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2013-08-21
|
Overstable Librations can account for the Paucity of Mean Motion Resonances among Exoplanet Pairs
|
We assess the multi-planet systems discovered by the Kepler satellite in
terms of current ideas about orbital migration and eccentricity damping due to
planet-disk interactions. Our primary focus is on mean motion resonances. Only
a few percent of planet pairs are in close proximity to a resonance. However,
predicted migration rates (parameterized by $\tau_n=n/{|\dot n|}$) imply that
during convergent migration most planets would have been captured into first
order resonances. Eccentricity damping (parameterized by $\tau_e=e/{|\dot e|}$)
offers a plausible resolution. Estimates suggest $\tau_e/\tau_n\sim (h/a)^2\sim
10^{-2}$, where $h/a$ is the ratio of disk thickness to radius. Together,
eccentricity damping and orbital migration give rise to an equilibrium
eccentricity, $e_{eq}\sim(\tau_e/\tau_n)^{1/2}$. Capture is permanent provided
$e_{eq}\lesssim \mu^{1/3}$, where $\mu$ denotes the planet to star mass ratio.
But for $e_{eq}\gtrsim \mu^{1/3}$, capture is only temporary because librations
around equilibrium are overstable and lead to passage through resonance on
timescale $\tau_e$. Most Kepler planet pairs have $e_{eq}>\mu^{1/3}$. Since
$\tau_n>> \tau_e$ is the timescale for migration between neighboring
resonances, only a modest percentage of pairs end up trapped in resonances
after the disk disappears. Planet pairs close to a mean motion resonance
typically exhibit period ratios 1-2% larger than those for exact resonance. The
direction of this shift undoubtedly reflects the same asymmetry that requires
convergent migration for resonance capture. Permanent resonance capture at
these separations from exact resonance would demand $\mu
(\tau_n/\tau_e)^{1/2}\gtrsim 0.01$, a value that estimates of $\mu$ from
transit data and $(\tau_e/\tau_n)^{1/2}$ from theory are insufficient to match.
Plausible alternatives involve eccentricity damping during or after disk
dispersal. (Abridged)
|
1308.4688v2
|
2013-08-30
|
Nested Head-Tail Vlasov Solver
|
Nested Head-Tail (NHT) is a Mathematica-based Vlasov solver for transverse
oscillations in multi-bunch beams. It takes into account azimuthal, radial,
coupled-bunch and beam-beam degrees of freedom, single- and inter-bunch dipole
wakes, an arbitrary damper, beam-beam effects and Landau damping.
|
1309.0044v3
|
2013-09-24
|
Attractors for damped quintic wave equations in bounded domains
|
The dissipative wave equation with a critical quintic nonlinearity in smooth
bounded three dimensional domain is considered. Based on the recent extension
of the Strichartz estimates to the case of bounded domains, the existence of a
compact global attractor for the solution semigroup of this equation is
established. Moreover, the smoothness of the obtained attractor is also shown.
|
1309.6272v1
|
2013-09-30
|
Harmonic oscillator: an analysis via Fourier series
|
The Fourier series method is used to solve the homogeneous equation governing
the motion of the harmonic oscillator. It is shown that the general solution to
the problem can be found in a surprisingly simple way for the case of the
simple harmonic oscillator. It is also shown that the damped harmonic
oscillator is susceptible to the analysis.
|
1309.7918v1
|
2013-10-01
|
Observations and predictions at CesrTA, and outlook for ILC
|
In this paper, we will describe some of the recent experimental measurements
[1, 2, 3] performed at CESRTA [4], and the supporting simulations, which probe
the interaction of the electron cloud with the stored beam. These experiments
have been done over a wide range of beam energies, emittances, bunch currents,
and fill patterns, to gather sufficient information to be able to fully
characterize the beam-electron-cloud interaction and validate the simulation
programs. The range of beam conditions is chosen to be as close as possible to
those of the ILC damping ring, so that the validated simulation programs can be
used to predict the performance of these rings with regard to electroncloud-
related phenomena. Using the new simulation code Synrad3D to simulate the
synchrotron radiation environment, a vacuum chamber design has been developed
for the ILC damping ring which achieves the required level of photoelectron
suppression. To determine the expected electron cloud density in the ring, EC
buildup simulations have been done based on the simulated radiation environment
and on the expected performance of the ILC damping ring chamber mitigation
prescriptions. The expected density has been compared with analytical estimates
of the instability threshold, to verify that the ILC damping ring vacuum
chamber design is adequate to suppress the electron cloud single-bunch
head-tail instability.
|
1310.0261v1
|
2013-10-21
|
A Critical History of Renormalization
|
The history of renormalization is reviewed with a critical eye, starting with
Lorentz's theory of radiation damping, through perturbative QED with Dyson,
Gell-Mann & Low, and others, to Wilson's formulation and Polchinski's
functional equation, and applications to "triviality", and dark energy in
cosmology.
|
1310.5533v1
|
2013-10-27
|
Fundamental limitations of half-metallicicity in spintronic materials
|
Zero-point spin fluctuations are shown to strongly influence the ground state
of ferromagnetic metals and to impose limitations for the fully spin polarized
state assumed in half-metallic ferromagnets, which may influence their
applications in spintronics. This phenomenon leads to the low-frequency Stoner
excitations and cause strong damping and softening of magnons in
magnetoresistive manganites observed experimentally.
|
1310.7174v1
|
2013-12-13
|
Probing Intergalactic Neutral Hydrogen by the Lyman Alpha Red Damping Wing of Gamma-Ray Burst 130606A Afterglow Spectrum at z = 5.913
|
The unprecedentedly bright optical afterglow of GRB 130606A located by Swift
at a redshift close to the reionization era (z = 5.913) provides a new
opportunity to probe the ionization status of intergalactic medium (IGM). Here
we present an analysis of the red Ly alpha damping wing of the afterglow
spectrum taken by Subaru/FOCAS during 10.4-13.2 hr after the burst. We find
that the minimal model including only the baseline power-law and HI absorption
in the host galaxy does not give a good fit, leaving residuals showing concave
curvature in 8400-8900 A with an amplitude of about 0.6% of the flux. Such a
curvature in the short wavelength range cannot be explained either by
extinction at the host with standard extinction curves, intrinsic curvature of
afterglow spectra, or by the known systematic uncertainties in the observed
spectrum. The red damping wing by intervening HI gas outside the host can
reduce the residual by about 3 sigma statistical significance. We find that a
damped Ly alpha system is not favored as the origin of this intervening HI
absorption, from the observed Ly beta and metal absorption features. Therefore
absorption by diffuse IGM remains as a plausible explanation. A fit by a simple
uniform IGM model requires HI neutral fraction of f_HI ~ 0.1-0.5 depending on
the distance to the GRB host, implying high f_HI IGM associated with the
observed dark Gunn-Peterson (GP) troughs. This gives a new evidence that the
reionization is not yet complete at z ~ 6.
|
1312.3934v3
|
2014-01-08
|
Dynamic exchange via spin currents in acoustic and optical modes of ferromagnetic resonance in spin-valve structures
|
Two ferromagnetic layers magnetically decoupled by a thick normal metal
spacer layer can be, nevertheless, dynamically coupled via spin currents
emitted by the spin-pump and absorbed through the spin-torque effects at the
neighboring interfaces. A decrease of damping in both layers due to a partial
compensation of the angular momentum leakage in each layer was previously
observed at the coincidence of the two ferromagnetic resonances. In case of
non-zero magnetic coupling, such a dynamic exchange will depend on the mutual
precession of the magnetic moments in the layers. A difference in the linewidth
of the resonance peaks is expected for the acoustic and optical regimes of
precession. However, the interlayer coupling hybridizes the resonance responses
of the layers and therefore can also change their linewidths. The interplay
between the two mechanisms has never been considered before. In the present
work, the joint influence of the hybridization and non-local damping on the
linewidth has been studied in weakly coupled NiFe/CoFe/Cu/CoFe/MnIr spin-valve
multilayers. It has been found that the dynamic exchange by spin currents is
different in the optical and acoustic modes, and this difference is dependent
on the interlayer coupling strength. In contrast to the acoustic precession
mode, the dynamic exchange in the optical mode works as an additional damping
source. A simulation in the framework of the Landau-Lifshitz-Gilbert formalism
for two ferromagnetic layers coupled magnetically and by spin currents has been
done to separate the effects of the non-local damping from the resonance modes
hybridization. In our samples both mechanisms bring about linewidth changes of
the same order of magnitude, but lead to a distinctly different angular
behavior. The obtained results are relevant for a broad class of coupled
magnetic multilayers with ballistic regime of the spin transport.
|
1401.1672v1
|
2014-02-01
|
Effects of stellar flybys on planetary systems: 3D modeling of the circumstellar disks damping effects
|
Stellar flybys in star clusters are suspected to affect the orbital
architecture of planetary systems causing eccentricity excitation and orbital
misalignment between the planet orbit and the equatorial plane of the star. We
explore whether the impulsive changes in the orbital elements of planets,
caused by an hyperbolic stellar flyby, can be fully damped by the circumstellar
disk surrounding the star. The time required to disperse stellar clusters is in
fact comparable to circumstellar disk's lifetime. We have modelled in 3D a
system made of a solar type star surrounded by a low density disk with a giant
planet embedded in it approached on a hyperbolic encounter trajectory by a
second star, of similar mass and with its own disk. We focus on extreme
configurations where a very deep stellar flyby perturbs a Jovian planet on an
external orbit. This allows to test in full the ability of the disk to erase
the effects of the stellar encounter. We find that the amount of mass lost by
the disk during the stellar flyby is less than in 2D models where a single disk
was considered due to the mass exchange between the two disks at the encounter.
