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2019-03-14 | A new class of accelerated regularization methods, with application to bioluminescence tomography | In this paper we propose a new class of iterative regularization methods for
solving ill-posed linear operator equations. The prototype of these iterative
regularization methods is in the form of second order evolution equation with a
linear vanishing damping term, which can be viewed not only as an extension of
the asymptotical regularization, but also as a continuous analog of the
Nesterov's acceleration scheme. New iterative regularization methods are
derived from this continuous model in combination with damped symplectic
numerical schemes. The regularization property as well as convergence rates and
acceleration effects under the H\"older-type source conditions of both
continuous and discretized methods are proven.
The second part of this paper is concerned with the application of the newly
developed accelerated iterative regularization methods to the diffusion-based
bioluminescence tomography, which is modeled as an inverse source problem in
elliptic partial differential equations with both Dirichlet and Neumann
boundary data. A relaxed mathematical formulation is proposed so that the
discrepancy principle can be applied to the iterative scheme without the usage
of Sobolev embedding constants. Several numerical examples, as well as a
comparison with the state-of-the-art methods, are given to show the accuracy
and the acceleration effect of the new methods. | 1903.05972v2 |
2019-05-15 | Stop-and-Go Suppression in Two-Class Congested Traffic | This paper develops boundary feedback control laws in order to damp out
traffic oscillations in the congested regime of the linearized two-class
Aw-Rascle (AR) traffic model. The macroscopic second-order two-class AR traffic
model consists of four hyperbolic partial differential equations (PDEs)
describing the dynamics of densities and velocities on freeway. The concept of
area occupancy is used to express the traffic pressure and equilibrium speed
relationship yielding a coupling between the two classes of vehicles. Each
vehicle class is characterized by its own vehicle size and driver's behavior.
The considered equilibrium profiles of the model represent evenly distributed
traffic with constant densities and velocities of both classes along the
investigated track section. After linearizing the model equations around those
equilibrium profiles, it is observed that in the congested traffic one of the
four characteristic speeds is negative, whereas the remaining three are
positive. Backstepping control design is employed to stabilize the $4 \times 4$
heterodirectional hyperbolic PDEs. The control input actuates the traffic flow
at outlet of the investigated track section and is realized by a ramp metering.
A full-state feedback is designed to achieve finite time convergence of the
density and velocity perturbations to the equilibrium at zero. This result is
then combined with an anti-collocated observer design in order to construct an
output feedback control law that damps out stop-and-go waves in finite time by
measuring the velocities and densities of both vehicle classes at the inlet of
the investigated track section. The performance of the developed controllers is
verified by simulation. | 1905.06476v1 |
2019-11-20 | Extreme events in a network of heterogeneous Josephson junctions | We report rare and recurrent large spiking events in a heterogeneous network
of superconducting Josephson junctions (JJ) connected through a resistive load
and driven by a radio-frequency (rf) current in addition to a constant bias.
The intermittent large spiking events show characteristic features of extreme
events (EE) since they are larger than a statistically defined significant
height. Under the influence of repulsive interactions and an impact of
heterogeneity of damping parameters, the network splits into three sub-groups
of junctions, one in incoherent rotational, another in coherent librational
motion and a third sub-group originating EE. We are able to scan the whole
population of junctions with their distinctive individual dynamical features
either in EE mode or non-EE mode in parameter space. EE migrates spatially from
one to another sub-group of junctions depending upon the repulsive strength and
the damping parameter. For a weak repulsive coupling, all the junctions
originate frequent large spiking events, in rotational motion when the average
inter-spike-interval (ISI) is small, but it increases exponentially with
repulsive interaction; it largely deviates from its exponential growth at a
break point where EE triggers in a sub-group of junctions. The probability
density of inter-event-intervals (IEI) in the subgroup exhibits a Poisson
distribution. EE originates via bubbling instability of in-phase
synchronization. | 1911.10040v1 |
2019-12-05 | Atypical Behavior of Collective Modes in Two-Dimensional Fermi Liquids | Using the Landau kinetic equation to study the non-equilibrium behavior of
interacting Fermi systems is one of the crowning achievements of Landau's Fermi
liquid theory. While thorough study of transport modes has been done for
standard three-dimensional Fermi liquids, an equally in-depth analysis for two
dimensional Fermi liquids is lacking. In applying the Landau kinetic equation
(LKE) to a two-dimensional Fermi liquid, we obtain unconventional behavior of
the zero sound mode $c_0$. As a function of the usual dimensionless parameter
$s=\omega/qv_F$, we find two peculiar results: First, for $|s|>1$ we see the
propagation of an undamped mode for weakly interacting systems. This differs
from the three dimensional case where an undamped mode only propagates for
repulsive interactions and the mode experiences Landau damping for any
arbitrary attractive interaction. Second, we find that regardless of
interaction strength, a propagating mode is forbidden for $|s|<1$. This is
profoundly different from the three-dimensional case where a mode can
propagate, albeit damped. In addition, we present a revised Pomeranchuk
instability condition for a two-dimensional Fermi liquid as well as equations
of motion for the fluid that follow directly from the LKE. In two dimensions,
we find a constant minimum for all Landau parameters for $\ell\geq 1$ which
differs from the three dimensional case. Finally we discuss the effect of a
Coulomb interaction on the system resulting in the plasmon frequency $\omega_p$
exhibiting a crossover to the zero sound mode. | 1912.02699v2 |
2020-01-30 | Ability of Markovian Master Equations to Model Quantum Computers and Other Systems Under Broadband Control | Most future quantum devices, including quantum computers, require control
that is broadband, meaning that the rate of change of the time-dependent
Hamiltonian is as fast or faster than the dynamics it generates. In many areas
of quantum physics, including quantum technology, one must include dissipation
and decoherence induced by the environment. While Markovian master equations
provide the only really efficient way to model these effects, these master
equations are derived for constant Hamiltonians (or those with a discrete set
of well-defined frequencies). In 2006, Alicky, Lidar, and Zanardi [Phys. Rev. A
73, 052311 (2006)] provided detailed qualitative arguments that Markovian
master equations could not describe systems under broadband control. Despite
apparently broad acceptance of these arguments, such master equations are
routinely used to model precisely these systems. This odd state of affairs is
likely due to a lack of quantitative results. Here we perform exact simulations
of two- and three-level systems coupled to an oscillator bath to obtain
quantitative results. Although we confirm that in general Markovian master
equations cannot predict the effects of damping under broadband control, we
find that there is a widely applicable regime in which they can. Master
equations are accurate for weak damping if both the Rabi frequencies and
bandwidth of the control are significantly smaller than the system's transition
frequencies. They also remain accurate if the bandwidth of control is as large
as the frequency of the driven transition so long as this bandwidth does not
overlap other transitions. Master equations are thus able to provide accurate
descriptions of many quantum information processing protocols for atomic
systems. | 2001.11160v1 |
2020-02-06 | Effects of transition-metal spacers on the spin-orbit torques, spin Hall magnetoresistance, and magnetic anisotropy of Pt/Co bilayers | We studied the effect of inserting 0.5 nm-thick spacer layers (Ti, V, Cr, Mo,
W) at the Pt/Co interface on the spin-orbit torques, Hall effect,
magnetoresistance, saturation magnetization, and magnetic anisotropy. We find
that the damping-like spin-orbit torque decreases substantially for all samples
with a spacer layer compared to the reference Pt/Co bilayer, consistently with
the opposite sign of the atomic spin-orbit coupling constant of the spacer
elements relative to Pt. The reduction of the damping-like torque is monotonic
with atomic number for the isoelectronic 3d, 4d, and 5d elements, with the
exception of V that has a stronger effect than Cr. The field-like spin-orbit
torque almost vanishes for all spacer layers irrespective of their composition,
suggesting that this torque predominantly originates at the Pt/Co interface.
The anomalous Hall effect, magnetoresistance, and saturation magnetization are
also all reduced substantially, whereas the sheet resistance is increased in
the presence of the spacer layer. Finally, we evidence a correlation between
the amplitude of the spin-orbit torques, the spin Hall-like magnetoresistance,
and the perpendicular magnetic anisotropy. These results highlight the
significant influence of ultrathin spacer layers on the magnetotransport
properties of heavy metal/ferromagnetic systems. | 2002.02162v1 |
2020-06-12 | Tidal Asteroseismology: Possible Evidence of Non-linear Mode Coupling in an Equilibrium State in Kepler Eclipsing Binary KIC 3230227 | Previously, a series of tidally-excited oscillations were discovered in the
eccentric eclipsing binary KIC 3230227. The pulsation amplitudes and phases
suggest the observed oscillations are prograde quadruple modes. In this paper,
we refine the analysis and extract more oscillation frequencies. We also study
the temporal variations of amplitudes and phases and show that almost all modes
have stable phases and amplitudes. We then focus on the non-orbital-harmonic
oscillations. We consider two formation mechanisms: 1) nonlinear response of
the surface convective layer, and 2) nonlinear three/multi-mode coupling.
Although the former can explain some of the observed features, we find the
latter mechanism is more probable. Assuming that these are coupled modes, the
constant amplitude/phase over four years can be explained by either an
equilibrium state in the mode coupling or modes undergoing limit cycles with
very long periods. The observed frequency detuning and the calculated damping
rates of the daughter modes favor the equilibrium-state interpretation. This is
verified by integrating the amplitude equations of three-mode coupling. We find
that the steady-state relation derived in Weinberg et al., which relates the
observed frequency detuning, phase detuning, and mode damping rates, is
approximately satisfied for one mode triplet. We also try to identify the
azimuthal number of the modes based on the observed mode amplitude ratios and
the selection rules in nonlinear three-mode coupling. We discuss further
implications of these observations on nonlinear tidal asteroseismology. | 2006.07417v1 |
2021-02-22 | Anisotropic cosmological models in Horndeski gravity | It was found recently that the anisotropies in the homogeneous Bianchi I
cosmology considered within the context of a specific Horndeski theory are
damped near the initial singularity instead of being amplified. In this work we
extend the analysis of this phenomenon to cover the whole of the Horndeski
family. We find that the phenomenon is absent in the K-essence and/or Kinetic
Gravity Braiding theories, where the anisotropies grow as one approaches the
singularity. The anisotropies are damped at early times only in more general
Horndeski models whose Lagrangian includes terms quadratic and cubic in second
derivatives of the scalar field. Such theories are often considered as being
inconsistent with the observations because they predict a non-constant speed of
gravitational waves. However, the predicted value of the speed at present can
be close to the speed of light with any required precision, hence the theories
actually agree with the present time observations. We consider two different
examples of such theories, both characterized by a late self-acceleration and
an early inflation driven by the non-minimal coupling. Their anisotropies show
a maximum at intermediate times and approach zero at early and late times. The
early inflationary stage exhibits an instability with respect to inhomogeneous
perturbations, suggesting that the initial state of the universe should be
inhomogeneous. However, more general Horndeski models may probably be stable. | 2102.10981v2 |
2021-03-18 | Size limit of superparamagnetic inclusions in dust grains and difficulty of magnetic grain alignment in protoplanetary disks | Alignment of non-spherical grains with magnetic fields is an important
problem as it lays the foundation of probing magnetic fields with polarized
dust thermal emissions. In this paper, we investigate the feasibility of
magnetic alignment in protoplanetary disks (PPDs). We use an alignment
condition that Larmor precession should be fast compared with the damping
timescale. We first show that the Larmor precession timescale is some three
orders of magnitude longer than the damping time for millimeter-sized grains
under conditions typical of PPDs, making the magnetic alignment unlikely. The
precession time can be shortened by superparamagnetic inclusions (SPIs), but
the reduction factor strongly depends on the size of the SPI clusters, which we
find is limited by the so-called "N\'{e}el's relaxation process." In
particular, the size limit of SPIs is set by the so-called "anisotropic energy
constant" of the SPI material, which describes the energy barrier needed to
change the direction of the magnetic moment of an SPI. For the most common
iron-bearing materials, we find maximum SPI sizes corresponding to a reduction
factor of the Larmor precession timescale of order $10^3$. We also find that
reaching this maximum reduction factor requires fine-tuning on the SPI sizes.
