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1996-08-14 | Ginzburg-Landau-Gor'kov Theory of Magnetic oscillations in a type-II 2-dimensional Superconductor | We investigate de Haas-van Alphen (dHvA) oscillations in the mixed state of a
type-II two-dimensional superconductor within a self-consistent Gor'kov
perturbation scheme. Assuming that the order parameter forms a vortex lattice
we can calculate the expansion coefficients exactly to any order. We have
tested the results of the perturbation theory to fourth and eight order against
an exact numerical solution of the corresponding Bogoliubov-de Gennes
equations. The perturbation theory is found to describe the onset of
superconductivity well close to the transition point $H_{c2}$. Contrary to
earlier calculations by other authors we do not find that the perturbative
scheme predicts any maximum of the dHvA-oscillations below $H_{c2}$. Instead we
obtain a substantial damping of the magnetic oscillations in the mixed state as
compared to the normal state. We have examined the effect of an oscillatory
chemical potential due to particle conservation and the effect of a finite
Zeeman splitting. Furthermore we have investigated the recently debated issue
of a possibility of a sign change of the fundamental harmonic of the magnetic
oscillations. Our theory is compared with experiment and we have found good
agreement. | 9608004v3 |
2007-10-04 | Detailed Examination of Transport Coefficients in Cubic-Plus-Quartic Oscillator Chains | We examine the thermal conductivity and bulk viscosity of a one-dimensional
(1D) chain of particles with cubic-plus-quartic interparticle potentials and no
on-site potentials. This system is equivalent to the FPU-alpha beta system in a
subset of its parameter space. We identify three distinct frequency regimes
which we call the hydrodynamic regime, the perturbative regime and the
collisionless regime. In the lowest frequency regime (the hydrodynamic regime)
heat is transported ballistically by long wavelength sound modes. The model
that we use to describe this behaviour predicts that as the frequency goes to
zero the frequency dependent bulk viscosity and the frequency dependent thermal
conductivity should diverge with the same power law dependence on frequency.
Thus, we can define the bulk Prandtl number as the ratio of the bulk viscosity
to the thermal conductivity (with suitable prefactors to render it
dimensionless). This dimensionless ratio should approach a constant value as
frequency goes to zero. We use mode-coupling theory to predict the zero
frequency limit. Values of the bulk Prandtl number from simulations are in
agreement with these predictions over a wide range of system parameters. In the
middle frequency regime, which we call the perturbative regime, heat is
transported by sound modes which are damped by four-phonon processes. We call
the highest frequency regime the collisionless regime since at these
frequencies the observing times are much shorter than the characteristic
relaxation times of phonons. The perturbative and collisionless regimes are
discussed in detail in the appendices. | 0710.1066v1 |
2008-01-01 | Radiative torques alignment in the presence of pinwheel torques | We study the alignment of grains subject to both radiative torques and
pinwheel torques while accounting for thermal flipping of grains. By pinwheel
torques we refer to all systematic torques that are fixed in grain body axes,
including the radiative torques arising from scattering and absorption of
isotropic radiation. We discuss new types of pinwheel torques, which are
systematic torques arising from infrared emission and torques arising from the
interaction of grains with ions and electrons in hot plasma. We show that both
types of torques are long-lived, i.e. may exist longer than gaseous damping
time. We compare these torques with the torques introduced by E. Purcell,
namely, torques due to H$_2$ formation, the variation of accommodation
coefficient for gaseous collisions and photoelectric emission. Furthermore, we
revise the Lazarian & Draine model for grain thermal flipping. We calculate
mean flipping timescale induced by Barnett and nuclear relaxation for both
paramagnetic and superparamagnetic grains, in the presence of stochastic
torques associated with pinwheel torques, e.g. the stochastic torques arising
from H$_2$ formation, and gas bombardment. We show that the combined effect of
internal relaxation and stochastic torques can result in fast flipping for
sufficiently small grains and, because of this, they get thermally trapped,
i.e. rotate thermally in spite of the presence of pinwheel torques. For
sufficiently large grains, we show that the pinwheel torques can increase the
degree of grain alignment achievable with the radiative torques by increasing
the magnitude of the angular momentum of low attractor points and/or by driving
grains to new high attractor points. | 0801.0266v2 |
2008-09-09 | Turbulent Convection in Stellar Interiors. II. The Velocity Field | We analyze stellar convection with the aid of 3D hydrodynamic simulations,
introducing the turbulent cascade into our theoretical analysis. We devise
closures of the Reynolds-decomposed mean field equations by simple physical
modeling of the simulations (we relate temperature and density fluctuations via
coefficients); the procedure (CABS, Convection Algorithms Based on Simulations)
is terrestrially testable and is amenable to systematic improvement. We develop
a turbulent kinetic energy equation which contains both nonlocal and time
dependent terms, and is appropriate if the convective transit time is shorter
than the evolutionary time scale. The interpretation of mixing-length theory
(MLT) as generally used in astrophysics is incorrect; MLT forces the mixing
length to be an imposed constant. Direct tests show that the damping associated
with the flow is that suggested by Kolmogorov. The eddy size is approximately
the depth of the convection zone, and this dissipation length corresponds to
the "mixing length". New terms involving local heating by turbulent dissipation
should appear in the stellar evolution equations. The enthalpy flux
("convective luminosity") is directly connected to the buoyant acceleration,
and hence the velocity scale. MLT tends to systematically underestimate this
velocity scale. Quantitative comparison with a variety of 3D simulations
reveals a previously recognized consistency. Examples of application to stellar
evolution will be presented in subsequent papers in this series. | 0809.1625v2 |
2011-04-04 | The underlying physical meaning of the $ν_{\rm max}-ν_{\rm c}$ relation | Asteroseismology of stars that exhibit solar-like oscillations are enjoying a
growing interest with the wealth of observational results obtained with the
CoRoT and Kepler missions. In this framework, scaling laws between
asteroseismic quantities and stellar parameters are becoming essential tools to
study a rich variety of stars. However, the physical underlying mechanisms of
those scaling laws are still poorly known. Our objective is to provide a
theoretical basis for the scaling between the frequency of the maximum in the
power spectrum ($\nu_{\rm max}$) of solar-like oscillations and the cut-off
frequency ($\nu_{\rm c}$). Using the SoHO GOLF observations together with
theoretical considerations, we first confirm that the maximum of the height in
oscillation power spectrum is determined by the so-called \emph{plateau} of the
damping rates. The physical origin of the plateau can be traced to the
destabilizing effect of the Lagrangian perturbation of entropy in the
upper-most layers which becomes important when the modal period and the local
thermal relaxation time-scale are comparable. Based on this analysis, we then
find a linear relation between $\nu_{\rm max}$ and $\nu_{\rm c}$, with a
coefficient that depends on the ratio of the Mach number of the exciting
turbulence to the third power to the mixing-length parameter. | 1104.0630v2 |
2012-04-09 | Global MRI with Braginskii viscosity in a galactic profile | We present a global-in-radius linear analysis of the axisymmetric
magnetorotational instability (MRI) in a collisional magnetized plasma with
Braginskii viscosity. For a galactic angular velocity profile $\Omega$ we
obtain analytic solutions for three magnetic field orientations: purely
azimuthal, purely vertical and slightly pitched (almost azimuthal). In the
first two cases the Braginskii viscosity damps otherwise neutrally stable
modes, and reduces the growth rate of the MRI respectively. In the final case
the Braginskii viscosity makes the MRI up to $2\sqrt{2}$ times faster than its
inviscid counterpart, even for \emph{asymptotically small} pitch angles. We
investigate the transition between the Lorentz-force-dominated and the
Braginskii viscosity-dominated regimes in terms of a parameter $\sim \Omega
\nub/B^2$ where $\nub$ is the viscous coefficient and $B$ the Alfv\'en speed.
In the limit where the parameter is small and large respectively we recover the
inviscid MRI and the magnetoviscous instability (MVI). We obtain asymptotic
expressions for the approach to these limits, and find the Braginskii viscosity
can magnify the effects of azimuthal hoop tension (the growth rate becomes
complex) by over an order of magnitude. We discuss the relevance of our results
to the local approximation, galaxies and other magnetized astrophysical
plasmas. Our results should prove useful for benchmarking codes in global
geometries. | 1204.1948v1 |
2012-10-25 | Gravitational bremsstrahlung in ultra-planckian collisions | A classical computation of gravitational bremsstrahlung in ultra-planckian
collisions of massive point particles is presented in an arbitrary number d of
toroidal or non-compact extra dimensions. Our method generalizes the
post-linear formalism of General Relativity to the multidimensional case. The
total emitted energy, as well as its angular and frequency distribution are
discussed in detail. In terms of the gravitational radius r_S of the collision
energy, the impact parameter b and the Lorentz factor in the CM frame, the
leading order radiation efficiency in the Lab frame is shown to be of order
(r_S/b)^{3(d+1)} gamma_{cm} for d=0, 1 and of order (r_S/b)^{3(d+1)}
gamma_{cm}^{2d-3} for d>1, up to a known d-dependent coefficient and a ln
gamma_{cm} factor for d=2, while the characteristic frequency of the radiation
is gamma/b. The contribution of the low frequency part of the radiation (soft
gravitons) to the total radiated energy is shown to be negligible for all
values of d. The domain of validity of the classical result is discussed.
Finally, it is shown that within the region of validity of our approach the
efficiency can obtain unnatural values greater than one, which is interpreted
to mean that the peripheral ultra-planckian collisions should be strongly
radiation damped. | 1210.6976v1 |
2013-07-29 | Shear shocks in fragile networks | A minimal model for studying the mechanical properties of amorphous solids is
a disordered network of point masses connected by unbreakable springs. At a
critical value of its mean connectivity, such a network becomes fragile: it
undergoes a rigidity transition signaled by a vanishing shear modulus and
transverse sound speed. We investigate analytically and numerically the linear
and non-linear visco-elastic response of these fragile solids by probing how
shear fronts propagate through them. Our approach, that we tentatively label
shear front rheology, provides an alternative route to standard oscillatory
rheology. In the linear regime, we observe at late times a diffusive broadening
of the fronts controlled by an effective shear viscosity that diverges at the
critical point. No matter how small the microscopic coefficient of dissipation,
strongly disordered networks behave as if they were over-damped because energy
is irreversibly leaked into diverging non-affine fluctuations. Close to the
transition, the regime of linear response becomes vanishingly small: the
tiniest shear strains generate strongly non-linear shear shock waves
qualitatively different from their compressional counterparts in granular
media. The inherent non-linearities trigger an energy cascade from low to high
frequency components that keep the network away from attaining the quasi-static
limit. This mechanism, reminiscent of acoustic turbulence, causes a
super-diffusive broadening of the shock width. | 1307.7665v1 |
2014-01-30 | From the Samuelson Volatility Effect to a Samuelson Correlation Effect: Evidence from Crude Oil Calendar Spread Options | We introduce a multi-factor stochastic volatility model based on the
CIR/Heston stochastic volatility process. In order to capture the Samuelson
effect displayed by commodity futures contracts, we add expiry-dependent
exponential damping factors to their volatility coefficients. The pricing of
single underlying European options on futures contracts is straightforward and
can incorporate the volatility smile or skew observed in the market. We
calculate the joint characteristic function of two futures contracts in the
model in analytic form and use the one-dimensional Fourier inversion method of
Caldana and Fusai (JBF 2013) to price calendar spread options. The model leads
to stochastic correlation between the returns of two futures contracts. We
illustrate the distribution of this correlation in an example. We then propose
analytical expressions to obtain the copula and copula density directly from
the joint characteristic function of a pair of futures. These expressions are
convenient to analyze the term-structure of dependence between the two futures
produced by the model. In an empirical application we calibrate the proposed
model to volatility surfaces of vanilla options on WTI. In this application we
provide evidence that the model is able to produce the desired stylized facts
in terms of volatility and dependence. In a separate appendix, we give guidance
for the implementation of the proposed model and the Fourier inversion results
by means of one and two-dimensional FFT methods. | 1401.7913v3 |
2014-02-04 | Complete Tidal Evolution of Pluto-Charon | Both Pluto and its satellite Charon have rotation rates synchronous with
their orbital mean motion. This is the theoretical end point of tidal evolution
where transfer of angular momentum has ceased. Here we follow Pluto's tidal
evolution from an initial state having the current total angular momentum of
the system but with Charon in an eccentric orbit with semimajor axis $a \approx
4R_P$ (where $R_P$ is the radius of Pluto), consistent with its impact origin.
Two tidal models are used, where the tidal dissipation function $Q \propto$
1/frequency and $Q=$ constant, where details of the evolution are strongly
model dependent. The inclusion of the gravitational harmonic coefficient
$C_{22}$ of both bodies in the analysis allows smooth, self consistent
evolution to the dual synchronous state, whereas its omission frustrates
successful evolution in some cases. The zonal harmonic $J_2$ can also be
included, but does not cause a significant effect on the overall evolution. The
ratio of dissipation in Charon to that in Pluto controls the behavior of the
orbital eccentricity, where a judicious choice leads to a nearly constant
eccentricity until the final approach to dual synchronous rotation. The tidal
models are complete in the sense that every nuance of tidal evolution is
realized while conserving total angular momentum - including temporary capture
into spin-orbit resonances as Charon's spin decreases and damped librations
about the same. | 1402.0625v1 |
2014-07-11 | Chiral Hall Effect and Chiral Electric Waves | We investigate the vector and axial currents induced by external
electromagnetic fields and chemical potentials in chiral systems at finite
temperature. Similar to the normal Hall effect, we find that an axial Hall
current is generated in the presence of the electromagnetic fields along with
an axial chemical potential, which may be dubbed as the "chiral Hall
effect"(CHE). The CHE is related to the interactions of chiral fermions and
exists with the a nonzero axial chemical potential. We argue that the CHE could
lead to nontrivial charge distributions at different rapidity in asymmetric
heavy ion collisions. Moreover, we study the chiral electric waves(CEW) led by
the fluctuations of the vector and axial chemical potentials along with the
chiral electric separation effect(CESE), where a density wave propagates along
the applied electric field. Combining with the normal/chiral Hall effects, the
fluctuations of chemical potentials thus result in Hall density waves. The Hall
density waves may survive even at zero chemical potentials and become
non-dissipative. We further study the transport coefficients including the Hall
conductivities, damping times, wave velocities, and diffusion constants of CEW
in a strongly coupled plasma via the AdS/CFT correspondence. | 1407.3168v3 |
2014-09-01 | Interface-resolved direct numerical simulation of the erosion of a sediment bed sheared by laminar channel flow | A numerical method based upon the immersed boundary technique for the
fluid-solid coupling and on a soft-sphere approach for solid-solid contact is
used to perform direct numerical simulation of the flow-induced motion of a
thick bed of spherical particles in a horizontal plane channel. The collision
model features a normal force component with a spring and a damper, as well as
a damping tangential component, limited by a Coulomb friction law. The standard
test case of a single particle colliding perpendicularly with a horizontal wall
in a viscous fluid is simulated over a broad range of Stokes numbers, yielding
values of the effective restitution coefficient in close agreement with
experimental data. The case of bedload particle transport by laminar channel
flow is simulated for 24 different parameter values covering a broad range of
the Shields number. Comparison of the present results with reference data from
the experiment of Aussillous et al. (J. Fluid Mech. 2013) yields excellent
agreement. It is confirmed that the particle flow rate varies with the third
power of the Shields number once the known threshold value is exceeded. The
present data suggests that the thickness of the mobile particle layer
(normalized with the height of the clear fluid region) increases with the
square of the normalized fluid flow rate. | 1409.0339v1 |
2014-10-28 | Equations of a Moving Mirror and the Electromagnetic Field | We consider a system composed of a mobile slab and the electromagnetic field.
