spectroscopic
information, VNA-FMR measurements can be used to quantify the magnitude and
phase of all AC charge currents in the sample, including those due to spin
pumping and spin-charge conversion. Our findings reveal that
Ni$_{80}$Fe$_{20}$/Pt bilayers exhibit both damping-like and field-like inverse
spin-orbit torques. While the magnitudes of both the damping-like and
field-like inverse spin-orbit torque are of comparable scale to prior reported
values for similar material systems, we observed a significant dependence of
the damping-like magnitude on the order of deposition. This suggests interface
quality plays an important role in the overall strength of the damping-like
spin-to-charge conversion. | 1611.05798v2 |
2016-12-30 | Spectroscopic evidence of Alfvén wave damping in the off-limb solar corona | We investigate off-limb active region and quiet Sun corona using
spectroscopic data. Active region is clearly visible in several spectral lines
formed in the temperature range of 1.1--2.8 MK. We derive electron number
density using line ratio method, and non-thermal velocity in the off-limb
region up to the distance of 140 Mm. We compare density scale heights derived
from several spectral line pairs with expected scale heights as per hydrostatic
equilibrium model. Using several isolated and unblended spectral line profiles,
we estimate non-thermal velocities in active region and quiet Sun. Non-thermal
velocities obtained from warm lines in active region first show increase and
later show either decrease or almost constant value with height in the far
off-limb region, whereas hot lines show consistent decrease. However, in the
quiet Sun region, non-thermal velocities obtained from various spectral lines
show either gradual decrease or remain almost constant with height. Using these
obtained parameters, we further calculate Alfv\'en wave energy flux in the both
active and quiet Sun regions. We find significant decrease in wave energy
fluxes with height, and hence provide evidence of Alfv\'en wave damping.
Furthermore, we derive damping lengths of Alfv\'en waves in the both regions
and find them to be in the range of 25-170 Mm. Different damping lengths
obtained at different temperatures may be explained as either possible
temperature dependent damping or measurements obtained in different coronal
structures formed at different temperatures along the line-of-sight.
Temperature dependent damping may suggest some role of thermal conduction in
the damping of Alfv\'en waves in the lower corona. | 1612.09551v2 |
2017-01-04 | Controlling plasmon modes and damping in buckled two-dimensional material open systems | Full ranges of both hybrid plasmon-mode dispersions and their damping are
studied systematically by our recently developed mean-field theory in open
systems involving a conducting substrate and a two-dimensional (2D) material
with a buckled honeycomb lattice, such as silicene, germanene, and a group
\rom{4} dichalcogenide as well. In this hybrid system, the single plasmon mode
for a free-standing 2D layer is split into one acoustic-like and one
optical-like mode, leading to a dramatic change in the damping of plasmon
modes. In comparison with gapped graphene, critical features associated with
plasmon modes and damping in silicene and molybdenum disulfide are found with
various spin-orbit and lattice asymmetry energy bandgaps, doping types and
levels, and coupling strengths between 2D materials and the conducting
substrate. The obtained damping dependence on both spin and valley degrees of
freedom is expected to facilitate measuring the open-system dielectric property
and the spin-orbit coupling strength of individual 2D materials. The unique
linear dispersion of the acoustic-like plasmon mode introduces additional
damping from the intraband particle-hole modes which is absent for a
free-standing 2D material layer, and the use of molybdenum disulfide with a
large bandgap simultaneously suppresses the strong damping from the interband
particle-hole modes. | 1701.01084v1 |
2017-04-05 | Stimulated Brillouin scattering behaviors in different species ignition hohlraum plasmas in high-temperature and high-density region | The presence of multiple ion species can add additional branches to the IAW
dispersion relation and change the Landau damping significantly. Different IAW
modes excited by stimulated Brillouin scattering (SBS) and different SBS
behaviors in several typical ignition hohlraum plasmas in the high-temperature
and high-density region have been researched by Vlasov-Maxwell simulation. The
slow mode in HeH or CH plasmas is the least damped mode and will be excited in
SBS, while the fast mode in AuB plasmas is the least damped mode and will be
excited in SBS. Due to strong Landau damping, the SBS in H or HeH plasmas is
strong convective instability, while the SBS in AuB plasmas is absolute
instability due to the weak Landau damping. However, although the SBS in CH
plasmas is weak convective instability in the linear theory, the SBS will
transform into absolute instability due to decreasing linear Landau damping by
particles trapping. These results give a detail research of the IAW modes
excitation and the properties of SBS in different species plasmas, thus
providing the possibility of controlling SBS by increasing the linear Landau
damping of the IAW by changing ion species. | 1704.02317v1 |
2017-06-29 | Resonant Absorption of Axisymmetric Modes in Twisted Magnetic Flux Tubes | It has been shown recently that magnetic twist and axisymmetric MHD modes are
ubiquitous in the solar atmosphere and therefore, the study of resonant
absorption for these modes have become a pressing issue as it can have
important consequences for heating magnetic flux tubes in the solar atmosphere
and the observed damping. In this investigation, for the first time, we
calculate the damping rate for axisymmetric MHD waves in weakly twisted
magnetic flux tubes. Our aim is to investigate the impact of resonant damping
of these modes for solar atmospheric conditions. This analytical study is based
on an idealized configuration of a straight magnetic flux tube with a weak
magnetic twist inside as well as outside the tube. By implementing the
conservation laws derived by \cite{Sakurai:1991aa} and the analytic solutions
for weakly twisted flux tubes obtained recently by \cite{Giagkiozis:2015apj},
we derive a dispersion relation for resonantly damped axisymmetric modes in the
spectrum of the Alfv\'{e}n continuum. We also obtain an insightful analytical
expression for the damping rate in the long wavelength limit. Furthermore, it
shown that both the longitudinal magnetic field and the density, which are
allowed to vary continuously in the inhomogeneous layer, have a significant
impact on the damping time. Given the conditions in the solar atmosphere,
resonantly damped axisymmetric modes are highly likely to be ubiquitous and
play an important role in energy dissipation.