Lastly, we illustrate the effects of the SPI size limits on magnetic alignment
of dust grains with a simple disk model, and we conclude that it is unlikely
for relatively large grains of order 100 $\mu$m or more to be aligned with
magnetic fields even with SPIs. | 2103.10243v1 |
2021-06-23 | The dynamical exponent of a quantum critical itinerant ferromagnet: a Monte Carlo study | We consider the effect of the coupling between 2D quantum rotors near an XY
ferromagnetic quantum critical point and spins of itinerant fermions. We
analyze how this coupling affects the dynamics of rotors and the self-energy of
fermions.A common belief is that near a $q=0$ ferromagnetic transition,
fermions induce an $\Omega/q$ Landau damping of rotors (i.e., the dynamical
critical exponent is $z=3$) and Landau overdamped rotors give rise to non-Fermi
liquid fermionic self-energy $\Sigma\propto \omega^{2/3}$. This behavior has
been confirmed in previous quantum Monte Carlo (QMC) studies.Here we show that
for the XY case the behavior is different.We report the results of large scale
quantum Monte Carlo simulations,which show that at small frequencies $z=2$ and
$\Sigma\propto \omega^{1/2}$. We argue that the new behavior is associated with
the fact that a fermionic spin is by itself not a conserved quantity due to
spin-spin coupling to rotors, and a combination of self-energy and vertex
corrections replaces $1/q$ in the Landau damping by a constant. We discuss the
implication of these results to experiments. | 2106.12601v3 |
2021-08-20 | Cosmic-Ray Transport in Simulations of Star-forming Galactic Disks | Cosmic ray transport on galactic scales depends on the detailed properties of
the magnetized, multiphase interstellar medium (ISM). In this work, we
post-process a high-resolution TIGRESS magnetohydrodynamic simulation modeling
a local galactic disk patch with a two-moment fluid algorithm for cosmic ray
transport. We consider a variety of prescriptions for the cosmic rays, from a
simple purely diffusive formalism with constant scattering coefficient, to a
physically-motivated model in which the scattering coefficient is set by
critical balance between streaming-driven Alfv\'en wave excitation and damping
mediated by local gas properties. We separately focus on cosmic rays with
kinetic energies of $\sim 1$ GeV (high-energy) and $\sim 30$~MeV (low-energy),
respectively important for ISM dynamics and chemistry. We find that
simultaneously accounting for advection, streaming, and diffusion of cosmic
rays is crucial for properly modeling their transport. Advection dominates in
the high-velocity, low-density, hot phase, while diffusion and streaming are
more important in higher density, cooler phases. Our physically-motivated model
shows that there is no single diffusivity for cosmic-ray transport: the
scattering coefficient varies by four or more orders of magnitude, maximal at
density $n_\mathrm{H} \sim 0.01\, \mathrm{cm}^{-3}$. Ion-neutral damping of
Alfv\'en waves results in strong diffusion and nearly uniform cosmic ray
pressure within most of the mass of the ISM. However, cosmic rays are trapped
near the disk midplane by the higher scattering rate in the surrounding
lower-density, higher-ionization gas. The transport of high-energy cosmic rays
differs from that of low-energy cosmic rays, with less effective diffusion and
greater energy losses for the latter. | 2108.09356v1 |
2021-12-24 | Excitation of ion-acoustic waves by non-linear finite-amplitude standing Alfvén waves | We investigate, using a multi-fluid approach, the main properties of standing
ion-acoustic modes driven by nonlinear standing Alfv\'en waves. The standing
character of the Alfv\'enic pump is because we study the superposition of two
identical circularly polarised counter-propagating waves. We consider parallel
propagation along the constant magnetic field and we find that left and
right-handed modes generate via ponderomotive forces the second harmonic of
standing ion-acoustic waves. We demonstrate that parametric instabilities are
not relevant in the present problem and the secondary ion-acoustic waves
attenuate by Landau damping in the absence of any other dissipative process.
Kinetic effects are included in our model where ions are considered as
particles and electrons as a massless fluid, and hybrid simulations are used to
complement the theoretical results. Analytical expressions are obtained for the
time evolution of the different physical variables in the absence of Landau
damping. From the hybrid simulations we find that the attenuation of the
generated ion-acoustic waves follows the theoretical predictions even under the
presence of a driver Alfv\'enic pump. Due to the nonlinear induced ion-acoustic
waves the system develops density cavities and an electric field parallel to
the magnetic field. Theoretical expressions for this density and electric field
fluctuations are derived. The implications of these results in the context of
standing slow mode oscillations in coronal loops is discussed. | 2112.13048v1 |
2021-12-25 | Internal modes and radiation damping for quadratic Klein-Gordon in 3D | We consider Klein-Gordon equations with an external potential $V$ and a
quadratic nonlinearity in $3+1$ space dimensions. We assume that $V$ is regular
and decaying and that the (massive) Schr\"odinger operator $H=-\Delta+V+m^2$
has a positive eigenvalue $\lambda^2<m^2$ with associated eigenfunction $\phi.$
This is a so-called internal mode and gives rise to time-periodic and spatially
localized solutions of the linear flow. We address the classical question of
whether such solutions persist under the full nonlinear flow, and describe the
behavior of all solutions in a suitable neighborhood of zero. Provided a
natural Fermi-Golden rule holds, our main result shows that a solution to the
nonlinear Klein-Gordon equation can be decomposed into a discrete component
$a(t)\phi$ where $a(t)$ decays over time, and a continuous component $v$ which
has some weak dispersive properties. We obtain precise asymptotic information
on these components such as the sharp rates of decay $\vert a(t) \vert \approx
t^{-1/2}$ and ${\| v(t) \|}_{L^\infty_x} \approx t^{-1}$, (where the implicit
constants are independent of the small size of the data) as well as the growth
of a natural weighted norm of the profile of $v.$ In particular, our result
extends the seminal work of Soffer-Weinstein for the cubic Klein-Gordon, and
shows that radiation damping also occurs in the quadratic case. | 2112.13163v2 |
2022-01-17 | Sizing of Energy Storage System for Virtual Inertia Emulation | The infusion of renewable energy sources into the conventional synchronous
generation system decreases the overall system inertia and negatively impacts
the stability of its primary frequency response. The lowered inertia is due to
the absence of inertia in some of the renewable energy-based systems. To
maintain the stability of the system, we need to keep the frequency in the
permissible limits and maintain low rotational inertia. Some authors in the
literature have used the virtual synchronous generators (VSG) as a solution to
this problem. Although the VSG based distributed recourses (DER) exhibits the
characteristics and behavior of synchronous generators (SG) such as inertia,
frequency droop functions and damping but it does not optimally solve the
question of frequency stability. This paper presents a solution for these
problems via an empirical model that sizes the Battery Energy Storage System
(BESS) required for the inertia emulation and damping control. The tested
system consists of a Photovoltaic (PV) based VSG that is connected to a 9-Bus
grid and the simulation experiments are carried out using EMTP software. The
VSG transient response is initiated by a symmetric fault on the grid side. Our
simulations show the battery energy sizing required to emulate the virtual
inertia corresponding to several design parameters, i.e., the droop gain,
K{\omega}, the droop coefficient, Kd, and the VSG time constant Ta. | 2201.06566v2 |
2022-04-26 | Galactic seismology: joint evolution of impact-triggered stellar and gaseous disc corrugations | Evidence for wave-like corrugations are well established in the Milky Way and
in nearby disc galaxies. These were originally detected as a displacement of
the interstellar medium about the midplane, either in terms of vertical
distance or vertical velocity. Over the past decade, similar patterns have
emerged in the Milky Way's stellar disc. We investigate how these vertical
waves are triggered by a passing satellite. Using high-resolution
N-body/hydrodynamical simulations, we systematically study how the corrugations
set up and evolve jointly in the stellar and gaseous discs. We find that the
gas corrugations follow the stellar corrugations, i.e. they are initially in
phase although, after a few rotation periods (500-700 Myr), the distinct waves
separate and thereafter evolve in different ways. The spatial and kinematic
amplitudes (and thus the energy) of the corrugations dampen with time, with the
gaseous corrugation settling at a faster rate (~800 Myr versus ~1 Gyr). In
contrast, the vertical energy of individual disc stars is fairly constant
throughout the galaxy's evolution. This difference arises because corrugations
are an emergent phenomenon supported by the collective, ordered motions of
co-spatial ensembles of stars. We show that the damping of the stellar
corrugations can be understood as a consequence of incomplete phase mixing,
while the damping of the gaseous corrugations is a natural consequence of the
dissipative nature of the gas. We suggest that - in the absence of further,
strong perturbations - the degree of correlation between the stellar and
gaseous waves may help to age-date the phenomenon. | 2204.12096v2 |
2022-04-28 | Low-frequency resolvent analysis of the laminar oblique shock wave / boundary layer interaction | Resolvent analysis is used to study the low-frequency behaviour of the
laminar oblique shock wave / boundary layer interaction (SWBLI). It is shown
that the computed optimal gain, which can be seen as a transfer function of the
system, follows a first-order low-pass filter equation, recovering the results
of Touber and Sandham (JFM, 2011). This behaviour is understood as proceeding
from the excitation of a single stable, steady global mode whose damping rate
sets the time scale of the filter. Different Mach and Reynolds numbers are
studied, covering different recirculation lengths $L$. This damping rate is
found to scale as $1/L$, leading to a constant Strouhal number $St_L$ as
observed in the literature. It is associated with a breathing motion of the
recirculation bubble. This analysis furthermore supports the idea that the
low-frequency dynamics of the SWBLI is a forced dynamics, in which background
perturbations continuously excite the flow. The investigation is then carried
out for 3D perturbations for which two regimes are identified. At low wave
numbers of the order of $L$, a modal mechanism similar to that of 2D
perturbations is found and exhibits larger values of the optimal gain. At
larger wave numbers of the order of the boundary layer thickness, the growth of
streaks, which results from a non-modal mechanism, is detected. No interaction
with the recirculation region is observed. Based on these results, the
potential prevalence of 3D effects in the low-frequency dynamics of the SWBLI
is discussed. | 2204.13527v1 |
2022-09-02 | Identical damped harmonic oscillators described by coherent states | Some aspects of quantum damped harmonic oscillator (DHO) obeying a Markovian
master equation are considered in the absence of thermal noise. The continuity
equation is derived and Bohmian trajectories are constructed. As a solution of
the master equation, we take a single coherent state and compute analytically
the relative entropy of coherence, $C_r$, in the energy, position and momentum
bases. Although $C_r$ is constant in both the position and the momentum bases,
it is a decreasing function of time in the energy basis becoming zero at long
times, revealing its role as the preferred basis. Then, quantum coherence is
computed for a superposition of two coherent states, a cat state, and also a
superposition of two cat states in the energy basis as a function of
separation, in the complex plane, between the two superposed states. It is seen
that the quantum coherence increases with this separation. Furthermore, quantum
coherence of superposition is compared to that of decomposed states in the
superposition. Finally, considering a system of two non-interacting DHOs, the
effect of quantum statistics is studied on the coherence of reduced
single-particle states, the joint detection probability and the mean square
separation of particles. Our computations show that the single-particle
coherence for antisymmetric states is always less than that of symmetric ones.
Furthermore, boson anti-bunching and fermion bunching is seen in this open
system. This behavior of bosons is the matter-wave analogue of photon
anti-bunching seen in a modified Hanbury Brown-Twiss (HBT) interferometer. | 2209.00914v2 |
2022-11-27 | Dynamic surface tension of the pure liquid-vapor interface subjected to the cyclic loads | We demonstrate a methodology for computationally investigating the mechanical
response of a pure molten lead surface system to the lateral mechanical cyclic
loads and try to answer the question: how dose the dynamically driven liquid
surface system follow the classical physics of the elastic-driven oscillation?