We assume that the slab is made of a material that has the following properties
when it is at rest: it is linear, isotropic, non-magnetizable, and ohmic with
zero free charge density. Using instantaneous Lorentz transformations, we
deduce the set of self-consistent equations governing the dynamics of the
system and we obtain approximate equations to first order in the velocity and
the acceleration of the slab. As a consequence of the motion of the slab, the
field must satisfy a wave equation with damping and slowly varying coefficients
plus terms that are small when the time-scale of the evolution of the mirror is
much smaller than that of the field. Also, the motion of the slab and its
interaction with the field introduce two effects in the slab's equation of
motion. The first one is a position- and time-dependent mass related to the
$\textit{effective mass}$ taken in phenomenological treatments of this type of
systems. The second one is a velocity-dependent force that can give rise to
friction and that is related to the much sought $\textit{cooling}$ of
mechanical objects. | 1410.7609v2 |
2014-12-17 | Fluctuation-dissipation dynamics of cosmological scalar fields | We show that dissipative effects have a significant impact on the evolution
of cosmological scalar fields, leading to friction, entropy production and
field fluctuations. We explicitly compute the dissipation coefficient for
different scalar fields within the Standard Model and some of its most widely
considered extensions, in different parametric regimes. We describe the generic
consequences of fluctuation-dissipation dynamics in the post-inflationary
universe, focusing in particular on friction and particle production, and
analyze in detail two important effects. Firstly, we show that dissipative
friction delays the process of spontaneous symmetry breaking and may even damp
the the motion of a Higgs field sufficiently to induce a late period of warm
inflation. Along with dissipative entropy production, this may parametrically
dilute the abundance of dangerous thermal relics. Secondly, we show that
dissipation can generate the observed baryon asymmetry without symmetry
restoration, and we develop in detail a model of dissipative leptogenesis. We
further show that this generically leads to characteristic baryon isocurvature
perturbations that can be tested with CMB observations. This work provides a
fundamental framework to go beyond the leading thermal equilibrium
semi-classical approximation in addressing fundamental problems in modern
cosmology. | 1412.5489v2 |
2014-12-22 | H$_2$ Lyman and Werner band lines and their sensitivity for a variation of the proton-electron mass ratio in the gravitational potential of white dwarfs | Recently an accurate analysis of absorption spectra of molecular hydrogen,
observed with the Cosmic Origins Spectrograph aboard the Hubble Space
Telescope, in the photosphere of white dwarf stars GD133 and GD29-38 was
published in a Letter [Phys. Rev. Lett. 113, 123002 (2014)], yielding a
constraint on a possible dependence of the proton-electron mass ratio on a
gravitational field of strength 10,000 times that at the Earth's surface. In
the present paper further details of that study are presented, in particular a
re-evaluation of the spectrum of the $B^1\Sigma_u^+ - X^1\Sigma_g^+ (v',v'')$
Lyman bands relevant for the prevailing temperatures (12,000 - 14,000 K) of the
photospheres. An emphasis is on the calculation of so-called
$K_i$-coefficients, that represent the sensitivity of each individual line to a
possible change in the proton-electron mass ratio. Such calculations were
performed by semi-empirical methods and by ab initio methods providing accurate
and consistent values. A full listing is provided for the molecular physics
data on the Lyman bands (wavelengths $\lambda_i$, line oscillator strengths
$f_i$, radiative damping rates $\Gamma_i$, and sensitivity coefficients $K_i$)
as required for the analyses of H$_2$-spectra in hot dwarf stars. A similar
listing of the molecular physics parameters for the $C^1\Pi_u - X^1\Sigma_g^+
(v',v'')$ Werner bands is provided for future use in the analysis of white
dwarf spectra. | 1412.6920v1 |
2014-12-11 | Modeling the Aerodynamic Lift Produced by Oscillating Airfoils at Low Reynolds Number | For present study, setting Strouhal Number (St) as control parameter,
numerical simulations for flow past oscillating NACA-0012 airfoil at 1,000
Reynolds Numbers (Re) are performed. Temporal profiles of unsteady forces; lift
and thrust, and their spectral analysis clearly indicate the solution to be a
period-1 attractor for low Strouhal numbers. This study reveals that
aerodynamic forces produced by plunging airfoil are independent of initial
kinematic conditions of airfoil that proves the existence of limit cycle.
Frequencies present in the oscillating lift force are composed of fundamental
(fs), even and odd harmonics (3fs) at higher Strouhal numbers. Using numerical
simulations, shedding frequencies (f_s) were observed to be nearly equal to the
excitation frequencies in all the cases. Unsteady lift force generated due to
the plunging airfoil is modeled by modified van der Pol oscillator. Using
method of multiple scales and spectral analysis of steady-state CFD solutions,
frequencies and damping terms in the van der Pol oscillator model are
estimated. We prove the applicability of this model to all planar motions of
airfoil; plunging, pitching and flapping. An important aspect of
currently-proposed model is capturing the time-averaged value of aerodynamic
lift coefficient. | 1502.06431v1 |
2015-03-09 | Boundedness in a quasilinear fully parabolic Keller-Segel system of higher dimension with logistic source | This paper deals with the higher dimension quasilinear parabolic-parabolic
Keller-Segel system involving a source term of logistic type $
u_t=\nabla\cdot(\phi(u)\nabla u)-\chi\nabla\cdot(u\nabla v)+g(u)$, $\tau
v_t=\Delta v-v+u$ in $\Omega\times (0,T)$, subject to nonnegative initial data
and homogeneous Neumann boundary condition, where $\Omega$ is smooth and
bounded domain in $\mathbb{R}^n$, $n\ge 2$, $\phi$ and $g$ are smooth and
positive functions satisfying $ks^p\le\phi$ when $s\ge s_0>1$, $g(s) \le as -
\mu s^2$ for $s>0$ with $g(0)\ge0$ and constants $a\ge 0$, $\tau,\chi,\mu>0$.
It was known that the model without the logistic source admits both bounded and
unbounded solutions, identified via the critical exponent $\frac{2}{n}$. On the
other hand, the model is just a critical case with the balance of logistic
damping and aggregation effects, for which the property of solutions should be
determined by the coefficients involved. In the present paper it is proved that
there is $\theta_0>0$ such that the problem admits global bounded classical
solutions, regardless of the size of initial data and diffusion whenever
$\frac{\chi}{\mu}<\theta_0$. This shows the substantial effect of the logistic
source to the behavior of solutions. | 1503.02387v1 |
2015-03-16 | Effect of primordial magnetic fields on the ionization history | Primordial magnetic fields (PMF) damp at scales smaller than the photon
diffusion and free-streaming scale. This leads to heating of ordinary matter
(electrons and baryons), which affects both the thermal and ionization history
of our Universe. Here, we study the effect of heating due to ambipolar
diffusion and decaying magnetic turbulence. We find that changes to the
ionization history computed with recfast are significantly overestimated when
compared with CosmoRec. The main physical reason for the difference is that the
photoionization coefficient has to be evaluated using the radiation temperature
rather than the matter temperature. A good agreement with CosmoRec is found
after changing this aspect. Using Planck 2013 data and considering only the
effect of PMF-induced heating, we find an upper limit on the r.m.s. magnetic
field amplitude of B0 < 1.1 nG (95% c.l.) for a stochastic background of PMF
with a nearly scale-invariant power spectrum. We also discuss uncertainties
related to the approximations for the heating rates and differences with
respect to previous studies. Our results are important for the derivation of
constraints on the PMF power spectrum obtained from measurements of the cosmic
microwave background anisotropies with full-mission Planck data. They may also
change some of the calculations of PMF-induced effects on the primordial
chemistry and 21cm signals. | 1503.04827v1 |
2015-11-18 | Gravito-inertial waves in a differentially rotating spherical shell | The gravito-inertial waves propagating over a shellular baroclinic flow
inside a rotating spherical shell are analysed using the Boussinesq
approximation. The wave properties are examined by computing paths of
characteristics in the non-dissipative limit, and by solving the full
dissipative eigenvalue problem using a high-resolution spectral method.
Gravito-inertial waves are found to obey a mixed-type second-order operator and
to be often focused around short-period attractors of characteristics or
trapped in a wedge formed by turning surfaces and boundaries. We also find
eigenmodes that show a weak dependence with respect to viscosity and heat
diffusion just like truly regular modes. Some axisymmetric modes are found
unstable and likely destabilized by baroclinic instabilities. Similarly, some
non-axisymmetric modes that meet a critical layer (or corotation resonance) can
turn unstable at sufficiently low diffusivities. In all cases, the instability
is driven by the differential rotation. For many modes of the spectrum, neat
power laws are found for the dependence of the damping rates with diffusion
coefficients, but the theoretical explanation for the exponent values remains
elusive in general. The eigenvalue spectrum turns out to be very rich and
complex, which lets us suppose an even richer and more complex spectrum for
rotating stars or planets that own a differential rotation driven by
baroclinicity. | 1511.05832v2 |
2016-02-02 | Reflected brownian motion: selection, approximation and linearization | We construct a family of SDEs whose solutions select a reflected Brownian
flow as well as a stochastic damped transport process (W\_t). The latter gives
a representation for the solutions to the heat equation for differential
1-forms with the absolute boundary conditions; it evolves pathwise by the Ricci
curvature in the interior, by the shape operator on the boundary and driven by
the boundary local time, and has its normal part erased on the boundary. On the
half line this construction selects the Skorohod solution (and its derivative
with respect to initial points), not the Tanaka solution. On the half space
this agrees with the construction of N. Ikeda and S. Watanabe
\cite{Ikeda-Watanabe} by Poisson point processes. This leads also to an
approximation for the boundary local time in the topology of uniform
convergence; not in the semi-martingale topology, indicating the difficulty for
the convergence of solutions of a family of random ODE's, with nice
coefficients, to the solution of an equation with jumps and driven by the local
time. In addition, We note that (W\_t) is the weak derivative of a family of
reflected Brownian motions with respect to the starting point. | 1602.00897v4 |
2016-02-06 | Basic Properties of Conductivity and Normal Hall Effect in the Periodic Anderson Model | Exact formulas of diagonal conductivity $\sigma_{xx}$ and Hall conductivity
$\sigma_{xy}$ are derived from the Kubo formula in hybridized two-orbital
systems with arbitrary band dispersions. On the basis of the theoretical
framework for the Fermi liquid based on these formulas, the ground-state
properties of the periodic Anderson model with electron correlation and weak
impurity scattering are studied on the square lattice. It is shown that
imbalance of the mass-renormalization factors in $\sigma_{xx}$ and
$\sigma_{xy}$ causes remarkable increase in the valence-fluctuation regime as
the f level increases while the cancellation of the renormalization factors
causes slight increase in $\sigma_{xx}$ and $\sigma_{xy}$ in the Kondo regime.
The Hall coefficient $R_{\rm H}$ shows almost constant behavior in both the
regimes. Near half filling, $R_{\rm H}$ is expressed by the total hole density
as $R_{\rm H}=1/(\bar{n}_{\rm hole}e)$ while $R_{\rm H}$ approaches zero near
quarter filling, which reflects the curvature of the Fermi surface. These
results hold as far as the damping rate for f electrons is less than about
$10~\%$ of the renormalized hybridization gap. From these results we discuss
pressure dependence of residual resistivity and normal Hall effect in Ce- and
Yb-based heavy electron systems. | 1602.02229v1 |
2016-03-28 | Kernelized Weighted SUSAN based Fuzzy C-Means Clustering for Noisy Image Segmentation | The paper proposes a novel Kernelized image segmentation scheme for noisy
images that utilizes the concept of Smallest Univalue Segment Assimilating
Nucleus (SUSAN) and incorporates spatial constraints by computing circular
colour map induced weights. Fuzzy damping coefficients are obtained for each
nucleus or center pixel on the basis of the corresponding weighted SUSAN area
values, the weights being equal to the inverse of the number of horizontal and
vertical moves required to reach a neighborhood pixel from the center pixel.
These weights are used to vary the contributions of the different nuclei in the
Kernel based framework. The paper also presents an edge quality metric obtained
by fuzzy decision based edge candidate selection and final computation of the
blurriness of the edges after their selection. The inability of existing
algorithms to preserve edge information and structural details in their
segmented maps necessitates the computation of the edge quality factor (EQF)
for all the competing algorithms. Qualitative and quantitative analysis have
been rendered with respect to state-of-the-art algorithms and for images ridden
with varying types of noises. Speckle noise ridden SAR images and Rician noise
ridden Magnetic Resonance Images have also been considered for evaluating the
effectiveness of the proposed algorithm in extracting important segmentation
information. | 1603.08564v1 |
2016-06-11 | Characterization of base roughness for granular chute flows | Base roughness plays an important role to the dynamics of granular flows but
is yet poorly understood due to the difficulty of its quantification. For a
bumpy base made by spheres, at least two factors should be considered to
characterize its geometric roughness, namely the size ratio of base- to
flow-particles and the packing of base particles. In this paper, we propose a
definition of base roughness, Ra, which is a function of both the size ratio
and the packing arrangement of base particles. The function is generalized for
random and regular packing of multi-layered spheres, where the range of
possible values of Ra is studied, along with the optimal values to create
maximum base roughness. The new definition is applied to granular flows down
chute in both two- and three-dimensional configurations. It is proven to be a
good indicator of slip condi- tion, and a transition occurs from slip to
non-slip condition as Ra increases. Critical values of Ra are identified for
the construction of a non-slip base. The effects of contact parameters on base
velocity are studied, and it is shown that while the coefficient of friction is
less influential, normal damping has more profound effect on base velocity at
lower values of Ra. The application of present definition to other base
geometries is also discussed. | 1606.03554v1 |
2016-06-22 | Non-linear diffusion of cosmic rays escaping from supernova remnants - I. The effect of neutrals | Supernova remnants are believed to be the main sources of galactic Cosmic
Rays (CR). Within this framework, particles are accelerated at supernova
remnant shocks and then released in the interstellar medium. The mechanism
through which CRs are released and the way in which they propagate still remain
open issues. The main difficulty is the high non-linearity of the problem: CRs
themselves excite the magnetic turbulence that confines them close to their
sources. We solve numerically the coupled differential equations describing the
evolution in space and time of the escaping particles and of the waves
generated through the CR streaming instability. The warm ionized and warm
neutral phases of the interstellar medium are considered. These phases occupy
the largest fraction of the disc volume, where most supernovae explode, and are
characterised by the significant presence of neutral particles. The friction
between those neutrals and ions results in a very effective wave damping
mechanism. It is found that streaming instability affects the propagation of
CRs even in the presence of ion-neutral friction. The diffusion coefficient can
be suppressed by more than a factor of $\sim 2$ over a region of few tens of pc
around the remnant. The suppression increases for smaller distances. The
propagation of $\approx 10$ GeV particles is affected for several tens of
kiloyears after escape, while $\approx 1$ TeV particles are affected for few
kiloyears. This might have a great impact on the interpretation of gamma-ray
observations of molecular clouds located in the vicinity of supernova remnants. | 1606.06902v2 |
2016-08-29 | Hilbert space hypocoercivity for the Langevin dynamics revisited | We provide a complete elaboration of the $L^2$-Hilbert space hypocoercivity
theorem for the degenerate Langevin dynamics via studying the longtime behavior
of the strongly continuous contraction semigroup solving the associated
Kolmogorov (backward) equation as an abstract Cauchy problem. This
hypocoercivity result is proven in previous works before by Dolbeault, Mouhot
and Schmeiser in the corresponding dual Fokker-Planck framework, but without
including domain issues of the appearing operators. In our elaboration, we
include the domain issues and additionally compute the rate of convergence in
dependence of the damping coefficient. Important statements for the complete
elaboration are the m-dissipativity results for the Langevin operator
established by Conrad and the first named author of this article as well as the
essential selfadjointness results for generalized Schr\"{o}dinger operators by
Wielens or Bogachev, Krylov and R\"{o}ckner. We emphasize that the chosen
Kolmogorov approach is natural. Indeed, techniques from the theory of
(generalized) Dirichlet forms imply a stochastic representation of the Langevin
semigroup as the transition kernel of diffusion process which provides a
martingale solution to the Langevin equation. Hence an interesting connection
between the theory of hypocoercivity and the theory of (generalized) Dirichlet
forms is established besides. | 1608.07889v1 |
2017-04-06 | Evolution of a proto-neutron star with a nuclear many-body equation of state: Neutrino luminosity and gravitational wave frequencies | In a core-collapse supernova, a huge amount of energy is released in the
Kelvin-Helmholtz phase subsequent to the explosion, when the proto-neutron star
cools and deleptonizes as it loses neutrinos. Most of this energy is emitted
through neutrinos, but a fraction of it can be released through gravitational
waves. We model the evolution of a proto-neutron star in the Kelvin-Helmholtz
phase using a general relativistic numerical code, and a recently proposed
finite temperature, many-body equation of state; from this we consistently
compute the diffusion coefficients driving the evolution. To include the
many-body equation of state, we develop a new fitting formula for the high
density baryon free energy at finite temperature and intermediate proton
fraction. We estimate the emitted neutrino signal, assessing its detectability
by present terrestrial detectors, and we determine the frequencies and damping
times of the quasi-normal modes which would characterize the gravitational wave
signal emitted in this stage. | 1704.01923v2 |
2017-05-16 | A Tube Dynamics Perspective Governing Stability Transitions: An Example Based on Snap-through Buckling | The equilibrium configuration of an engineering structure, able to withstand
a certain loading condition, is usually associated with a local minimum of the
underlying potential energy. However, in the nonlinear context, there may be
other equilibria present, and this brings with it the possibility of a
transition to an alternative (remote) minimum. That is, given a sufficient
disturbance, the structure might buckle, perhaps suddenly, to another shape.