The damping in eccentricity is slightly faster than in 2D models and it occurs
on timescales of the order of a few kyr. The only trace of the flyby left in
the planet system, after about 10^4 yr, is a small misalignment, lower than 9
degrees, between the star equatorial plane and the planet orbit. In a realistic
model based on 3D simulations of star--planet--disk interactions, we find that
stellar flybys cannot excite significant eccentricities and inclinations of
planets in stellar clusters. The circumstellar disks hosting the planets damp
on a short timescale all the step changes in the two orbital parameters
produced during any stellar encounter. All records of past encounters are
erased.
|
1402.0077v1
|
2014-02-21
|
Damping of electron Zitterbewegung in carbon nanotubes
|
Zitterbewegung (ZB, trembling motion) of electrons in semiconductor carbon
nanotubes is described taking into account dephasing processes. The density
matrix formalism is used for the theory. Differences between decay of ZB
oscillations due to electron localization and that due to dephasing are
discussed.
|
1402.5393v1
|
2014-04-18
|
Exponential mixing for the white - forced damped nonlinear wave equation
|
The paper is devoted to studying the stochastic nonlinear wave (NLW) equation
in a bounded domain D $\subset$ R3. We show that the Markov process associated
with the flow of solution has a unique stationary measure $\mu$, and the law of
any solution converges to $\mu$ with exponential rate in the dual-Lipschitz
norm
|
1404.4697v1
|
2014-04-22
|
A unique continuation result for the plate equation and an application
|
In this paper, we prove the unique continuation property for the weak
solution of the plate equation with non-smooth coefficients. Then, we apply
this result to study the global attractor for the semilinear plate equation
with a localized damping.
|
1404.5586v3
|
2014-05-13
|
Magneto-seismological insights into the penumbral chromosphere and evidence for wave damping in spicules
|
The observation of propagating magneto-hydrodynamic kink waves in magnetic
structures and measurement of their properties (amplitude, phase speed) can be
used to diagnose the plasma conditions in the neighbourhood of the magnetic
structure via magneto-seismology (MS). We aim to reveal properties of the
chromosphere/Transition Region above the sunspot penumbra using this technique.
Hinode observed a sunspot as it was crossing the limb, providing a unique side
on view of the sunspot atmosphere. The presence of large spicule-like jets is
evident in \ion{Ca}{II} H images. The jets are found to support transverse wave
motions that displace the central axis, which can be interpreted as a kink
wave. The properties of a wave event are measured and used to determine the
magnetic and density stratification along the structure. We also measure the
width of the spicule and the intensity profile along the structure. The
measured wave properties reveal an initial rapid increase in amplitude with
height above the solar surface, followed by a decrease in amplitude. The MS
inversion suggests this initial increase corresponds to large changes in
density and magnetic field strength. In addition, we provide the first
measurements of spicule width with height, which confirm that the spicule under
goes rapid expansion. The measured expansion shows good agreement with the
results from the MS. The observed variations in plasma parameters are suggested
to be partly due to the presence of a gravitational stratified, ambient
atmosphere. Combining width measurements with phase speed measurements implies
the observed decrease in wave amplitude at greater heights can be explained by
wave damping. Hence, we provide the first direct evidence of wave damping in
chromospheric spicules and the quality factor of the damping is found to be
significantly smaller than estimated coronal values.
|
1405.3203v1
|
2014-05-27
|
Interior feedback stabilization of wave equations with dynamic boundary delay
|
In this paper we consider an interior stabilization problem for the wave
equation with dynamic boundary delay.We prove some stability results under the
choice of damping operator. The proof of the main result is based on a
frequency domain method and combines a contradiction argument with the
multiplier technique to carry out a special analysis for the resolvent.
|
1405.6865v2
|
2014-07-11
|
Remark on stabilization of second order evolution equations by unbounded dynamic feedbacks and applications
|
In this paper we consider second order evolution equations with unbounded
dynamic feedbacks. Under a regularity assumption we show that observability
properties for the undamped problem imply decay estimates for the damped
problem. We consider both uniform and non uniform decay properties.
|
1407.3070v1
|
2014-09-11
|
Eliminating flutter for clamped von Karman plates immersed in subsonic flows
|
We address the long-time behavior of a non-rotational von Karman plate in an
inviscid potential flow. The model arises in aeroelasticity and models the
interaction between a thin, nonlinear panel and a flow of gas in which it is
immersed [6, 21, 23]. Recent results in [16, 18] show that the plate component
of the dynamics (in the presence of a physical plate nonlinearity) converge to
a global compact attracting set of finite dimension; these results were
obtained in the absence of mechanical damping of any type. Here we show that,
by incorporating mechanical damping the full flow-plate system, full
trajectories---both plate and flow---converge strongly to (the set of)
stationary states. Weak convergence results require "minimal" interior damping,
and strong convergence of the dynamics are shown with sufficiently large
damping. We require the existence of a "good" energy balance equation, which is
only available when the flows are subsonic. Our proof is based on first showing
the convergence properties for regular solutions, which in turn requires
propagation of initial regularity on the infinite horizon. Then, we utilize the
exponential decay of the difference of two plate trajectories to show that full
flow-plate trajectories are uniform-in-time Hadamard continuous. This allows us
to pass convergence properties of smooth initial data to finite energy type
initial data. Physically, our results imply that flutter (a non-static end
behavior) does not occur in subsonic dynamics. While such results were known
for rotational (compact/regular) plate dynamics [14] (and references therein),
the result presented herein is the first such result obtained for
non-regularized---the most physically relevant---models.
|
1409.3308v5
|
2014-12-15
|
Optomechanical laser cooling with mechanical modulations
|
We theoretically study the laser cooling of cavity optomechanics when the
mechanical resonance frequency and damping depend on time. In the regime of
weak optomechanical coupling we extend the theory of laser cooling using an
adiabatic approximation. We discuss the modifications of the cooling dynamics
and compare it with numerical simulations in a wide range of modulation
frequencies.
|
1412.4497v1
|
2015-03-08
|
An Analytical Formulation of Power System Oscillation Frequency
|
This letter proposes an analytical approach to formulate the power system
oscillation frequency under a large disturbance. A fact is revealed that the
oscillation frequency is only the function of the oscillation amplitude when
the system's model and operating condition are fixed. Case studies also show
that this function is damping-insensitive and could be applied to an inter-area
model of a multi-machine power system.
|
1503.07554v1
|
2015-04-07
|
Generation of coherent spin-wave modes in Yttrium Iron Garnet microdiscs by spin-orbit torque
|
Spin-orbit effects [1-4] have the potential of radically changing the field
of spintronics by allowing transfer of spin angular momentum to a whole new
class of materials. In a seminal letter to Nature [5], Kajiwara et al. showed
that by depositing Platinum (Pt, a normal metal) on top of a 1.3 $\mu$m thick
Yttrium Iron Garnet (YIG, a magnetic insulator), one could effectively transfer
spin angular momentum through the interface between these two different
materials. The outstanding feature was the detection of auto-oscillation of the
YIG when enough dc current was passed in the Pt. This finding has created a
great excitement in the community for two reasons: first, one could control
electronically the damping of insulators, which can offer improved properties
compared to metals, and here YIG has the lowest damping known in nature;
second, the damping compensation could be achieved on very large objects, a
particularly relevant point for the field of magnonics [6,7] whose aim is to
use spin-waves as carriers of information. However, the degree of coherence of
the observed auto-oscillations has not been addressed in ref. [5]. In this
work, we emphasize the key role of quasi-degenerate spin-wave modes, which
increase the threshold current. This requires to reduce both the thickness and
lateral size in order to reach full damping compensation [8] , and we show
clear evidence of coherent spin-orbit torque induced auto-oscillation in
micron-sized YIG discs of thickness 20 nm.
|
1504.01512v1
|
2015-05-01
|
Periodic solutions for nonlinear hyperbolic evolution systems
|
We shall deal with the periodic problem for nonlinear perturbations of
abstract hyperbolic evolution equations generating an evolution system of
contractions. We prove an averaging principle for the translation along
trajectories operator associated to the nonlinear evolution system, expressed
in terms of the topological degree. The abstract results shall be applied to
the damped hyperbolic partial differential equation.
|
1505.00150v1
|
2015-05-28
|
Moore-Gibson-Thompson equation with memory, part I: exponential decay of energy
|
We are interested in the Moore-Gibson-Thompson(MGT) equation with memory
\begin{equation}\nonumber \tau u_{ttt}+ \alpha u_{tt}+c^2\A u+b\A u_t
-\int_0^tg(t-s)\A w(s)ds=0. \end{equation} We first classify the memory into
three types. Then we study how a memory term creates damping mechanism and how
the memory causes energy decay.
|
1505.07523v1
|
2015-05-29
|
Fission barriers heights in A$\sim$ 200 mass region
|
Statistical model analysis has been carried out for $p$ and $\alpha$ induced
fission reactions using a consistent description for fission barrier and level
density in A $\sim$ 200 mass region. A continuous damping of shell correction
with excitation energy have been considered. Extracted fission barriers agree
well with the recent microscopic-macroscopic model. The shell corrections at
the saddle point were found to be not significant.
|
1505.08026v1
|
2015-06-16
|
Revisit on How to Derive Asymptotic Profiles to Some Evolution Equations
|
We consider the Cauchy problem in ${\bf R}^{n}$ for heat and damped wave
equations. We derive asymptotic profiles to those solutions with weighted
$L^{1,1}({\bf R}^{n})$ data by presenting a simple method.
|
1506.04858v1
|
2015-06-21
|
Predicting the Influence of Plate Geometry on the Eddy Current Pendulum
|
We quantitatively analyze a familiar classroom demonstration, Van
Waltenhofen's eddy current pendulum, to predict the damping effect for a
variety of plate geometries from first principles. Results from conformal
mapping, finite element simulations and a simplified model suitable for
introductory classes are compared with experiments.
|
1506.06401v1
|
2015-07-19
|
Alfvén wave phase-mixing in flows: Why over-dense, solar coronal, open magnetic field structures are cool?
|
The motivation for this study is to include the effect of plasma flow in
Alfv\'en wave (AW) damping via phase mixing and to explore the observational
implications. Our magnetohydrodynamic (MHD) simulations and analytical
calculations show that, when a background flow is present, mathematical
expressions for the AW damping via phase mixing are modified by the following
substitution: $C_A^\prime(x) \to C_A^\prime(x)+V_0^\prime(x)$, where $C_A$ and
$V_0$ are AW phase and the flow speeds, and the prime denotes a derivative in
the direction across the background magnetic field. In uniform magnetic fields
and over-dense plasma structures, where $C_A$ is smaller than in the
surrounding plasma, the flow, which is confined to the structure and going in
the same direction as the AW, reduces the effect of phase-mixing, because on
the edges of the structure $C_A^\prime$ and $V_0^\prime$ have opposite signs.