The steady-state oscillation of the dynamic surface tension under cyclic load,
including the excitation of high frequency vibration mode at different driving
frequencies and amplitudes, was compared with the classical theory of
single-body driven damped oscillator. Under the highest studied frequency (50
GHz) and amplitude (5%) of the load, the increase of the (mean value) dynamic
surface tension could reach ~5%. The peak and trough values of the
instantaneous dynamic surface tension could reach (up to) 40% increase and (up
to) 20% decrease compared to the equilibrium surface tension, respectively. The
extracted generalized natural frequencies and the generalized damping constants
seem to be intimately related to the intrinsic timescales of the atomic
temporal-spatial correlation functions of the liquids both in the bulk region
and in the outermost surface layers. These insights uncovered could be helpful
for quantitative manipulation of the liquid surface tension using ultrafast
shockwaves or laser pulses. | 2211.14766v1 |
2023-11-07 | Strong electron-phonon coupling in Ba$_{1-x}$Sr$_x$Ni$_2$As$_2$ | The charge density wave (CDW) or nematicity has been found to coexist with
superconductivity in many systems. It is thus interesting that the
superconducting transition temperature $T_c$ in the doped BaNi$_2$As$_2$ system
can be enhanced up to six times as the CDW or nematicity in the undoped
compound is suppressed. Here we show that the transverse acoustic phonons of
Ba$_{1-x}$Sr$_x$Ni$_2$As$_2$ are strongly damped in a wide doping range and
over the whole $Q$ range, which excludes its origin from either CDW or
nematicity. The damping of TA phonons can be understood as large
electron-phonon coupling and possible strong hybridization between acoustic and
optical phonons as shown by the first-principle calculations. The
superconductivity can be quantitatively reproduced by the change of
electron-phonon coupling constant calculated by the McMillan equation in the
BCS framework, which suggests that no quantum fluctuations of any order is
needed to promote the superconductivity. On the contrary, the change of $T_c$
in this system should be understood as the six-fold suppression of
superconductivity in undoped compounds. | 2311.03649v2 |
2023-11-21 | Numerical modelling of bulk viscosity in neutron stars | The early post-merger phase of a binary neutron-star coalescence is shaped by
characteristic rotational velocities as well as violent density oscillations
and offers the possibility to constrain the properties of neutron star matter
by observing the gravitational wave emission. One possibility to do so is the
investigation of gravitational wave damping through the bulk viscosity which
originates from violations of weak chemical equilibrium. Motivated by these
prospects, we present a comprehensive report about the implementation of the
self-consistent and second-order formulation of the equations of relativistic
hydrodynamics for dissipative fluids proposed by M\"uller, Israel and Stewart.
Furthermore, we report on the results of two test problems, namely the viscous
damping of linear density oscillations of isolated nonrotating neutron stars
and the viscous migration test, both of which confirm our implementation and
can be used for future code tests. Finally, we present fully
general-relativistic simulations of viscous binary neutron-star mergers. We
explore the structural and thermal properties of binary neutron-star mergers
with a constant bulk viscosity prescription and investigate the impact of bulk
viscosity on dynamical mass ejection. We find that inverse Reynolds numbers of
order $\sim 1\%$ can be achieved for the highest employed viscosity thereby
suppressing the dynamically ejected mass by a factor of $\sim 5$ compared to
the inviscid case. | 2311.13027v1 |
2023-12-24 | Transient growth of wavelet-based resolvent modes in the buffer layer of wall-bounded turbulence | In this work, we study the transient growth of the principal resolvent modes
in the minimal flow unit using a reformulation of resolvent analysis in a
time-localized wavelet basis. We target the most energetic spatial wavenumbers
for the minimal flow unit and obtain modes that are constant in the streamwise
direction and once-periodic in the spanwise direction. The forcing modes are in
the shape of streamwise rolls, though pulse-like in time, and the response
modes are in the form of transiently growing streaks. We inject the principal
transient forcing mode at different intensities into a simulation of the
minimal flow unit and compare the resulting nonlinear response to the linear
one. The peak energy amplification scales quadratically with the intensity of
the injected mode, and this peak occurs roughly at the same time for all
forcing intensities. However, the larger energy amplification intensifies the
magnitude of the nonlinear terms, which play an important role in damping the
energy growth and accelerating energy decay of the principal resolvent mode. We
also observe that the damping effect of the nonlinearities is less prominent
close to the wall. Finally, we find that the principal resolvent forcing mode
is more effective than other structures at amplifying the streak energy in the
turbulent minimal-flow unit. In addition to lending support to the claim that
linear mechanisms are important to near-wall turbulence, this work identifies
time scales for the nonlinear breakdown of linearly-generated streaks. | 2312.15465v1 |
2024-02-27 | Fourier analysis of near-field patterns generated by propagating polaritons | Scattering-type scanning near-field optical microscope (s-SNOM) has become an
essential tool to study polaritons - quasiparticles of light coupled to
collective charge oscillations - via direct probing of their near field with a
spatial resolution far beyond the diffraction limit. However, extraction of the
polariton complex propagation constant from the near-field images requires
subtle considerations that have not received necessary attention so far. In
this study, we discuss important yet overlooked aspects of the near-field
analysis. First, we experimentally demonstrate that the sample orientation
inside the s-SNOM may significantly affect the near-field interference pattern
of mid-infrared polaritons, leading to an error in momentum measurement up to
7.7% even for the modes with effective index of 12.5. Second, we establish a
methodology to correctly extract the polariton damping rate from the
interference fringes depending on their origin - the s-SNOM nano-tip or the
material edge. Overall, our work provides a unified framework for the accurate
extraction of the polariton momentum and damping from the near-field
interference fringes. | 2402.17225v2 |
2011-03-31 | The ACS Nearby Galaxy Survey Treasury VII. The NGC 4214 Starburst and the Effects of Star Formation History on Dwarf Morphology | We present deep Hubble Space Telescope Wide Field Planetary Camera 2 (WFPC2)
optical observations obtained as part of the ACS Nearby Galaxy Survey Treasury
(ANGST) as well as early release Wide Field Camera 3 (WFC3) ultra-violet and
infrared observations of the nearby dwarf starbursting galaxy NGC 4214. Our
data provide a detailed example of how covering such a broad range in
wavelength provides a powerful tool for constraining the physical properties of
stellar populations. The deepest data reach the ancient red clump at M_F814W
-0.2. All of the optical data reach the main sequence turnoff for stars younger
than ~300 Myr, and the blue He burning sequence for stars younger than 500 Myr.
The full CMD-fitting analysis shows that all three fields in our data set are
consistent with ~75% of the stellar mass being older than 8 Gyr, in spite of
showing a wide range in star formation rates at the present day. Thus, our
results suggest that the scale length of NGC 4214 has remained relatively
constant for many Gyr. As previously noted by others, we also find the galaxy
has recently ramped up production, consistent with its bright UV luminosity and
its population of UV-bright massive stars. In the central field we find UV
point sources with F336W magnitudes as bright as -9.9. These are as bright as
stars with masses of at least 52-56 M_sun and ages near 4 Myr in stellar
evolution models. Assuming a standard IMF, our CMD is well-fitted by an
increase in star formation rate beginning 100 Myr ago. The stellar populations
of this late-type dwarf are compared with those of NGC 404, an early-type dwarf
that is also the most massive galaxy in its local environment. The late-type
dwarf appears to have a similar high fraction of ancient stars, suggesting that
these dominant galaxies may form at early epochs even if they have low total
mass and very different present-day morphologies. | 1104.0033v1 |
2012-01-23 | The Star Formation History of Leo T from Hubble Space Telescope Imaging | We present the star formation history (SFH) of the faintest known
star-forming galaxy, Leo T, based on imaging taken with the Hubble Space
Telescope (HST) Wide Field Planetary Camera 2 (WFPC2). The HST/WFPC2
color-magnitude diagram (CMD) of Leo T is exquisitely deep, extending ~ 2
magnitudes below the oldest main sequence turnoff, permitting excellent
constraints on star formation at all ages. We use a maximum likelihood CMD
fitting technique to measure the SFH of Leo T assuming three different sets of
stellar evolution models: Padova (solar-scaled metallicity) and BaSTI (both
solar-scaled and alpha-enhanced metallicities). The resulting SFHs are
remarkably consistent at all ages, indicating that our derived SFH is robust to
the choice of stellar evolution model. From the lifetime SFH of Leo T, we find
that 50% of the total stellar mass formed prior to z ~ 1 (7.6 Gyr ago).
Subsequent to this epoch, the SFH of Leo T is roughly constant until the most
recent ~ 25 Myr, where the SFH shows an abrupt drop. This decrease could be due
to a cessation of star formation or stellar initial mass function sampling
effects, but we are unable to distinguish between the two scenarios. Overall,
our measured SFH is consistent with previously derived SFHs of Leo T. However,
the HST-based solution provides improved age resolution and reduced
uncertainties at all epochs. The SFH, baryonic gas fraction, and location of
Leo T are unlike any of the other recently discovered faint dwarf galaxies in
the Local Group, and instead bear strong resemblance to gas-rich dwarf galaxies
(irregular or transition), suggesting that gas-rich dwarf galaxies may share
common modes of star formation over a large range of stellar mass (~ 10^5-10^9
Msun). | 1201.4859v1 |
2015-08-02 | Optimal Radio Frequency Energy Harvesting with Limited Energy Arrival Knowledge | In this paper, we develop optimal policies for deciding when a wireless node
with radio frequency (RF) energy harvesting (EH) capabilities should try and
harvest ambient RF energy. While the idea of RF-EH is appealing, it is not
always beneficial to attempt to harvest energy; in environments where the
ambient energy is low, nodes could consume more energy being awake with their
harvesting circuits turned on than what they can extract from the ambient radio
signals; it is then better to enter a sleep mode until the ambient RF energy
increases. Towards this end, we consider a scenario with intermittent energy
arrivals and a wireless node that wakes up for a period of time (herein called
the time-slot) and harvests energy. If enough energy is harvested during the
time-slot, then the harvesting is successful and excess energy is stored;
however, if there does not exist enough energy the harvesting is unsuccessful
and energy is lost.
We assume that the ambient energy level is constant during the time-slot, and
changes at slot boundaries. The energy level dynamics are described by a
two-state Gilbert-Elliott Markov chain model, where the state of the Markov
chain can only be observed during the harvesting action, and not when in sleep
mode. Two scenarios are studied under this model. In the first scenario, we
assume that we have knowledge of the transition probabilities of the Markov
chain and formulate the problem as a Partially Observable Markov Decision
Process (POMDP), where we find a threshold-based optimal policy. In the second
scenario, we assume that we don't have any knowledge about these parameters and
formulate the problem as a Bayesian adaptive POMDP; to reduce the complexity of
the computations we also propose a heuristic posterior sampling algorithm. The
performance of our approaches is demonstrated via numerical examples. | 1508.00285v1 |
2012-02-13 | Internal Stellar Kinematics of M32 from the SPLASH Survey: Dark Halo Constraints and the Formation of Compact Elliptical Galaxies | As part of the SPLASH survey of the Andromeda galaxy (M31) and its neighbors,
we have obtained Keck/DEIMOS spectra of the compact elliptical (cE) satellite
M32. This is the first resolved-star kinematical study of any cE galaxy. In
contrast to previous studies that extended out to r<30"~1Re~100pc, we measure
the rotation curve and velocity dispersion profile out to r~250" and higher
order Gauss-Hermite moments out to r~70". We achieve this by combining
integrated-light spectroscopy at small radii (where crowding/blending are
severe) with resolved stellar spectroscopy at larger radii, using spatial and
kinematical information to statistically account for M31 contamination. The
rotation curve and velocity dispersion profile extend well beyond the radius
(r~150") where the isophotes are distorted. Unlike NGC 205, another close dwarf
companion of M31, M32's kinematic are regular and symmetric and do not show
obvious sharp gradients across the region of isophotal elongation and twists.
We interpret M32's kinematics using three-integral axisymmetric dynamical
equilibrium models constructed using Schwarzschild's orbit superposition
technique. Models with a constant M/L can fit the data remarkably well.
However, since such a model requires an increasing tangential anisotropy with
radius, invoking the presence of an extended dark halo may be more plausible.