This paper considers the dynamic mechanisms under which such transitions
(typically via saddle points) occur. A two-mode Hamiltonian is developed for a
shallow arch/buckled beam. The resulting form of the potential energy---two
stable wells connected by rank-1 saddle points---shows an analogy with
resonance transitions in celestial mechanics or molecular reconfigurations in
chemistry, whereas here the transition corresponds to switching between two
stable structural configurations. Then, from Hamilton's equations, the
analytical equilibria are determined and linearization of the equations of
motion about the saddle is obtained. After computing the eigenvalues and
eigenvectors of the coefficient matrix associated with the linearization, a
symplectic transformation is given which puts the Hamiltonian into normal form
and simplifies the equations, allowing us to use the conceptual framework known
as tube dynamics. The flow in the equilibrium region of phase space as well as
the invariant manifold tubes in position space are discussed. Also, we account
for the addition of damping in the tube dynamics framework, which leads to a
richer set of behaviors in transition dynamics than previously explored. | 1705.05903v2 |
2018-02-13 | Acoustic Disturbances in Galaxy Clusters | Galaxy cluster cores are pervaded by hot gas which radiates at far too high a
rate to maintain any semblance of a steady state; this is referred to as the
cooling flow problem. Of the many heating mechanisms that have been proposed to
balance radiative cooling, one of the most attractive is dissipation of
acoustic waves generated by Active Galactic Nuclei (AGN). Fabian (2005) showed
that if the waves are nearly adiabatic, wave damping due to heat conduction and
viscosity must be well below standard Coulomb rates in order to allow the waves
to propagate throughout the core. Because of the importance of this result, we
have revisited wave dissipation under galaxy cluster conditions in a way that
accounts for the self limiting nature of dissipation by electron thermal
conduction, allows the electron and ion temperature perturbations in the waves
to evolve separately, and estimates kinetic effects by comparing to a
semi-collisionless theory. While these effects considerably enlarge the toolkit
for analyzing observations of wavelike structures and developing a quantitative
theory for wave heating, the drastic reduction of transport coefficients
proposed in Fabian (2005) remains the most viable path to acoustic wave heating
of galaxy cluster cores. | 1802.04808v2 |
2018-04-23 | Dissipation-Based Continuation Method for Multiphase Flow in Heterogeneous Porous Media | In reservoir simulation, solution of the coupled systems of nonlinear
algebraic equations that are associated with fully-implicit (backward Euler)
discretization is challenging. Having a robust and efficient nonlinear solver
is necessary in order for reservoir simulation to serve as the primary tool for
managing the recovery processes of large-scale reservoirs. Here, we develop a
continuation method based on the use of a dissipation operator. We focus on
nonlinear two-phase flow and transport in heterogeneous formations in the
presence of viscous, gravitational, and capillary forces. The homotopy is
constructed by adding numerical dissipation to the coupled discrete
conservation equations. A continuation parameter is introduced to control the
amount of dissipation. Numerical evidence of multi-dimensional models and
detailed analysis of single-cell problems are used to explain how the
dissipation operator improves the nonlinear convergence of the coupled system
of equations. An adaptive strategy to determine the dissipation coefficient is
proposed. The dissipation level is computed locally for each cell interface. We
demonstrate the efficiency of the dissipation-based continuation (DBC)
nonlinear solver using several examples, including 1D scalar transport and 2D
heterogeneous problems with fully-coupled flow and transport. The DBC solver
has better convergence properties compared with the standard damped-Newton
solvers used in reservoir simulation. | 1804.08538v2 |
2018-05-08 | A fast adhesive discrete element method for random packings of fine particles | Introducing a reduced particle stiffness in discrete element method (DEM)
allows for bigger time steps and therefore fewer total iterations in a
simulation. Although this approach works well for dry non-adhesive particles,
it has been shown that for fine particles with adhesion, system behaviors are
drastically sensitive to the particle stiffness. Besides, a simple and
applicable principle to set the parameters in adhesive DEM is also lacking. To
solve these two problems, we first propose a fast DEM based on scaling laws to
reduce particle Young's modulus, surface energy and to modify rolling and
sliding resistances simultaneously in the framework of Johnson-Kendall-Roberts
(JKR)-based contact theory. A novel inversion method is then presented to help
users to quickly determine the damping coefficient, particle stiffness and
surface energy to reproduce a prescribed experimental result. After validating
this inversion method, we apply the fast adhesive DEM to packing problems of
microparticles. Measures of packing fraction, averaged coordination number and
distributions of local packing fraction and contact number of each particle are
in good agreement with results simulated using original value of particle
properties. The new method should be helpful to accelerate DEM simulations for
systems associated with aggregates or agglomerates. | 1805.03025v2 |
2019-01-13 | Stochastic resonance and bifurcation of order parameter in a coupled system of underdamped Duffing oscillators | The long-term mean-field dynamics of coupled underdamped Duffing oscillators
driven by an external periodic signal with Gaussian noise is investigated. A
Boltzmann-type H-theorem is proved for the associated nonlinear Fokker-Planck
equation to ensure that the system can always be relaxed to one of the
stationary states as time is long enough. Based on a general framework of the
linear response theory, the linear dynamical susceptibility of the system order
parameter is explicitly deduced. With the spectral amplification factor as a
quantifying index, calculation by the method of moments discloses that both
mono-peak and double-peak resonance might appear, and that noise can greatly
signify the peak of the resonance curve of the coupled underdamped system as
compared with a single-element bistable system. Then, with the input signals
taken from laboratory experiments, further observations show that the
mean-field coupled stochastic resonance system can amplify the periodic input
signal. Also, it reveals that for some driving frequencies, the optimal
stochastic resonance parameter and the critical bifurcation parameter have a
close relationship. Moreover, it is found that the damping coefficient can also
give rise to nontrivial non-monotonic behaviors of the resonance curve, and the
resultant resonant peak attains its maximal height if the noise intensity or
the coupling strength takes the critical value. The new findings reveal the
role of the order parameter in a coupled system of chaotic oscillators. | 1901.03955v2 |
2019-03-19 | Conservative Discontinuous Galerkin Schemes for Nonlinear Fokker-Planck Collision Operators | We present a novel discontinuous Galerkin algorithm for the solution of a
class of Fokker-Planck collision operators. These operators arise in many
fields of physics, and our particular application is for kinetic plasma
simulations. In particular, we focus on an operator often known as the
`Lenard-Bernstein,' or `Dougherty,' operator. Several novel algorithmic
innovations are reported. The concept of weak-equality is introduced and used
to define weak-operators to compute primitive moments needed in the updates.
Weak-equality is also used to determine a reconstruction procedure that allows
an efficient and accurate discretization of the diffusion term. We show that
when two integration by parts are used to construct the discrete weak-form, and
finite velocity-space extents are accounted for, a scheme that conserves
density, momentum and energy exactly is obtained. One novel feature is that the
requirements of momentum and energy conservation lead to unique formulas to
compute primitive moments. Careful definition of discretized moments also
ensure that energy is conserved in the piecewise linear case, even though the
$v^2$ term is not included in the basis-set used in the discretization. A
series of benchmark problems are presented and show that the scheme conserves
momentum and energy to machine precision. Empirical evidence also indicates
that entropy is a non-decreasing function. The collision terms are combined
with the Vlasov equation to study collisional Landau damping and plasma heating
via magnetic pumping. We conclude with an outline of future work, in particular
with some indications of how the algorithms presented here can be extended to
use the Rosenbluth potentials to compute the drag and diffusion coefficients. | 1903.08062v1 |
2019-03-20 | Limits of flexural wave absorption by open lossy resonators: reflection and transmission problems | The limits of flexural wave absorption by open lossy resonators are
analytically and numerically reported in this work for both the reflection and
transmission problems. An experimental validation for the reflection problem is
presented. The reflection and transmission of flexural waves in 1D resonant
thin beams are analyzed by means of the transfer matrix method. The hypotheses,
on which the analytical model relies, are validated by experimental results.
The open lossy resonator, consisting of a finite length beam thinner than the
main beam, presents both energy leakage due to the aperture of the resonators
to the main beam and inherent losses due to the viscoelastic damping. Wave
absorption is found to be limited by the balance between the energy leakage and
the inherent losses of the open lossy resonator. The perfect compensation of
these two elements is known as the critical coupling condition and can be
easily tuned by the geometry of the resonator. On the one hand, the scattering
in the reflection problem is represented by the reflection coefficient. A
single symmetry of the resonance is used to obtain the critical coupling
condition. Therefore the perfect absorption can be obtained in this case. On
the other hand, the transmission problem is represented by two eigenvalues of
the scattering matrix, representing the symmetric and anti-symmetric parts of
the full scattering problem. In the geometry analyzed in this work, only one
kind of symmetry can be critically coupled, and therefore, the maximal
absorption in the transmission problem is limited to 0.5. The results shown in
this work pave the way to the design of resonators for efficient flexural wave
absorption. | 1903.08522v1 |
2019-04-18 | Emergence of hydrodynamical behavior in expanding quark-gluon plasmas | We use a set of simple angular moments to solve the Boltzmann equation in the
relaxation time approximation for a boost invariant longitudinally expanding
gluonic plasma. The transition from the free streaming regime at early time to
the hydrodynamic regime at late time is well captured by the first two-moments,
corresponding to the monopole and quadrupole components of the momentum
distribution, or equivalently to the energy density and the difference between
the longitudinal and the transverse pressures. We relate this property to the
existence of fixed points in the infinite hierarchy of equations satisfied by
the moments. These fixed points are already present in the two-moment
truncations and are only moderately affected by the coupling to higher moments.
Collisions contribute to a damping of all the non trivial moments. At late
time, when the hydrodynamic regime is entered, only the monopole and quadrupole
moments are significant and remain strongly coupled, the decay of the
quadrupole moment being delayed by the expansion, causing in turn a delay in
the full isotropization of the system. The two-moment truncation contains
second order viscous hydrodynamics, in its various variants, and third order
hydrodynamics, together with explicit values of the relevant transport
coefficients, can be easily obtained from the three-moment truncation. | 1904.08677v1 |
2019-04-29 | A nonlinear subgrid-scale model for large-eddy simulations of rotating turbulent flows | Rotating turbulent flows form a challenging test case for large-eddy
simulation (LES). We, therefore, propose and validate a new subgrid-scale (SGS)
model for such flows. The proposed SGS model consists of a dissipative eddy
viscosity term as well as a nondissipative term that is nonlinear in the
rate-of-strain and rate-of-rotation tensors. The two corresponding model
coefficients are a function of the vortex stretching magnitude. Therefore, the
model is consistent with many physical and mathematical properties of the
Navier-Stokes equations and turbulent stresses, and is easy to implement. We
determine the two model constants using a nondynamic procedure that takes into
account the interaction between the model terms. Using detailed direct
numerical simulations (DNSs) and LESs of rotating decaying turbulence and
spanwise-rotating plane-channel flow, we reveal that the two model terms
respectively account for dissipation and backscatter of energy, and that the
nonlinear term improves predictions of the Reynolds stress anisotropy near
solid walls. We also show that the new SGS model provides good predictions of
rotating decaying turbulence and leads to outstanding predictions of
spanwise-rotating plane-channel flow over a large range of rotation rates for
both fine and coarse grid resolutions. Moreover, the new nonlinear model
performs as well as the dynamic Smagorinsky and scaled anisotropic
minimum-dissipation models in LESs of rotating decaying turbulence and
outperforms these models in LESs of spanwise-rotating plane-channel flow,
without requiring (dynamic) adaptation or near-wall damping of the model
constants. | 1904.12748v1 |
2019-04-29 | Dynamics of scalar fields in an expanding/contracting cosmos at finite temperature | This paper extends the study of the quantum dissipative effects of a
cosmological scalar field by taking into account the cosmic expansion and
contraction. Cheung, Drewes, Kang and Kim calculated the effective action and
quantum dissipative effects of a cosmological scalar field. The analytic
expressions for the effective potential and damping coefficient were presented
using a simple scalar model with quartic interaction. Their work was done using
Minkowski-space propagators in loop diagrams. In this work we incorporate the
Hubble expansion and contraction of the comic background, and focus on the
thermal dynamics of a scalar field in a regime where the effective potential
changes slowly. We let the Hubble parameter, $H$, attain a small but non-zero
value and carry out calculations to first order in $H$. If we set $H=0$ all
results match those obtained previously in flat spacetime [1]. Interestingly we
have to integrate over the resonances, which in turn leads to an amplification
of the effects of a non-zero $H$. This is an intriguing phenomenon which cannot
be uncovered in flat spacetime. The implications on particle creations in the
early universe will be studied in a forthcoming work. | 1904.12941v2 |
2019-05-09 | Global Robustness vs. Local Vulnerabilities in Complex Synchronous Networks | In complex network-coupled dynamical systems, two questions of central
importance are how to identify the most vulnerable components and how to devise
a network making the overall system more robust to external perturbations. To
address these two questions, we investigate the response of complex networks of
coupled oscillators to local perturbations. We quantify the magnitude of the
resulting excursion away from the unperturbed synchronous state through
quadratic performance measures in the angle or frequency deviations. We find
that the most fragile oscillators in a given network are identified by
centralities constructed from network resistance distances. Further defining
the global robustness of the system from the average response over ensembles of
homogeneously distributed perturbations, we find that it is given by a family
of topological indices known as generalized Kirchhoff indices. Both resistance
centralities and Kirchhoff indices are obtained from a spectral decomposition
of the stability matrix of the unperturbed dynamics and can be expressed in
terms of resistance distances. We investigate the properties of these
topological indices in small-world and regular networks. In the case of
oscillators with homogeneous inertia and damping coefficients, we find that
inertia only has small effects on robustness of coupled oscillators. Numerical
results illustrate the validity of the theory. | 1905.03582v1 |
2019-05-20 | Out of time ordered effective dynamics of a quartic oscillator | We study the dynamics of a quantum Brownian particle weakly coupled to a
thermal bath. Working in the Schwinger-Keldysh formalism, we develop an
effective action of the particle up to quartic terms. We demonstrate that this
quartic effective theory is dual to a stochastic dynamics governed by a
non-linear Langevin equation. The Schwinger-Keldysh effective theory, or the
equivalent non-linear Langevin dynamics, is insufficient to determine the out
of time order correlators (OTOCs) of the particle. To overcome this limitation,
we construct an extended effective action in a generalised Schwinger-Keldysh
framework. We determine the additional quartic couplings in this OTO effective
action and show their dependence on the bath's 4-point OTOCs. We analyse the
constraints imposed on the OTO effective theory by microscopic reversibility
and thermality of the bath. We show that these constraints lead to a
generalised fluctuation-dissipation relation between the non-Gaussianity in the
distribution of the thermal noise experienced by the particle and the thermal
jitter in its damping coefficient. The quartic effective theory developed in
this work provides extension of several results previously obtained for the
cubic OTO dynamics of a Brownian particle. | 1905.08307v6 |
2019-06-11 | Instability of flux flow and production of vortex-antivortex pairs by current-driven Josephson vortices in layered superconductors | We report numerical simulations of the nonlinear dynamics of Josephson
vortices driven by strong dc currents in layered superconductors. Dynamic
equations for interlayer phase differences in a stack of coupled
superconducting layers were solved to calculate a drag coefficient $\eta(J)$ of
the vortex as a function of the perpendicular dc current density $J$. It is
shown that Cherenkov radiation produced by a moving vortex causes significant
radiation drag increasing $\eta(v)$ at high vortex velocities $v$ and striking
instabilities of driven Josephson vortices moving faster than a terminal
velocity $v_c$. The steady-state flux flow breaks down at $v>v_c$ as the vortex
starts producing a cascade of expanding vortex-antivortex pairs evolving into
either planar macrovortex structures or branching flux patterns propagating
both along and across the layers. The pair production triggered by a rapidly
moving vortex is most pronounced in a stack of underdamped planar junctions
where it can occur at $J>J_s$ well below the interlayer Josephson critical
current density. Both $v_c$ and $J_s$ were calculated as functions of the
quasiparticle damping parameter, and the dc magnetic field applied parallel to
the layers. The effects of vortex interaction on the Cherenkov instability of
moving vortex chains and lattices in annular stacks of Josephson junctions were
considered. It is shown that a vortex driven by a current density $J>J_s$ in a
multilayer of finite length excites self-sustained large-amplitude standing
waves of magnetic flux, resulting in temporal oscillations of the total
magnetic moment. We evaluated a contribution of this effect to the power $W$
radiated by the sample and showed that $W$ increases strongly as the number of
layers increases. | 1906.04783v1 |
2020-01-22 | Probing XY phase transitions in a Josephson junction array with tunable frustration | The seminal theoretical works of Berezinskii, Kosterlitz, and Thouless
presented a new paradigm for phase transitions in condensed matter that are
driven by topological excitations. These transitions have been extensively
studied in the context of two-dimensional XY models -- coupled compasses -- and
have generated interest in the context of quantum simulation. Here, we use a
circuit quantum-electrodynamics architecture to study the critical behavior of
engineered XY models through their dynamical response. In particular, we
examine not only the unfrustrated case but also the fully-frustrated case which
leads to enhanced degeneracy associated with the spin rotational [U$(1)$] and
discrete chiral ($Z_2$) symmetries. The nature of the transition in the
frustrated case has posed a challenge for theoretical studies while direct
experimental probes remain elusive. Here we identify the transition
temperatures for both the unfrustrated and fully-frustrated XY models by
probing a Josephson junction array close to equilibrium using weak microwave
excitations and measuring the temperature dependence of the effective damping
obtained from the complex reflection coefficient. We argue that our probing
technique is primarily sensitive to the dynamics of the U$(1)$ part. | 2001.07877v2 |
2020-01-30 | Electrical spectroscopy of forward volume spin waves in perpendicularly magnetized materials | We study the potential of all-electrical inductive techniques for the
spectroscopy of propagating forward volume spin waves. We develop a
one-dimensional model to account for the electrical signature of spin-wave
reflection and transmission between inductive antennas and validate it with
experiments on a perpendicularly magnetized Co/Ni multilayer. We describe the
influence of the antenna geometry and antenna-to-antenna separation, as well as
that of the material parameters on the lineshape of the inductive signals. For
a finite damping, the broadband character of the antenna emission in the wave
vector space imposes to take into account the growing decoherence of the
magnetization waves upon their spatial propagation. The transmission signal can
be viewed as resulting from two contributions: a first one from propagating
spin-waves leading to an oscillatory phase of the broadband transmission
coefficient, and another one originating from the distant induction of
ferromagnetic resonance because of the long-range stray fields of realistic
antennas. Depending on the relative importance of these two contributions, the
decay of the transmitted signal with the propagation distance may not be
exponential and the oscillatory character of the spin-wave phase upon
propagation may be hidden. Our model and its experimental validation allow to
define geometrical and material specifications to be met to enable the use of
forward volume spin waves as efficient information carriers. | 2001.11483v1 |
2020-02-27 | Dipole polarizability of time-varying particles | Invariance under time translation (or stationarity) is probably one of the
most important assumptions made when investigating electromagnetic phenomena.