We also suggest that given the character of these waves, it is likely that
they have already been observed in the guise of Alfv\'{e}n waves. | 1706.09665v1 |
2017-08-16 | Damping of an oscillating scalar field indirectly coupled to a thermal bath | The damping process of a homogeneous oscillating scalar field that indirectly
interacts with a thermal bath through a mediator field is investigated over a
wide range of model parameters. We consider two types of mediator fields, those
that can decay to the thermal bath and those that are individually stable but
pair annihilate. The former case has been extensively studied in the literature
by treating the damping as a local effect after integrating out the assumed
close-to-equilibrium mediator field. The same approach does not apply if the
mediator field is stable and freezes out of equilibrium. To account for the
latter case, we adopt a non-local description of damping that is only
meaningful when we consider full half-oscillations of the field being damped.
The damping rates of the oscillating scalar field and the corresponding heating
rate of the thermal bath in all bulk parameter regions are calculated in both
cases, corroborating previous results in the direct decay case. Using the
obtained results, the time it takes for the amplitude of the scalar field to be
substantially damped is estimated. | 1708.04865v2 |
2018-09-14 | Continuous and discrete damping reduction for systems with quadratic interaction | We study the connection between Lagrangian and Hamiltonian descriptions of
closed/open dynamics, for a collection of particles with quadratic interaction
(closed system) and a sub-collection of particles with linear damping (open
system). We consider both continuous and discrete versions of mechanics. We
define the Damping Reduction as the mapping from the equations of motion of the
closed system to those of the open one. As variational instruments for the
obtention of these equations we use the Hamilton's principle (closed dynamics)
and Lagrange-d'Alembert principle (open dynamics). We establish the
commutativity of the branches Legendre transform + Damping Reduction and
Damping Reduction+Legendre transform, where the Legendre transform is the usual
mapping between Lagrangian and Hamiltonian mechanics. At a discrete level, this
commutativity provides interesting insight about the resulting integrators.
More concretely, Discrete Damping Reduction yields particular numerical schemes
for linearly damped systems which are not symplectic anymore, but preserve some
of the features of their symplectic counterparts from which they proceed (for
instance the semi-implicitness in some cases). The theoretical results are
illustrated with the examples of the heat bath and transmission lines. In the
latter case some simulations are displayed, showing a better performance of the
integrators with variational origin. | 1809.05532v1 |
2019-03-02 | Complex Stiffness Model of Physical Human-Robot Interaction: Implications for Control of Performance Augmentation Exoskeletons | Human joint dynamic stiffness plays an important role in the stability of
performance augmentation exoskeletons. In this paper, we consider a new
frequency domain model of the human joint dynamics which features a complex
value stiffness. This complex stiffness consists of a real stiffness and a
hysteretic damping. We use it to explain the dynamic behaviors of the human
connected to the exoskeleton, in particular the observed non-zero low frequency
phase shift and the near constant damping ratio of the resonant as stiffness
and inertia vary. We validate this concept by experimenting with an elbow-joint
exoskeleton testbed on a subject while modifying joint stiffness behavior,
exoskeleton inertia, and strength augmentation gains. We compare three
different models of elbow-joint dynamic stiffness: a model with real stiffness,
viscous damping and inertia, a model with complex stiffness and inertia, and a
model combining the previous two models. Our results show that the hysteretic
damping term improves modeling accuracy, using a statistical F-test. Moreover
this improvement is statistically more significant than using classical viscous
damping term. In addition, we experimentally observe a linear relationship
between the hysteretic damping and the real part of the stiffness which allows
us to simplify the complex stiffness model as a 1-parameter system. Ultimately,
we design a fractional order controller to demonstrate how human hysteretic
damping behavior can be exploited to improve strength amplification performance
while maintaining stability. | 1903.00704v4 |
2020-05-31 | Optimal decay rates of the compressible Euler equations with time-dependent damping in $\mathbb R^n$: (II) over-damping case | This paper is concerned with the multi-dimensional compressible Euler
equations with time-dependent over-damping of the form
$-\frac{\mu}{(1+t)^\lambda}\rho\boldsymbol u$ in $\mathbb R^n$, where $n\ge2$,
$\mu>0$, and $\lambda\in[-1,0)$. This continues our previous work dealing with
the under-damping case for $\lambda\in[0,1)$. We show the optimal decay
estimates of the solutions such that for $\lambda\in(-1,0)$ and $n\ge2$,
$\|\rho-1\|_{L^2(\mathbb R^n)}\approx(1+t)^{-\frac{1+\lambda}{4}n}$ and
$\|\boldsymbol u\|_{L^2(\mathbb R^n)}\approx
(1+t)^{-\frac{1+\lambda}{4}n-\frac{1-\lambda}{2}}$, which indicates that a
stronger damping gives rise to solutions decaying optimally slower. For the
critical case of $\lambda=-1$, we prove the optimal logarithmical decay of the
perturbation of density for the damped Euler equations such that
$\|\rho-1\|_{L^2(\mathbb R^n)}\approx |\ln(e+t)|^{-\frac{n}{4}}$ and
$\|\boldsymbol u\|_{L^2(\mathbb R^n)}\approx
(1+t)^{-1}\cdot|\ln(e+t)|^{-\frac{n}{4}-\frac{1}{2}}$ for $n\ge7$. The
over-damping effect reduces the decay rates of the solutions to be slow, which
causes us some technical difficulty in obtaining the optimal decay rates by the
Fourier analysis method and the Green function method. Here, we propose a new
idea to overcome such a difficulty by artfully combining the Green function
method and the time-weighted energy method. | 2006.00403v1 |
2020-07-07 | Nonlinear viscoelastic isolation for seismic vibration mitigation | The aim of this paper is to assess the effectiveness of nonlinear
viscoelastic damping in controlling base-excited vibrations. Specifically, the