Such an extended dark halo is definitely required to bind a half-dozen
fast-moving stars observed at the largest radii, but these stars may not be an
equilibrium component of M32. The observed regularity of the stellar
kinematics, as well as the possible detection of an extended dark halo, are
unexpected if M31 tides are significant at large radii. While these findings by
themselves do not rule out tidal models for cE formation, they suggest that
tidal stripping may not be as significant for shaping cE galaxies as has often
been argued. | 1202.2897v3 |
2014-04-28 | The Star Formation Histories of Local Group Dwarf Galaxies I. Hubble Space Telescope / Wide Field Planetary Camera 2 Observations | We present uniformly measured star formation histories (SFHs) of 40 Local
Group dwarf galaxies based on color-magnitude diagram (CMD) analysis from
archival Hubble Space Telescope imaging. We demonstrate that accurate SFHs can
be recovered from CMDs that do not reach the oldest main sequence turn-off
(MSTO), but emphasize that the oldest MSTO is critical for precisely
constraining the earliest epochs of star formation. We find that: (1) the
average lifetime SFHs of dwarf spheroidals (dSphs) can be approximated by an
exponentially declining SFH with $\tau$ $\sim$ 5 Gyr; (2) lower luminosity
dSphs are less likely to have extended SFHs than more luminous dSphs; (3) the
average SFHs of dwarf irregulars (dIrrs), transition dwarfs (dTrans), and dwarf
ellipticals (dEs) can be approximated by the combination of an exponentially
declining SFH ($\tau$ $\sim$ 3-4 Gyr) for lookback ages $>$ 10-12 Gyr ago and a
constant SFH thereafter; (4) the observed fraction of stellar mass formed prior
to z=2 ranges considerably (80\% for galaxies with M $<$ 10$^5$ M$_{\odot}$ to
30\% for galaxies with M$>$10$^7$ M$_{\odot}$) and is largely explained by
environment; (5) the distinction between "ultra-faint" and "classical" dSphs is
arbitrary; (6) LG dIrrs formed a significantly higher fraction of stellar mass
prior to z=2 than the SDSS galaxies from Leiter 2012 and the SFHs from the
abundance matching models of Behroozi et al. 2013. This may indicate higher
than expected star-formation efficiencies at early times in low mass galaxies.
Finally, we provide all the SFHs in tabulated electronic format for use by the
community. | 1404.7144v1 |
2016-12-22 | Eroding dipoles and vorticity growth for Euler flows in $ \scriptstyle{\mathbb{R}}^3$: The hairpin geometry as a model for finite-time blowup | A theory of an eroding "hairpin" vortex dipole structure in three dimensions
is developed, extending our previous study of an axisymmetric eroding dipole
without swirl. The hairpin is here similarly proposed as a model to produce
large "self-stretching" of vorticity, with the possibility of finite-time
blow-up. We derive a system of partial differential equations of "generalized"
form, involving contour averaging of a locally two-dimensional Euler flow. We
do not attempt here to solve the system exactly, but point out that
non-existence of physically acceptable solutions would most probably be a
result of the axial flow. Because of the axial flow the vorticity distribution
within the dipole eddies is no longer of the simple Sadovskii type (vorticity
constant over a cross-section) obtained in the axisymmetric problem. Thus the
solution of the system depends upon the existence of a larger class of
propagating two-dimensional dipoles.
The hairpin model is obtained by formal asymptotic analysis. As in the
axisymmetric problem a local transformation to "shrinking" coordinates is
introduced, but now in a self-similar form appropriate to the study of a
possible finite-time singularity. We discuss some properties of the model,
including a study of the helicity and a first step in iterating toward a
solution from the Sadovskii structure. We also present examples of
two-dimensional propagating dipoles not previously studied, which have a
vorticity profile consistent with our model. Although no rigorous results can
be given, and analysis of the system is only partial, the formal calculations
are consistent with the possibility of a finite time blowup of vorticity at a
point of vanishing circulation of the dipole eddies, but depending upon the
existence of the necessary two-dimensional propagating dipole. | 1612.07709v2 |
2019-04-23 | Spin injection and pumping generated by a direct current flowing through a magnetic tunnel junction | A charge flow through a magnetic tunnel junction (MTJ) leads to the
generation of a spin-polarized current which exerts a spin-transfer torque
(STT) on the magnetization. When the density of applied direct current exceeds
some critical value, the STT excites high-frequency magnetization precession in
the "free" electrode of MTJ. Such precession gives rise to microwave output
voltage and, furthermore, can be employed for spin pumping into adjacent normal
metal or semiconductor. Here we describe theoretically the spin dynamics and
charge transport in the CoFeB/MgO/CoFeB/Au tunneling heterostructure connected
to a constant-current source. The magnetization dynamics in the free CoFeB
layer with weak perpendicular anisotropy is calculated by numerical integration
of the Landau-Lifshitz-Gilbert-Slonczewski equation accounting for both STT and
voltage controlled magnetic anisotropy associated with the CoFeB|MgO interface.
It is shown that a large-angle magnetization precession, resulting from
electrically induced dynamic spin reorientation transition, can be generated in
a certain range of relatively low current densities. An oscillating spin
current, which is pumped into the Au overlayer owing to such precession, is
then evaluated together with the injected spin current. Considering both the
driving spin-polarized charge current and the pumped spin current, we also
describe the charge transport in the CoFeB/Au bilayer with the account of
anomalous and inverse spin Hall effects. An electric potential difference
between the lateral sides of the CoFeB/Au bilayer is calculated as a function
of distance from the CoFeB|MgO interface. It is found that this transverse
voltage signal in Au is large enough for experimental detection, which
indicates significant efficiency of the proposed current-driven spin injector. | 1904.10361v1 |
2020-01-07 | X-ray Observations of the Peculiar Cepheid V473 Lyr Identify A Low-Mass Companion | V473 Lyr is a classical Cepheid which is unique in having substantial
amplitude variations with a period of approximately 3.3 years, thought to be
similar to the Blazhko variations in RR Lyrae stars. We obtained an {\it
XMM-Newton} observation of this star to followup a previous detection in
X-rays. Rather than the X-ray burst and rapid decline near maximum radius seen
in $\delta$ Cephei itself, the X-ray flux in V473 Lyr remained constant for a
third of the pulsation cycle covered by the observation. Thus the X-rays are
most probably not produced by the changes around the pulsation cycle. The X-ray
spectrum is soft (kT = 0.6 keV), with
X-ray properties which are consistent with a young low mass companion.
Previously there was no evidence of a companion in radial velocities or in {\it
Gaia} and {\it Hipparcos} proper motions. While this rules out companions which
are very close or very distant, a binary companion at a separation between 30
and 300 AU is possible. This is an example of an X-ray observation revealing
evidence of a low mass companion, which is important in completing the mass
ratio statistics of binary Cepheids. Furthermore, the detection of a young
X-ray bright companion is a further indication that the Cepheid (primary) is a
Population I star, even though its pulsation behavior differs from other
classical Cepheids. | 2001.02253v1 |
2020-10-07 | Fairness in Influence Maximization through Randomization | The influence maximization paradigm has been used by researchers in various
fields in order to study how information spreads in social networks. While
previously the attention was mostly on efficiency, more recently fairness
issues have been taken into account in this scope. In this paper, we propose to
use randomization as a mean for achieving fairness. Similar to previous works
like Fish et al. (WWW '19) and Tsang et al. (IJCAI '19), we study the maximin
criterion for (group) fairness. In contrast to their work however, we model the
problem in such a way that, when choosing the seed sets, probabilistic
strategies are possible rather than only deterministic ones. We introduce two
different variants of this probabilistic problem, one that entails
probabilistic strategies over nodes (node-based problem) and a second one that
entails probabilistic strategies over sets of nodes (set-based problem). While
the original deterministic problem involving the maximin criterion has been
shown to be inapproximable, interestingly, we show that both probabilistic
variants permit approximation algorithms that achieve a constant multiplicative
factor of 1-1/e plus an additive arbitrarily small error that is due to the
simulation of the information spread. For an experimental study, we provide
implementations of multiplicative-weight routines for both problems and compare
the achieved fairness values to existing methods. Maybe non-surprisingly, we
show that the ex-ante values of the computed probabilistic strategies are
significantly larger than the (ex-post) fairness values of previous methods.
This indicates that studying fairness via randomization is a worthwhile path to
follow. Interestingly and maybe more surprisingly, we observe that even the
ex-post fairness values computed by our routines, dominate over the fairness
achieved by previous methods on most of the instances tested. | 2010.03438v4 |
2020-10-29 | Group-Harmonic and Group-Closeness Maximization -- Approximation and Engineering | Centrality measures characterize important nodes in networks. Efficiently
computing such nodes has received a lot of attention. When considering the
generalization of computing central groups of nodes, challenging optimization
problems occur. In this work, we study two such problems, group-harmonic
maximization and group-closeness maximization both from a theoretical and from
an algorithm engineering perspective.
On the theoretical side, we obtain the following results. For group-harmonic
maximization, unless $P=NP$, there is no polynomial-time algorithm that
achieves an approximation factor better than $1-1/e$ (directed) and $1-1/(4e)$
(undirected), even for unweighted graphs. On the positive side, we show that a
greedy algorithm achieves an approximation factor of $\lambda(1-2/e)$
(directed) and $\lambda(1-1/e)/2$ (undirected), where $\lambda$ is the ratio of
minimal and maximal edge weights. For group-closeness maximization, the
undirected case is $NP$-hard to be approximated to within a factor better than
$1-1/(e+1)$ and a constant approximation factor is achieved by a local-search
algorithm. For the directed case, however, we show that, for any
$\epsilon<1/2$, the problem is $NP$-hard to be approximated within a factor of
$4|V|^{-\epsilon}$.
From the algorithm engineering perspective, we provide efficient
implementations of the above greedy and local search algorithms. In our
experimental study we show that, on small instances where an optimum solution
can be computed in reasonable time, the quality of both the greedy and the
local search algorithms come very close to the optimum. On larger instances,
our local search algorithms yield results with superior quality compared to
existing greedy and local search solutions, at the cost of additional running
time. We thus advocate local search for scenarios where solution quality is of
highest concern. | 2010.15435v1 |
2021-12-16 | A Complete Linear Programming Hierarchy for Linear Codes | A longstanding open problem in coding theory is to determine the best
(asymptotic) rate $R_2(\delta)$ of binary codes with minimum constant
(relative) distance $\delta$. An existential lower bound was given by Gilbert
and Varshamov in the 1950s. On the impossibility side, in the 1970s McEliece,
Rodemich, Rumsey and Welch (MRRW) proved an upper bound by analyzing Delsarte's
linear programs. To date these results remain the best known lower and upper
bounds on $R_2(\delta)$ with no improvement even for the important class of
linear codes. Asymptotically, these bounds differ by an exponential factor in
the blocklength.
In this work, we introduce a new hierarchy of linear programs (LPs) that
converges to the true size $A^{\text{Lin}}_2(n,d)$ of an optimum linear binary
code (in fact, over any finite field) of a given blocklength $n$ and distance
$d$.
This hierarchy has several notable features:
(i) It is a natural generalization of the Delsarte LPs used in the first MRRW
bound.
(ii) It is a hierarchy of linear programs rather than semi-definite programs
potentially making it more amenable to theoretical analysis.
(iii) It is complete in the sense that the optimum code size can be retrieved
from level $O(n^2)$.
(iv) It provides an answer in the form of a hierarchy (in larger dimensional
spaces) to the question of how to cut Delsarte's LP polytopes to approximate
the true size of linear codes.
We obtain our hierarchy by generalizing the Krawtchouk polynomials and
MacWilliams inequalities to a suitable "higher-order" version taking into
account interactions of $\ell$ words. Our method also generalizes to
translation schemes under mild assumptions. | 2112.09221v1 |
2022-03-30 | Shock Hugoniot of diamond from 3 to 80 TPa | The principal Hugoniot of carbon, initially diamond, was measured from 3 to
80 TPa (30 to 800 million atmospheres), the highest pressure ever achieved,
using radiography of spherically-converging shocks. The shocks were generated
by ablation of a plastic coating by soft x-rays in a laser-heated hohlraum at
the National Ignition Facility (NIF). Experiments were performed with low and
high drive powers, spanning different but overlapping pressure ranges. The
radius-time history of the shock, and the profile of mass density behind, were
determined by profile-matching from a time-resolved x-ray radiograph across the
diameter of the sphere. Above ~50 TPa, the heating induced by the shock was
great enough to ionize a significant fraction of K-shell electrons, reducing
the opacity to the 10.2 keV probe x-rays. The opacity and mass density were
deduced simultaneously using the constraint that the total mass of the sample
was constant. The Hugoniot and opacity were consistent with density functional
theory calculations of the electronic states and equation of state (EOS), and
varied significantly from theoretical Hugoniots based on Thomas-Fermi theory.