Breaking this assumption is expected to open up novel possibilities and result
in exceeding conventional limitations. However, to explore the field of
time-varying electromagnetic structures, we primarily need to contemplate the
fundamental principles and concepts from a nonstationarity perspective. Here,
we revisit one of those key concepts: The polarizability of a small particle,
assuming that its properties vary in time. We describe the creation of induced
dipole moment by external fields in a nonstationary, causal way, and introduce
a complex-valued function, called temporal complex polarizability, for
elucidating a nonstationary Hertzian dipole under time-harmonic illumination.
This approach can be extended to any subwavelength particle exhibiting electric
response. In addition, we also study the classical model of the polarizability
of an oscillating electron using the equation of motion whose damping
coefficient and natural frequency are changing in time. Next, we theoretically
derive the effective permittivity corresponding to time-varying media
(comprising free or bound electrons, or dipolar meta-atoms) and explicitly show
the differences with the conventional macroscopic Drude-Lorentz model. This
paper will hopefully pave the road towards better understanding of
nonstationary scattering from small particles and homogenization of
time-varying materials, metamaterials, and metasurfaces. | 2002.12297v3 |
2020-02-25 | The Casimir densities for a sphere in the Milne universe | The influence of a spherical boundary on the vacuum fluctuations of a massive
scalar field is investigated in background of $(D+1)$-dimensional Milne
universe, assuming that the field obeys Robin boundary condition on the sphere.
The normalized mode functions are derived for the regions inside and outside
the sphere and different vacuum states are discussed. For the conformal vacuum,
the Hadamard function is decomposed into boundary-free and sphere-induced
contributions and an integral representation is obtained for the latter in both
the interior and exterior regions. As important local characteristics of the
vacuum state the vacuum expectation values (VEVs) of the field squared and of
the energy-momentum tensor are investigated. It is shown that the vacuum
energy-momentum tensor has an off-diagonal component that corresponds to the
energy flux along the radial direction. Depending on the coefficient in Robin
boundary condition the sphere-induced contribution to the vacuum energy and the
energy flux can be either positive or negative. At late stages of the expansion
and for a massive field the decay of the sphere-induced VEVs, as functions of
time, is damping oscillatory. The geometry under consideration is conformally
related to that for a static spacetime with negative constant curvature space
and the sphere-induced contributions in the corresponding VEVs are compared. | 2003.05372v2 |
2020-04-15 | On the cavity evolution and the Rayleigh--Plesset equation in superfluid helium | On the basis of the two-fluid hydrodynamics, an analogue of the famous
Rayleigh-Plesse equation for the dynamics of a spherical bubble in superfluid
helium is obtained. The mass flow velocity $v$ and the velocity of the normal
component $v_{n}$ were chosen as independent variables. Due to the two-fluid
nature of HeII, the cross terms in the evolution equation for the boundary
position $\ R(t)$ appeared, which were absent in classical Rayleigh-Plesset
equation in ordinary fluids. One of them renormilizes the coefficient in front
of $(dR/dt)^{2}$. Another additional term formally coinciding with the viscous
term, describes the attenuation of the boundary oscillations. This
"extra-damping" term, greatly exceeding the usual viscous term, leads to a
significant difference in the dynamics of cavity compared to HeI. In
particular, this results in the interesting effect of abnormal suppression of
oscillations of the vapor--liquid boundary observed in many works. There is
also an additional term proportional to the squared velocity of the normal
component, which is independent of the derivative $dR/dt$, and can be included
in the pressure drop. Its physical meaning is that it describes a "Bernoulli"
-like pressure created by the flow of a normal component. The obtained result
declares that some results on the dynamics of the cavity in superfluid helium
should be reviewed | 2004.06893v1 |
2020-05-30 | Spiral defect chaos in Rayleigh-Bénard convection: Asymptotic and numerical studies of azimuthal flows induced by rotating spirals | Rotating spiral patterns in Rayleigh-B\'enard convection are known to induce
azimuthal flows, which raises the question of how different neighboring spirals
interact with each other in spiral chaos, and the role of hydrodynamics in this
regime. Far from the core, we show that spiral rotations lead to an azimuthal
body force that is irrotational and of magnitude proportional to the
topological index of the spiral and its angular frequency. The force, although
irrotational, cannot be included in the pressure field as it would lead to a
nonphysical, multivalued pressure. We calculate the asymptotic dependence of
the resulting flow, and show that it leads to a logarithmic dependence of the
azimuthal velocity on distance r away from the spiral core in the limit of
negligible damping coefficient. This solution dampens to approximately $1/r$
when accounting for no-slip boundary conditions for the convection cell's
plate. This flow component can provide additional hydrodynamic interactions
among spirals including those observed in spiral defect chaos. We show that the
analytic prediction for the azimuthal velocity agrees with numerical results
obtained from both two-dimensional generalized Swift-Hohenberg and
three-dimensional Boussinesq models, and find that the velocity field is
affected by the size and charges of neighboring spirals. Numerically, we
identify a correlation between the appearance of spiral defect chaos and the
balancing between the mean-flow advection and the diffusive dynamics related to
roll unwinding. | 2006.00147v1 |
2020-06-16 | Learning Rates as a Function of Batch Size: A Random Matrix Theory Approach to Neural Network Training | We study the effect of mini-batching on the loss landscape of deep neural
networks using spiked, field-dependent random matrix theory. We demonstrate
that the magnitude of the extremal values of the batch Hessian are larger than
those of the empirical Hessian. We also derive similar results for the
Generalised Gauss-Newton matrix approximation of the Hessian. As a consequence
of our theorems we derive an analytical expressions for the maximal learning
rates as a function of batch size, informing practical training regimens for
both stochastic gradient descent (linear scaling) and adaptive algorithms, such
as Adam (square root scaling), for smooth, non-convex deep neural networks.
Whilst the linear scaling for stochastic gradient descent has been derived
under more restrictive conditions, which we generalise, the square root scaling
rule for adaptive optimisers is, to our knowledge, completely novel. %For
stochastic second-order methods and adaptive methods, we derive that the
minimal damping coefficient is proportional to the ratio of the learning rate
to batch size. We validate our claims on the VGG/WideResNet architectures on
the CIFAR-$100$ and ImageNet datasets. Based on our investigations of the
sub-sampled Hessian we develop a stochastic Lanczos quadrature based on the fly
learning rate and momentum learner, which avoids the need for expensive
multiple evaluations for these key hyper-parameters and shows good preliminary
results on the Pre-Residual Architecure for CIFAR-$100$. | 2006.09092v6 |
2020-07-20 | Hydrodynamic and thermal characteristics of a freely-vibrating circular cylinder in mixed convection flow | The hydrodynamic and thermal characteristics of a freely-vibrating circular
cylinder in mixed convection flow are numerically investigated at low Reynolds
numbers. The numerical investigations are conducted for a range of parameters,
Ur = [2.0, 10], Pr = [0.7, 10] and Ri = [0.5, 2.0]. Whereas the Reynolds
number, the mass ratio and the damping ratio are fixed. A secondary VIV lock-in
region is found in the cases of high Richardson number Ri=2.0 for high reduced
velocity values, in which the buoyancy-driven flow is non-trivial. A wide VIV
lock-in region is formed with tremendous energy transfer between fluid and
structure, which is extremely meaningful for hydropower harvesting. The
influences of Prandtl and Richardson numbers on the hydrodynamics, structural
dynamics and heat transfer are discussed in detail. The temperature contours
are concentrated around cylinder for the cases of high Prandtl number, which
are associated with high mean Nusselt values. The influence on heat transfer
efficiency over the cylinder's surface is quantified via the calculation of
mean Nusselt number and its fluctuation for different circumstances. The energy
transfer coefficient is employed to quantify the energy transfer between fluid
and structure in mixed convection flow. The phase angle difference between the
transverse displacement of cylinder and the lift force is used to support the
discussions of energy transfer. A stabilized finite element formulation in
Arbitrary Lagrangian-Eulerian description is derived. The structural dynamics
and vortex-induced vibration are documented for various environments, e.g.,
different reduced velocity, Prandtl numbers and Richardson numbers. The
influence of structural dynamics on the heat transfer efficiency over a heated
cylinder is recorded and discussed as well. The obtained numerical results
match well with literature and the established empirical formula. | 2007.10091v2 |
2020-07-29 | Delayed Rebounds in the Two-Ball Bounce Problem | In the classroom demonstration of a tennis ball dropped on top of a
basketball, the surprisingly high bounce of the tennis ball is typically
explained using momentum conservation for elastic collisions, with the
basketball-floor collision treated as independent from the collision between
the two balls. This textbook explanation is extended to inelastic collisions by
including a coefficient of restitution. This independent contact model (ICM),
as reviewed in this paper, is accurate for a wide variety of cases, even when
the collisions are not truly independent. However, it is easy to explore
situations that are not explained by the ICM, such as swapping the tennis ball
for a ping-pong ball. In this paper, we study the conditions that lead to a
"delayed rebound effect," a small first bounce followed by a higher second
bounce, using techniques accessible to an undergraduate student. The dynamical
model is based on the familiar solution of the damped harmonic oscillator. We
focus on making the equations of motion dimensionless for numerical simulation,
and reducing the number of parameters and initial conditions to emphasize
universal behavior. The delayed rebound effect is found for a range of
parameters, most commonly in cases where the first bounce is lower than the ICM
prediction. | 2007.15005v2 |
2020-08-08 | Axial Gravitational Waves in Bianchi I Universe | In this paper, we have studied the propagation of axial gravitational waves
in Bianchi I universe using the Regge-Wheeler gauge. In this gauge, there are
only two non-zero components of $ h_{\mu\nu} $ in the case of axial waves:
$h_0(t,r)$ and $h_1(t,r)$. The field equations in absence of matter have been
derived both for the unperturbed as well as axially perturbed metric. These
field equations are solved simultaneously by assuming the expansion scalar
$\Theta$ to be proportional to the shear scalar $\sigma$ (so that $a= b^n$,
where $a$, $b$ are the metric coefficients and $n$ is an arbitrary constant),
and the wave equation for the perturbation parameter $h_0(t,r)$ have been
derived. We used the method of separation of variables to solve for this
parameter, and have subsequently determined $h_1(t,r)$. We then discuss a few
special cases in order to interpret the results. We find that the anisotropy of
the background spacetime is responsible for the damping of the gravitational
waves as they propagate through this spacetime. The perturbations depend on the
values of the angular momentum $l$. The field equations in the presence of
matter reveal that the axially perturbed spacetime leads to perturbations only
in the azimuthal velocity of the fluid leaving the matter field undisturbed. | 2008.04780v2 |
2020-11-13 | Hopf Bifurcation for General 1D Semilinear Wave Equations with Delay | We consider boundary value problems for 1D autonomous damped and delayed
semilinear wave equations of the type $$ \partial^2_t u(t,x)-
a(x,\lambda)^2\partial_x^2u(t,x)=
b(x,\lambda,u(t,x),u(t-\tau,x),\partial_tu(t,x),\partial_xu(t,x)), \; x \in
(0,1) $$ with smooth coefficient functions $a$ and $b$ such that
$a(x,\lambda)>0$ and $b(x,\lambda,0,0,0,0) = 0$ for all $x$ and $\lambda$. We
state conditions ensuring Hopf bifurcation, i.e., existence, local uniqueness
(up to time shifts), regularity (with respect to $t$ and $x$) and smooth
dependence (on $\tau$ and $\lambda$) of small non-stationary time-periodic
solutions, which bifurcate from the stationary solution $u=0$, and we derive a
formula which determines the bifurcation direction with respect to the
bifurcation parameter $\tau$.
To this end, we transform the wave equation into a system of partial integral
equations by means of integration along characteristics, and then we apply a
Lyapunov-Schmidt procedure and a generalized implicit function theorem to this
system. The main technical difficulties, which have to be managed, are typical
for hyperbolic PDEs (with or without delay): small divisors and the "loss of
derivatives" property.
We do not use any properties of the corresponding initial-boundary value
problem. In particular, our results are true also for negative delays $\tau$. | 2011.06824v1 |
2020-12-01 | Digital Light Processing in a Hybrid Atomic Force Microscope: In situ, Nanoscale Characterization of the Printing Process | Stereolithography (SLA) and digital light processing (DLP) are powerful
additive manufacturing techniques that address a wide range of applications
including regenerative medicine, prototyping, and manufacturing. Unfortunately,
these printing processes introduce micrometer-scale anisotropic inhomogeneities
due to the resin absorptivity, diffusivity, reaction kinetics, and swelling
during the requisite photoexposure. Previously, it has not been possible to
characterize high-resolution mechanical heterogeneity as it develops during the
printing process. By combining DLP 3D printing with atomic force microscopy in
a hybrid instrument, heterogeneity of a single, in situ printed voxel is
characterized. Here, we describe the instrument and demonstrate three
modalities for characterizing voxels during and after printing. Sensing
Modality I maps the mechanical properties of just-printed, resin-immersed
voxels, providing the framework to study the relationships between voxel sizes,
print exposure parameters, and voxel-voxel interactions. Modality II captures
the nanometric, in situ working curve and is the first demonstration of in situ
cure depth measurement. Modality III dynamically senses local rheological
changes in the resin by monitoring the viscoelastic damping coefficient of the
resin during patterning. Overall, this instrument equips researchers with a
tool to develop rich insight into resin development, process optimization, and
fundamental printing limits. | 2012.00496v1 |
2021-02-23 | Cosmic Ray Transport in the Ionized and Neutral ISM: MHD-PIC Simulations and Effective Fluid Treatments | Cosmic rays (CRs) have critical impacts in the multiphase interstellar medium
(ISM), driving dynamical motions in low-density plasma and modifying the
ionization state, temperature, and chemical composition of higher-density
atomic and molecular gas. We present a study of CR propagation between the
ionized ISM and a neutral cloud. Using one-dimensional magnetohydrodynamic
particle-in-cell simulations which include ion-neutral drag to damp
Alfv$\acute{\text{e}}$n waves in the cloud, we self-consistently evolve the
kinetic physics of CRs and fluid dynamics of the multiphase gas. By introducing
the cloud in our periodic domain, our simulations break translational symmetry
and allow the emergence of spatial structure in the CR distribution function. A
negative spatial gradient forms across the fully-ionized ISM region while a
positive gradient forms across the neutral cloud. We connect our results with
CR hydrodynamics formulations by computing the wave-particle scattering rates
as predicted by quasilinear, fluid, and Fokker-Planck theory. For momenta where
the mean free path is short relative to the box size, we find excellent
agreement among all scattering rates. By exploring different cloud sizes and
ion-neutral collision rates, we show that our results are robust. Our work
provides a first-principles verification of CR hydrodynamics when particles
stream down their pressure gradient, and opens a pathway toward comprehensive
calibrations of transport coefficients from self-generated
Alfv$\acute{\text{e}}$n wave scattering with CRs. | 2102.11877v1 |
2021-03-10 | Quasi-solid state microscopic dynamics in equilibrium classical liquids: Self-consisnent relaxation theory | In the framework of the concept of time correlation functions, we develop a
self-consistent relaxation theory of the transverse collective particle
dynamics in liquids. The theory agrees with well-known results in both the
short-wave (free particle dynamics) and the long-wave (hydrodynamic) limits. We
obtain a general expression for the spectral density~$C_T(k,\omega)$ of
transverse particle current realized in the range of wave numbers $k$. In
domain of microscopic spatial scales comparable to action scale of effective
forces of interparticle interaction, the theory reproduces a transition from a
regime with typical equilibrium liquid dynamics to a regime with collective
particle dynamics where properties similar to solid-state properties appear:
effective shear stiffness and transverse (shear) acoustic waves. In the
framework of the corresponding approximations, we obtain expressions for the
spectral density of transverse particle current for all characteristic regimes
in equilibrium collective dynamics. We obtain expressions for dispersion law
for transverse (shear) acoustic waves and also relations for the kinematic
shear viscosity $\nu$, the transverse speed of sound $v^{(T)}$, and the
corresponding sound damping coefficient $\Gamma^{(T)}$. We compare the
theoretical results with the results of atomic dynamics simulations of liquid
lithium near the melting point. | 2103.06241v1 |
2021-04-01 | Brownian motion under intermittent harmonic potentials | We study the effects of an intermittent harmonic potential of strength $\mu =
\mu_0 \nu$ -- that switches on and off stochastically at a constant rate
$\gamma$, on an overdamped Brownian particle with damping coefficient $\nu$.