Thus, the wave damps by means of slower phase-mixing compared to the case
without the flow. This is the result of the co-directional flow that reduces
the wave front stretching in the transverse direction. We apply our findings to
addressing the question why over-dense solar coronal open magnetic field
structures (OMFS) are cooler than the background plasma. Observations show that
the over-dense OMFS (e.g. solar coronal polar plumes) are cooler than
surrounding plasma and that, in these structures, Doppler line-broadening is
consistent with bulk plasma motions, such as AW. If over-dense solar coronal
OMFS are heated by AW damping via phase-mixing, we show that, co-directional
with AW, plasma flow in them reduces the phase-mixing induced-heating, thus
providing an explanation of why they appear cooler than the background.
|
1507.05293v2
|
2015-09-28
|
Linear inviscid damping for a class of monotone shear flow in Sobolev spaces
|
In this paper, we prove the decay estimates of the velocity and $H^1$
scattering for the 2D linearized Euler equations around a class of monotone
shear flow in a finite channel. Our result is consistent with the decay rate
predicted by Case in 1960.
|
1509.08228v1
|
2015-10-09
|
Energy Dissipation and Landau Damping in Two- and Three-Dimensional Plasma Turbulence
|
Plasma turbulence is ubiquitous in space and astrophysical plasmas, playing
an important role in plasma energization, but the physical mechanisms leading
to dissipation of the turbulent energy remain to be definitively identified.
Kinetic simulations in two dimensions (2D) have been extensively used to study
the dissipation process. How the limitation to 2D affects energy dissipation
remains unclear. This work provides a model of comparison between two- and
three-dimensional (3D) plasma turbulence using gyrokinetic simulations; it also
explores the dynamics of distribution functions during the dissipation process.
It is found that both 2D and 3D nonlinear gyrokinetic simulations of a low-beta
plasma generate electron velocity-space structures with the same
characteristics as that of linear Landau damping of Alfv\'en waves in a 3D
linear simulation. The continual occurrence of the velocity-space structures
throughout the turbulence simulations suggests that the action of Landau
damping may be responsible for the turbulent energy transfer to electrons in
both 2D and 3D, and makes possible the subsequent irreversible heating of the
plasma through collisional smoothing of the velocity-space fluctuations.
Although, in the 2D case where variation along the equilibrium magnetic field
is absent, it may be expected that Landau damping is not possible, a common
trigonometric factor appears in the 2D resonant denominator, leaving the
resonance condition unchanged from the 3D case. The evolution of the 2D and 3D
cases is qualitatively similar. However, quantitatively the nonlinear energy
cascade and subsequent dissipation is significantly slower in the 2D case.
|
1510.02842v2
|
2015-10-10
|
Boundary layers and incompressible Navier-Stokes-Fourier limit of the Boltzmann Equation in Bounded Domain (I)
|
We establish the incompressible Navier-Stokes-Fourier limit for solutions to
the Boltzmann equation with a general cut-off collision kernel in a bounded
domain. Appropriately scaled families of DiPerna-Lions-(Mischler) renormalized
solutions with Maxwell reflection boundary conditions are shown to have
fluctuations that converge as the Knudsen number goes to zero. Every limit
point is a weak solution to the Navier-Stokes-Fourier system with different
types of boundary conditions depending on the ratio between the accommodation
coefficient and the Knudsen number. The main new result of the paper is that
this convergence is strong in the case of Dirichlet boundary condition. Indeed,
we prove that the acoustic waves are damped immediately, namely they are damped
in a boundary layer in time. This damping is due to the presence of viscous and
kinetic boundary layers in space. As a consequence, we also justify the first
correction to the infinitesimal Maxwellian that one obtains from the
Chapman-Enskog expansion with Navier-Stokes scaling.
This extends the work of Golse and Saint-Raymond \cite{Go-Sai04, Go-Sai05}
and Levermore and Masmoudi \cite{LM} to the case of a bounded domain. The case
of a bounded domain was considered by Masmoudi and Saint-Raymond \cite{M-S} for
linear Stokes-Fourier limit and Saint-Raymond \cite{SRM} for Navier-Stokes
limit for hard potential kernels. Both \cite{M-S} and \cite{SRM} didn't study
the damping of the acoustic waves. This paper extends the result of \cite{M-S}
and \cite{SRM} to the nonlinear case and includes soft potential kernels. More
importantly, for the Dirichlet boundary condition, this work strengthens the
convergence so as to make the boundary layer visible. This answers an open
problem proposed by Ukai \cite{Ukai}.
|
1510.02977v1
|
2015-11-18
|
Temperature cooling in quantum dissipation channel and the correspondimg thermal vacuum state
|
We examine temperature cooling of optical chaotic light in a quantum
dissipation channel with the damping parameter k.The way we do it is by
introducing its thermal vacuum state which can expose entangling effect between
the system and the reservoir. The temperature cooling formula is derived, which
depends on the parameter k, by adjusting k one can control temperature.
|
1511.05777v1
|
2016-01-30
|
Quantum Dynamics of Complex Hamiltonians
|
Non hermitian Hamiltonians play an important role in the study of dissipative
quantum systems. We show that using states with time dependent normalization
can simplify the description of such systems especially in the context of the
classical limit. We apply this prescription to study the damped harmonic
oscillator system. This is then used to study the problem of radiation in leaky
cavity.
|
1602.00157v2
|
2016-02-17
|
Instability of a witness bunch in a plasma bubble
|
The stability of a trailing witness bunch, accelerated by a plasma wake
accelerator (PWA) in a blow-out regime, is discussed. The instability growth
rate as well as the energy spread, required for BNS damping, are obtained. A
relationship between the PWA power efficiency and the BNS energy spread is
derived.
|
1602.05260v2
|
2016-02-25
|
Strong Ly alpha Emission in the Proximate Damped Ly alpha Absorption Trough toward the Quasar SDSS J095253.83+011422.0
|
SDSS J095253.83+011422.0 (SDSS J0952+0114) was reported by Hall et al. (2004)
as an exotic quasar at $z_{\rm em}=3.020$. In contrast to prominent broad
metal--line emissions with FWHM~9000 km/s, only a narrow Ly \alpha emission
line is present with FWHM~1000 km/s. The absence of broad Ly alpha emission
line has been a mystery for more than a decade. In this paper, we demonstrate
that this is due to dark Proximate Damped Ly alpha Absorption (PDLA) at $z_{\rm
abs}=3.010$ by identifying associated Lyman absorption line series from the
damped Ly beta up to Ly9, as well as the Lyman limit absorption edge. The PDLA
cloud has a column density of $\log N_{\rm H\,I}({\rm cm}^{-2})=21.8\pm0.2$, a
metallicity of [Zn/H]$>-1.0$, and a spatial extent exceeding the Narrow
Emission Line Region (NELR) of the quasar. With a luminosity of $L_{{\rm
Ly}\alpha}\sim10^{45}$ erg s$^{-1}$, the residual Ly alpha emission superposed
on the PDLA trough is of two orders of magnitude stronger than previous
reports. This is best explained as re-radiated photons arising from the quasar
outflowing gas at a scale larger than the NELR. The PDLA here, acting like a
natural coronagraph, provides us with a good insight into the illuminated gas
in the vicinity of the quasar, which are usually hard to resolve due to their
small size and "seeing fuzz" of bright quasars. Notably, SDSS J0952+0114
analogs might be easily omitted in the spectroscopic surveys of DLAs and PDLAs,
as their damped Ly alpha troughs can be fully filled by additional strong Ly
alpha emissions. Our preliminary survey shows that such systems are not very
rare. They are potentially a unique sample for probing strong quasar feedback
phenomena in the early universe.
|
1602.07880v2
|
2016-03-27
|
Evolution of One-Dimensional Wind-Driven Sea Spectra
|
We analyze modern operational models of wind wave prediction on the subject
for compliance dissipation. Our numerical simulations from the "first
principle" demonstrate that heuristic formulas for damping rate of free wind
sea due to "white capping" (or wave breaking) dramatically exaggerates the role
of this effect in these models.
|
1603.08229v1
|
2016-03-07
|
Faddeev-Jackiw Quantization of Non-Autonomous Singular Systems
|
We extend the quantization \`a la Faddeev-Jackiw for non-autonomous singular
systems. This leads to a generalization of the Schr\"odinger equation for those
systems. The method is exemplified by the quantization of the damped harmonic
oscillator and the relativistic particle in an external electromagnetic field.
|
1603.08407v1
|
2016-05-06
|
Existence of invariant measures for the stochastic damped Schrödinger equation
|
In this paper, we address the long time behaviour of solutions of the
stochastic Schrodinger equation in $\mathbb{R}^d$. We prove the existence of an
invariant measure and establish asymptotic compactness of solutions, implying
in particular the existence of an ergodic measure.
|
1605.02014v1
|
2016-05-25
|
Dynamic analysis of simultaneous adaptation of force, impedance and trajectory
|
When carrying out tasks in contact with the environment, humans are found to
concurrently adapt force, impedance and trajectory. Here we develop a robotic
model of this mechanism in humans and analyse the underlying dynamics. We
derive a general adaptive controller for the interaction of a robot with an
environment solely characterised by its stiffness and damping, using Lyapunov
theory.
|
1605.07834v1
|
2016-06-24
|
Mixing for the Burgers equation driven by a localised two-dimensional stochastic forcing
|
We consider the one-dimensional Burgers equation perturbed by a stochastic
forcing, which is assumed to be white in time and localised and low-dimensional
in space. We establish a mixing property for the Markov process associated with
the problem in question. The proof is based on a general criterion for mixing
and a recent result on global approximate controllability to trajectories for
damped conservation laws.
|
1606.07763v1
|
2016-07-01
|
Randomized block proximal damped Newton method for composite self-concordant minimization
|
In this paper we consider the composite self-concordant (CSC) minimization
problem, which minimizes the sum of a self-concordant function $f$ and a
(possibly nonsmooth) proper closed convex function $g$. The CSC minimization is
the cornerstone of the path-following interior point methods for solving a
broad class of convex optimization problems. It has also found numerous
applications in machine learning. The proximal damped Newton (PDN) methods have
been well studied in the literature for solving this problem that enjoy a nice
iteration complexity. Given that at each iteration these methods typically
require evaluating or accessing the Hessian of $f$ and also need to solve a
proximal Newton subproblem, the cost per iteration can be prohibitively high
when applied to large-scale problems. Inspired by the recent success of block
coordinate descent methods, we propose a randomized block proximal damped
Newton (RBPDN) method for solving the CSC minimization. Compared to the PDN
methods, the computational cost per iteration of RBPDN is usually significantly
lower. The computational experiment on a class of regularized logistic
regression problems demonstrate that RBPDN is indeed promising in solving
large-scale CSC minimization problems. The convergence of RBPDN is also
analyzed in the paper. In particular, we show that RBPDN is globally convergent
when $g$ is Lipschitz continuous. It is also shown that RBPDN enjoys a local
linear convergence. Moreover, we show that for a class of $g$ including the
case where $g$ is Lipschitz differentiable, RBPDN enjoys a global linear
convergence. As a striking consequence, it shows that the classical damped
Newton methods [22,40] and the PDN [31] for such $g$ are globally linearly
convergent, which was previously unknown in the literature. Moreover, this
result can be used to sharpen the existing iteration complexity of these
methods.
|
1607.00101v1
|
2016-11-09
|
Witnessing quantum capacities of correlated channels
|
We test a general method to detect lower bounds of the quantum channel
capacity for two-qubit correlated channels. We consider in particular
correlated dephasing, depolarising and amplitude damping channels. We show that
the method is easily implementable, it does not require a priori knowledge
about the channels, and it is very efficient, since it does not rely on full
quantum process tomography.
|
1611.02857v1
|
2017-03-20
|
Recovery of the starting times of delayed signals
|
We present a new method to locate the starting points in time of an arbitrary
number of (damped) delayed signals. For a finite data sequence, the method
permits to first locate the starting point of the component with the longest
delay, and then --by iteration-- all the preceding ones. Numerical examples are
given and noise sensitivity is tested for weak noise.
|
1703.07001v1
|
2017-05-13
|
Eigenvalues of one-dimensional non-self-adjoint Dirac operators and applications
|
We analyze eigenvalues emerging from thresholds of the essential spectrum of
one-dimensional Dirac operators perturbed by complex and non-symmetric
potentials. In the general non-self-adjoint setting we establish the existence
and asymptotics of weakly coupled eigenvalues and Lieb-Thirring inequalities.