Theoretical models used to predict the compressibility of diamond ablator
experiments at the NIF, producing the highest neutron yields so far from
inertial confinement fusion experiments, are qualitatively consistent with our
EOS measurements but appear to overpredict the compressibility slightly. These
measurements help to evaluate theoretical techniques and constrain wide-range
EOS models applicable to white dwarf stars, which are the ultimate evolutionary
form of at least 97% of stars in the galaxy. | 2203.16065v1 |
2023-08-04 | Quench Risk Increase With Radiation Damage | Superconducting magnets are often proposed to confine plasma in fusion
reactors. Superconducting material enables the magnets to carry current
densities that would melt materials with non-zero resistance. Quench occurs
when superconductivity is lost and the current starts to generate heat. Unless
prevented with a fast enough control system, the heat generated during a quench
can cause catastrophic damage to the coils. This work describes a less-studied
heating mechanism that increases the likelihood and aggressiveness of fusion
magnet quenches. Defects accumulate in the magnet structural material under
irradiation by the fusion process. The defects store energy in the material and
change thermal and normal state electrical properties. Wigner energy is
released when defects anneal. After a 0.9 mDPA neutron irradiation, a 10 K
disturbance from 20 K is predicted to release enough energy to result in a
final temperature of 40 K. Irradiation damage also reduces the quench time
constant by increasing normal state resistivity and thus Ohmic heating. The
continuous operation of a fusion reactor produces an increasingly unstable
thermodynamic system in superconducting magnets by changing electrical and
thermal properties with irradiation damage. The temperature margin between
operation and quench runaway reduces with irradiation. The next steps are to
include these observations in quench models and validate the predictions
experimentally. Implications of this work is felt by all fusion powerplant
projects planning to leverage superconducting magnets. Designs will recognize
this risk with more stringent specifications on quench control systems and
maximum duration of coil operation at cryogenic temperature between periodic
releases of Wigner energy to avoid catastrophic quench failures. | 2308.03794v2 |
2024-02-15 | Partial synchrony for free? New bounds for Byzantine agreement via a generic transformation across network models | Byzantine consensus allows n processes to decide on a common value, in spite
of arbitrary failures. The seminal Dolev-Reischuk bound states that any
deterministic solution to Byzantine consensus exchanges Omega(n^2) bits. In
recent years, great advances have been made in deterministic Byzantine
agreement for partially synchronous networks, with state-of-the-art
cryptographic solutions achieving O(n^2 \kappa) bits (where $\kappa$ is the
security parameter) and nearly matching the lower bound. In contrast, for
synchronous networks, optimal solutions with O(n^2) bits, with no cryptography
and the same failure tolerance, have been known for more than three decades.
Can this gap in network models be closed?
In this paper, we present Repeater, the first generic transformation of
Byzantine agreement algorithms from synchrony to partial synchrony. Repeater is
modular, relying on existing and novel algorithms for its sub-modules. With the
right choice of modules, Repeater requires no additional cryptography, is
optimally resilient (n = 3t+1, where t is the maximum number of failures) and,
for constant-size inputs, preserves the worst-case per-process bit complexity
of the transformed synchronous algorithm. Leveraging Repeater, we present the
first partially synchronous algorithm that (1) achieves optimal bit complexity
(O(n^2) bits), (2) resists a computationally unbounded adversary (no
cryptography), and (3) is optimally-resilient (n = 3t+1), thus showing that the
Dolev-Reischuk bound is tight in partial synchrony. Moreover, we adapt Repeater
for long inputs, introducing several new algorithms with improved complexity
and weaker (or completely absent) cryptographic assumptions. | 2402.10059v3 |
2000-09-11 | Numerical Studies on Locally Damped Structures | In the JLC/NLC X-band linear collider, it is essential to reduce the
long-range dipole wakefields in the accelerator structure to prevent beam break
up (BBU) and emittance degradation. The two methods of reducing the long-range
wakefields are detuning and damping. Detuning reduces the wakefields rapidly as
the dipole modes de-cohere but, with a finite number of modes, the wakefield
will grow again as the modes re-cohere. In contrast, damping suppresses the
wakefields at a longer distance. There are two principal damping schemes:
synchronous damping using HOM manifolds such as that used in the RDDS1
structure and local damping similar to that used in the CLIC structure. In a
locally damped scheme, one can obtain almost any Q value, however, the damping
can have significant effects on the accelerating mode. In this paper, we
present a medium local-damping scheme where the wakefields are controlled to
meet the BBU requirement while minimizing the degradations of the fundamental
rf parameters. We will address the load design and pulse heating issues
associated with the medium damping scheme. | 0009039v1 |
2015-03-13 | A one-step optimal energy decay formula for indirectly nonlinearly damped hyperbolic systems coupled by velocities | In this paper, we consider the energy decay of a damped hyperbolic system of
wave-wave type which is coupled through the velocities. We are interested in
the asymptotic properties of the solutions of this system in the case of
indirect nonlinear damping, i.e. when only one equation is directly damped by a
nonlinear damping. We prove that the total energy of the whole system decays as
fast as the damped single equation. Moreover, we give a one-step general
explicit decay formula for arbitrary nonlinearity. Our results shows that the
damping properties are fully transferred from the damped equation to the
undamped one by the coupling in velocities, different from the case of
couplings through displacements as shown in \cite{AB01, ACK01, AB02, AL12} for
the linear damping case, and in \cite{AB07} for the nonlinear damping case. The
proofs of our results are based on multiplier techniques, weighted nonlinear
integral inequalities and the optimal-weight convexity method of \cite{AB05,
AB10}. | 1503.04126v1 |
2015-08-21 | Radiative damping in wave guide based FMR measured via analysis of perpendicular standing spin waves in sputtered Permalloy films | The damping $\alpha$ of the spinwave resonances in 75 nm, 120 nm, and 200nm
-thick Permalloy films is measured via vector-network-analyzer
ferromagnetic-resonance (VNA-FMR) in the out-of-plane geometry. Inductive
coupling between the sample and the waveguide leads to an additional radiative
damping term. The radiative contribution to the over-all damping is determined
by measuring perpendicular standing spin waves (PSSWs) in the Permalloy films,
and the results are compared to a simple analytical model. The damping of the
PSSWs can be fully explained by three contributions to the damping: The
intrinsic damping, the eddy-current damping, and the radiative damping. No
other contributions were observed. Furthermore, a method to determine the
radiative damping in FMR measurements with a single resonance is suggested. | 1508.05265v1 |
2022-09-28 | Tunable nonlinear damping in parametric regime | Nonlinear damping plays a significant role in several area of physics and it
is becoming increasingly important to understand its underlying mechanism.
However, microscopic origin of nonlinear damping is still a debatable topic.
Here, we probe and report nonlinear damping in a highly tunable MoS2 nano
mechanical drum resonator using electrical homodyne actuation and detection
technique. In our experiment, we achieve 2:1 internal resonance by tuning
resonance frequency and observe enhanced non-linear damping. We probe the
effect of non-linear damping by characterizing parametric gain. Geometry and
tunability of the device allow us to reduce the effect of other prominent
Duffing non-linearity to probe the non-linear damping effectively. The enhanced
non-linear damping in the vicinity of internal resonance is also observed in
direct drive, supporting possible origin of non-linear damping. Our experiment
demonstrates, a highly tunable 2D material based nanoresonator offers an
excellent platform to study the nonlinear physics and exploit nonlinear damping
in parametric regime. | 2209.14120v1 |
2005-11-07 | The Effects of Alfven Waves and Radiation Pressure in Dusty Winds of Late-Type Stars. II. Dust-Cyclotron Damping | There are in the literature several theories to explain the mass loss in
stellar winds. In particular, for late-type stars, some authors have proposed a
wind model driven by an outward-directed flux of damped Alfven waves. The winds
of these stars present great amounts of dust particles that, if charged, can
give rise to new wave modes or modify the pre-existing ones. In this work, we
study how the dust can affect the propagation of Alfven waves in these winds
taking into account a specific damping mechanism, dust-cyclotron damping. This
damping affects the Alfven wave propagation near the dust-cyclotron frequency.
Hence, if we assume a dust size distribution, the damping occurs over a broad
band of wave frequencies. In this work, we present a model of Alfven
wave-driven winds using the dust-cyclotron damping mechanism. On the basis of
coronal holes in the Sun, which present a superradial expansion, our model also
assumes a diverging geometry for the magnetic field. Thus, the mass, momentum,
and energy equations are obtained and then solved in a self-consistent
approach. Our results of wind velocity and temperature profiles for a typical
K5 supergiant star shows compatibility with observations. We also show that,
considering the presence of charged dust particles, the wave flux is less
damped due to the dust-cyclotron damping than it would be if we consider some
other damping mechanisms studied in the literature, such as nonlinear damping,
resonant surface damping, and turbulent damping. | 0511192v2 |
2013-09-11 | Initial versus tangent stiffness-based Rayleigh damping in inelastic time history seismic analyses | In the inelastic time history analyses of structures in seismic motion, part
of the seismic energy that is imparted to the structure is absorbed by the
inelastic structural model, and Rayleigh damping is commonly used in practice
as an additional energy dissipation source. It has been acknowledged that
Rayleigh damping models lack physical consistency and that, in turn, it must be
carefully used to avoid encountering unintended consequences as the appearance
of artificial damping. There are concerns raised by the mass proportional part
of Rayleigh damping, but they are not considered in this paper. As far as the
stiffness proportional part of Rayleigh damping is concerned, either the
initial structural stiffness or the updated tangent stiffness can be used. The
objective of this paper is to provide a comprehensive comparison of these two
types of Rayleigh damping models so that a practitioner (i) can objectively
choose the type of Rayleigh damping model that best fits her/his needs and (ii)
is provided with useful analytical tools to design Rayleigh damping model with
good control on the damping ratios throughout inelastic analysis. To that end,
a review of the literature dedicated to Rayleigh damping within these last two
decades is first presented; then, practical tools to control the modal damping
ratios throughout the time history analysis are developed; a simple example is
finally used to illustrate the differences resulting from the use of either
initial or tangent stiffness-based Rayleigh damping model. | 1309.2741v1 |
2017-07-14 | Damping of gravitational waves by matter | We develop a unified description, via the Boltzmann equation, of damping of
gravitational waves by matter, incorporating collisions. We identify two
physically distinct damping mechanisms -- collisional and Landau damping. We
first consider damping in flat spacetime, and then generalize the results to
allow for cosmological expansion. In the first regime, maximal collisional
damping of a gravitational wave, independent of the details of the collisions
in the matter is, as we show, significant only when its wavelength is
comparable to the size of the horizon. Thus damping by intergalactic or
interstellar matter for all but primordial gravitational radiation can be
neglected. Although collisions in matter lead to a shear viscosity, they also
act to erase anisotropic stresses, thus suppressing the damping of
gravitational waves. Damping of primordial gravitational waves remains
possible. We generalize Weinberg's calculation of gravitational wave damping,
now including collisions and particles of finite mass, and interpret the
collisionless limit in terms of Landau damping. While Landau damping of
gravitational waves cannot occur in flat spacetime, the expansion of the
universe allows such damping by spreading the frequency of a gravitational wave
of given wavevector. | 1707.05192v2 |
2001-08-28 | Galaxy number counts in the Hubble Deep Field as a strong constraint on a hierarchical galaxy formation model | Number counts of galaxies are re-analyzed using a semi-analytic model (SAM)
of galaxy formation based on the hierarchical clustering scenario. We have
determined the astrophysical parameters in the SAM that reproduce observations
of nearby galaxies, and used them to predict the number counts and redshifts of
faint galaxies for three cosmological models for (1) the standard cold dark
matter (CDM) universe, (2) a low-density flat universe with nonzero
cosmological constant, and (3) a low-density open universe with zero
cosmological constant. The novelty of our SAM analysis is the inclusion of
selection effects arising from the cosmological dimming of surface brightness
of high-redshift galaxies, and also from the absorption of visible light by
internal dust and intergalactic \ion{H}{1} clouds. Contrary to previous SAM
analyses which do not take into account such selection effects, we find, from
comparison with observed counts and redshifts of faint galaxies in the Hubble
Deep Field (HDF), that the standard CDM universe is {\it not} preferred, and a
low-density universe either with or without cosmological constant is favorable,
as suggested by other recent studies. Moreover, we find that a simple
prescription for the time scale of star formation (SF), being proportional to
the dynamical time scale of the formation of the galactic disk, is unable to
reproduce the observed number- redshift relation for HDF galaxies, and that the
SF time scale should be nearly independent of redshift, as suggested by other
SAM analyses for the formation of quasars and the evolution of damped
Ly-$\alpha$ systems. | 0108433v1 |
2010-05-07 | Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order | We present a field-theoretic renormalization group analysis of Abanov and
Chubukov's model of the spin density wave transition in two dimensional metals.