This can be thought of as a realistic model for realisation of stochastic
resetting. We show that this dynamics admits a stationary solution in all
parameter regimes and compute the full time dependent variance for the position
distribution and find the characteristic relaxation time. We find the exact
non-equilibrium stationary state distributions in the limits -- (i)
$\gamma\ll\mu_0 $ which shows a non-trivial distribution, in addition as
$\mu_0\to\infty$, we get back the result for resetting with refractory period;
(ii) $\gamma\gg\mu_0$ where the particle relaxes to a Boltzmann distribution of
an Ornstein-Uhlenbeck process with half the strength of the original potential
and (iii) intermediate $\gamma=2n\mu_0$ for $n=1, 2$. The mean first passage
time (MFPT) to find a target exhibits an optimisation with the switching rate,
however unlike instantaneous resetting the MFPT does not diverge but reaches a
stationary value at large rates. MFPT also shows similar behavior with respect
to the potential strength. Our results can be verified in experiments on
colloids using optical tweezers. | 2104.00609v2 |
2021-04-29 | Resonant Chains of Exoplanets: Libration Centers for Three-body Angles | Resonant planetary systems contain at least one planet pair with orbital
periods librating at a near-integer ratio (2/1, 3/2, 4/3, etc.) and are a
natural outcome of standard planetary formation theories. Systems with multiple
adjacent resonant pairs are known as resonant chains and can exhibit three-body
resonances -- characterized by a critical three-body angle. Here we study
three-body angles as a diagnostic of resonant chains through tidally-damped
N-body integrations. For each combination of the 2:1, 3:2, 4:3, and 5:4 mean
motion resonances (the most common resonances in the known resonant chains), we
characterize the three-body angle equilibria for several mass schemes,
migration timescales, and initial separations. We find that under our
formulation of the three-body angle, which does not reduce coefficients, 180
deg is the preferred libration center, and libration centers shifted away from
180 deg are associated with non-adjacent resonances. We then relate these
angles to observables, by applying our general results to two transiting
systems: Kepler-60 and Kepler-223. For these systems, we compare N-body models
of the three-body angle to the zeroth order in e approximation accessible via
transit phases, used in previous publications. In both cases, we find the
three-body angle during the Kepler observing window is not necessarily
indicative of the long-term oscillations and stress the role of dynamical
models in investigating three-body angles. We anticipate our results will
provide a useful diagnostic in the analysis of resonant chains. | 2104.14665v1 |
2021-04-30 | Complete modeling of hydrodynamic bearings with a boundary parameterization approach | The present work aims to revisit the simplifications made in the
Navier-Stokes equations for the flow between two cylinders with a small
thickness of lubricating oil film. Through a dimensionless analysis, the terms
of these equations are mapped and ordered by importance for the hydrodynamic
bearing application. An effective parameterization of the geometry is proposed,
enabling a more detailed description of the problem and its adaptation to other
contexts. At the end, an elliptical partial differential equation is reached
and solved by the centered finite difference method, whose solution is the
pressure field between the cylinders. To illustrate the effectiveness of the
proposed approach, the model is applied to hydrodynamic bearings, where the
pressure field and some parameters resulting from it, such as stiffness and
damping coefficients, are computed. Based on the facilities offered by the
parameterization of the geometry, two different configurations are presented:
(1) elliptical and (2) worn bearings. Their responses are evaluated and a
comparative analysis is performed. The modeling exposed in this text, as well
as all its simulations were developed to integrate Ross-Rotordynamics, an open
library in Python, available on the GitHub platform. | 2105.00118v3 |
2021-07-27 | Performance-based optimal distribution of viscous dampers in structure using hysteretic energy compatible endurance time excitations | Performance-based optimization of energy dissipation devices in structures
necessitates massive and repetitive dynamic analyses. In the endurance time
method known as a rather fast dynamic analysis procedure, structures are
subjected to intensifying dynamic excitations and their response at multiple
intensity levels is estimated by a minimal number of analyses. So, this method
significantly reduces computational endeavors. In this paper, the endurance
time method is employed to determine the optimal placement of viscous dampers
in a weak structure to achieve the desired performance at various hazard
levels, simultaneously. The viscous damper is one of the energy dissipation
systems which can dissipate a large amount of seismic input energy to the
structure. To this end, hysteretic energy compatible endurance time excitation
functions are used and the validity of the results is investigated by comparing
them with the results obtained from a suite of ground motions. To optimize the
placement of the dampers, the genetic algorithm is used. The damping
coefficients of the dampers are considered as design variables in the
optimization procedure and determined in such a way that the sum of them has a
minimum value. The behavior of the weak structure before and after
rehabilitation is also investigated using endurance time and nonlinear time
history analysis procedures in different hazard levels. | 2107.12983v1 |
2021-08-18 | Velocity auto correlation function of a confined Brownian particle | Motivated by the simple models of molecular motor obeying a linear
force-velocity relation, we have studied the stochastic dynamics of a Brownian
particle in the presence of a linear velocity dependent force,
$f_s(1-\frac{v}{v_0})$ where $f_{s}$ is a constant. The position and velocity
auto correlation functions in different situations of the dynamics are
calculated exactly. We observed that the velocity auto correlation function
shows an exponentially decaying behaviour with time and saturates to a constant
value in the time asymptotic limit, for a fixed $f_s$. It attains saturation
faster with increase in the $f_{s}$ value. When the particle is confined in a
harmonic well, the spectral density exhibits a symmetric behaviour and the
corresponding velocity auto correlation function shows a damped oscillatory
behaviour before decaying to zero in the long time limit. With viscous
coefficient, a non-systematic variation of the velocity auto correlation
function is observed. Further, in the presence of a sinusoidal driving force,
the correlation in velocities increases with increase in the amplitude of
driving in the transient regime. For the particle confined in a harmonic well,
the correlation corresponding to the shift relative to the average position is
basically the thermal contribution to the total position correlation. Moreover,
in the athermal regime, the total correlation is entirely due to the velocity
dependent force. | 2108.07922v1 |
2021-10-08 | Relationship between low-discrepancy sequence and static solution to multi-bodies problem | The main interest of this paper is to study the relationship between the
low-discrepancy sequence and the static solution to the multi-bodies problem in
high-dimensional space. An assumption that the static solution to the
multi-bodies problem is a low-discrepancy sequence is proposed. Considering the
static solution to the multi-bodies problem corresponds to the minimum
potential energy principle, we further assume that the distribution of the
bodies is the most uniform when the potential energy is the smallest. To verify
the proposed assumptions, a dynamical evolutionary model (DEM) based on the
minimum potential energy is established to find out the static solution. The
central difference algorithm is adopted to solve the DEM and an evolutionary
iterative scheme is developed. The selection of the mass and the damping
coefficient to ensure the convergence of the evolutionary iteration is
discussed in detail. Based on the DEM, the relationship between the potential
energy and the discrepancy during the evolutionary iteration process is
studied. It is found that there is a significant positive correlation between
them, which confirms the proposed assumptions. We also combine the DEM with the
restarting technique to generate a series of low-discrepancy sequences. These
sequences are unbiased and perform better than other low-discrepancy sequences
in terms of the discrepancy, the potential energy, integrating eight test
functions and computing the statistical moments for two practical stochastic
problems. Numerical examples also show that the DEM can not only generate
uniformly distributed sequences in cubes, but also in non-cubes. | 2110.03918v1 |
2021-12-08 | Resolving Hall and dissipative viscosity ambiguities via boundary effects | We examine the physical implications of the viscous redundancy of
two-dimensional anisotropic fluids, where different components of the viscosity
tensor lead to identical effects in the bulk of a system [Rao and Bradlyn,
Phys. Rev. X $\textbf{10}$, 021005 (2020)]. We first re-introduce the
redundancy, show how it reflects a lack of knowledge of microscopic information
of a system, and give microscopic examples. Next, we show that fluid flow in
systems with a boundary can distinguish between otherwise redundant viscosity
coefficients. In particular, we show how the dispersion and damping of
gravity-dominated surface waves can be used to resolve the redundancies between
both dissipative and Hall viscosities, and discuss how these results apply to
recent experiments in chiral active fluids with nonvanishing Hall viscosity.
Our results highlight the importance of divergenceless, magnetization-like
contributions to the stress (which we dub ``contact terms''). Finally, we apply
our results to the hydrodynamics of quantum Hall fluids, and show that the
extra contribution to the action that renders the bulk Wen-Zee action gauge
invariant in systems with a boundary can be reinterpreted in terms of the bulk
viscous redundancy. | 2112.04545v2 |
2021-12-25 | Transport and modeling of subgrid-scale turbulent kinetic energy in channel flows | To develop a more convenient subgrid-scale (SGS) model that performs well
even in coarse grid cases, we investigate the transport and modeling of SGS
turbulent kinetic energy (hereafter SGS energy) in turbulent channel flows
based on the stabilized mixed model (SMM). In this paper, we try to increase
the convenience of the SMM by replacing the modeled transport equation for the
SGS energy with an algebraic model. The SMM quantitatively adequately predicts
the total turbulent kinetic energy of the direct numerical simulation (DNS)
even in coarse grid cases. For both the filtered DNS (fDNS) and large-eddy
simulation (LES), the statistically averaged production term balances with the
dissipation in the region away from the wall in the SGS energy transport
equation. In contrast, we reveal that the correlation coefficient between the
production and dissipation terms is high for the modeled transport equation in
LES, whereas that for the fDNS is low. Based on the high correlation or local
equilibrium between the production and dissipation observed in the LES, we
demonstrate the reduction of the SMM into a zero-equation SMM (ZE-SMM). We
construct a new damping function based on the grid-scale Kolmogorov length to
reproduce the near-wall behavior of the algebraic model for the SGS energy. The
ZE-SMM provides quantitatively the same performance as the original SMM that
employs the SGS energy transport model. This result suggests that the local
equilibrium model for the SGS energy provides the equivalent performance as the
transport model in wall-bounded turbulent flows even in coarse grid cases. | 2112.13200v3 |
2022-01-08 | Local Gyrokinetic Collisional Theory of the Ion-Temperature Gradient Mode | We present a study of the linear properties of ion temperature gradient (ITG)
modes with collisions modelled by the linearized gyrokinetic (GK) Coulomb
collision operator (Frei et al. 2021) in the local limit. The study is based on
a Hermite-Laguerre polynomial expansion of the perturbed ion distribution
function applied to the linearized GK Boltzmann equation, yielding a hierarchy
of coupled equations for the expansion coefficients, referred to as
gyro-moments. We explore analytically the collisionless and high-collisional
limits of the gyro-moment hierarchy. Parameter scans revealing the dependence
of the ITG growth rate on the collisionality are reported, showing strong
damping at small scales as the collisionality increases. These properties are
compared with the predictions based on the Sugama, the momentum-conserving
pitch-angle scattering, the Hirshman- Sigmar-Clarke, and the Daugherty
collision operators. The importance of finite Larmor radius (FLR) terms in the
collision operators is pointed out by the appearance of a short wavelength (SW)
ITG branch when collisional FLR terms are neglected, this branch being
completely suppressed by collisional FLR effects. We demonstrate that energy
diffusion is important at high collisionality and small scale lengths and that,
among the collision operators considered in this work, the GK Sugama collision
operator yields, in general, the smallest deviation on the ITG growth rate
compared to the GK Coulomb collision operator. Convergence studies of the
gyro-moment method are reported. | 2201.02860v2 |
2022-02-11 | Cosmic-ray generated bubbles around their sources | Cosmic rays are thought to escape their sources streaming along the local
magnetic field lines. We show that this phenomenon generally leads to the
excitation of both resonant and non-resonant streaming instabilities. The
self-generated magnetic fluctuations induce particle diffusion in extended
regions around the source, so that cosmic rays build up a large pressure
gradient. By means of two-dimensional (2D) and three-dimensional (3D) hybrid
particle-in-cell simulations, we show that such a pressure gradient excavates a
cavity around the source and leads to the formation of a cosmic-ray dominated
bubble, inside which diffusivity is strongly suppressed. Based on the trends
extracted from self-consistent simulations, we estimate that, in the absence of
severe damping of the self-generated magnetic fields, the bubble should keep
expanding until pressure balance with the surrounding medium is reached,
corresponding to a radius of $\sim 10-50$ pc. The implications of the formation
of these regions of low diffusivity for sources of Galactic cosmic rays are
discussed. Special care is devoted to estimating the self-generated diffusion
coefficient and the grammage that cosmic rays might accumulate in the bubbles
before moving into the interstellar medium. Based on the results of 3D
simulations, general considerations on the morphology of the $\gamma$-ray and
synchrotron emission from these extended regions also are outlined. | 2202.05814v1 |
2022-02-22 | Criterion of Bari basis property for $2 \times 2$ Dirac-type operators with strictly regular boundary conditions | The paper is concerned with the Bari basis property of a boundary value
problem associated in $L^2([0,1]; \mathbb{C}^2)$ with the following $2 \times
2$ Dirac-type equation for $y = {\rm col}(y_1, y_2)$: $$L_U(Q) y =-i B^{-1} y'
+ Q(x) y = \lambda y , \quad B = \begin{pmatrix} b_1 & 0 \\ 0 & b_2
\end{pmatrix}, \quad b_1 < 0 < b_2, $$ with a potential matrix $Q \in
L^2([0,1]; \mathbb{C}^{2 \times 2})$ and subject to the strictly regular
boundary conditions $Uy :=\{U_1, U_2\}y=0$. If $b_2 = -b_1 =1$ this equation is
equivalent to one dimensional Dirac equation. We show that the system of root
vectors $\{f_n\}_{n \in \mathbb{Z}}$ of the operator $L_U(Q)$ forms a Bari
basis in $L^2([0,1]; \mathbb{C}^2)$ if and only if the unperturbed operator
$L_U(0)$ is self-adjoint. We also give explicit conditions for this in terms of
coefficients in the boundary conditions. The Bari basis criterion is a
consequence of our more general result: Let $Q \in L^p([0,1]; \mathbb{C}^{2
\times 2})$, $p \in [1,2]$, boundary conditions be strictly regular, and let
$\{g_n\}_{n \in \mathbb{Z}}$ be the sequence biorthogonal to the system of root
vectors $\{f_n\}_{n \in \mathbb{Z}}$ of the operator $L_U(Q)$. Then $$ \{\|f_n
- g_n\|_2\}_{n \in \mathbb{Z}} \in (\ell^p(\mathbb{Z}))^*
\quad\Leftrightarrow\quad L_U(0) = L_U(0)^*. $$ These abstract results are
applied to non-canonical initial-boundary value problem for a damped string
equation. | 2202.11148v1 |
2022-03-22 | Hydromagnetic waves in an expanding universe -- cosmological MHD code tests using analytic solutions | We describe how analytic solutions for linear hydromagnetic waves can be used
for testing cosmological magnetohydrodynamic (MHD) codes. We start from the
comoving MHD equations and derive analytic solutions for the amplitude
evolution of linear hydromagnetic waves in a matter-dominated, flat
Einstein-de-Sitter (EdS) universe. The waves considered are comoving, linearly
polarized Alfv\'en waves and comoving, magnetosonic (fast) waves modified by
self-gravity. The solution for compressible waves is found for a general
adiabatic index and we consider the limits of hydrodynamics without
self-gravity in addition to the full solution. In addition to these analytic
solutions, the linearized equations are solved numerically for a $\Lambda$CDM
cosmology. We use the analytic and numeric solutions to compare with results
obtained using the cosmological MHD code AREPO and find good agreement when
using a sufficient number of grid points. We interpret the numerical damping
clearly evident in simulations with few grid points by further deriving the
Alfv\'en wave solution including physical Navier-Stokes viscosity. A comparison
between Alfv\'en wave simulations and theory reveals that the dissipation can
be described by a numerical viscosity coefficient $\eta_\mathrm{num} \propto
a^{-5/2}$ where $a$ is the scale factor. We envision that our examples could be
useful when developing a new cosmological MHD code or for regression testing of
existing codes. | 2203.11887v2 |
2022-03-22 | Cosmic-Ray Transport in Varying Galactic Environments | We study the propagation of mildly-relativistic cosmic rays (CRs) in
multiphase interstellar medium environments with conditions typical of nearby
disk galaxies. We employ the techniques developed in Armillotta+21 to
post-process three high-resolution TIGRESS magnetohydrodynamic simulations
modeling local patches of star-forming galactic disks. Together, the three
simulations cover a wide range of gas surface density, gravitational potential,
and star formation rate (SFR). Our prescription for CR propagation includes the
effects of advection by the background gas, streaming along the magnetic field
at the local ion Alfv\'en speed, and diffusion relative to the Alfv\'en waves,
with the diffusion coefficient set by the balance between streaming-driven
Alfv\'en wave excitation and damping mediated by local gas properties. We find
that the combined transport processes are more effective in environments with
higher SFR. These environments are characterized by higher-velocity hot
outflows (created by clustered supernovae) that rapidly advect CRs away from
the galactic plane. As a consequence, the ratio of midplane CR pressure to
midplane gas pressures decreases with increasing SFR. We also use the
post-processed simulations to make predictions regarding potential dynamical
impacts of CRs. The relatively flat CR pressure profiles near the midplane
argue that they would not provide significant support against gravity for most
of the ISM mass. However, the CR pressure gradients are larger than the other
pressure gradients in the extra-planar region (|z|>0.5 kpc), suggesting that
CRs may affect the dynamics of galactic fountains and/or winds. The degree of
this impact is expected to increase in environments with lower SFR. | 2203.11949v1 |
2022-05-23 | Universal mechanical response of metallic glasses during strain-rate-dependent uniaxial compression | Experimental data on the compressive strength $\sigma_{\rm max}$ versus
strain rate ${\dot \varepsilon}_{\rm eng}$ for metallic glasses undergoing
uniaxial compression shows significantly different behavior for different
alloys. For some metallic glasses, $\sigma_{\rm max}$ decreases with increasing
${\dot \varepsilon}_{\rm eng}$, for others, $\sigma_{\rm max}$ increases with
increasing ${\dot \varepsilon}_{\rm eng}$, and for others $\sigma_{\rm max}$
versus ${\dot \varepsilon}_{\rm eng}$ is nonmonotonic. Using numerical
simulations of metallic glasses undergoing uniaxial compression at nonzero
strain rate and temperature, we show that they obey a universal relation for
the compressive strength versus temperature, which determines their mechanical
response. At low ${\dot \varepsilon}_{\rm eng}$, increasing strain rate leads
to increases in temperature and decreases in $\sigma^*_{\rm max}$, whereas at
high ${\dot \varepsilon}_{\rm eng}$, increasing strain rate leads to decreases
in temperature and increases in $\sigma^*_{\rm max}$. This non-monotonic
behavior of $\sigma^*_{\rm max}$ versus temperature causes the nonmonotonic
behavior of $\sigma^*_{\rm max}$ versus ${\dot \varepsilon}_{\rm eng}$.