focus is on investigating the robustness of the nonlinear base isolation
performance in controlling the system response due to a wide set of possible
excitation spectra. The dynamic model is derived to study a simple structure
whose base isolation is provided via a Rubber-Layer Roller Bearing (RLRB)
(rigid cylinders rolling on rigid plates with highly damping rubber coatings)
equipped with a nonlinear cubic spring, thus presenting both nonlinear damping
and stiffness. We found that, under periodic loading, due to the non-monotonic
bell-shaped viscoelastic damping arising from the viscoelastic rolling
contacts, different dynamic regimes occur mostly depending on whether the
damping peak is overcome or not. Interestingly, in the former case, poorly
damped self-excited vibrations may be triggered by the steep damping decrease.
Moreover, in order to investigate the robustness of the isolation performance,
we consider a set of real seismic excitations, showing that tuned nonlinear
RLRB provide loads isolation in a wider range of excitation spectra, compared
to generic linear isolators. This is peculiarly suited for applications (such
as seismic and failure engineering) in which the specific excitation spectrum
is unknown a priori, and blind design on statistical data has to be employed. | 2007.04378v1 |
2021-01-20 | Damped perturbations in stellar systems: Genuine modes and Landau-damped waves | This research was stimulated by the recent studies of damping solutions in
dynamically stable spherical stellar systems. Using the simplest model of the
homogeneous stellar medium, we discuss nontrivial features of stellar systems.
Taking them into account will make it possible to correctly interpret the
results obtained earlier and will help to set up decisive numerical experiments
in the future. In particular, we compare the initial value problem versus the
eigenvalue problem. It turns out that in the unstable regime, the Landau-damped
waves can be represented as a superposition of van Kampen modes {\it plus} a
discrete damped mode, usually ignored in the stability study. This mode is a
solution complex conjugate to the unstable Jeans mode. In contrast, the
Landau-damped waves are not genuine modes: in modes, eigenfunctions depend on
time as $\exp (-{\rm i} \omega t)$, while the waves do not have eigenfunctions
on the real $v$-axis at all. However, `eigenfunctions' on the complex
$v$-contours do exist. Deviations from the Landau damping are common and can be
due to singularities or cut-off of the initial perturbation above some fixed
value in the velocity space. | 2101.08287v2 |
2021-03-10 | Dynamical Pose Estimation | We study the problem of aligning two sets of 3D geometric primitives given
known correspondences. Our first contribution is to show that this primitive
alignment framework unifies five perception problems including point cloud
registration, primitive (mesh) registration, category-level 3D registration,
absolution pose estimation (APE), and category-level APE. Our second
contribution is to propose DynAMical Pose estimation (DAMP), the first general
and practical algorithm to solve primitive alignment problem by simulating
rigid body dynamics arising from virtual springs and damping, where the springs
span the shortest distances between corresponding primitives. We evaluate DAMP
in simulated and real datasets across all five problems, and demonstrate (i)
DAMP always converges to the globally optimal solution in the first three
problems with 3D-3D correspondences; (ii) although DAMP sometimes converges to
suboptimal solutions in the last two problems with 2D-3D correspondences, using
a scheme for escaping local minima, DAMP always succeeds. Our third
contribution is to demystify the surprising empirical performance of DAMP and
formally prove a global convergence result in the case of point cloud
registration by charactering local stability of the equilibrium points of the
underlying dynamical system. | 2103.06182v3 |
2021-04-13 | Apparent nonlinear damping triggered by quantum fluctuations | Nonlinear damping, the change in damping rate with the amplitude of
oscillations plays an important role in many electrical, mechanical and even
biological oscillators. In novel technologies such as carbon nanotubes,
graphene membranes or superconducting resonators, the origin of nonlinear
damping is sometimes unclear. This presents a problem, as the damping rate is a
key figure of merit in the application of these systems to extremely precise
sensors or quantum computers. Through measurements of a superconducting
resonator, we show that from the interplay of quantum fluctuations and the
nonlinearity of a Josephson junction emerges a power-dependence in the
resonator response which closely resembles nonlinear damping. The phenomenon
can be understood and visualized through the flow of quasi-probability in phase
space where it reveals itself as dephasing. Crucially, the effect is not
restricted to superconducting circuits: we expect that quantum fluctuations or
other sources of noise give rise to apparent nonlinear damping in systems with
a similar conservative nonlinearity, such as nano-mechanical oscillators or
even macroscopic systems. | 2104.06464v2 |
2023-07-26 | Improving frequency response with synthetic damping available from fleets of distributed energy resources | With the increasing use of renewable generation in power systems, responsive
resources will be necessary to support primary frequency control in future
low-inertia/under-damped power systems. Flexible loads can provide
fast-frequency response services if coordinated effectively. However, practical
implementations of such synthetic damping services require both effective local
sensing and control at the device level and an ability to accurately estimate
online and predict the available synthetic damping from a fleet. In addition,
the inherent trade-off between a fleet being available for fast frequency
response while providing other ancillary services needs to be characterized. In
this context, the manuscript presents a novel, fully decentralized,
packet-based controller for diverse flexible loads that dynamically prioritizes
and interrupts loads to engender synthetic damping suitable for primary
frequency control. Moreover, the packet-based control methodology is shown to
accurately characterize the available synthetic damping in real-time, which is
useful to aggregators and system operators. Furthermore, spectral analysis of