As physical applications we investigate the damped wave equation and armchair
graphene nanoribbons.
|
1705.04833v1
|
2017-09-07
|
The driven oscillator, with friction
|
This paper develops further the semi-classical theory of an harmonic
oscillator acted on by a Gaussian white noise force discussed in
(arXiv:1508.02379). Here I add to that theory the effects of Brownian damping
(friction). Albeit semi-classical, the theory can be used to model quantum
expectations and probabilities. I consider several examples.
|
1709.03391v1
|
2017-11-16
|
Correlations in the three-dimensional Lyman-alpha forest contaminated by high column density absorbers
|
Correlations measured in three dimensions in the Lyman-alpha forest are
contaminated by the presence of the damping wings of high column density (HCD)
absorbing systems of neutral hydrogen (HI; having column densities
$N(\mathrm{HI}) > 1.6\times10^{17}\,\mathrm{atoms}\,\mathrm{cm}^{-2}$), which
extend significantly beyond the redshift-space location of the absorber. We
measure this effect as a function of the column density of the HCD absorbers
and redshift by measuring 3D flux power spectra in cosmological hydrodynamical
simulations from the Illustris project. Survey pipelines exclude regions
containing the largest damping wings. We find that, even after this procedure,
there is a scale-dependent correction to the 3D Lyman-alpha forest flux power
spectrum from residual contamination. We model this residual using a simple
physical model of the HCD absorbers as linearly biased tracers of the matter
density distribution, convolved with their Voigt profiles and integrated over
the column density distribution function. We recommend the use of this model
over existing models used in data analysis, which approximate the damping wings
as top-hats and so miss shape information in the extended wings. The simple
'linear Voigt model' is statistically consistent with our simulation results
for a mock residual contamination up to small scales ($|k| <
1\,h\,\mathrm{Mpc}^{-1}$). It does not account for the effect of the highest
column density absorbers on the smallest scales (e.g., $|k| >
0.4\,h\,\mathrm{Mpc}^{-1}$ for small damped Lyman-alpha absorbers; HCD
absorbers with $N(\mathrm{HI}) \sim
10^{21}\,\mathrm{atoms}\,\mathrm{cm}^{-2}$). However, these systems are in any
case preferentially removed from survey data. Our model is appropriate for an
accurate analysis of the baryon acoustic oscillations feature. It is
additionally essential for reconstructing the full shape of the 3D flux power
spectrum.
|
1711.06275v2
|
2017-12-08
|
An algorithm to resolve γ-rays from charged cosmic rays with DAMPE
|
The DArk Matter Particle Explorer (DAMPE), also known as Wukong in China,
launched on December 17, 2015, is a new high energy cosmic ray and {\gamma}-ray
satellite-borne observatory in space. One of the main scientific goals of DAMPE
is to observe GeV-TeV high energy {\gamma}-rays with accurate energy, angular,
and time resolution, to indirectly search for dark matter particles and for the
study of high energy astrophysics. Due to the comparatively higher fluxes of
charged cosmic rays with respect to {\gamma}-rays, it is challenging to
identify {\gamma}-rays with sufficiently high efficiency minimizing the amount
of charged cosmic ray contamination. In this work we present a method to
identify {\gamma}-rays in DAMPE data based on Monte Carlo simulations, using
the powerful electromagnetic/hadronic shower discrimination provided by the
calorimeter and the veto detection of charged particles provided by the plastic
scintillation detector. Monte Carlo simulations show that after this selection
the number of electrons and protons that contaminate the selected {\gamma}-ray
events at $\sim10$ GeV amounts to less than 1% of the selected sample. Finally,
we use flight data to verify the effectiveness of the method by highlighting
known {\gamma}-ray sources in the sky and by reconstructing preliminary light
curves of the Geminga pulsar.
|
1712.02939v1
|
2017-12-27
|
A simple and natural interpretations of the DAMPE cosmic-ray electron/positron spectrum within two sigma deviations
|
The DArk Matter Particle Explorer (DAMPE) experiment has recently announced
the first results for the measurement of total electron plus positron fluxes
between 25 GeV and 4.6 TeV. A spectral break at about 0.9 TeV and a tentative
peak excess around 1.4 TeV have been found. However, it is very difficult to
reproduce both the peak signal and the smooth background including spectral
break simultaneously. We point out that the numbers of events in the two energy
ranges (bins) close to the 1.4 TeV excess have $1\sigma$ deficits. With the
basic physics principles such as simplicity and naturalness, we consider the
$-2\sigma$, $+2\sigma$, and $-1\sigma$ deviations due to statistical
fluctuations for the 1229.3~GeV bin, 1411.4~GeV bin, and 1620.5~GeV bin.
Interestingly, we show that all the DAMPE data can be explained consistently
via both the continuous distributed pulsar and dark matter interpretations,
which have $\chi^{2} \simeq 17.2 $ and $\chi^{2} \simeq 13.9$ (for all the 38
points in DAMPE electron/positron spectrum with 3 of them revised),
respectively. These results are different from the previous analyses by
neglecting the 1.4 TeV excess. At the same time, we do a similar global fitting
on the newly released CALET lepton data, which could also be interpreted by
such configurations. Moreover, we present a $U(1)_D$ dark matter model with
Breit-Wigner mechanism, which can provide the proper dark matter annihilation
cross section and escape the CMB constraint. Furthermore, we suggest a few ways
to test our proposal.
|
1712.09586v6
|
2018-03-21
|
Well-posedness and stabilization of the Benjamin-Bona-Mahony equation on star-shaped networks
|
We study the stabilization issue of the Benjamin-Bona-Mahony (BBM) equation
on a finite star-shaped network with a damping term acting on the central node.
In a first time, we prove the well-posedness of this system. Then thanks to the
frequency domain method, we get the asymptotic stabilization result.
|
1803.07914v1
|
2018-04-05
|
Finite time blow up for wave equations with strong damping in an exterior domain
|
We consider the initial boundary value problem in exterior domain for
semilinear wave equations with power-type nonlinearity |u| p. We will establish
blow-up results when p is less than or equal to Strauss' exponent which is the
same one for the whole space case R n .
|
1804.01689v1
|
2018-04-13
|
Well-posedness and long time behavior of singular Langevin stochastic differential equations
|
In this paper, we study damped Langevin stochastic differential equations
with singular velocity fields. We prove the strong well-posedness of such
equations. Moreover, by combining the technique of Lyapunov functions with
Krylov's estimate, we also establish the exponential ergodicity for the unique
strong solution.
|
1804.05086v2
|
2018-04-27
|
Contribution of phase-mixing of Alfvén waves to coronal heating in multi-harmonic loop oscillations
|
Kink oscillations of a coronal loop are observed and studied in detail
because they provide a unique probe into the structure of coronal loops through
MHD seismology and a potential test of coronal heating through the phase-mixing
of Alfv\'en waves. In particular, recent observations show that standing
oscillations of loops often involve also higher harmonics, beside the
fundamental mode. The damping of these kink oscillations is explained by mode
coupling with Alfv\'en waves. We investigate the consequences for wave-based
coronal heating of higher harmonics and what coronal heating observational
signatures we may use to infer the presence of higher harmonic kink
oscillations. We perform a set of non-ideal MHD simulations where the damping
of the kink oscillation of a flux tube via mode coupling is modelled. Our MHD
simulation parameters are based on the seismological inversion of an
observation for which the first three harmonics are detected. We study the
phase-mixing of Alfv\'en waves that leads to the deposition of heat in the
system, and we apply the seismological inversion techniques to the MHD
simulation output. We find that the heating due to phase-mixing of the Alfv\'en
waves triggered by the damping of the kink oscillation is relatively small,
however we can illustrate i) how the heating location drifts due to the
subsequent damping of lower order harmonics. We also address the role of the
higher order harmonics and the width of the boundary shell in the energy
deposition. We conclude that the coronal heating due to phase-mixing seems not
to provide enough energy to maintain the thermal structure of the solar corona
even when multi-harmonics oscillations are included, and these oscillations
play an inhibiting role in the development of smaller scale structures.
|
1804.10562v1
|
2018-05-23
|
Effect of time varying transmission rates on coupled dynamics of epidemic and awareness over multiplex network
|
In the present work, a non-linear stochastic model is presented to study the
effect of time variation of transmission rates on the co-evolution of epidemics
and its corresponding awareness over a two layered multiplex network. In this
model, the infection transmission rate of a given node in the epidemic layer
depends upon its awareness probability in the awareness layer. Similarly, the
infection information transmission rate of a node in the awareness layer
depends upon its infection probability in the epidemic layer. The spread of
disease resulting from physical contacts is described in terms of SIS
(Susceptible Infected Susceptible) process over the epidemic layer and the
spread of information about the disease outbreak is described in terms of UAU
(Unaware Aware Unaware) process over the virtual interaction mediated awareness
layer. The time variation of the transmission rates and the resulting
co-evolution of these mutually competing processes is studied in terms of a
network topology depend parameter({\alpha}). Using a second order linear theory
it has been shown that in the continuous time limit, the co-evolution of these
processes can be described in terms of damped and driven harmonic oscillator
equations. From the results of the Monte-Carlo simulation, it is shown that for
the suitable choice of parameter({\alpha}), the two process can either exhibit
sustained oscillatory or damped dynamics. The damped dynamics corresponds to
the endemic state. Further, for the case of endemic state it is shown that the
inclusion of awareness layer significantly lowers the disease transmission rate
and reduces the size of epidemic. The endemic state infection probability of a
given node corresponding to the damped dynamics is found to have dependence
upon both the transmission rates as well as on both absolute intra-layer and
relative inter-layer degree of the individual nodes.