We identify the independent field scale and coupling constant renormalizations
in a local field theory, and argue that the damping constant of spin density
wave fluctuations tracks the renormalization of the local couplings. The
divergences at two-loop order overdetermine the renormalization constants, and
are shown to be consistent with our renormalization scheme. We describe the
physical consequences of our renormalization group equations, including the
breakdown of Fermi liquid behavior near the "hot spots" on the Fermi surface.
In particular, we find that the dynamical critical exponent z receives
corrections to its mean-field value z = 2. At higher orders in the loop
expansion, we find infrared singularities similar to those found by S.-S. Lee
for the problem of a Fermi surface coupled to a gauge field. A treatment of
these singularities implies that an expansion in 1/N, (where N is the number of
fermion flavors) fails for the present problem. We also discuss the
renormalization of the pairing vertex, and find an enhancement which scales as
logarithm-squared of the energy scale. A similar enhancement is also found for
a modulated bond order which is locally an Ising-nematic order. | 1005.1288v2 |
2023-09-10 | Scalar fields around a loop quantum gravity black hole in de Sitter spacetime: Quasinormal modes, late-time tails and strong cosmic censorship | Loop quantum gravity, as one branch of quantum gravity, holds the potential
to explore the fundamental nature of black holes. Recently, according to the
quantum Oppenheimer-Snyder model in loop quantum cosmology, a novel loop
quantum corrected black hole in de Sitter spacetime has been discovered. Here,
we first investigate the corresponding quasinormal modes and late-time behavior
of massless neutral scalar field perturbations based on such a quantum-modified
black hole in de Sitter spacetime. The frequency and time domain analysis of
the lowest-lying quasinormal modes is derived by Prony method, Matrix method as
well as WKB approximation. The influences of loop quantum correction, the black
hole mass ratio, and the cosmological constant on the quasinormal frequencies
are studied in detail. The late-time behaviors of quantum-modified black holes
possess an exponential decay, which is mainly determined not only by the
multipole number but also by the cosmological constant. The impact of loop
quantum correction on the late-time tail is negligible, but it has a
significant impact on damping oscillation. To explore spacetime singularities,
we examine the validity of strong cosmic censorship for a near-extremal
quantum-modified black hole in de Sitter spacetime. As a result, it is found
that the strong cosmic censorship is destroyed as the black hole approaches the
near-extremal limit, but the violation becomes weaker as the cosmological
constant and the loop quantum correction increase. | 2309.04962v2 |
2024-03-13 | The q-ary Gilbert-Varshamov bound can be improved for all but finitely many positive integers q | For any positive integer $q\geq 2$ and any real number $\delta\in(0,1)$, let
$\alpha_q(n,\delta n)$ denote the maximum size of a subset of $\mathbb{Z}_q^n$
with minimum Hamming distance at least $\delta n$, where
$\mathbb{Z}_q=\{0,1,\dotsc,q-1\}$ and $n\in\mathbb{N}$. The asymptotic rate
function is defined by $ R_q(\delta) =
\limsup_{n\rightarrow\infty}\frac{1}{n}\log_q\alpha_q(n,\delta n).$ The famous
$q$-ary asymptotic Gilbert-Varshamov bound, obtained in the 1950s, states that
\[ R_q(\delta) \geq 1 -
\delta\log_q(q-1)-\delta\log_q\frac{1}{\delta}-(1-\delta)\log_q\frac{1}{1-\delta}
\stackrel{\mathrm{def}}{=}R_\mathrm{GV}(\delta,q) \] for all positive integers
$q\geq 2$ and $0<\delta<1-q^{-1}$. In the case that $q$ is an even power of a
prime with $q\geq 49$, the $q$-ary Gilbert-Varshamov bound was firstly improved
by using algebraic geometry codes in the works of Tsfasman, Vladut, and Zink
and of Ihara in the 1980s. These algebraic geometry codes have been modified to
improve the $q$-ary Gilbert-Varshamov bound $R_\mathrm{GV}(\delta,q)$ at a
specific tangent point $\delta=\delta_0\in (0,1)$ of the curve
$R_\mathrm{GV}(\delta,q)$ for each given integer $q\geq 46$. However, the
$q$-ary Gilbert-Varshamov bound $R_\mathrm{GV}(\delta,q)$ at $\delta=1/2$,
i.e., $R_\mathrm{GV}(1/2,q)$, remains the largest known lower bound of
$R_q(1/2)$ for infinitely many positive integers $q$ which is a generic prime
and which is a generic non-prime-power integer. In this paper, by using codes
from geometry of numbers introduced by Lenstra in the 1980s, we prove that the
$q$-ary Gilbert-Varshamov bound $R_\mathrm{GV}(\delta,q)$ with $\delta\in(0,1)$
can be improved for all but finitely many positive integers $q$. It is shown
that the growth defined by $\eta(\delta)=
\liminf_{q\rightarrow\infty}\frac{1}{\log q}\log[1-\delta-R_q(\delta)]^{-1}$
for every $\delta\in(0,1)$ has actually a nontrivial lower bound. | 2403.08727v2 |
2006-05-22 | The entanglement of damped noon-state and its performance in phase measurement | The state evolution of the initial optical \textit{noon} state is
investigated. The residue entanglement of the state is calculated after it is
damped by amplitude and phase damping. The relative entropy of entanglement of
the damped state is exactly obtained. The performance of direct application of
the damped \textit{noon} state is compared with that of firstly distilling the
docoherence damped state then applying it in measurement. | 0605184v1 |
2007-10-04 | Channel-Adapted Quantum Error Correction for the Amplitude Damping Channel | We consider error correction procedures designed specifically for the
amplitude damping channel. We analyze amplitude damping errors in the
stabilizer formalism. This analysis allows a generalization of the [4,1]
`approximate' amplitude damping code of quant-ph/9704002. We present this
generalization as a class of [2(M+1),M] codes and present quantum circuits for
encoding and recovery operations. We also present a [7,3] amplitude damping
code based on the classical Hamming code. All of these are stabilizer codes
whose encoding and recovery operations can be completely described with
Clifford group operations. Finally, we describe optimization options in which
recovery operations may be further adapted according to the damping probability
gamma. | 0710.1052v1 |
2011-11-30 | Local phase damping of single qubits sets an upper bound on the phase damping rate of entangled states | I derive an inequality in which the phase damping rates of single qubits set
an upper bound for the phase damping rate of entangled states of many qubits.
The derivation is based on two assumptions: first, that the phase damping can
be described by a dissipator in Lindblad form and, second, that the phase
damping preserves the population of qubit states in a given basis. | 1111.7152v2 |
2012-05-11 | Quantum dynamics of the damped harmonic oscillator | The quantum theory of the damped harmonic oscillator has been a subject of
continual investigation since the 1930s. The obstacle to quantization created
by the dissipation of energy is usually dealt with by including a discrete set
of additional harmonic oscillators as a reservoir. But a discrete reservoir
cannot directly yield dynamics such as Ohmic damping (proportional to velocity)
of the oscillator of interest. By using a continuum of oscillators as a
reservoir, we canonically quantize the harmonic oscillator with Ohmic damping
and also with general damping behaviour. The dynamics of a damped oscillator is
determined by an arbitrary effective susceptibility that obeys Kramers-Kronig
relations. This approach offers an alternative description of nano-mechanical
oscillators and opto-mechanical systems. | 1205.2545v1 |
2014-02-28 | Escape rate for the power-law distribution in low-to-intermediate damping | Escape rate in the low-to-intermediate damping connecting the low damping
with the intermediate damping is established for the power-law distribution on
the basis of flux over population theory. We extend the escape rate in the low
damping to the low-to-intermediate damping, and get an expression for the
power-law distribution. Then we apply the escape rate for the power-law
distribution to the experimental study of the excited-state isomerization, and
show a good agreement with the experimental value. The extra current and the
improvement of the absorbing boundary condition are discussed. | 1402.7194v2 |
2015-03-21 | On damping created by heterogeneous yielding in the numerical analysis of nonlinear reinforced concrete frame elements | In the dynamic analysis of structural engineering systems, it is common
practice to introduce damping models to reproduce experimentally observed
features. These models, for instance Rayleigh damping, account for the damping
sources in the system altogether and often lack physical basis. We report on an
alternative path for reproducing damping coming from material nonlinear
response through the consideration of the heterogeneous character of material
mechanical properties. The parameterization of that heterogeneity is performed
through a stochastic model. It is shown that such a variability creates the
patterns in the concrete cyclic response that are classically regarded as
source of damping. | 1503.07122v1 |
2016-01-20 | Introduction to Landau Damping | The mechanism of Landau damping is observed in various systems from plasma
oscillations to accelerators. Despite its widespread use, some confusion has
been created, partly because of the different mechanisms producing the damping
but also due to the mathematical subtleties treating the effects. In this
article the origin of Landau damping is demonstrated for the damping of plasma
oscillations. In the second part it is applied to the damping of coherent
oscillations in particle accelerators. The physical origin, the mathematical
treatment leading to the concept of stability diagrams and the applications are
discussed. | 1601.05227v1 |
2018-07-25 | Regularity and asymptotic behaviour for a damped plate-membrane transmission problem | We consider a transmission problem where a structurally damped plate equation
is coupled with a damped or undamped wave equation by transmission conditions.