historical frequency regulation data is used to produce a probabilistic bound
on the expected available synthetic damping for primary frequency control from
a fleet and the trade-off from concurrently providing secondary frequency
control services. Finally, numerical simulation on IEEE test networks
demonstrates the effectiveness of the proposed methodology. | 2307.14498v1 |
2023-12-11 | Possible Contamination of the Intergalactic Medium Damping Wing in ULAS J1342+0928 by Proximate Damped Ly$α$ Absorption | The red damping wing from neutral hydrogen in the intergalactic medium is a
smoking-gun signal of ongoing reionization. One potential contaminant of the
intergalactic damping wing signal is dense gas associated with foreground
galaxies, which can give rise to proximate damped Ly$\alpha$ absorbers. The
Ly$\alpha$ imprint of such absorbers on background quasars is indistinguishable
from the intergalactic medium within the uncertainty of the intrinsic quasar
continuum, and their abundance at $z\gtrsim7$ is unknown. Here we show that the
complex of low-ionization metal absorption systems recently discovered by deep
JWST/NIRSpec observations in the foreground of the $z=7.54$ quasar
ULAS~J1342$+$0928 can potentially reproduce the quasar's spectral profile close
to rest-frame Ly$\alpha$ without invoking a substantial contribution from the
intergalactic medium, but only if the absorbing gas is extremely metal-poor
($[{\rm O}/{\rm H}]\sim-3.5$). Such a low oxygen abundance has never been
observed in a damped Ly$\alpha$ absorber at any redshift, but this possibility
still complicates the interpretation of the spectrum. Our analysis highlights
the need for deep spectroscopy of high-redshift quasars with JWST or ELT to
"purify" damping wing quasar samples, an exercise which is impossible for much
fainter objects like galaxies. | 2312.06747v1 |
2024-02-13 | Forecasts for Constraining Lorentz-violating Damping of Gravitational Waves from Compact Binary Inspirals | Violation of Lorentz symmetry can result in two distinct effects in the
propagation of the gravitational waves (GWs). One is a modified dispersion
relation and another is a frequency-dependent damping of GWs. While the former
has been extensively studied in the literature, in this paper we concentrate on
the frequency-dependent damping effect that arises from several specific
Lorentz-violating theories, such as spatial covariant gravities,
Ho\v{r}ava-Lifshitz gravities, etc. This Lorentz-violating damping effect
changes the damping rate of GWs at different frequencies and leads to an
amplitude correction to the GW waveform of compact binary inspiral systems.
With this modified waveform, we then use the Fisher information matrix to
investigate the prospects of constraining the Lorentz-violating damping effect
with GW observations. We consider both ground-based and space-based GW
detectors, including the advanced LIGO, Einstein Telescope, Cosmic Explorer
(CE), Taiji, TianQin, and LISA. Our results indicate that the ground-based
detectors in general give tighter constraints than those from the space-based
detectors. Among the considered three ground-based detectors, CE can give the
tightest constraints on the Lorentz-violating damping effect, which improves
the current constraint from LIGO-Virgo-KAGRA events by about 8 times. | 2402.08240v1 |
2024-03-13 | Thermal Hall effect incorporating magnon damping in localized spin systems | We propose a theory for thermal Hall transport mediated by magnons to address
the impact of their damping resulting from magnon-magnon interactions in
insulating magnets. This phenomenon is anticipated to be particularly
significant in systems characterized by strong quantum fluctuations,
exemplified by spin-1/2 systems. Employing a nonlinear flavor-wave theory, we
analyze a general model for localized electron systems and develop a
formulation for thermal conductivity based on a perturbation theory, utilizing
bosonic Green's functions with a nonzero self-energy. We derive the expression
of the thermal Hall conductivity incorporating magnon damping. To demonstrate
the applicability of the obtained representation, we adopt it to two $S=1/2$
quantum spin models on a honeycomb lattice. In calculations for these systems,
we make use of the self-consistent imaginary Dyson equation approach at finite
temperatures for evaluating the magnon damping rate. In both systems, the
thermal Hall conductivity is diminished due to the introduction of magnon
damping over a wide temperature range. This effect arises due to the smearing
of magnon spectra with nonzero Berry curvatures. We also discuss the relation
to the damping of chiral edge modes of magnons. Our formulation can be applied
to various localized electron systems as we begin with a general Hamiltonian
for these systems. Our findings shed light on a new aspect of topological
magnonics emergent from many-body effects and will stimulate further
investigations on the impact of magnon damping on topological phenomena. | 2403.08478v1 |
2024-04-02 | A recipe for eccentricity and inclination damping for partial gap opening planets in 3D disks | In a previous paper we showed that, like the migration speed, the
eccentricity damping efficiency is modulated linearly by the depth of the
partial gap a planet carves in the disk surface density profile, resulting in
less efficient $e$-damping compared to the prescription commonly used in
population synthesis works. Here, we extend our analysis to 3D, refining our
$e$-damping formula and studying how the inclination damping efficiency is also
affected. We perform high resolution 3D locally isothermal hydrodynamical
simulations of planets with varying masses embedded in disks with varying
aspect ratios and viscosities. We extract the gap profile and orbital damping
timescales for fixed eccentricities and inclinations up to the disk scale
height. The limit in gap depths below which vortices appear, in the
low-viscosity case, happens roughly at the transition between classical type-I
and type-II migration regimes. The orbital damping timescales can be described
by two linear trends with a break around gap depths $\sim80\%$ and with slopes
and intercepts depending on the eccentricity and inclination. These trends are
understood on physical grounds and are reproduced by simple fitting formulas
whose error is within the typically uncertainty of type-I torque formulas.