Variations in the internal dissipation change the characteristic strain rate at
which the nonmonotonic behavior occurs. These results are general for a wide
range of metallic glasses with different atomic interactions, damping
coefficients, and chemical compositions. | 2205.11340v1 |
2022-05-29 | Negative cavity photon spectral function in an optomechanical system with two parametrically-driven mechanical modes | We propose an experimentally feasible optomechanical scheme to realize a
negative cavity photon spectral function (CPSF) which is equivalent to a
negative absorption. The system under consideration is an optomechanical system
consisting of two mechanical (phononic) modes which are linearly coupled to a
common cavity mode via the radiation pressure while parametrically driven
through the coherent time-modulation of their spring coefficients. Using the
equations of motion for the cavity retarded Green's function obtained in the
framework of the generalized linear response theory, we show that in the
red-detuned and weak-coupling regimes a frequency-dependent effective cavity
damping rate (ECDR) corresponding to a negative CPSF can be realized by
controlling the cooperativities and modulation parameters while the system
still remains in the stable regime. Nevertheless, such a negativity which acts
as an optomechanical gain never occurs in a standard (an unmodulated bare)
cavity optomechanical system. Besides, we find that the presence of two
modulated mechanical degrees of freedom provides more controllability over the
magnitude and bandwidth of the negativity of CPSF, in comparison to the setup
with a single modulated mechanical oscillator. Interestingly, the introduced
negativity may open a new platform to realize an extraordinary (modified)
optomechanically induced transparency (in which the input signal is amplified
in the output) leading to a perfect tunable optomechanical filter with
switchable bandwidth which can be used as an optical transistor. | 2205.15314v3 |
2022-06-27 | Diffusion in the Presence of Correlated Returns in a Two-dimensional Energy Landscape and non-Monotonic Friction Dependence: Examination of Simulation Results by a Random Walk Model | Diffusion in a multidimensional energy surface with minima and barriers is a
problem of importance in statistical mechanics and also has wide applications,
such as protein folding. To understand it in such a system, we carry out theory
and simulations of a tagged particle moving on a two-dimensional periodic
potential energy surface, both in the presence and absence of noise. Langevin
dynamics simulations at multiple temperatures are carried out to obtain the
diffusion coefficient of a solute particle. Friction is varied from zero to
large values. Diffusive motion emerges in the limit of long times, even in the
absence of noise, although the trajectory is found to remain correlated over a
long time. This correlation is manifested in correlated returns to the starting
minima following a scattering by surrounding maxima. Noise destroys this
correlation, induces chaos, and increases diffusion at small friction.
Diffusion thus exhibits a non-monotonic friction dependence at the intermediate
value of the damping, ultimately converging to our theoretically predicted
value. The latter is obtained by using the well-established relation between
diffusion and random walk. An excellent agreement is obtained between theory
and simulations in the high friction limit, but not so in the intermediate
regime. The rate of escape from one cell to another is obtained from the
multidimensional rate theory of Langer. We find that enhanced dimensionality
plays an important role. In order to quantify the effects of noise on the
potential-imposed coherence on the trajectories, we calculate the Lyapunov
exponent. At small friction values, the Lyapunov exponent mimics the friction
dependence of the rate. | 2206.13565v1 |
2022-07-14 | The Damped Wave Equation with Acoustic Boundary Conditions and Non-locally Reacting Surfaces | The aim of the paper is to study the problem $$u_{tt}+du_t-c^2\Delta u=0
\qquad \text{in $\mathbb{R}\times\Omega$,}$$ $$\mu v_{tt}- \text{div}_\Gamma
(\sigma \nabla_\Gamma v)+\delta v_t+\kappa v+\rho u_t =0\qquad \text{on
$\mathbb{R}\times \Gamma_1$,}$$ $$v_t =\partial_\nu u\qquad \text{on
$\mathbb{R}\times \Gamma_1$,}$$ $$\partial_\nu u=0 \text{on $\mathbb{R}\times
\Gamma_0$,}$$ $$u(0,x)=u_0(x),\quad u_t(0,x)=u_1(x)\quad \text{in $\Omega$,}$$
$$v(0,x)=v_0(x),\quad v_t(0,x)=v_1(x) \quad \text{on $\Gamma_1$,}$$ where
$\Omega$ is a open domain of $\mathbb{R}^N$ with uniformly $C^r$ boundary
($N\ge 2$, $r\ge 1$), $\Gamma=\partial\Omega$, $(\Gamma_0,\Gamma_1)$ is a
relatively open partition of $\Gamma$ with $\Gamma_0$ (but not $\Gamma_1$)
possibly empty. Here $\text{div}_\Gamma$ and $\nabla_\Gamma$ denote the
Riemannian divergence and gradient operators on $\Gamma$, $\nu$ is the outward
normal to $\Omega$, the coefficients $\mu,\sigma,\delta, \kappa, \rho$ are
suitably regular functions on $\Gamma_1$ with $\rho,\sigma$ and $\mu$ uniformly
positive, $d$ is a suitably regular function in $\Omega$ and $c$ is a positive
constant.
In this paper we first study well-posedness in the natural energy space and
give regularity results. Hence we study asymptotic stability for solutions when
$\Omega$ is bounded, $\Gamma_1$ is connected, $r=2$, $\rho$ is constant and
$\kappa,\delta,d\ge 0$. | 2207.07047v2 |
2022-08-01 | Stochastic Galerkin particle methods for kinetic equations of plasmas with uncertainties | The study of uncertainty propagation is of fundamental importance in plasma
physics simulations. To this end, in the present work we propose a novel
stochastic Galerkin (sG) particle {method} for collisional kinetic models of
plasmas under the effect of uncertainties. This class of methods is based on a
generalized polynomial chaos (gPC) expansion of the particles' position and
velocity. In details, we introduce a stochastic particle approximation for the
Vlasov-Poisson system with a BGK term describing plasma collisions. A careful
reformulation of such dynamics is needed to perform the sG projection and to
obtain the corresponding system for the gPC coefficients. We show that the sG
particle method preserves the main physical properties of the problem, such as
conservations and positivity of the solution, while achieving spectral accuracy
for smooth solutions in the random space. Furthermore, in the fluid limit the
sG particle solver is designed to possess the asymptotic-preserving property
necessary to obtain a sG particle scheme for the limiting Euler-Poisson system,
thus avoiding the loss of hyperbolicity typical of conventional sG methods
based on finite differences or finite volumes. We tested the schemes
considering the classical Landau damping problem in the presence of both small
and large initial uncertain perturbations, the two stream instability and the
Sod shock tube problems under uncertainties. The results show that the proposed
method is able to capture the correct behavior of the system in all test cases,
even when the relaxation time scale is very small. | 2208.00692v2 |
2022-08-02 | Diagrammatic perturbation theory for Stochastic nonlinear oscillators | We consider the stochastically driven one dimensional nonlinear oscillator
$\ddot{x}+2\Gamma\dot{x}+\omega^2_0 x+\lambda x^3 = f(t)$ where f(t) is a
Gaussian noise which, for the bulk of the work, is delta correlated (white
noise). We construct the linear response function in frequency space in a
systematic Feynman diagram-based perturbation theory. As in other areas of
physics, this expansion is characterized by the number of loops in the diagram.
This allows us to show that the damping coefficient acquires a correction at
$O(\lambda^2)$ which is the two loop order. More importantly, it leads to the
numerically small but conceptually interesting finding that the response is a
function of the frequency at which a stochastic system is probed. The method is
easily generalizable to different kinds of nonlinearity and replacing the
nonlinear term in the above equation by $\mu x^2$ , we can discuss the issue of
noise driven escape from a potential well. If we add a periodic forcing to the
cubic nonlinearity situation, then we find that the response function can have
a contribution jointly proportional to the strength of the noise and the
amplitude of the periodic drive. To treat the stochastic Kapitza problem in
perturbation theory we find that it is necessary to have a coloured noise. | 2208.01349v2 |
2022-08-09 | Pulsar radio emission mechanism II. On the origin of relativistic Langmuir solitons in pulsar plasma | Observations suggest that coherent radio emission from pulsars is excited in
a dense pulsar plasma by curvature radiation from charge bunches. Numerous
studies propose that these charge bunches are relativistic charge solitons
which are solutions of the non-linear Schr\"{o}dinger equation (NLSE) with a
group velocity dispersion ($G$), cubic-nonlinearity($q$) and non-linear Landau
damping ($s$). The formation of stable solitons crucially depends on the
parameters $G, q$ and $s$ and the particle distribution function. In this work,
we use realistic pulsar plasma parameters obtained from observational
constraints to explore the parameter space of NLSE for two representative
distribution functions (DF) of particles' momenta: Lorentzian (long-tailed) and
Gaussian (short-tailed). The choice of DF critically affects the value of
$|s/q|$, which, in turn, determines whether solitons can form. Numerical
simulations show that well-formed solitons are obtained only for small values
of $|s/q| \lesssim 0.1$ while for moderate and higher values of $|s/q| \gtrsim
0.5$ soliton formation is suppressed. Small values for $|s/q| \sim 0.1$ are
readily obtained for long-tailed DF for a wide range of plasma temperatures. On
the other hand, short-tailed DF provides these values only for some narrow
range of plasma parameters. Thus, the presence of a prominent high-energy tail
in the particle DF favours soliton formation for a wide range of plasma
parameters. Besides pair plasma, we also include an iron ion component and find
that they make a negligible contribution in either modifying the NLSE
coefficients or contributing to charge separation. | 2208.04894v1 |
2022-08-24 | Analysis of point-contact models of the bounce of a hard spinning ball on a compliant frictional surface | Inspired by the turf-ball interaction in golf, this paper seeks to understand
the bounce of a ball that can be modelled as a rigid sphere and the surface as
supplying an elasto-plastic contact force in addition to Coulomb friction. A
general formulation is proposed that models the finite time interval of bounce
from touch-down to lift-off. Key to the analysis is understanding transitions
between slip and roll during the bounce. Starting from the rigid-body limit
with a an energetic or Poisson coefficient of restitution, it is shown that
slip reversal during the contact phase cannot be captured in this case, which
result generalises to the case of pure normal compliance. Yet, the introduction
of linear tangential stiffness and damping, does enable slip reversal. This
result is extended to general weakly nonlinear normal and tangential
compliance. An analysis using Filippov theory of piecewise-smooth systems leads
to an argument in a natural limit that lift-off while rolling is non-generic
and that almost all trajectories that lift off, do so under slip conditions.
Moreover, there is a codimension-one surface in the space of incoming velocity
and spin which divides balls that lift off with backspin from those that lift
off with topspin. The results are compared with recent experimental
measurements on golf ball bounce and the theory is shown to capture the main
features of the data. | 2208.11685v1 |
2022-08-31 | Reynolds number effects on the bistable flows over a wavy circular cylinder | The wake of wavy cylinder has been shown to exhibit bistability. Depending on
the initial condition, the final state of the wake can either develop into a
steady flow (state I), or periodic shedding (state II). In this paper, we
perform direct numerical simulations to reveal the Reynolds number effects on
these two wake states. With increasing Reynolds number, the steady vortical
structures in state I wake sways back and forth in the spanwise direction,
resulting in low-frequency fluctuations in drag forces, but not in lift. For
state II, the increase in Reynolds number is associated with the emergence of
another spectral peak in the lift coefficient. The secondary frequency is
associated with highly three-dimensional vortical structures in the wake. For
both states, the wakes transition to turblent flows at higher Reynolds numbers,
with the development of small-scale vortices. We further study the streamwise
gust flows over the wavy cylinder. The time-varying inflow velocity results in
a wide range of instantaneous Reynolds number spanning from the absolutely
unstable flow regime to the bistable regime. Depending on the period of the
inflow velocity variation, the wake perturbations grown at the absolutely
unstable flow regime can be damped out in state I wake, or grow large enough to
trigger the transition state II, resulting in loss of flow control efficacy.
The above analyses reveal novel flow physics of the bistable states at
unexplored Reynolds numbers, and showcase the complex transition behavior
between the two states in unsteady flows. The insights gained from this study
improve the understanding of the wake dynamics of the wavy cylinder. | 2208.14606v1 |
2022-09-13 | Do Periods of Decayless Kink Oscillations of Solar Coronal Loops Depend on Noise? | Decayless kink oscillations of solar coronal loops are studied in terms of a
low-dimensional model based on a randomly driven Rayleigh oscillator with
coefficients experiencing random fluctuations. The model considers kink
oscillations as natural modes of coronal loops, decaying by linear resonant
absorption. The damping is counteracted by random motions of the loop
footpoints and the interaction of the loop with external quasi-steady flows
with random fluctuations. In other words, the model combines the
self-oscillatory and randomly driven mechanisms for the decayless behaviour.
The random signals are taken to be of the stationary red noise nature. In the
noiseless case, the model has an asymptotically stationary oscillatory
solution, i.e., a kink self-oscillation. It is established that the kink
oscillation period is practically independent of noise. This finding justifies
the seismological estimations of the kink and Alfv\'en speeds and the magnetic
field in an oscillating loop by kink oscillations, based on the observed
oscillation period. The oscillatory patterns are found to be almost harmonic.