|
1805.08947v2
|
2018-06-09
|
Recovery Analysis of Damped Spectrally Sparse Signals and Its Relation to MUSIC
|
One of the classical approaches for estimating the frequencies and damping
factors in a spectrally sparse signal is the MUSIC algorithm, which exploits
the low-rank structure of an autocorrelation matrix. Low-rank matrices have
also received considerable attention recently in the context of optimization
algorithms with partial observations, and nuclear norm minimization (NNM) has
been widely used as a popular heuristic of rank minimization for low-rank
matrix recovery problems. On the other hand, it has been shown that NNM can be
viewed as a special case of atomic norm minimization (ANM), which has achieved
great success in solving line spectrum estimation problems. However, as far as
we know, the general ANM (not NNM) considered in many existing works can only
handle frequency estimation in undamped sinusoids. In this work, we aim to fill
this gap and deal with damped spectrally sparse signal recovery problems. In
particular, inspired by the dual analysis used in ANM, we offer a novel
optimization-based perspective on the classical MUSIC algorithm and propose an
algorithm for spectral estimation that involves searching for the peaks of the
dual polynomial corresponding to a certain NNM problem, and we show that this
algorithm is in fact equivalent to MUSIC itself. Building on this connection,
we also extend the classical MUSIC algorithm to the missing data case. We
provide exact recovery guarantees for our proposed algorithms and quantify how
the sample complexity depends on the true spectral parameters. In particular,
we provide a parameter-specific recovery bound for low-rank matrix recovery of
jointly sparse signals rather than use certain incoherence properties as in
existing literature. Simulation results also indicate that the proposed
algorithms significantly outperform some relevant existing methods (e.g., ANM)
in frequency estimation of damped exponentials.
|
1806.03511v5
|
2018-07-13
|
N-body simulations of structure formation in thermal inflation cosmologies
|
Thermal inflation models (which feature two inflationary stages) can display
damped primordial curvature power spectra on small scales which generate damped
matter fluctuations. For a reasonable choice of parameters, thermal inflation
models naturally predict a suppression of the matter power spectrum on galactic
and sub-galactic scales, mimicking the effect of warm or interacting dark
matter. Matter power spectra in these models are also characterised by an
excess of power (w.r.t. the standard $\Lambda$CDM power spectrum) just below
the suppression scale. By running a suite of N-body simulations we investigate
the non-linear growth of structure in models of thermal inflation. We measure
the non-linear matter power spectrum and extract halo statistics, such as the
halo mass function, and compare these quantities with those predicted in the
standard $\Lambda$CDM model and in other models with damped matter
fluctuations. We find that the thermal inflation models considered here produce
measurable differences in the matter power spectrum from $\Lambda$CDM at
redshifts $z>5$, while the halo mass functions are appreciably different at all
redshifts. The halo mass function at $z=0$ for thermal inflation displays an
enhancement of around $\sim 20\%$ w.r.t. $\Lambda$CDM and a damping at lower
halo masses, with the position of the enhancement depending on the value of the
free parameter in the model. The enhancement in the halo mass function (w.r.t.
$\Lambda$CDM ) increases with redshift, reaching $\sim 40\%$ at $z=5$. We also
study the accuracy of the analytical Press-Schechter approach, using different
filters to smooth the density field, to predict halo statistics for thermal
inflation. We find that the predictions with the smooth-$k$ filter agree with
the simulation results over a wider range of halo masses than is the case with
other filters commonly used in the literature.
|
1807.04980v2
|
2018-07-16
|
Global existence for semilinear damped wave equations in relation with the Strauss conjecture
|
We study the global existence of solutions to semilinear wave equations with
power-type nonlinearity and general lower order terms on $n$ dimensional
nontrapping asymptotically Euclidean manifolds, when $n=3, 4$. In addition, we
prove almost global existence with sharp lower bound of the lifespan for the
four dimensional critical problem.
|
1807.05908v1
|
2018-07-20
|
Effect of correlated noise channels on quantum speed limit
|
We study the effect of correlated Markovian noise channels on the quantum
speed limit of an open system. This is done for correlated dephasing and
amplitude damping channels for a two qubit atomic model. Our model serves as a
platform for a detailed study of speed of quantum evolution in correlated open
systems.
|
1807.07782v2
|
2018-08-20
|
Local existence of Strong solutions for a fluid-structure interaction model
|
We are interested in studying a system coupling the compressible
Navier-Stokes equations with an elastic structure located at the boundary of
the fluid domain. Initially the fluid domain is rectangular and the beam is
located on the upper side of the rectangle. The elastic structure is modeled by
an Euler-Bernoulli damped beam equation. We prove the local in time existence
of strong solutions for that coupled system.
|
1808.06716v1
|
2018-09-04
|
Creation of bipartite steering correlations by a fast damped auxiliary mode
|
We consider a three-mode system and show how steering correlations can be
created between two modes of the system using the fast dissipation of the third
mode. These correlations result in a directional form of entanglement, called
quantum or EPR steering. We illustrate this on examples of the interactions
among damped radiation modes in an optomechanical three-mode system. By
assuming that one of the modes undergoes fast dissipation, we show that the
coupling of that mode to one or two other modes of the system may result in
one- or two-way quantum steering. Explicit analytical results are given for the
steering parameters. We find that two modes coupled by the parametric-type
interaction and damped with the same rates can be entangled but cannot exhibit
quantum steering. When, in addition, one of the modes is coupled to a fast
damped mode, steering correlations are created and the modes then exhibit
one-way steering. The creation of the steering correlations is interpreted in
the context of the variances of the quadrature components of the modes that the
steering correlations result from an asymmetry in the variances of the
quadrature components of the modes induced by the auxiliary mode. It is found
that the fluctuations act directionally that quantum steering may occur only
when the variance of the steering mode is larger that the variance of the
steered mode. The scheme is shown to be quite robust against the thermal
excitation of the modes if the fluctuations of the steering mode are larger
than the fluctuations of the steered mode.
|
1809.01176v1
|
2018-10-06
|
Global Well-Posedness and Global Attractor for Two-dimensional Zakharov-Kuznetsov Equation
|
The initial value problem for two-dimensional Zakharov-Kuznetsov equation is
shown to be globally well-posed in $H^s({\mathbb{R}^2})$ for all
$\frac{5}{7}<s<1$ via using $I$-method in the context of atomic spaces. By
means of the increment of modified energy, the exsitence of global attractor
for weakly damped, forced Zakharov-Kuznetsov equation is also established in
$H^s({\mathbb{R}^2})$ for $\frac{10}{11}<s<1$.
|
1810.02984v1
|
2018-10-07
|
Uniform attractors for measure-driven quintic wave equation with periodic boundary conditions
|
We give a detailed study of attractors for measure driven quintic damped wave
equations with periodic boundary conditions. This includes uniform
energy-to-Strichartz estimates, the existence of uniform attractors in a weak
or strong topology in the energy phase space, the possibility to present them
as a union of all complete trajectories, further regularity, etc.
|
1810.03149v1
|
2018-10-13
|
Exponential Decay in a Timoshenko-type System of Thermoelasticity of Type III with Frictional versus Viscoelatic Damping and Delay
|
In this work, a Timoshenko system of type III of thermoelasticity with
frictional versus viscoelastic under Dirichlet-Dirichlet-Neumann boundary
conditions was considered. By exploiting energy method to produce a suitable
Lyapunov functional, we establish the global existence, exponential decay of
Type-III case.
|
1810.05820v1
|
2018-12-22
|
Damping of acoustic waves in straight ducts and turbulent flow conditions
|
In this paper the propagation of acoustic plane waves in turbulent, fully
developed flow is studied by means of an experimental investigation carried out
in a straight, smooth-walled duct.The presence of a coherent perturbation, such
as an acoustic wave in a turbulent confined flow, generates the oscillation of
the wall shear stress. In this circumstance a shear wave is excited and
superimposed on the sound wave. The turbulent shear stress is modulated by the
shear wave and the wall shear stress is strongly affected by the turbulence.
From the experimental point of view, it results in a measured damping strictly
connected to the ratio between the thickness of the acoustic sublayer, which is
frequency dependent, and the thickness of the viscous sublayer of the turbulent
mean flow, the last one being dependent on the Mach number. By reducing the
turbulence, the viscous sublayer thickness increases and the wave propagation
is mainly dominated by convective effects. In the present work, the damping and
wall impedance have been extracted from the measured complex wavenumber, which
represents the most important parameter used to characterize the wave
propagation. An experimental approach, referred to as iterative plane wave
decomposition, has been used in order to obtain the results. The investigations
have been carried out at low Mach number turbulent flows, low Helmholtz numbers
and low shear wavenumbers. The aim is to overcome a certain lack of
experimental results found by the authors of the most recent models for the
plane wave propagation in turbulent flows, such as Knutsson et al. (The effect
of turbulence damping on acoustic wave propagation in tubes, Journal of Sound
and Vibration, Vol. 329, No. 22, 2010), and Weng et al. (The attenuation of
sound by turbulence in internal flows, The Journal of the Acoustical Society of
America 133(6), 2013).
|
1812.11063v1
|
2019-01-30
|
Transverse waves in coronal flux tubes with thick boundaries: The effect of longitudinal flows
|
Observations show that transverse magnetohydrodynamic (MHD) waves and flows
are often simultaneously present in magnetic loops of the solar corona. The
waves are resonantly damped in the Alfv\'en continuum because of plasma and/or
magnetic field nonuniformity across the loop. The resonant damping is relevant
in the context of coronal heating, since it provides a mechanism to cascade
energy down to the dissipative scales. It has been theoretically shown that the
presence of flow affects the waves propagation and damping, but most of the
studies rely on the unjustified assumption that the transverse nonuniformity is
confined to a boundary layer much thinner than the radius of the loop. Here we
present a semi-analytic technique to explore the effect of flow on resonant MHD
waves in coronal flux tubes with thick nonuniform boundaries. We extend a
published method, which was originally developed for a static plasma, in order
to incorporate the effect of flow. We allowed the flow velocity to continuously
vary within the nonuniform boundary from the internal velocity to the external
velocity. The analytic part of the method is based on expressing the wave
perturbations in the thick nonuniform boundary of the loop as a Frobenius
series that contains a singular term accounting for the Alfv\'en resonance,
while the numerical part of the method consists of solving iteratively the
transcendental dispersion relation together with the equation for the Alfv\'en
resonance position. As an application of this method, we investigated the
impact of flow on the phase velocity and resonant damping length of MHD kink
waves. We consistently recover results in the thin boundary approximation
obtained in previous studies. We have extended those results to the case of
thick boundaries. We also explored the error associated with the use of the
thin boundary approximation beyond its regime of applicability.