Thus, our recipes for the gap depth and orbital damping efficiencies yield a
simple description for planet-disk interactions to use in N-body codes in the
case of partial gap opening planets that is consistent with high-resolution 3D
hydro-simulations. Finally, we show examples of how our novel orbital damping
prescription can affect the outcome of population synthesis experiments. | 2404.02247v1 |
2009-08-21 | Surface Alfven Wave Damping in a 3D Simulation of the Solar Wind | Here we investigate the contribution of surface Alfven wave damping to the
heating of the solar wind in minima conditions. These waves are present in
regions of strong inhomogeneities in density or magnetic field (e. g., the
border between open and closed magnetic field lines). Using a 3-dimensional
Magnetohydrodynamics (MHD) model, we calculate the surface Alfven wave damping
contribution between 1-4 solar radii, the region of interest for both
acceleration and coronal heating. We consider waves with frequencies lower than
those that are damped in the chromosphere and on the order of those dominating
the heliosphere. In the region between open and closed field lines, within a
few solar radii of the surface, no other major source of damping has been
suggested for the low frequency waves we consider here. This work is the first
to study surface Alfven waves in a 3D environment without assuming a priori a
geometry of field lines or magnetic and density profiles. We determine that
waves with frequencies >2.8x10^-4 Hz are damped between 1-4 solar radii. In
quiet sun regions, surface Alfven waves are damped at further distances
compared to active regions, thus carrying additional wave energy into the
corona. We compare the surface Alfven wave contribution to the heating by a
variable polytropic index and find that it an order of magnitude larger than
needed for quiet sun regions. For active regions the contribution to the
heating is twenty percent. As it has been argued that a variable gamma acts as
turbulence, our results indicate that surface Alfven wave damping is comparable
to turbulence in the lower corona. This damping mechanism should be included
self consistently as an energy driver for the wind in global MHD models. | 0908.3146v1 |
2017-11-21 | Determination of spin Hall effect and spin diffusion length of Pt from self-consistent fitting of damping enhancement and inverse spin-orbit torque measurements | Understanding the evolution of spin-orbit torque (SOT) with increasing
heavy-metal thickness in ferromagnet/normal metal (FM/NM) bilayers is critical
for the development of magnetic memory based on SOT. However, several
experiments have revealed an apparent discrepancy between damping enhancement
and damping-like SOT regarding their dependence on NM thickness. Here, using
linewidth and phase-resolved amplitude analysis of vector network analyzer
ferromagnetic resonance (VNA-FMR) measurements, we simultaneously extract
damping enhancement and both field-like and damping-like inverse SOT in
Ni$_{80}$Fe$_{20}$/Pt bilayers as a function of Pt thickness. By enforcing an
interpretation of the data which satisfies Onsager reciprocity, we find that
both the damping enhancement and damping-like inverse SOT can be described by a
single spin diffusion length ($\approx$ 4 nm), and that we can separate the
spin pumping and spin memory loss (SML) contributions to the total damping.
This analysis indicates that less than 40% of the angular momentum pumped by
FMR through the Ni$_{80}$Fe$_{20}$/Pt interface is transported as spin current
into the Pt. On account of the SML and corresponding reduction in total spin
current available for spin-charge transduction in the Pt, we determine the Pt
spin Hall conductivity ($\sigma_\mathrm{SH} = (2.36 \pm 0.04)\times10^6
\Omega^{-1} \mathrm{m}^{-1}$) and bulk spin Hall angle
($\theta_\mathrm{SH}=0.387 \pm0.008$) to be larger than commonly-cited values.