We show that exponential stability holds in the damped-damped situation and
polynomial stability (but no exponential stability) holds in the
damped-undamped case. Additionally, we show that the solutions first defined by
the weak formulation, in fact have higher Sobolev space regularity. | 1807.09730v1 |
2021-08-04 | Nonlinear fluid damping of elastically mounted pitching wings in quiescent water | We experimentally study the nonlinear fluid damping of a rigid but
elastically mounted pitching wing in the absence of a freestream flow. The
dynamics of the elastic mount are simulated using a cyber-physical system. We
perturb the wing and measure the fluid damping coefficient from damped
oscillations over a large range of pitching frequencies, pitching amplitudes,
pivot locations and sweep angles. A universal fluid damping scaling is proposed
to incorporate all these parameters. Flow fields obtained using particle image
velocimetry are analyzed to explain the nonlinear behaviors of the fluid
damping. | 2108.02090v1 |
2019-06-18 | Phase dynamics of effective drag and lift in vortex-induced vibration at low mass-damping | In this work, we investigate the dynamics of vortex-induced vibration of an
elastically mounted cylinder with very low values of mass and damping. We use
two methods to investigate this canonical problem: first we calculate the
instantaneous phase between the cylinder motion and the fluid forcing; second
we decompose the total hydrodynamic force into drag and lift components that
act along and normal to, respectively, the instantaneous effective angle of
attack. We focus on the phase dynamics in the large-amplitude-response range,
consisting of the initial, upper and lower branches of response. The
instantaneous phase between the transverse force and displacement shows
repeated phase slips separating periods of constant, or continuous-drifting,
phase in the second half of the upper branch. The phase between the lift
component and displacement shows strong phase locking throughout the
large-amplitude range - the average phase varies linearly with the primary
frequency - however the modulation of this phase is largest in the second half
of the upper branch. These observations suggest that the
large-amplitude-response dynamics is driven by two distinct limit cycles - one
that is stable over a very small range of reduced velocity at the beginning of
the upper branch, and another that consists of the lower branch. The chaotic
oscillation between them - the majority of the upper branch - occurs when
neither limit cycle is stable. The transition between the upper and lower
branches is marked by intermittent switching with epochs of time where
different states exist at a constant reduced velocity. These different states
are clearly apparent in the phase between the lift and displacement,
illustrating the utility of the force decomposition employed. | 1906.07375v2 |
2002-11-03 | Damping of coupled phonon--plasmon modes | The effect of free carriers on dispersion and damping of coupled
phonon-plasmon modes is considered in the long-wave approximation. The electron
and phonon scattering rate as well as Landau damping are taken into account. | 0211040v1 |
2002-02-01 | On "the authentic damping mechanism" of the phonon damping model | Some general features of the phonon damping model are presented. It is
concluded that the fits performed within this model have no physical content. | 0202006v1 |
2010-12-20 | Global attractors for the one dimensional wave equation with displacement dependent damping | We study the long-time behavior of solutions of the one dimensional wave
equation with nonlinear damping coefficient. We prove that if the damping
coefficient function is strictly positive near the origin then this equation
possesses a global attractor. | 1012.4455v1 |
2018-01-28 | Observations of excitation and damping of transversal oscillation in coronal loops by AIA/SDO | The excitation and damping of transversal coronal loop oscillations and
quantitative relation between damping time, damping quality (damping time per
period), oscillation amplitude, dissipation mechanism and the wake phenomena
are investigated. The observed time series data with the \textit{Atmospheric
Imaging Assembly} (AIA) telescope on NASA's \textit{Solar Dynamics Observatory}
(SDO) satellite on 2015 March 2, consisting of 400 consecutive images with 12
seconds cadence in the 171 $ \rm{{\AA}}$ pass band is analyzed for evidence of
transversal oscillations along the coronal loops by Lomb-Scargle periodgram. In
this analysis signatures of transversal coronal loop oscillations that are
damped rapidly were found with dominant oscillation periods in the range of
$\rm{P=12.25-15.80}$ minutes. Also, damping times and damping qualities of
transversal coronal loop oscillations at dominant oscillation periods are
estimated in the range of $ \rm{\tau_d=11.76-21.46}$ minutes and $
\rm{\tau_d/P=0.86-1.49}$, respectively. The observational results of this
analysis show that damping qualities decrease slowly with increasing the
amplitude of oscillation, but periods of oscillations are not sensitive
function of amplitude of oscillations. The order of magnitude of the damping
qualities and damping times are in good agreement with previous findings and
the theoretical prediction for damping of kink mode oscillations by dissipation
mechanism. Furthermore, oscillation of loop segments attenuate with time
roughly as $t^{-\alpha}$ that magnitude values of $\alpha$ for 30 different
segments change from 0.51 to 0.75. | 1801.09217v1 |
1999-11-16 | Probing supernovae ejecta by Halpha damping wings | It is predicted that H$\alpha$ emission line at the early nebular epoch of
type II-P supernovae may display robust observational effects of damping wings.
This is illustrated by Monte-Carlo simulations. The strength of damping wing
effects may be used to constrain parameters of the line-emitting zone. An
anomalous redshift, width and red wing of H$\alpha$ revealed by SN 1997D on day
150 are explained in terms of damping wing effects. | 9911300v1 |
2009-01-23 | Rheological Interpretation of Rayleigh Damping | Damping is defined through various terms such as energy loss per cycle (for
cyclic tests), logarithmic decrement (for vibration tests), complex modulus,
rise-time or spectrum ratio (for wave propagation analysis), etc. For numerical
modeling purposes, another type of damping is frequently used : it is called
Rayleigh damping. It is a very convenient way of accounting for damping in
numerical models, although the physical or rheological meaning of this approach
is not clear. A rheological model is proposed to be related to classical
Rayleigh damping : it is a generalized Maxwell model with three parameters. For
moderate damping (<25%), this model perfectly coincide with Rayleigh damping
approach since internal friction has the same expression in both cases and
dispersive phenomena are negligible. This is illustrated by finite element
(Rayleigh damping) and analytical (generalized Maxwell model) results in a
simple one-dimensional case. | 0901.3717v1 |
2015-05-06 | Remarks on the asymptotic behavior of the solution of an abstract damped wave equation | We study an abstract damped wave equation. We prove that the solution of the
damped wave equation becomes closer to the solution of a heat type equation as
time tend to infinity. As an application of our approach, we also study the
asymptotic behavior of the damped wave equation in Euclidean space under the
geometric control condition. | 1505.01794v2 |
2017-01-18 | Two types of spurious damping forces potentially modeled in numerical seismic nonlinear response history analysis | The purpose of this paper is to provide practitioners with further insight
into spurious damping forces that can be generated in nonlinear seismic
response history analyses (RHA). The term 'spurious' is used to refer to
damping forces that are not present in an elastic system and appear as
nonlinearities develop: such damping forces are not necessarily intended and
appear as a result of modifications in the structural properties as it yields
or damages due to the seismic action. In this paper, two types of spurious
damping forces are characterized. Each type has often been treated separately
in the literature, but each has been qualified as 'spurious', somehow blurring
their differences. Consequently, in an effort to clarify the consequences of
choosing a particular viscous damping model for nonlinear RHA, this paper shows
that damping models that avoid spurious damping forces of one type do not
necessarily avoid damping forces of the other type. | 1701.05092v1 |
2017-02-02 | Exponential stability for a coupled system of damped-undamped plate equations | We consider the transmission problem for a coupled system of undamped and
structurally damped plate equations in two sufficiently smooth and bounded
subdomains. It is shown that, independently of the size of the damped part, the
damping is strong enough to produce uniform exponential decay of the energy of
the coupled system. | 1702.00637v1 |
2019-08-19 | Spectral determinant for the damped wave equation on an interval | We evaluate the spectral determinant for the damped wave equation on an
interval of length $T$ with Dirichlet boundary conditions, proving that it does
not depend on the damping. This is achieved by analysing the square of the
damped wave operator using the general result by Burghelea, Friedlander, and
Kappeler on the determinant for a differential operator with matrix
coefficients. | 1908.06862v1 |
2017-09-11 | Comparison of damping mechanisms for transverse waves in solar coronal loops | We present a method to assess the plausibility of alternative mechanisms to
explain the damping of magnetohydrodynamic (MHD) transverse waves in solar
coronal loops. The considered mechanisms are resonant absorption of kink waves
in the Alfv\'en continuum, phase-mixing of Alfv\'en waves, and wave leakage.
Our methods make use of Bayesian inference and model comparison techniques. We
first infer the values for the physical parameters that control the wave
damping, under the assumption of a particular mechanism, for typically observed
damping time-scales. Then, the computation of marginal likelihoods and Bayes
factors enable us to quantify the relative plausibility between the alternative
mechanisms. We find that, in general, the evidence is not large enough to
support a single particular damping mechanism as the most plausible one.
Resonant absorption and wave leakage offer the most probable explanations in
strong damping regimes, while phase mixing is the best candidate for
weak/moderate damping. When applied to a selection of 89 observed transverse
loop oscillations, with their corresponding measurements of damping times
scales and taking into account data uncertainties, we find that only in a few
cases positive evidence for a given damping mechanism is available. | 1709.03347v1 |
2019-03-25 | Distributed Inter-Area Oscillation Damping Control for Power Systems by Using Wind Generators and Load Aggregators | This paper investigates the potential of wind turbine generators (WTGs) and
load aggregators (LAs) to provide supplementary damping control services for
low frequency inter-area oscillations (LFOs) through the additional distributed
damping control units (DCUs) proposed in their controllers. In order to provide
a scalable methodology for the increasing number of WTGs and LAs, a novel
distributed control framework is proposed to coordinate damping controllers.
Firstly, a distributed algorithm is designed to reconstruct the system Jacobian
matrix for each damping bus (buses with damping controllers). Thus, the
critical LFO can be identified locally at each damping bus by applying
eigen-analysis to the obtained system Jacobian matrix. Then, if the damping
ratio of the critical LFO is less than a preset threshold, the control
parameters of DCUs will be tuned in a distributed and coordinated manner to
improve the damping ratio and minimize the total control cost at the same time.
The proposed control framework is tested in a modified IEEE 39-bus test system.
The simulation results with and without the proposed control framework are
compared to demonstrate the effectiveness of the proposed framework. | 1903.10135v1 |
2020-10-12 | Decays rates for Kelvin-Voigt damped wave equations II: the geometric control condition | We study in this article decay rates for Kelvin-Voigt damped wave equations
under a geometric control condition. We prove that when the damping coefficient
is sufficiently smooth ($C^1$ vanishing nicely) we show that exponential decay
follows from geometric control conditions (see~\cite{BuCh, Te12} for similar
results under stronger assumptions on the damping function). | 2010.05614v2 |
2020-12-05 | On Periodical Damping Ratio of a Controlled Dynamical System with Parametric Resonances | This report provides an interpretation on the periodically varying damping
ratio of a dynamical system with direct control of oscillation or vibration
damping. The principal parametric resonance of the system and a new type of
parametric resonance, named "zero-th order" parametric resonance, are
investigated by using the method of multiple scales to find approximate,
analytical solutions of the system, which provide an interpretation on such
damping variations. | 2012.02932v1 |
2021-06-09 | Grammage of cosmic rays in the proximity of supernova remnants embedded in a partially ionized medium | We investigate the damping of Alfv\'en waves generated by the cosmic ray
resonant streaming instability in the context of the cosmic ray escape and
propagation in the proximity of supernova remnants. We consider ion-neutral
damping, turbulent damping and non linear Landau damping in the warm ionized
and warm neutral phases of the interstellar medium. For the ion-neutral
damping, up-to-date damping coefficients are used. We investigate in particular
whether the self-confinement of cosmic rays nearby sources can appreciably
affect the grammage. We show that the ion-neutral damping and the turbulent
damping effectively limit the residence time of cosmic rays in the source
proximity, so that the grammage accumulated near sources is found to be
negligible. Contrary to previous results, this also happens in the most extreme
scenario where ion-neutral damping is less effective, namely in a medium with
only neutral helium and fully ionized hydrogen. Therefore, the standard
picture, in which CR secondaries are produced during the whole time spent by
cosmic rays throughout the Galactic disk, need not to be deeply revisited. | 2106.04948v1 |
2021-06-22 | Sharp decay rate for the damped wave equation with convex-shaped damping | We revisit the damped wave equation on two-dimensional torus where the damped
region does not satisfy the geometric control condition. We show that if the
damping vanishes as a H\"older function $|x|^{\beta}$, and in addition, the
boundary of the damped region is strictly convex, the wave is stable at rate
$t^{-1+\frac{2}{2\beta+7}}$, which is better than the known optimal decay rate
$t^{-1+\frac{1}{\beta+3}}$ for strip-shaped dampings of the same H\"older
regularity. Moreover, we show by example that the decay rate is optimal. This
illustrates the fact that the energy decay rate depends not only on the order
of vanishing of the damping, but also on the shape of the damped region. The
main ingredient of the proof is the averaging method (normal form reduction)
developed by Hitrick and Sj\"ostrand (\cite{Hi1}\cite{Sj}). | 2106.11782v3 |
2021-08-09 | Effect of stepwise adjustment of Damping factor upon PageRank | The effect of adjusting damping factor {\alpha}, from a small initial value
{\alpha}0 to the final desired {\alpha}f value, upon then iterations needed for
PageRank computation is observed. Adjustment of the damping factor is done in
one or more steps. Results show no improvement in performance over a fixed
damping factor based PageRank. | 2108.04150v1 |
2021-08-17 | Asymptotic behaviour of the wave equation with nonlocal weak damping, anti-damping and critical nonlinearity | In this paper we prove the existence of the global attractor for the wave
equation with nonlocal weak damping, nonlocal anti-damping and critical
nonlinearity. | 2108.07395v2 |
2023-02-23 | Buckling Metamaterials for Extreme Vibration Damping | Damping mechanical resonances is a formidable challenge in an increasing
number of applications. Many of the passive damping methods rely on using low
stiffness dissipative elements, complex mechanical structures or electrical
systems, while active vibration damping systems typically add an additional
layer of complexity. However, in many cases, the reduced stiffness or
additional complexity and mass render these vibration damping methods
unfeasible. Here, we introduce a method for passive vibration damping by
allowing buckling of the primary load path, which sets an upper limit for
vibration transmission: the transmitted acceleration saturates at a maximum
value, no matter what the input acceleration is. This nonlinear mechanism leads
to an extreme damping coefficient tan delta ~0.23 in our metal
metamaterial|orders of magnitude larger than the linear damping of traditional
lightweight structural materials. We demonstrate this principle experimentally
and numerically in free-standing rubber and metal mechanical metamaterials over
a range of accelerations, and show that bi-directional buckling can further
improve its performance. Buckling metamaterials pave the way towards extreme
vibration damping without mass or stiffness penalty, and as such could be
applicable in a multitude of high-tech applications, including aerospace
structures, vehicles and sensitive instruments. | 2302.11968v1 |
1997-11-20 | Symmetric matrices and quantum codes | This paper has been withdrawn since a Gilbert-Varshamov bound for general
quantum codes has already appeared in Ekert and Macchiavello, Prys. Rev. Lett.