|
1901.10785v1
|
2019-02-07
|
Violent relaxation in the Hamiltonian Mean Field model: I. Cold collapse and effective dissipation
|
In $N$-body systems with long-range interactions mean-field effects dominate
over binary interactions (collisions), so that relaxation to thermal
equilibrium occurs on time scales that grow with $N$, diverging in the
$N\to\infty$ limit. However, a faster and non-collisional relaxation process,
referred to as violent relaxation, sets in when starting from generic initial
conditions: collective oscillations (referred to as virial oscillations)
develop and damp out on timescales not depending on the system's size. After
the damping of such oscillations the system is found in a quasi-stationary
state that survives virtually forever when the system is very large. During
violent relaxation the distribution function obeys the collisionless Boltzmann
(or Vlasov) equation, that, being invariant under time reversal, does not
"naturally" describe a relaxation process. Indeed, the dynamics is moved to
smaller and smaller scales in phase space as time goes on, so that observables
that do not depend on small-scale details appear as relaxed after a short time.
We propose an approximation scheme to describe collisionless relaxation, based
on the introduction of moments of the distribution function, and apply it to
the Hamiltonian Mean Field (HMF) model. To the leading order, virial
oscillations are equivalent to the motion of a particle in a one-dimensional
potential. Inserting higher-order contributions in an effective way, inspired
by the Caldeira-Leggett model of quantum dissipation, we derive a dissipative
equation describing the damping of the oscillations, including a
renormalization of the effective potential and yielding predictions for
collective properties of the system after the damping in very good agreement
with numerical simulations. Here we restrict ourselves to "cold" initial
conditions; generic initial conditions will be considered in a forthcoming
paper.
|
1902.02436v2
|
2019-05-16
|
Boundary control of partial differential equations using frequency domain optimization techniques
|
We present a frequency domain based $H_\infty$-control strategy to solve
boundary control problems for systems governed by parabolic or hyperbolic
partial differential equation, where controllers are constrained to be
physically implementable and of simple structure suited for practical
applications. The efficiency of our technique is demonstrated by controlling a
reaction-diffusion equation with input delay, and a wave equation with boundary
anti-damping.
|
1905.06786v1
|
2019-05-20
|
Sharp Bounds for Oscillatory Integral Operators with Homogeneous Polynomial Phases
|
We obtain sharp $L^p$ bounds for oscillatory integral operators with generic
homogeneous polynomial phases in several variables. The phases considered in
this paper satisfy the rank one condition which is an important notion
introduced by Greenleaf, Pramanik and Tang. Under certain additional
assumptions, we can establish sharp damping estimates with critical exponents
to prove endpoint $L^p$ estimates.
|
1905.07980v1
|
2019-06-06
|
Well-posedness and exponential decay estimates for a Korteweg-de Vries-Burgers equation with time-delay
|
We consider the KdV-Burgers equation and its linear version in presence of a
delay feedback. We prove well-posedness of the models and exponential decay
estimates under appropriate conditions on the damping coefficients. Our
arguments rely on a Lyapunov functional approach combined with a step by step
procedure and semigroup theory.
|
1906.02488v1
|
2019-06-19
|
Accurate Lindblad-Form Master Equation for Weakly Damped Quantum Systems Across All Regimes
|
Realistic models of quantum systems must include dissipative interactions
with an environment. For weakly-damped systems the Lindblad-form Markovian
master equation is invaluable for this task due to its tractability and
efficiency. This equation only applies, however, when the frequencies of any
subset of the system's transitions are either equal (degenerate), or their
differences are much greater than the transitions' linewidths (far-detuned).
Outside of these two regimes the only available efficient description has been
the Bloch-Redfield (B-R) master equation, the efficacy of which has long been
controversial due to its failure to guarantee the positivity of the density
matrix. The ability to efficiently simulate weakly-damped systems across all
regimes is becoming increasingly important, especially in the area of quantum
technologies. Here we solve this long-standing problem. We discover that a
condition on the slope of the spectral density is sufficient to derive a
Lindblad form master equation that is accurate for all regimes. We further show
that this condition is necessary for weakly-damped systems to be described by
the B-R equation or indeed any Markovian master equation. We thus obtain a
replacement for the B-R equation over its entire domain of applicability that
is no less accurate, simpler in structure, completely positive, allows
simulation by efficient quantum trajectory methods, and unifies the previous
Lindblad master equations. We also show via exact simulations that the new
master equation can describe systems in which slowly-varying transition
frequencies cross each other during the evolution. System identification tools,
developed in systems engineering, play an important role in our analysis. We
expect these tools to prove useful in other areas of physics involving complex
systems.
|
1906.08279v2
|
2019-07-10
|
Heuristic construction of codeword stabilized codes
|
The family of codeword stabilized codes encompasses the stabilizer codes as
well as many of the best known nonadditive codes. However, constructing optimal
$n$-qubit codeword stabilized codes is made difficult by two main factors. The
first of these is the exponential growth with $n$ of the number of graphs on
which a code can be based. The second is the NP-hardness of the maximum clique
search required to construct a code from a given graph. We address the second
of these issues through the use of a heuristic clique finding algorithm. This
approach has allowed us to find $((9,97\leq K\leq100,2))$ and $((11,387\leq
K\leq416,2))$ codes, which are larger than any previously known codes. To
address the exponential growth of the search space, we demonstrate that graphs
that give large codes typically yield clique graphs with a large number of
nodes. The number of such nodes can be determined relatively efficiently, and
we demonstrate that $n$-node graphs yielding large clique graphs can be found
using a genetic algorithm. This algorithm uses a novel spectral bisection based
crossover operation that we demonstrate to be superior to more standard
crossover operations. Using this genetic algorithm approach, we have found
$((13,18,4))$ and $((13,20,4))$ codes that are larger than any previously known
code. We also consider codes for the amplitude damping channel. We demonstrate
that for $n\leq9$, optimal codeword stabilized codes correcting a single
amplitude damping error can be found by considering standard form codes that
detect one of only three of the $3^{n}$ possible equivalent error sets. By
combining this error set selection with the genetic algorithm approach, we have
found $((11,68))$ and $((11,80))$ codes capable of correcting a single
amplitude damping error and $((11,4))$, $((12,4))$, $((13,8))$, and $((14,16))$
codes capable of correcting two amplitude damping
|
1907.04537v2
|
2019-07-10
|
Exponential stability for the nonlinear Schrödinger equation on a star-shaped network
|
In this paper, we prove the exponential stability of the solution of the
nonlinear dissipative Schr\"odinger equation on a star-shaped network and where
the damping is localized on one branch and at the infinity.
|
1907.04950v1
|
2019-07-22
|
Role of charge equilibration in multinucleon transfer in damped collisions of heavy ions
|
In this work, the charge equilibration process has been analyzed within the
Langevin-type dynamical approach. Its duration and energy dependence are
discussed. We have analyzed the isotopic distributions of final products
obtained in the isospin-asymmetric 58Ni,40Ca + 208Pb reactions. Comparison of
58Ni,64Ni + 208Pb systems have been done in order to analyze the final yields
of neutron-rich heavy nuclides.
|
1907.09352v1
|
2019-09-25
|
Neutrino decoherence in a fermion and scalar background
|
We consider the decoherence effects in the propagation of neutrinos in a
background composed of a scalar particle and a fermion due to the non-forward
neutrino scattering processes. Using a simple model for the coupling of the
form $\bar f_R\nu_L\phi$ we calculate the contribution to the imaginary part of
the neutrino self-energy arising from the non-forward neutrino scattering
processes in such backgrounds, from which the damping terms are determined. In
the case we are considering, in which the initial neutrino state is depleted
but does not actually disappear (the initial neutrino transitions into a
neutrino of a different flavor but does not decay into a $f\phi$ pair, for
example), we associate the damping terms with decoherence effects. For this
purpose we give a precise prescription to identify the decoherence terms, as
used in the context of the master or Linblad equation, in terms of the damping
terms we have obtained from the calculation of the imaginary part of the
neutrino self-energy from the non-forward neutrino scattering processes. The
results can be directly useful in the context of Dark Matter-neutrino
interaction models in which the scalar and/or fermion constitute the
dark-matter, and can also serve to guide the generalizations to other models
and/or situations in which the decoherence effects in the propagation of
neutrinos originate from the non-forward scattering processes may be important.