These results suggest that Pt can be an extremely useful source of SOT if the
FM/NM interface can be engineered to minimize SML. Lastly, we find that
self-consistent fitting of the damping and SOT data is best achieved by a model
with Elliott-Yafet spin relaxation and extrinsic inverse spin Hall effect, such
that both the spin diffusion length and spin Hall conductivity are proportional
to the Pt charge conductivity. | 1711.07654v2 |
2019-09-19 | Nonlinear energy loss in the oscillations of coated and uncoated bubbles: Role of thermal, radiation damping and encapsulating shell at various excitation pressures | A simple generalized model (GM) for coated bubbles accounting for the effect
of compressibility of the liquid is presented. The GM was then coupled with
nonlinear ODEs that account for the thermal effects. Starting with mass and
momentum conservation equations for a bubbly liquid and using the GM, nonlinear
pressure dependent terms were derived for energy dissipation due to thermal
damping (Td), radiation damping (Rd) and dissipation due to the viscosity of
liquid (Ld) and coating (Cd). The dissipated energies were solved for uncoated
and coated 2- 20 $\mu m$ bubbles over a frequency range of $0.25f_r-2.5f_r$
($f_r$ is the bubble resonance) and for various acoustic pressures
(1kPa-300kPa). Thermal effects were examined for air and C3F8 gas cores in each
case. For uncoated bubbles with an air gas core and a diameter larger than 4
$\mu m$, thermal damping is the strongest damping factor. When pressure
increases, the contributions of Rd grow faster and become the dominant damping
mechanism for pressure dependent resonance frequencies (e.g. fundamental and
super harmonic resonances). For coated bubbles, Cd is the strongest damping
mechanism. As pressure increases Rd contributes more to damping compared to Ld
and Td. In case of air bubbles, as pressure increases, the linear thermal model
largely deviates from the nonlinear model and accurate modeling requires
inclusion of the full thermal model. However, for coated C3F8 bubbles of
diameter 1-8 $\mu m$, typically used in medical ultrasound, thermal effects
maybe neglected even at higher pressures. We show that the scattering to
damping ratio (STDR), a measure of the effectiveness of the bubble as contrast
agent, is pressure dependent and can be maximized for specific frequency ranges
and pressures. | 1909.08793v1 |
2020-11-20 | The effect of magnetic field on the damping of slow waves in the solar corona | Slow magnetoacoustic waves are routinely observed in astrophysical plasma
systems such as the solar corona. As a slow wave propagates through a plasma,
it modifies the equilibrium quantities of density, temperature, and magnetic
field. In the corona and other plasma systems, the thermal equilibrium is
comprised of a balance between continuous heating and cooling processes, the
magnitudes of which vary with density, temperature and magnetic field. Thus the
wave may induce a misbalance between these competing processes. Its back
reaction on the wave has been shown to lead to dispersion, and amplification or
damping, of the wave. In this work the importance of the effect of magnetic
field in the rapid damping of slow waves in the solar corona by heating/cooling
misbalance is evaluated and compared to the effects of thermal conduction. The
two timescales characterising the effect of misbalance are derived and
calculated for plasma systems with a range of typical coronal conditions. The
predicted damping times of slow waves from thermal misbalance in the solar
corona are found to be of the order of 10-100 minutes, coinciding with the wave
periods and damping times observed. Moreover the slow wave damping by thermal
misbalance is found to be comparable to the damping by field-aligned thermal
conduction. We show that in the infinite field limit, the wave dynamics is
insensitive to the dependence of the heating function on the magnetic field,
and this approximation is found to be valid in the corona so long as the
magnetic field strength is greater than 10G for quiescent loops and plumes and
100G for hot and dense loops. In summary thermal misbalance may damp slow
magnetoacoustic waves rapidly in much of the corona, and its inclusion in our
understanding of slow mode damping may resolve discrepancies between
observations and theory relying on compressive viscosity and thermal conduction
alone. | 2011.10437v1 |
1997-11-25 | Abundances of Heavy Elements and CO Molecules in High Redshift Damped Lyman-alpha Galaxies | Damped Lyman-alpha systems seen in spectra of background quasars are
generally thought to represent high redshift counterparts of present-day
galaxies. We summarize observations of heavy element abundances in damped
Lyman-alpha systems. The results of a systematic search for CO and C II*
absorption in 17 damped Lyman-alpha systems are also presented using
observations obtained with the 10m Keck telescopes. The latter provides a
useful constraint on the expected strength of [C II] 158 micron emission from
damped Lyman-alpha galaxies. It is hoped that these results will be useful for
planning future radio to millimeter wave observations of high redshift galaxies
using next generation instruments which are now being built. | 9711298v1 |
1997-12-05 | Magnetohydrodynamics in the Early Universe and the Damping of Non-linear Alfven Waves | The evolution and viscous damping of cosmic magnetic fields in the early
universe, is analysed. Using the fact that the fluid, electromagnetic, and
shear viscous energy-momentum tensors are all conformally invariant, the
evolution is transformed from the expanding universe setting into that in flat
spacetime. Particular attention is paid to the evolution of nonlinear Alfven
modes. For a small enough magnetic field, which satisfies our observational
constraints, these wave modes either oscillate negligibly or, when they do
oscillate, become overdamped. Hence they do not suffer Silk damping on galactic
and subgalactic scales. The smallest scale which survives damping depends on
the field strength and is of order a dimensionless Alfven velocity times the
usual baryon-photon Silk damping scale. After recombination, nonlinear effects
can convert the Alfven mode into compressional, gravitationally unstable waves
and seed cosmic structures if the cosmic magnetic field is sufficiently strong. | 9712083v1 |
2001-08-09 | Are Simulations of CDM Consistent with Galactic-Scale Observations at High Redshift? | We compare new observations on the kinematic characteristics of the damped
Lya systems against results from numerical SPH simulations to test the