Noisy fluctuations of external flows modulate the amplitude of the almost
monochromatic oscillatory pattern symmetrically, while random motions of the
loop footpoints cause antisymmetric amplitude modulation. Such modulations are
also consistent with the observed behaviour. | 2209.06343v1 |
2022-10-11 | Switching Dynamics of Shallow Arches | This paper presents an analytical method to predict the delayed switching
dynamics of nonlinear shallow arches while switching from one state to another
state for different loading cases. We study an elastic arch subject to static
loading and time-dependent loading separately. In particular, we consider a
time-dependent loading that evolves linearly with time at a constant rate. In
both cases, we observed that the switching does not occur abruptly when the
load exceeds the static switching load, rather the time scale of the dynamics
drastically slows down; hence there is a delay in switching. For
time-independent loading, this delay increases as the applied load approach the
static switching load. Whereas for a time-dependent loading, the delay is
proportional to the rate of the applied load. Other than the loading
parameters, the delay switching time also depends on the local curvature of the
force-displacement function at the static switching point and the damping
coefficient of the arch material. The delay switching occurs due to the
flatness of the energy curve at static switching load. Therefore, we linearize
the arch near the static switching point and get a reduced nonlinear ordinary
differential equation to study the switching dynamics of the arch. This reduced
equation allows us to derive analytical expressions for the delay switching
time of the. We further compare the derived analytical results with the
numerical solutions and observed a good agreement between them. Finally, the
derived analytical formulae can be used to design arches for self-offloading
dynamic footwear for diabetics. | 2210.05734v2 |
2022-10-11 | Moment-Based Approach to the Flux-Tube linear Gyrokinetic Model | This work reports on the development and numerical implementation of the
linear electromagnetic gyrokinetic (GK) model in a tokamak flux-tube geometry
using a moment approach based on the expansion of the perturbed distribution
function on a velocity-space Hermite-Laguerre polynomials basis. A hierarchy of
equations of the expansion coefficients, referred to as the gyro-moments (GM),
is derived. We verify the numerical implementation of the GM hierarchy in the
collisionless limit by performing a comparison with the continuum GK code GENE,
recovering the linear properties of the ion-temperature gradient, trapped
electron, kinetic ballooning, and microtearing modes, as well as the
collisionless damping of zonal flows. The present investigation reveals the
ability of the GM approach to describe fine velocity-space scale structures
appearing near the trapped and passing boundary and kinetic effects associated
with parallel and perpendicular particle drifts. In addition, the effects of
collisions are studied using advanced collision operators, including the GK
Coulomb collision operator. The main findings are that the number of GMs
necessary for convergence decreases with plasma collisionality and is lower for
pressure gradient-driven modes, such as in H-mode pedestal regions, compared to
instabilities driven by trapped particles and magnetic gradient drifts often
found in the core. The accuracy of approximations often used to model
collisions (relative to the GK Coulomb operator) is studied, showing
differences between collision operator models that increase with collisionality
and electron temperature gradient in the case of TEM. The present linear
analysis demonstrates that the GM approach efficiently describes the plasma
dynamics for typical parameters of the tokamak boundary, ranging from the
low-collisionality banana H-mode to the high-collisionality Pfirsch-Schl\"uter
conditions. | 2210.05799v1 |
2022-10-17 | Pion dynamics in a soft-wall AdS-QCD model | Pseudo-Goldstone modes appear in many physical systems and display robust
universal features. First, their mass $m$ obeys the so-called
Gell-Mann-Oakes-Renner (GMOR) relation $f^2\,m^2=H\,\bar{\sigma}$, with $f$ the
Goldstone stiffness, $H$ the explicit breaking scale and $\bar{\sigma}$ the
spontaneous condensate. More recently, it has been shown that their damping
$\Omega$ is constrained to follow the relation $\Omega=m^2 D_\varphi$, where
$D_\varphi$ is the Goldstone diffusivity in the purely spontaneous phase. Pions
are the most paradigmatic example of pseudo-Goldstone modes and they are
related to chiral symmetry breaking in QCD. In this work, we consider a
bottom-up soft-wall AdS-QCD model with broken ${\rm{SU}}(2)_L \times
{\rm{SU}}(2)_R$ symmetry and we study the nature of the associated
pseudo-Goldstone modes -- the pions. In particular, we perform a detailed
investigation of their dispersion relation in presence of dissipation, of the
role of the explicit breaking induced by the quark masses and of the dynamics
near the critical point. Taking advantage of the microscopic information
provided by the holographic model, we give quantitative predictions for all the
coefficients appearing in the effective description. In particular, we estimate
the finite temperature behavior of the kinetic parameter $\mathfrak{r^2}$
defined as the ration between the Goldstone diffusivity $D_\varphi$ and the
pion attenuation constant $D_A$. Interestingly, we observe important deviations
from the value $\mathfrak{r^2}=3/4$ computed in chiral perturbation theory in
the limit of zero temperature. | 2210.09088v1 |
2022-11-03 | Viscous attenuation of gravitational waves propagating through an inhomogeneous background | We consider the propagation of gravitational waves in the late-time Universe
in the presence of matter distribution inhomogeneities, and we also consider
the cosmic fluid to be viscous. In this work, we investigate the cumulative
effect of inhomogeneities and viscosity of the cosmic-fluid on the observables
associated with the sources of the gravitational waves. Employing Buchert's
averaging procedure in the backreaction framework, we consider a model of
spacetime in which matter is distributed in-homogeneously across space. Using
the modified redshift versus distance relation, through the averaging process
in the context of the model, we study the variation of the redshift-dependent
part of the observed gravitational wave amplitude for different combinations of
our model parameters while simultaneously considering damping of the
gravitational wave amplitude due to viscosity of the cosmic-fluid. Then, we
investigate the differences occurring in the variation of the
redshift-dependent part of the observed gravitational wave amplitude due to
consideration of viscous attenuation. We show that there are significant
deviations after the inclusion of viscous attenuation in our analysis,
depending on the chosen value of the coefficient of viscosity. Our result
signifies the importance of the effect of viscosity, within the model of an
inhomogeneous Universe, on precision measurements of parameters of
compact-binary sources of gravitational waves. | 2211.01652v3 |
2022-11-07 | Three-Dimensionality in the flow of an elastically mounted circular cylinder with two-degree-of-freedom vortex-induced-vibrations | The study numerically investigates the three-dimensionality in the flow and
two-degree-of-freedom (2 DOF) vortex-induced-vibrations (VIV) characteristics
of an elastically mounted circular cylinder. The cylinder is allowed to vibrate
in both streamwise and transverse directions. A low value of mass-ratio with
the zero damping coefficient is taken for the simulations. The primary aim is
to understand the vortex shedding behind the cylinder and the transition
characteristics of the wake-flow from two-dimensional (2D) to three-dimensional
(3D). The Reynolds number (Re) is varied from 150 (fully 2D flow) to 1000
(fully 3D flow), which lies inside the laminar range. The reduced velocity is
varied which covers all three major VIV branches (Initial Branch (IB), Upper
Branch (UB), and the Lower Branch (LB)). The oscillating cylinder sweeps the
figure-eight trajectory. Two branches (IB, LB) and three branches (IB, UB, LB)
amplitude responses are obtained for the low and high Re values, respectively.
The wake behind the cylinder with 2-DOF VIV undergoes the mode-C transition of
2D to 3D flow as opposed to the direct mode-B transition observed for
transverse only VIV in the literature. The critical Re range of the 2D to 3D
transition for the 2-DOF VIV cylinder at a reduced velocity of 6 is around 250,
less than the 1-DOF VIV. Also, this range varies with the variation in and the
streamwise to transverse oscillation frequency ratio. A map is proposed for the
2-DOF VIV, highlighting the different modes of transition obtained for
combinations of reduced frequency and Re. | 2211.03307v1 |
2022-11-10 | Nonreciprocal nanoparticle refrigerators: design principles and constraints | We study the heat transfer between two nanoparticles held at different
temperatures that interact through nonreciprocal forces, by combining molecular
dynamics simulations with stochastic thermodynamics. Our simulations reveal
that it is possible to construct nano refrigerators that generate a net heat
transfer from a cold to a hot reservoir at the expense of power exerted by the
nonreciprocal forces. Applying concepts from stochastic thermodynamics to a
minimal under-damped Langevin model, we derive exact analytical expressions
predictions for the fluctuations of work, heat, and efficiency, which reproduce
thermodynamic quantities extracted from the molecular dynamics simulations. The
theory only involves a single unknown parameter, namely an effective friction
coefficient, which we estimate fitting the results of the molecular dynamics
simulation to our theoretical predictions. Using this framework, we also
establish design principles which identify the minimal amount of entropy
production that is needed to achieve a certain amount of uncertainty in the
power fluctuations of our nano refrigerator. Taken together, our results shed
light on how the direction and fluctuations of heat flows in natural and
artificial nano machines can be accurately quantified and controlled by using
nonreciprocal forces. | 2211.05502v3 |
2022-11-11 | Chemical Mixing Induced by Internal Gravity Waves in Intermediate Mass Stars | Internal gravity waves (IGWs) can cause mixing in the radiative interiors of
stars. We study this mixing by introducing tracer particles into two -
dimensional (2D) hydrodynamic simulations. Following the work of Rogers &
McElwaine (2017), arXiv:1709.04920, we extend our study to different masses (3
M$_{\odot}$, 7 M$_{\odot}$ and 20 M$_{\odot}$) and ages (ZAMS, midMS and TAMS).
The diffusion profiles of these models are influenced by various parameters
such as the Brunt-V\"ais\"al\"a frequency, density, thermal damping, the
geometric effect and the frequencies of waves contributing to these mixing
profiles. We find that the mixing profile changes dramatically across age. In
younger stars, we noted that the diffusion coefficient increases towards the
surface, whereas in older stars the initial increase in the diffusion profile
is followed by a decreasing trend. We also find that mixing is stronger in more
massive stars. Hence, future stellar evolution models should include this
variation. In order to aid the inclusion of this mixing in one-dimensional (1D)
stellar evolution models, we determine the dominant waves contributing to these
mixing profiles and present a prescription that can be included in 1D models. | 2211.06432v1 |
2023-06-20 | A revised gap-averaged Floquet analysis of Faraday waves in Hele-Shaw cells | Existing theoretical analyses of Faraday waves in Hele-Shaw cells rely on the
Darcy approximation and assume a parabolic flow profile in the narrow
direction. However, Darcy's model is known to be inaccurate when convective or
unsteady inertial effects are important. In this work, we propose a
gap-averaged Floquet theory accounting for inertial effects induced by the
unsteady terms in the Navier-Stokes equations, a scenario that corresponds to a
pulsatile flow where the fluid motion reduces to a two-dimensional oscillating
Poiseuille flow, similarly to the Womersley flow in arteries. When
gap-averaging the linearized Navier-Stokes equation, this results in a modified
damping coefficient, which is a function of the ratio between the Stokes
boundary layer thickness and the cell's gap, and whose complex value depends on
the frequency of the wave response specific to each unstable parametric region.
We first revisit the standard case of horizontally infinite rectangular
Hele-Shaw cells by also accounting for a dynamic contact angle model. A
comparison with existing experiments shows the predictive improvement brought
by the present theory and points out how the standard gap-averaged model often
underestimates the Faraday threshold. The analysis is then extended to the less
conventional case of thin annuli. A series of dedicated experiments for this
configuration highlights how Darcy's thin-gap approximation overlooks a
frequency detuning that is essential to correctly predict the locations of the
Faraday tongues in the frequency-amplitude parameter plane. These findings are
well rationalized and captured by the present model. | 2306.11501v1 |
2023-07-04 | Exponential stability of Euler-Bernoulli beam under boundary controls in rotation and angular velocity | This paper addresses the analysis of a boundary feedback system involving a
non-homogeneous Euler-Bernoulli beam governed by the equation
$m(x)u_{tt}+\mu(x)u_{t}$$+\left(r(x)u_{xx}\right)_{xx}=0$, subject to the
initial $u(x,0)=u_0(x)$, $u_t(x,0)=v_0(x)$ and boundary conditions $u(0,t)=0$,
$\left (-r(x)u_{xx}(x,t)\right )_{x=0}=-k^{-}_r u_{x}(0,t)-k^{-}_a
u_{xt}(0,t)$, $u(\ell,t)=0$, $\left (-r(x)u_{xx}(x,t)\right )_{x=\ell}=-k^{+}_r
u_{x}(\ell,t)-k^{+}_a u_{xt}(\ell,t)$, with boundary control at both ends
resulting from the rotation and angular velocity. The approach proposed in this
study relies on the utilization of regular weak solutions, energy identity, and
a physically motivated Lyapunov function. By imposing natural assumptions
concerning physical parameters and other inputs, which ensure the existence of
a regular weak solution, we successfully derive a uniform exponential decay
estimate for the system's energy. The decay rate constant featured in this
estimate is solely dependent on the physical and geometric properties of the
beam. These properties encompass crucial parameters such as the viscous
external damping coefficient $\mu(x)$, as well as the boundary springs
$k^{-}_r,k^+_r $ and dampers $k^{-}_a,k^+_a$. To illustrate the practical
effectiveness of our theoretical findings, numerical examples are provided.
These examples serve to demonstrate the applicability and relevance of our
derived results in real-world scenarios. | 2307.01518v1 |
2023-07-10 | Full-F Turbulent Simulation in a Linear Device using a Gyro-Moment Approach | Simulations of plasma turbulence in a linear plasma device configuration are
presented. These simulations are based on a simplified version of the
gyrokinetic (GK) model proposed by B. J. Frei et al. [J. Plasma Phys. 86,
905860205 (2020)] where the full-F distribution function is expanded on a
velocity-space polynomial basis allowing us to reduce its evolution to the
solution of an arbitrary number of fluid-like equations for the expansion
coefficients, denoted as the gyro-moments (GM). By focusing on the
electrostatic and neglecting finite Larmor radius effects, a full-F GM
hierarchy equation is derived to evolve the ion dynamics, which includes a
nonlinear Dougherty collision operator, localized sources, and Bohm sheath
boundary conditions. An electron fluid Braginskii model is used to evolve the
electron dynamics, coupled to the full-F ion GM hierarchy equation via a
vorticity equation where the Boussinesq approximation is used. A set of full-F
turbulent simulations are then performed using the parameters of the LArge
Plasma Device (LAPD) experiments with different numbers of ion GMs and
different values of collisionality. The ion distribution function is analyzed
illustrating the convergence properties of the GM approach. In particular, we
show that higher-order GMs are damped by collisions in the high-collisional
regime relevant to LAPD experiments. The GM results are then compared with
those from two-fluid Braginskii simulations, finding qualitative agreement in
the time-averaged profiles and statistical turbulent properties. | 2307.04562v2 |
2023-07-12 | Robust scalable initialization for Bayesian variational inference with multi-modal Laplace approximations | For predictive modeling relying on Bayesian inversion, fully independent, or
``mean-field'', Gaussian distributions are often used as approximate
probability density functions in variational inference since the number of
variational parameters is twice the number of unknown model parameters. The
resulting diagonal covariance structure coupled with unimodal behavior can be
too restrictive when dealing with highly non-Gaussian behavior, including
multimodality. High-fidelity surrogate posteriors in the form of Gaussian
mixtures can capture any distribution to an arbitrary degree of accuracy while
maintaining some analytical tractability. Variational inference with Gaussian
mixtures with full-covariance structures suffers from a quadratic growth in
variational parameters with the number of model parameters. Coupled with the
existence of multiple local minima due to nonconvex trends in the loss
functions often associated with variational inference, these challenges
motivate the need for robust initialization procedures to improve the
performance and scalability of variational inference with mixture models.
In this work, we propose a method for constructing an initial Gaussian
mixture model approximation that can be used to warm-start the iterative
solvers for variational inference. The procedure begins with an optimization
stage in model parameter space in which local gradient-based optimization,
globalized through multistart, is used to determine a set of local maxima,
which we take to approximate the mixture component centers. Around each mode, a
local Gaussian approximation is constructed via the Laplace method. Finally,
the mixture weights are determined through constrained least squares
regression. Robustness and scalability are demonstrated using synthetic tests.