As a guide to estimating such decoherence effects, the contributions to the
absorptive part of the self-energy and the corresponding damping terms are
computed explicitly in the context of the model we consider, for several
limiting cases of the momentum distribution functions of the background
particles.
|
1909.11271v2
|
2019-11-21
|
Special Itô maps and an $L^2$ Hodge theory for one forms on path spaces
|
We prove a Kodaira-Hodge decomposition on differential 1-forms on the space
of non-smooth paths over a Riemannian manifold, allowing us to define the
corresponding first cohomology group. This uses the It\^o map of a Brownian
system and damped stochastic parallel translation.
|
1911.09618v1
|
2019-12-03
|
The global classical solution to compressible Euler system with velocity alignment
|
In this paper, the compressible Euler system with velocity alignment and
damping is considered, where the influence matrix of velocity alignment is not
positive definite. Sound speed is used to reformulate the system into symmetric
hyperbolic type. The global existence and uniqueness of smooth solution for
small initial data is provided.
|
1912.01374v1
|
2019-12-23
|
Signal Analysis using Born-Jordan-type Distribution
|
In this note we exhibit recent advances in signal analysis via time-frequency
distributions. New members of the Cohen class, generalizing the Wigner
distribution, reveal to be effective in damping artefacts of some signals. We
will survey their main properties and drawbacks and present open problems
related to such phenomena.
|
1912.11387v1
|
2020-01-15
|
Weak pseudo-bosons
|
We show how the notion of {\em pseudo-bosons}, originally introduced as
operators acting on some Hilbert space, can be extended to a distributional
settings. In doing so, we are able to construct a rather general framework to
deal with generalized eigenvectors of the multiplication and of the derivation
operators. Connections with the quantum damped harmonic oscillator are also
briefly considered.
|
2001.05219v1
|
2020-02-18
|
Boundary feedback control of an anti-stable wave equation
|
We discuss boundary control of a wave equation with a non-linear anti-damping
boundary condition. We design structured finite-dimensional $H_\infty$-output
feedback controllers which stabilize the infinite dimensional system
exponentially in closed loop. The method is applied to control torsional
vibrations in drilling systems with the goal to avoid slip-stick.
|
2002.07567v1
|
2020-03-23
|
Critical exponent for the wave equation with a time-dependent scale invariant damping and a cubic convolution
|
In the present paper, we study the Cauchy problem for the wave equation with
a time-dependent scale invariant damping $\frac{2}{1+t}\partial_t v$ and a
cubic convolution $(|x|^{-\gamma}*v^2)v$ with $\gamma\in
\left(-\frac{1}{2},3\right)$ in three spatial dimension for initial data
$\left(v(x,0),\partial_tv(x,0)\right)\in C^2(\mathbb{R}^3)\times
C^1(\mathbb{R}^3)$ with a compact support, where $v=v(x,t)$ is an unknown
function to the problem on $\mathbb{R}^3\times[0,T)$. Here $T$ denotes a
maximal existence time of $v$.
The first aim of the present paper is to prove unique global existence of the
solution to the problem and asymptotic behavior of the solution in the
supercritical case $\gamma\in (0,3)$, and show a lower estimate of the lifespan
in the critical or subcritical case $\gamma\in \left(-\frac{1}{2},0\right]$.
The essential part for their proofs is to derive a weaker estimate under the
weaker condition than the case without damping and to recover the weakness by
the effect of the dissipative term.
The second aim of the present paper is to prove a small data blow-up and the
almost sharp upper estimate of the lifespan for positive data with a compact
support in the subcritical case $\gamma\in \left(-\frac{1}{2},0\right)$. The
essential part for the proof is to refine the argument for the proof of Theorem
6.1 in \cite{H20} to obtain the upper estimate of the lifespan.
Our two results determine that a critical exponent $\gamma_c$ which divides
global existence and blow-up for small solutions is $0$, namely $\gamma_c=0$.
As the result, we can see that the critical exponent shift from $2$ to $0$ due
to the effect of the scale invariant damping term.
|
2003.10329v2
|
2020-06-29
|
General decay and blow-up of solutions for a nonlinear wave equation with memory and fractional boundary damping terms
|
The paper studies the global existence and general decay of solutions using
Lyaponov functional for a nonlinear wave equation, taking into account the
fractional derivative boundary condition and memory term. In addition, we
establish the blow up of solutions with nonpositive initial energy.
|
2006.16325v1
|
2020-07-19
|
Entanglement-Coherence and Discord-Coherence analytical relations for X states
|
In this work we derive analytical relations between Entanglement and
Coherence as well as between Discord and Coherence, for Bell-diagonal states
and for X states, evolving under the action of several noise channels: Bit
Flip, Phase Damping and Depolarizing. We demonstrate that for these families,
Coherence is the fundamental correlation, that is: Coherence is necessary for
the presence of Entanglement and Discord.
|
2007.09792v1
|
2020-08-08
|
Linear Stability of the 2D Irrotational Circulation Flow around An Elliptical Cylinder
|
In this article we prove a linear inviscid damping result with optimal decay
rates of the 2D irrotational circulation flow around an elliptical cylinder. In
our result, all components of the asymptotic velocity field do not vanish and
the asymptotic flow lines are not ellipse any more.
|
2008.03451v1
|
2020-08-29
|
Exploring a quantum-information-relevant magnonic material: Ultralow damping at low temperature in the organic ferrimagnet V[TCNE]x
|
Quantum information science and engineering requires novel low-loss magnetic
materials for magnon-based quantum-coherent operations. The search for low-loss
magnetic materials, traditionally driven by applications in microwave
electronics near room-temperature, has gained additional constraints from the
need to operate at cryogenic temperatures for many applications in quantum
information science and technology. Whereas yttrium iron garnet (YIG) has been
the material of choice for decades, the emergence of molecule-based materials
with robust magnetism and ultra-low damping has opened new avenues for
exploration. Specifically, thin-films of vanadium tetracyanoethylene (V[TCNE]x)
can be patterned into the multiple, connected structures needed for hybrid
quantum elements and have shown room-temperature Gilbert damping ({\alpha} = 4
\times 10^-5) that rivals the intrinsic (bulk) damping otherwise seen only in
highly-polished YIG spheres (far more challenging to integrate into arrays).
Here, we present a comprehensive and systematic study of the low-temperature
magnetization dynamics for V[TCNE]x thin films, with implications for their
application in quantum systems. These studies reveal a temperature-driven,
strain-dependent magnetic anisotropy that compensates the thin-film shape
anisotropy, and the recovery of a magnetic resonance linewidth at 5 K that is
comparable to room-temperature values (roughly 2 G at 9.4 GHz). We can account
for these variations of the V[TCNE]x linewidth within the context of scattering
from very dilute paramagnetic impurities, and anticipate additional linewidth
narrowing as the temperature is further reduced.
|
2008.13061v3
|
2020-09-01
|
On the first $δ$ Sct--roAp hybrid pulsator and the stability of p and g modes in chemically peculiar A/F stars
|
Strong magnetic fields in chemically peculiar A-type (Ap) stars typically
suppress low-overtone pressure modes (p modes) but allow high-overtone p modes
to be driven. KIC 11296437 is the first star to show both. We obtained and
analysed a Subaru spectrum, from which we show that KIC 11296437 has abundances
similar to other magnetic Ap stars, and we estimate a mean magnetic field
modulus of $2.8\pm0.5$ kG. The same spectrum rules out a double-lined
spectroscopic binary, and we use other techniques to rule out binarity over a
wide parameter space, so the two pulsation types originate in one $\delta$
Sct--roAp hybrid pulsator. We construct stellar models depleted in helium and
demonstrate that helium settling is second to magnetic damping in suppressing
low-overtone p modes in Ap stars. We compute the magnetic damping effect for
selected p and g modes, and find that modes with frequencies similar to the
fundamental mode are driven for polar field strengths $\lesssim4$ kG, while
other low-overtone p modes are driven for polar field strengths up to $\sim$1.5
kG. We find that the high-order g modes commonly observed in $\gamma$ Dor stars
are heavily damped by polar fields stronger than 1--4 kG, with the damping
being stronger for higher radial orders. We therefore explain the observation
that no magnetic Ap stars have been observed as $\gamma$ Dor stars. We use our
helium-depleted models to calculate the $\delta$ Sct instability strip for
metallic-lined A (Am) stars, and find that driving from a Rosseland mean
opacity bump at $\sim$$5\times10^4$ K caused by the discontinuous H-ionization
edge in bound-free opacity explains the observation of $\delta$ Sct pulsations
in Am stars.
|
2009.00730v1
|
2020-09-24
|
The eccentricity distribution of giant planets and their relation to super-Earths in the pebble accretion scenario
|
Observations of the population of cold Jupiter planets ($r>$1 AU) show that
nearly all of these planets orbit their host star on eccentric orbits. For
planets up to a few Jupiter masses, eccentric orbits are thought to be the
outcome of planet-planet scattering events taking place after gas dispersal. We
simulate the growth of planets via pebble and gas accretion as well as the
migration of multiple planetary embryos in their gas disc. We then follow the
long-term dynamical evolution of our formed planetary system up to 100 Myr
after gas disc dispersal. We investigate the importance of the initial number
of protoplanetary embryos and different damping rates of eccentricity and
inclination during the gas phase for the final configuration of our planetary
systems. We constrain our model by comparing the final dynamical structure of
our simulated planetary systems to that of observed exoplanet systems. Our
results show that the initial number of planetary embryos has only a minor
impact on the final orbital eccentricity distribution of the giant planets, as
long as damping of eccentricity and inclination is efficient. If damping is
inefficient (slow), systems with a larger initial number of embryos harbor
larger average eccentricities. In addition, for slow damping rates, we observe
that scattering events already during the gas disc phase are common and that
the giant planets formed in these simulations match the observed giant planet
eccentricity distribution best. These simulations also show that massive giant
planets (above Jupiter mass) on eccentric orbits are less likely to host inner
super-Earths as these get lost during the scattering phase, while systems with
less massive giant planets on nearly circular orbits should harbor systems of
inner super-Earths. Finally, our simulations predict that giant planets are on
average not single, but live in multi-planet systems.
|
2009.11725v3
|
2020-10-12
|
Period Estimates for Autonomous Evolution Equations with Lipschitz Nonlinearities
|
We derive an estimate for the minimal period of autonomous strongly damped
hyperbolic problems. Our result corresponds to the works by Yorke, Busenberg et
al. for ordinary differential equations as well as Robinson and Vidal-Lopez for
parabolic problems. A general approach is developed for treating both
hyperbolic and parabolic problems. An example of application to a class of beam
equations is provided.
|
2010.05829v1
|
2020-12-16
|
Observation of anti-damping spin-orbit torques generated by in-plane and out-of-plane spin polarizations in MnPd3
|
High spin-orbit torques (SOTs) generated by topological materials and heavy
metals interfaced with a ferromagnetic layer show promise for next generation
magnetic memory and logic devices. SOTs generated from the in-plane spin
polarization along y-axis originated by the spin Hall and Edelstein effects can
switch magnetization collinear with the spin polarization in the absence of
external magnetic fields. However, an external magnetic field is required to
switch the magnetization along x and z-axes via SOT generated by y-spin
polarization. Here, we present that the above limitation can be circumvented by
unconventional SOT in magnetron-sputtered thin film MnPd3. In addition to the
conventional in-plane anti-damping-like torque due to the y-spin polarization,
out-of-plane and in-plane anti-damping-like torques originating from z-spin and
x-spin polarizations, respectively have been observed at room temperature. The
spin torque efficiency corresponding to the y-spin polarization from MnPd3 thin
films grown on thermally oxidized silicon substrate and post annealed at 400
Deg C is 0.34 - 0.44. Remarkably, we have demonstrated complete external
magnetic field-free switching of perpendicular Co layer via unconventional
out-of-plane anti-damping-like torque from z-spin polarization. Based on the
density functional theory calculations, we determine that the observed x- and
z- spin polarizations with the in-plane charge current are due to the low
symmetry of the (114) oriented MnPd3 thin films. Taken together, the new
material reported here provides a path to realize a practical spin channel in
ultrafast magnetic memory and logic devices.
|
2012.09315v1
|
2021-02-15
|
A transmission problem for waves under time-varying delay and nonlinear weight
|
This manuscript focus on in the transmission problem for one dimensional
waves with nonlinear weights on the frictional damping and time-varying delay.