predictions of hierarchical galaxy formation. This exercise is particularly
motivated by recent numerical results on the cross-section of damped Lya
systems. Our analysis focuses on the velocity widths of ~50 low-ion absorption
profiles from our sample of z>1.5 damped Lya systems. The results indicate that
current numerical simulations fail to match the damped Lya observations at high
confidence levels (>99.9%). Although we do not believe that our results present
an insurmountable challenge to the paradigm of hierarchical cosmology, the
damped Lya observations suggest that current numerical SPH simulations overlook
an integral aspect of galaxy formation. | 0108154v1 |
2003-03-19 | Distinct Abundance Patterns in Multiple Damped Ly-alpha Galaxies: Evidence for Truncated Star Formation? | (abridged) Following our previous work on metal abundances of a double damped
Ly-alpha system with a line-of-sight separation ~2000 km/s (Ellison & Lopez
2001), we present VLT UVES abundances of 3 new systems spanning a total of
\~6000 km/s at z~2.5 toward the southern QSO CTQ247. These abundances are
supplemented with echelle observations of another `double' damped Ly-alpha
system in the literature. We propose a definition in terms of velocity shift of
the sub-class 'multiple damped Ly-alpha system', which is motivated by its
possible connection with large-scale structure. We find that the abundance
ratio alpha/Fe is systematically low in multiple systems compared with single
systems, and with a small scatter. The same behavior is found in 2 more single
DLA systems taken from the literature that show evidence of belonging to a
galaxy group. After a careful investigation of possible sources of systematic
errors, we conclude that the low alpha/Fe ratios in multiple DLAs have a
nucleosynthetic origin. We suggest that they could be explained by reduced star
formation in multiple damped Ly-alpha systems, possibly due to environmental
effects. | 0303441v1 |
2003-05-16 | New Damped Lya Metallicities from ESI Spectroscopy of Five Palomar Sky Survey Quasars | This paper presents chemical abundance measurements for 12 new z>3 damped Lya
systems discovered toward five quasars from the Palomar Sky Survey. We
determine HI column densities from profile fits to the observed damped Lya
profiles and measure ionic column densities and limits for all observed
metal-line transitions. This dataset, acquired with the Echellette Spectrograph
and Imager on the KeckII telescope, adds to the rapidly growing database of
damped Lya abundances. It will impact studies of chemical evolution in the
early universe and help identify candidates for detailed follow-up observations
with echelle spectrographs. We report the discovery of the first quasar
sightline with four cosmologically distinct damped Lya systems. | 0305313v1 |
2006-07-06 | Ekman layer damping of r-modes revisited | We investigate the damping of neutron star r-modes due to the presence of a
viscous boundary (Ekman) layer at the interface between the crust and the core.
Our study is motivated by the possibility that the gravitational-wave driven
instability of the inertial r-modes may become active in rapidly spinning
neutron stars, eg. in low-mass X-ray binaries, and the fact that a viscous
Ekman layer at the core-crust interface provides an efficient damping mechanism
for these oscillations. We review various approaches to the problem and carry
out an analytic calculation of the effects due to the Ekman layer for a rigid
crust. Our analytic estimates support previous numerical results, and provide
further insight into the intricacies of the problem. We add to previous work by
discussing the effect that compressibility and composition stratification have
on the boundary layer damping. We show that, while stratification is
unimportant for the r-mode problem, composition suppresses the damping rate by
about a factor of two (depending on the detailed equation of state). | 0607105v2 |
1997-11-05 | Hydrodynamic damping in trapped Bose gases | Griffin, Wu and Stringari have derived the hydrodynamic equations of a
trapped dilute Bose gas above the Bose-Einstein transition temperature. We give
the extension which includes hydrodynamic damping, following the classic work
of Uehling and Uhlenbeck based on the Chapman-Enskog procedure. Our final
result is a closed equation for the velocity fluctuations $\delta v$ which
includes the hydrodynamic damping due to the shear viscosity $\eta$ and the
thermal conductivity $\kappa$. Following Kavoulakis, Pethick and Smith, we
introduce a spatial cutoff in our linearized equations when the density is so
low that the hydrodynamic description breaks down. Explicit expressions are
given for $\eta$ and $\kappa$, which are position-dependent through dependence
on the local fugacity when one includes the effect of quantum degeneracy of the
trapped gas. We also discuss a trapped Bose-condensed gas, generalizing the
work of Zaremba, Griffin and Nikuni to include hydrodynamic damping due to the
(non-condensate) normal fluid. | 9711036v4 |
1998-05-01 | Finite Temperature Perturbation Theory for a Spatially Inhomogeneous Bose-condensed Gas | We develop a finite temperature perturbation theory (beyond the mean field)
for a Bose-condensed gas and calculate temperature-dependent damping rates and
energy shifts for Bogolyubov excitations of any energy. The theory is
generalized for the case of excitations in a spatially inhomogeneous (trapped)
Bose-condensed gas, where we emphasize the principal importance of
inhomogeneouty of the condensate density profile and develop the method of
calculating the self-energy functions. The use of the theory is demonstrated by
calculating the damping rates and energy shifts of low-energy quasiclassical
excitations, i.e. the quasiclassical excitations with energies much smaller
than the mean field interaction between particles. In this case the boundary
region of the condensate plays a crucial role, and the result for the damping
rates and energy shifts is completely different from that in spatially
homogeneous gases. We also analyze the frequency shifts and damping of sound
waves in cylindrical Bose condensates and discuss the role of damping in the
recent MIT experiment on the sound propagation. | 9805015v2 |
2003-10-18 | Experiment and Dynamic Simulations of Radiation Damping of Laser-polarized liquid 129Xe at low magnetic field in a flow system | Radiation damping is generally observed when the sample with high spin
concentration and high gyro-magnetic ratio is placed in a high magnetic field.