The methodology is applied to an inversion problem in structural dynamics
involving unknown viscous damping coefficients. | 2307.06424v1 |
2023-09-26 | Universal Pairwise Interatomic van der Waals Potentials Based on Quantum Drude Oscillators | Repulsive short-range and attractive long-range van der Waals (vdW) forces
have an appreciable role in the behavior of extended molecular systems. When
using empirical force fields - the most popular computational methods applied
to such systems - vdW forces are typically described by Lennard-Jones-like
potentials, which unfortunately have a limited predictive power. Here, we
present a universal parameterization of a quantum-mechanical vdW potential,
which requires only two free-atom properties - the static dipole polarizability
$\alpha_1$ and the dipole-dipole $C_6$ dispersion coefficient. This is achieved
by deriving the functional form of the potential from the quantum Drude
oscillator (QDO) model, employing scaling laws for the equilibrium distance and
the binding energy as well as applying the microscopic law of corresponding
states. The vdW-QDO potential is shown to be accurate for vdW binding energy
curves, as demonstrated by comparing to ab initio binding curves of 21
noble-gas dimers. The functional form of the vdW-QDO potential has the correct
asymptotic behavior both at zero and infinite distances. In addition, it is
shown that the damped vdW-QDO potential can accurately describe vdW
interactions in dimers consisting of group II elements. Finally, we demonstrate
the applicability of the atom-in-molecule vdW-QDO model for predicting accurate
dispersion energies for molecular systems. The present work makes an important
step towards constructing universal vdW potentials, which could benefit
(bio)molecular computational studies. | 2309.14910v1 |
2023-10-18 | Quartic scaling of sound attenuation with frequency in vitreous silica | Several theoretical approaches to disordered media predict that acoustic
waves should undergo a quartic increase in their attenuation coefficient with
increasing frequency in the sub-terahertz region. Such Rayleigh-type scattering
would be related to the anomalous low-temperature plateau in the thermal
conductivity and to the so-called boson peak, i.e. an excess of vibrational
modes above the Debye density of states at around 1 THz. Brillouin scattering
of light allows the measurement of sound absorption and velocity dispersion up
to about 0.1 THz while inelastic x-ray scattering is limited to frequencies
larger than about 1 THz. We take advantage of the advent of ultrafast optical
techniques to explore the acoustical properties of amorphous SiO2 layers in the
difficult but crucial frequency region within this gap. A quartic scaling law
with frequency is clearly revealed between 0.2 and 0.9 THz, which is further
shown to be independent of temperature. This strongly damped regime is
accompanied by a decrease in the sound velocity already starting from about 0.5
THz, in line with theories. Our study assists to clarify the anomalous
acoustical properties in glasses at frequencies entering the boson peak region. | 2310.11832v1 |
2023-11-11 | Effects of wave parameters on load reduction performance for amphibious aircraft with V-hydrofoil | An investigation of the influence of the hydrofoil on load reduction
performance during an amphibious aircraft landing on still and wavy water is
conducted by solving the Unsteady Reynolds-Averaged Navier-Stokes equations
coupled with the standard $k-\omega$ turbulence model in this paper. During the
simulations, the numerical wave tank is realized by using the velocity-inlet
boundary wave maker coupled with damping wave elimination technique on the
outlet, while the volume of fluid model is employed to track the water-air
interface. Subsequently, the effects of geometric parameters of hydrofoil have
been first discussed on still water, which indicates the primary factor
influencing the load reduction is the static load coefficient of hydrofoil.
Furthermore, the effects of descent velocity, wave length and wave height on
load reduction are comprehensively investigated. The results show that the
vertical load reduces more than 55$\%$ at the early stage of landing on the
still water through assembling the hydrofoil for different descent velocity
cases. Meanwhile, for the amphibious aircraft with high forward velocity, the
bottom of the fuselage will come into close contact with the first wave when
landing on crest position, and then the forebody will impact the next wave
surface with extreme force. In this circumstance, the load reduction rate
decreases to around 30$\%$, which will entail a further decline with the
increase of wave length or wave height. | 2311.06516v1 |
2023-11-17 | Simulating X-ray Reverberation in the UV-Emitting Regions of Active Galactic Nuclei Accretion Disks with 3D Multi-Frequency Magnetohydrodynamic Simulations | Active galactic nuclei (AGN) light curves observed with different wavebands
show that the variability in longer wavelength bands lags the variability in
shorter wavelength bands. Measuring these lags, or reverberation mapping, is
used to measure the radial temperature profile and extent of AGN disks,
typically with a reprocessing model that assumes X-rays are the main driver of
the variability in other wavelength bands. To demonstrate how this reprocessing
works with realistic accretion disk structures, we use 3D local shearing box
multi-frequency radiation magnetohydrodynamic (MHD) simulations to model the
UV-emitting region of an AGN disk, which is unstable to the magnetorotational
instability (MRI) and convection. At the same time, we inject hard X-rays
($>1$~keV) into the simulation box to study the effects of X-ray irradiation on
the local properties of the turbulence and the resulting variability of the
emitted UV light curve. We find that disk turbulence is sufficient to drive
intrinsic variability in emitted UV light curves and that a damped random walk
(DRW) model is a good fit to this UV light curve for timescales $>5$~days.
Meanwhile, the injected X-rays have almost no impact on the power spectrum of
the emitted UV light curve. In addition, the injected X-ray and emitted UV
light curves are only correlated if there is X-ray variability on timescales
$>1$~day, in which case we find a correlation coefficient $r=0.52$. These
results suggest that hard X-rays with scattering dominated opacity are likely
not the main driver of the reverberation signals. | 2311.10820v1 |
2023-11-25 | Ultrasensitive vibrational resonance induced by small disturbances | We have found two kinds of ultra-sensitive vibrational resonance in coupled
nonlinear systems. It is particularly worth pointing out that this
ultra-sensitive vibrational resonance is a transient behavior caused by
transient chaos. Considering long-term response, the system will transform from
transient chaos to periodic response. The pattern of vibrational resonance will
also transform from ultra-sensitive vibrational resonance to conventional
vibrational resonance. This article focuses on the transient ultra-sensitive
vibrational resonance phenomenon. It is induced by a small disturbance of the
high-frequency excitation and the initial simulation conditions, respectively.
The damping coefficient and the coupling strength are the key factors to induce
the ultra-sensitive vibrational resonance. By increasing these two parameters,
the vibrational resonance pattern can be transformed from an ultra-sensitive
vibrational resonance to a conventional vibrational resonance. The reason for
different vibrational resonance patterns to occur lies in the state of the
system response. The response usually presents transient chaotic behavior when
the ultra-sensitive vibrational resonance appears and the plot of the response
amplitude versus the controlled parameters shows a highly fractalized pattern.
When the response is periodic or doubly-periodic, it usually corresponds to the
conventional vibrational resonance. The ultra-sensitive vibrational resonance
not only occurs at the excitation frequency, but it also occurs at some more
nonlinear frequency components. The ultra-sensitive vibrational resonance as a
transient behavior and the transformation of vibrational resonance patterns are
new phenomena in coupled nonlinear systems. | 2312.11474v1 |
2024-02-13 | Hyperballistic transport in dense ionized matter under external AC electric fields | The Langevin equation is ubiquitously employed to numerically simulate
plasmas and dusty plasmas. However, the usual assumption of white noise becomes
untenable when the system is subject to an external AC electric field. This is
because the charged particles in the plasma, which provide the thermal bath for
the particle transport, become themselves responsive to the AC field and the
thermal noise is field-dependent and non-Markovian. We theoretically study the
particle diffusivity in a Langevin transport model for a tagged charged
particle immersed in a dense plasma of charged particles that act as the
thermal bath, under an external AC electric field, by properly accounting for
the effects of the AC field on the thermal bath statistics. We analytically
derive the time-dependent generalized diffusivity $D(t)$ for different initial
conditions. The generalized diffusivity exhibits damped oscillatory-like
behaviour with initial very large peaks, where the generalized diffusion
coefficient is enhanced by orders of magnitude with respect to the
infinite-time steady-state value. The latter coincides with the Stokes-Einstein
diffusivity in the absence of external field. For initial conditions where the
external field is already on at $t=0$ and the system is thermalized under DC
conditions for $t \leq 0$, the short-time behaviour is hyperballistic, $MSD
\sim t^4$ (where MSD is the mean-squared displacement), leading to giant
enhancement of the particle transport. Finally, the theory elucidates the role
of medium polarization on the local Lorentz field, and allows for estimates of
the effective electric charge due to polarization by the surrounding charges. | 2402.08519v2 |
2024-02-15 | Tracer dynamics in polymer networks: generalized Langevin description | Tracer diffusion in polymer networks and hydrogels is relevant in biology and
technology, while it also constitutes an interesting model process for the
dynamics of molecules in fluctuating, heterogeneous soft matter. Here, we study
systematically the time-dependent dynamics and (non-Markovian) memory effects
of tracers in polymer networks based on (Markovian) implicit-solvent Langevin
simulations. In particular, we consider spherical tracer solutes at high
dilution in regular, tetrafunctional bead-spring polymer networks, and control
the tracer-network Lennard-Jones (LJ) interactions and the polymer density.
Based on the analysis of the memory (friction) kernels, we recover the expected
long-time transport coefficients, and demonstrate how the short-time tracer
dynamics, polymer fluctuations, and the viscoelastic response are interlinked.
Further, we fit the characteristic memory modes of the tracers with damped
harmonic oscillations and identify LJ contributions, bond vibrations, and slow
network relaxations, which enter the kernel with an almost linear scaling with
the LJ attractions. This procedure proposes a reduced functional form for the
tracer memory, allowing for a convenient inter- and extrapolation of the memory
kernels. This leads eventually to highly efficient simulations utilizing the
generalized Langevin equation (GLE), in which the polymer network acts as an
additional thermal bath with tuneable intensity. | 2402.10148v1 |
2024-02-21 | Obstacle crossing strategies for high-speed 4WD small-scale vehicle | Unmanned ground vehicle obstacle crossing generally relies on two strategies:
(i) applying a wheel torque for climbing and (ii) modifying the vehicle shape
by using a wheel-leg or wheel-paddle to lift the wheel on top of the obstacle.
However, most of those strategies sacrifice speed in order to have a longer
contact duration between the wheels and the obstacle. This paper investigates
the behaviour of a 4WD high-speed vehicle while crossing a step obstacle using
a design of experiment (DoE). A 3D multibody vehicle model is equipped with a
novel 2-DoF suspension system, which horizontal damping coefficient is modify
to dampen wheel motion in longitudinal and vertical directions in relation to
the chassis, for a given speed and obstacle height. The DoE results allow to
propose a novel high-speed obstacle crossing strategy based on three metrics:
(i) the kinetic energy variation of the vehicle, (ii) the contact duration
between the wheel and the obstacle, and (iii) the pitch rate at the start of
the ballistic phase. Experimental function are proposed to be able modify these
metric in real time. | 2402.13650v1 |
2001-08-02 | Dielectronic Recombination (via N=2 --> N'=2 Core Excitations) and Radiative Recombination of Fe XX: Laboratory Measurements and Theoretical Calculations | We have measured the resonance strengths and energies for dielectronic
recombination (DR) of Fe XX forming Fe XIX via N=2 --> N'=2 (Delta_N=0) core
excitations. We have also calculated the DR resonance strengths and energies
using AUTOSTRUCTURE, HULLAC, MCDF, and R-matrix methods, four different
state-of-the-art theoretical techniques. On average the theoretical resonance
strengths agree to within <~10% with experiment. However, the 1 sigma standard
deviation for the ratios of the theoretical-to-experimental resonance strengths
is >~30% which is significantly larger than the estimated relative experimental
uncertainty of <~10%. This suggests that similar errors exist in the calculated
level populations and line emission spectrum of the recombined ion. We confirm
that theoretical methods based on inverse-photoionization calculations (e.g.,
undamped R-matrix methods) will severely overestimate the strength of the DR
process unless they include the effects of radiation damping. We also find that
the coupling between the DR and radiative recombination (RR) channels is small.
We have used our experimental and theoretical results to produce
Maxwellian-averaged rate coefficients for Delta_N=0 DR of Fe XX. For kT>~1 eV,
which includes the predicted formation temperatures for Fe XX in an optically
thin, low-density photoionized plasma with cosmic abundances, our experimental
and theoretical results are in good agreement. We have also used our R-matrix
results, topped off using AUTOSTRUCTURE for RR into J>=25 levels, to calculate
the rate coefficient for RR of Fe XX. Our RR results are in good agreement with
previously published calculations. | 0108048v1 |
2003-10-21 | Self-Consistent R-matrix Approach To Photoionization And Unified Electron-Ion Recombination | A unified scheme using the R-matrix method has been developed for
electron-ion recombination subsuming heretofore separate treatments of
radiative and dielectronic recombination (RR and DR). The ab initio coupled
channel approach unifies resonant and non-resonant phenomena, and enables a
general and self-consistent treatment of photoionization and electron-ion
recombination employing idential wavefunction expansion. Detailed balance takes
account of interference effects due to resonances in cross sections, calculated
explicitly for a large number of recombined (e+ion) bound levels over extended
energy regions. The theory of DR by Bell and Seaton is adapted for high-n
resonances in the region below series limits. The R-matrix method is employed
for (A) partial and total photoionization and photorecombination cross sections
of (e+ion) bound levels, and (B) DR and (e+ion) scattering cross sections.
Relativistic effects and fine structure are considered in the Breit-Pauli
approximation. Effects such as radiation damping may be taken into account
where necessary. Unfiied recombination cross sections are in excellent
agreement with measurements on ion storage rings to about 10-20%. In addition
to high accuracy, the strengths of the method are: (I) both total and
level-specific cross sections and rate coefficients are obtained, and (II) a
single (e+ion) recombination rate coefficient for any given atom or ion is
obtained over the entire temperature range of practical importance in
laboratory and astrophysical plasmas, (III) self-consistent results are
obtained for photoionization and recombination; comprehensive datasets have
been computed for over 50 atoms and ions. Selected data are presented for iron
ions. | 0310624v1 |
2001-10-19 | A Survey of Numerical Solutions to the Coagulation Equation | We present the results of a systematic survey of numerical solutions to the
coagulation equation for a rate coefficient of the form A_ij \propto (i^mu j^nu
+ i^nu j^mu) and monodisperse initial conditions. The results confirm that
there are three classes of rate coefficients with qualitatively different
solutions. For nu \leq 1 and lambda = mu + nu \leq 1, the numerical solution
evolves in an orderly fashion and tends toward a self-similar solution at large
time t. The properties of the numerical solution in the scaling limit agree
with the analytic predictions of van Dongen and Ernst. In particular, for the
subset with mu > 0 and lambda < 1, we disagree with Krivitsky and find that the
scaling function approaches the analytically predicted power-law behavior at
small mass, but in a damped oscillatory fashion that was not known previously.
For nu \leq 1 and lambda > 1, the numerical solution tends toward a
self-similar solution as t approaches a finite time t_0. The mass spectrum n_k
develops at t_0 a power-law tail n_k \propto k^{-tau} at large mass that
violates mass conservation, and runaway growth/gelation is expected to start at
t_crit = t_0 in the limit the initial number of particles n_0 -> \infty. The
exponent tau is in general less than the analytic prediction (lambda + 3)/2,
and t_0 = K/[(lambda - 1) n_0 A_11] with K = 1--2 if lambda > 1.1. For nu > 1,
the behaviors of the numerical solution are similar to those found in a
previous paper by us. They strongly suggest that there are no self-consistent
solutions at any time and that runaway growth is instantaneous in the limit n_0
-> \infty. They also indicate that the time t_crit for the onset of runaway
growth decreases slowly toward zero with increasing n_0. | 0110411v1 |
2003-11-08 | Memory effects in superfluid vortex dynamics | The dissipative dynamics of a vortex line in a superfluid is investigated
within the frame of a non-Markovian quantal Brownian motion model. Our starting
point is a recently proposed interaction Hamiltonian between the vortex and the
superfluid quasiparticle excitations, which is generalized to incorporate the
effect of scattering from fermion impurities ($^3$He atoms). Thus, a
non-Markovian equation of motion for the mean value of the vortex position
operator is derived within a weak-coupling approximation. Such an equation is
shown to yield, in the Markovian and elastic scattering limits, a $^3$He
contribution to the longitudinal friction coefficient equivalent to that
arising from the Rayfield-Reif formula. Simultaneous Markov and elastic
scattering limits are found, however, to be incompatible, since an unexpected
breakdown of the Markovian approximation is detected at low cyclotron
frequencies. Then, a non-Markovian expression for the longitudinal friction
coefficient is derived and computed as a function of temperature and $^3$He
concentration. Such calculations show that cyclotron frequencies within the
range 0.01$-$0.03 ps$^{-1}$ yield a very good agreement to the longitudinal
friction figures computed from the Iordanskii and Rayfield-Reif formulas for
pure $^4$He, up to temperatures near 1 K. A similar performance is found for
nonvanishing $^3$He concentrations, where the comparison is also shown to be
very favorable with respect to the available experimental data. Memory effects
are shown to be weak and increasing with temperature and concentration. | 0311179v3 |
2015-09-03 | Evidence of thermal conduction suppression in a solar flaring loop by coronal seismology of slow-mode waves | Analysis of a longitudinal wave event observed by the Atmospheric Imaging
Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) is presented. A
time sequence of 131 A images reveals that a C-class flare occurred at one
footpoint of a large loop and triggered an intensity disturbance (enhancement)
propagating along it. The spatial features and temporal evolution suggest that
a fundamental standing slow-mode wave could be set up quickly after meeting of
two initial disturbances from the opposite footpoints. The oscillations have a
period of ~12 min and a decay time of ~9 min. The measured phase speed of
500$\pm$50 km/s matches the sound speed in the heated loop of ~10 MK,
confirming that the observed waves are of slow mode. We derive the
time-dependent temperature and electron density wave signals from six AIA
extreme-ultraviolet (EUV) channels, and find that they are nearly in phase.The
measured polytropic index from the temperature and density perturbations is
1.64$\pm$0.08 close to the adiabatic index of 5/3 for an ideal monatomic gas.
The interpretation based on a 1D linear MHD model suggests that the thermal
conductivity is suppressed by at least a factor of 3 in the hot flare loop at 9
MK and above. The viscosity coefficient is determined by coronal seismology
from the observed wave when only considering the compressive viscosity
dissipation. We find that to interpret the rapid wave damping, the classical
compressive viscosity coefficient needs to be enhanced by a factor of 15 as the
upper limit. | 1509.00920v2 |
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