We prove global existence of solutions using Kato's variable norm technique and
we show the exponential stability by the energy method with the construction of
a suitable Lyapunov functional.
|
2102.07829v1
|
2021-05-16
|
Linear stability analysis of the Couette flow for the two dimensional non-isentropic compressible Euler equations
|
This note is devoted to the linear stability of the Couette flow for the
non-isentropic compressible Euler equations in a domain $\mathbb{T}\times
\mathbb{R}$. Exploiting the several conservation laws originated from the
special structure of the linear system, we obtain a Lyapunov type instability
for the density, the temperature, the compressible part of the velocity field,
and also obtain an inviscid damping for the incompressible part of the velocity
field.
|
2105.07395v1
|
2021-05-21
|
Effects of ambipolar diffusion on waves in the solar chromosphere
|
The chromosphere is a partially ionized layer of the solar atmosphere, the
transition between the photosphere where the gas motion is determined by the
gas pressure and the corona dominated by the magnetic field. We study the
effect of partial ionization for 2D wave propagation in a gravitationally
stratified, magnetized atmosphere with properties similar to the solar
chromosphere. We adopt an oblique uniform magnetic field in the plane of
propagation with strength suitable for a quiet sun region. The theoretical
model used is a single fluid magnetohydrodynamic approximation, where
ion-neutral interaction is modeled by the ambipolar diffusion term. Magnetic
energy can be converted into internal energy through the dissipation of the
electric current produced by the drift between ions and neutrals. We use
numerical simulations where we continuously drive fast waves at the bottom of
the atmosphere. The collisional coupling between ions and neutrals decreases
with the decrease of the density and the ambipolar effect becomes important.
Fast waves excited at the base of the atmosphere reach the equipartition layer
and reflect or transmit as slow waves. While the waves propagate through the
atmosphere and the density drops, the waves steepen into shocks. The main
effect of ambipolar diffusion is damping of the waves. We find that for the
parameters chosen in this work, the ambipolar diffusion affects the fast wave
before it is reflected, with damping being more pronounced for waves which are
launched in a direction perpendicular to the magnetic field. Slow waves are
less affected by ambipolar effects. The damping increases for shorter periods
and larger magnetic field strengths. Small scales produced by the nonlinear
effects and the superposition of different types of waves created at the
equipartition height are efficiently damped by ambipolar diffusion.
|
2105.10285v1
|
2021-05-26
|
Global Attractor for the Periodic Generalized Korteweg-de Vries Equation Through Smoothing
|
We establish a smoothing result for the generalized KdV (gKdV) on the torus
with polynomial non-linearity, damping, and forcing that matches the smoothing
level for the gKdV at $H^1$. As a consequence, we establish the existence of a
global attractor for this equation as well as its compactness in
$H^s(\mathbb{T})$, $s\in (1,2).$
|
2105.13405v2
|
2021-06-01
|
On the Well-Posedness of Two Driven-Damped Gross Pitaevskii-Type Models for Exciton-Polariton Condensates
|
We study the well-posedness of two systems modeling the non-equilibrium
dynamics of pumped decaying Bose-Einstein condensates. In particular, we
present the local theory for rough initial data using the Fourier restricted
norm method introduced by Bourgain. We extend the result globally for initial
data in $L^2$.
|
2106.00438v1
|
2021-06-23
|
On generalized damped Klein-Gordon equation with nonlinear memory
|
In this paper we consider the Cauchy problem for linear dissipative
generalized Klein-Gordon equations with nonlinear memory in the right hand
side. Our goal is to study the effect of this nonlinearity on both the decay
estimates of global solutions as well as the admissible range of the exponent
p.
|
2106.12296v1
|
2021-08-29
|
A note on the energy transfer in coupled differential systems
|
We study the energy transfer in the linear system $$ \begin{cases} \ddot
u+u+\dot u=b\dot v\\ \ddot v+v-\epsilon \dot v=-b\dot u \end{cases} $$ made by
two coupled differential equations, the first one dissipative and the second
one antidissipative. We see how the competition between the damping and the
antidamping mechanisms affect the whole system, depending on the coupling
parameter $b$.
|
2108.12776v1
|
2021-08-29
|
Well-posedness and stability for semilinear wave-type equations with time delay
|
In this paper we analyze a semilinear abstract damped wave-type equation with
time delay. We assume that the delay feedback coefficient is variable in time
and belonging to $L^1_{loc}([0, +\infty)).$ Under suitable assumptions, we show
well-posedness and exponential stability for small initial data. Our strategy
combines careful energy estimates and continuity arguments. Some examples
illustrate the abstract results.
|
2108.12786v1
|
2021-08-30
|
Application of Rothe's method to a nonlinear wave equation on graphs
|
We study a nonlinear wave equation on finite connected weighted graphs. Using
Rothe's and energy methods, we prove the existence and uniqueness of solution
under certain assumption. For linear wave equation on graphs, Lin and Xie
\cite{Lin-Xie} obtained the existence and uniqueness of solution. The main
novelty of this paper is that the wave equation we considered has the nonlinear
damping term $|u_t|^{p-1}\cdot u_t$ ($p>1$).
|
2108.12980v1
|
2021-09-08
|
Stabilisation of Waves on Product Manifolds by Boundary Strips
|
We show that a transversely geometrically controlling boundary damping strip
is sufficient but not necessary for $t^{-1/2}$-decay of waves on product
manifolds. We give a general scheme to turn resolvent estimates for impedance
problems on cross-sections to wave decay on product manifolds.
|
2109.03928v1
|
2021-09-10
|
Smoothing effect and large time behavior of solutions to nonlinear elastic wave equations with viscoelastic term
|
The Cauchy problem for a nonlinear elastic wave equations with viscoelastic
damping terms is considered on the 3 dimensional whole space. Decay and
smoothing properties of the solutions are investigated when the initial data
are sufficiently small; and asymptotic profiles as $t \to \infty$ are also
derived.
|
2109.04628v3
|
2021-10-04
|
Overdamped limit at stationarity for non-equilibrium Langevin diffusions
|
In this note, we establish that the stationary distribution of a possibly
non-equilibrium Langevin diffusion converges, as the damping parameter goes to
infinity (or equivalently in the Smoluchowski-Kramers vanishing mass limit),
toward a tensor product of the stationary distribution of the corresponding
overdamped process and of a Gaussian distribution.
|
2110.01238v2
|
2021-10-22
|
p-Laplacian wave equations in non-cylindrical domains
|
This paper is devoted to studying the stability of p-Laplacian wave equations
with strong damping in non-cylindrical domains. The method of proof based on
some estimates for time-varying coefficients rising from moving boundary and a
modified Kormonik inequality. Meanwhile, by selecting appropriate auxiliary
functions, finally we obtain the polynomial stability (p > 2) and exponential
stability (p = 2) for such systems in some unbounded development domains.
|
2110.11547v1
|
2021-11-17
|
Transverse kink oscillations of inhomogeneous prominence threads: numerical analysis and H$α$ forward modelling
|
Prominence threads are very long and thin flux tubes which are partially
filled with cold plasma. Observations have shown that transverse oscillations
are frequent in these solar structures. The observations are usually
interpreted as the fundamental kink mode, while the detection of the first
harmonic remains elusive. Here, we aim to study how the density inhomogeneity
in the longitudinal and radial directions modify the periods and damping times
of kink oscillations, and how this effect would be reflected in observations.
We solve the ideal magnetohydrodynamics equations through two different
methods: a) performing 3D numerical simulations, and b) solving a 2D
generalised eigenvalue problem. We study the dependence of the periods, damping
times and amplitudes of transverse kink oscillations on the ratio between the
densities at the centre and at the ends of the tube, and on the average
density. We apply forward modelling on our 3D simulations to compute synthetic
H$\alpha$ profiles. We confirm that the ratio of the period of the fundamental
oscillation mode to the period of the first harmonic increases as the ratio of
the central density to the footpoint density is increased or as the averaged
density of the tube is decreased. We find that the damping times due to
resonant absorption decrease as the central to footpoint density ratio
increases. Contrary to the case of longitudinally homogeneous tubes, we find
that the damping time to period ratio also increases as the density ratio is
increased or the average density is reduced. We present snapshots and
time-distance diagrams of the emission in the H$\alpha$ line. The results
presented here have implications for the field of prominence seismology. While
the H$\alpha$ emission can be used to detect the fundamental mode, the first
harmonic is barely detectable in H$\alpha$. This may explain the lack of
detections of the first harmonic.
|
2111.09036v1
|
2021-11-26
|
A novel measurement of marginal Alfvén Eigenmode stability during high power auxiliary heating in JET
|
The interaction of Alfv\'{e}n Eigenmodes (AEs) and energetic particles is one
of many important factors determining the success of future tokamaks. In JET,
eight in-vessel antennas were installed to actively probe stable AEs with
frequencies ranging 25-250 kHz and toroidal mode numbers $\vert n \vert < 20$.
During the 2019-2020 deuterium campaign, almost 7500 resonances and their
frequencies $f_0$, net damping rates $\gamma < 0$, and toroidal mode numbers
were measured in almost 800 plasma discharges. From a statistical analysis of
this database, continuum and radiative damping are inferred to increase with
edge safety factor, edge magnetic shear, and when including non-ideal effects.
Both stable AE observations and their associated damping rates are found to
decrease with $\vert n \vert$. Active antenna excitation is also found to be
ineffective in H-mode as opposed to L-mode; this is likely due to the increased
edge density gradient's effect on accessibility and ELM-related noise's impact
on mode identification. A novel measurement is reported of a marginally stable,
edge-localized Ellipticity-induced AE probed by the antennas during high-power
auxiliary heating (ICRH and NBI) up to 25 MW. NOVA-K kinetic-MHD simulations
show good agreement with experimental measurements of $f_0$, $\gamma$, and $n$,
indicating the dominance of continuum and electron Landau damping in this case.
Similar experimental and computational studies are planned for the recent
hydrogen and ongoing tritium campaigns, in preparation for the upcoming DT
campaign.
|
2111.13569v1
|
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