However, we firstly observed liquid state 129Xe radiation damping using
laser-enhanced nuclear polarization at low magnetic field in a flow system in
which the polarization enhancement factor for the liquid state 129Xe was
estimated to be 5000, and furthermore theoretically simulated the envelopes of
the 129Xe FID and spectral lineshape in the presence of both relaxation and
radiation damping with different pulse flip angles and ratios of T2*/Trd. The
radiation damping time constant Trd of 5 ms was derived based on the
simulations. The reasons of depolarization and the further possible
improvements were also discussed. | 0310435v1 |
2004-03-25 | XMCD characterization of rare-earth dopants in Ni$_{81}$Fe$_{19}$(50nm): microscopic basis of engineered damping | We present direct evidence for the contribution of local orbital moments to
the damping of magnetization precession in magnetic thin films. Using x-ray
magnetic circular dichroism (XMCD) characterization of rare-earth (RE)
M$_{4,5}$ edges in Ni$_{81}$Fe$_{19}$ doped with $<$ 2% Gd and Tb, we show that
the enhancement of GHz precessional relaxation is accompanied by a significant
orbital moment fraction on the RE site. Tb impurities, which enhance the
Landau-Lifshitz(-Gilbert) LL(-G) damping $\lambda(\alpha)$, show a spin to
orbital number ratio of 1.5$\pm$0.3; Gd impurities, which have no effect on
damping, show a spin to orbital number ratio of zero within experimental error.
The results indicate that the dopant-based control of magnetization damping in
RE-doped ferromagnets is an atomistic effect, arising from spin-lattice
coupling, and thus scalable to nanometer dimensions. | 0403627v1 |
2005-02-08 | Landau Damping of Spin Waves in Trapped Boltzmann Gases | A semiclassical method is used to study Landau damping of transverse
pseudo-spin waves in harmonically trapped ultracold gases in the collisionless
Boltzmann limit. In this approach, the time evolution of a spin is calculated
numerically as it travels in a classical orbit through a spatially dependent
mean field. This method reproduces the Landau damping results for spin-waves in
unbounded systems obtained with a dielectric formalism. In trapped systems, the
simulations indicate that Landau damping occurs for a given spin-wave mode
because of resonant phase space trajectories in which spins are "kicked out" of
the mode (in spin space). A perturbative analysis of the resonant and nearly
resonant trajectories gives the Landau damping rate, which is calculated for
the dipole and quadrupole modes as a function of the interaction strength. The
results are compared to a numerical solution of the kinetic equation by Nikuni
et al. | 0502189v1 |
2005-06-01 | Landau damping of Bogoliubov excitations in optical lattices at finite temperature | We study the damping of Bogoliubov excitations in an optical lattice at
finite temperatures. For simplicity, we consider a Bose-Hubbard tight-binding
model and limit our analysis to the lowest excitation band. We use the Popov
approximation to calculate the temperature dependence of the number of
condensate atoms $n^{\rm c 0}(T)$ in each lattice well. We calculate the Landau
damping of a Bogoliubov excitation in an optical lattice due to coupling to a
thermal cloud of excitations. While most of the paper concentrates on 1D
optical lattices, we also briefly present results for 2D and 3D lattices. For
energy conservation to be satisfied, we find that the excitations in the
collision process must exhibit anomalous dispersion ({\it i.e.} the excitation
energy must bend upward at low momentum), as also exhibited by phonons in
superfluid $^4\rm{He}$. This leads to the sudden disappearance of all damping
processes in $D$-dimensional simple cubic optical lattice when $U n^{\rm c
0}\ge 6DJ$, where $U$ is the on-site interaction, and $J$ is the hopping matrix
element. Beliaev damping in a 1D optical lattice is briefly discussed. | 0506016v1 |
2006-06-15 | Landau damping: instability mechanism of superfluid Bose gases moving in optical lattices | We investigate Landau damping of Bogoliubov excitations in a dilute Bose gas
moving in an optical lattice at finite temperatures. Using a 1D tight-binding
model, we explicitly obtain the Landau damping rate, the sign of which
determines the stability of the condensate. We find that the sign changes at a
certain condensate velocity, which is exactly the same as the critical velocity
determined by the Landau criterion of superfluidity. This coincidence of the
critical velocities reveals the microscopic mechanism of the Landau
instability. This instability mechanism is also consistent with the recent
experiment suggesting that a thermal cloud plays a crucial role in breakdown of
superfluids, since the thermal cloud is also vital in the Landau damping
process. We also examine the possibility of simultaneous disappearance of all
damping processes. | 0606398v2 |
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