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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