77, p. 2585, and a Gilbert-Varshamov bound for stabilizer codes connected with
orthogonal geometry, or equivalently, with symmetric matrices as in this paper,
has been proved by Calredbank, Rains, Shor and Sloane, Phys. Rev. Lett. 78, p.
405. I would like to thank Robert Calderbank for pointing out these references
to me. | 9711026v2 |
1994-06-09 | Black Holes from Blue Spectra | Blue primordial power spectra with a spectral index $n>1$ can lead to a
significant production of primordial black holes in the very early Universe.
The evaporation of these objects leads to a number of observational
consequences and a model independent upper limit of $n \approx 1.4$. In some
cases this limit is strengthened to $n=1.3$. Such limits may be employed to
define the boundary to the region of parameter space consistent with
generalized inflationary predictions. [To appear in Proceedings of the CASE
WESTERN CMB WORKSHOP, April 22-24 1994. Figures available on request from
J.H.Gilbert@qmw.ac.uk] | 9406028v1 |
1995-06-14 | Inversions in astronomy and the SOLA method | This paper was presented at the Institute for Mathematics and its
Applications workshop "Inverse problems in wave propagation" and will appear in
the series IMA volumes (Springer). A brief overview of applications of
inversions within astronomy is presented and also an inventory of techniques
commonly in use. Most of this paper is focussed on the method of Subtractive
Optimally Localized Averages (SOLA) which is an adaptation of the Backus and
Gilbert method. This method was originally developed for use in helioseismology
where the Backus and Gilbert method is computationally too slow. Since then it
has also been applied to the problem of reverberation mapping of active
galactic nuclei and the differences between this inverse problem and the ones
of helioseismology are also discussed. | 9506084v1 |
1997-11-11 | No Need for MACHOS in the Halo | A simple interpretation of the more than dozen microlensing events seen in
the direction of the LMC is a halo population of MACHOs which accounts for
about half of the mass of the Galaxy. Such an interpretation is not without its
problems, and we show that current microlensing data can, with some advantage,
be explained by dark components of the disk and spheroid, whose total mass is
only about 10% of the mass of the Galaxy. | 9711110v1 |
2006-02-11 | Likelihood Functions for Galaxy Cluster Surveys | Galaxy cluster surveys offer great promise for measuring cosmological
parameters, but survey analysis methods have not been widely studied. Using
methods developed decades ago for galaxy clustering studies, it is shown that
nearly exact likelihood functions can be written down for galaxy cluster
surveys. The sparse sampling of the density field by galaxy clusters allows
simplifications that are not possible for galaxy surveys. An application to
counts in cells is explicitly tested using cluster catalogs from numerical
simulations and it is found that the calculated probability distributions are
very accurate at masses above several times 10^{14}h^{-1} solar masses at z=0
and lower masses at higher redshift. | 0602251v3 |
2000-03-25 | Thermokinetic approach of the generalized Landau-Lifshitz-Gilbert equation with spin polarized current | In order to describe the recently observed effect of current induced
magnetization reversal in magnetic nanostructures, the thermokinetic theory is
applied to a metallic ferromagnet in contact with a reservoir of spin polarized
conduction electrons. The spin flip relaxation of the conduction electrons is
described thermodynamically as a chemical reaction. The diffusion equation of
the chemical potential (or the giant magnetoresistance) and the usual
Landau-Lifshitz-Gilbert (LLG) equation are derived from the entropy variation.
The expression of the conservation laws of the magnetic moments, including spin
dependent scattering processes, leads then to the generalized LLG equation with
spin polarized current. The equation is applied to the measurements obtained on
single magnetic Ni nanowires. | 0003409v1 |
2004-05-26 | Nonequilibrium Extension of the Landau-Lifshitz-Gilbert Equation for Magnetic Systems | Using the invariant operator method for an effective Hamiltonian including
the radiation-spin interaction, we describe the quantum theory for
magnetization dynamics when the spin system evolves nonadiabatically and out of
equilibrium, $d \hat{\rho}/dt \neq 0$. It is shown that the vector parameter of
the invariant operator and the magnetization defined with respect to the
density operator, both satisfying the quantum Liouville equation, still obey
the Landau-Lifshitz-Gilbert equation. | 0405599v1 |
2006-10-16 | Properties of Codes with the Rank Metric | In this paper, we study properties of rank metric codes in general and
maximum rank distance (MRD) codes in particular. For codes with the rank
metric, we first establish Gilbert and sphere-packing bounds, and then obtain
the asymptotic forms of these two bounds and the Singleton bound. Based on the
asymptotic bounds, we observe that asymptotically Gilbert-Varsharmov bound is
exceeded by MRD codes and sphere-packing bound cannot be attained. We also
establish bounds on the rank covering radius of maximal codes, and show that
all MRD codes are maximal codes and all the MRD codes known so far achieve the
maximum rank covering radius. | 0610099v2 |
1994-08-26 | On the Dirichlet problem for harmonic maps with prescribed singularities | Let $\M$ be a classical Riemannian globally symmetric space of rank one and
non-compact type. We prove the existence and uniqueness of solutions to the
Dirichlet problem for harmonic maps into $\M$ with prescribed singularities
along a closed submanifold of the domain. This generalizes our previous work
where such maps into the hyperbolic plane were constructed. This problem, in
the case where $\M$ is the complex-hyperbolic plane, has applications to
equilibrium configurations of co-axially rotating charged black holes in
General Relativity. | 9408005v1 |
1997-08-15 | One-Loop Minimization Conditions in the Minimal Supersymmetric Standard Model | We study, in the Minimal Supersymmetric Standard Model, the electroweak
symmetry breaking conditions obtained from the one-loop effective potential.
Novel model-independent lower and upper bounds on $\tan \beta$, involving the
other free parameters of the model, are inferred and determined analytically.
We discuss briefly some of the related issues and give an outlook for further
applications. | 9708368v1 |
2004-05-31 | On a Penrose Inequality with Charge | We construct a time-symmetric asymptotically flat initial data set to the
Einstein-Maxwell Equations which satisfies the inequality: m - 1/2(R + Q^2/R) <
0, where m is the total mass, R=sqrt(A/4) is the area radius of the outermost
horizon and Q is the total charge. This yields a counter-example to a natural
extension of the Penrose Inequality to charged black holes. | 0405602v3 |
2004-07-26 | Automorphisms of free groups have asymptotically periodic dynamics | We show that every automorphism $\alpha$ of a free group $F_k$ of finite rank
$k$ has {\it asymptotically periodic} dynamics on $F_k$ and its boundary
$\partial F_k$: there exists a positive power $\alpha^q$ such that every
element of the compactum $F_k \cup \partial F_k$ converges to a fixed point
under iteration of $\alpha^q$. | 0407437v2 |
2004-12-30 | The Construction of a Partially Regular Solution to the Landau-Lifshitz-Gilbert Equation in $\mathbb{R}^2$ | We establish a framework to construct a global solution in the space of
finite energy to a general form of the Landau-Lifshitz-Gilbert equation in
$\mathbb{R}^2$. Our characterization yields a partially regular solution,
smooth away from a 2-dimensional locally finite Hausdorff measure set. This
construction relies on approximation by discretization, using the special
geometry to express an equivalent system whose highest order terms are linear
and the translation of the machinery of linear estimates on the fundamental
solution from the continuous setting into the discrete setting. This method is
quite general and accommodates more general geometries involving targets that
are compact smooth hypersurfaces. | 0412534v1 |
2002-01-13 | Inverse Cascade Regime in Shell Models of 2-Dimensional Turbulence | We consider shell models that display an inverse energy cascade similar to
2-dimensional turbulence (together with a direct cascade of an enstrophy-like
invariant). Previous attempts to construct such models ended negatively,
stating that shell models give rise to a "quasi-equilibrium" situation with
equipartition of the energy among the shells. We show analytically that the
quasi-equilibrium state predicts its own disappearance upon changing the model
parameters in favor of the establishment of an inverse cascade regime with K41
scaling. The latter regime is found where predicted, offering a useful model to
study inverse cascades. | 0201020v1 |
2002-04-23 | Algebraic decay in hierarchical graphs | We study the algebraic decay of the survival probability in open hierarchical
graphs. We present a model of a persistent random walk on a hierarchical graph
and study the spectral properties of the Frobenius-Perron operator. Using a
perturbative scheme, we derive the exponent of the classical algebraic decay in
terms of two parameters of the model. One parameter defines the geometrical
relation between the length scales on the graph, and the other relates to the
probabilities for the random walker to go from one level of the hierarchy to
another. The scattering resonances of the corresponding hierarchical quantum
graphs are also studied. The width distribution shows the scaling behavior
$P(\Gamma) \sim 1/\Gamma$. | 0204056v1 |
2004-03-11 | Statistics of active vs. passive advections in magnetohydrodynamic turbulence | Active turbulent advection is considered in the context of
magneto-hydrodynamics. In this case, an auxiliary passive field bears no
apparent connection to the active field. The scaling properties of the two
fields are different. In the framework of a shell model, we show that the
two-point structure function of the passive field has a unique zero mode,
characterizing the scaling of this field only. In other words, the existence of
statistical invariants for the decaying passive field carries no information on
the scaling properties of the active field. | 0403017v1 |
1997-11-20 | Quantum self-dual codes and symmetric matrices | This paper has been withdrawn since a Gilbert-Varshamov bound for general
quantum codes has already appeared in Ekert and Macchiavello, Prys. Rev. Lett.
77, p. 2585, and a Gilbert-Varshamov bound for stabilizer codes connected with
orthogonal geometry, or equivalently, with symmetric matrices as in this paper,
has been proved by Calredbank, Rains, Shor and Sloane, Phys. Rev. Lett. 78, p.
405. I would like to thank Robert Calderbank for pointing out these references
to me. | 9711047v2 |
2001-06-06 | Constraints on Eavesdropping on the BB84 Protocol | An undetected eavesdropping attack must produce count rate statistics that
are indistinguishable from those that would arise in the absence of such an
attack. In principle this constraint should force a reduction in the amount of
information available to the eavesdropper. In this paper we illustrate, by
considering a particular class of eavesdropping attacks, how the general
analysis of this problem may proceed. | 0106034v2 |
2007-09-14 | A complete proof of The Graceful Tree Conjecture using the concept of Edge Degree | We show the Graceful Tree Conjecture holds. | 0709.2201v9 |
2007-09-24 | An extension of a result concerning convex geometric graphs | We show a general result known as the Erdos_Sos Conjecture: if
$E(G)>{1/2}(k-1)n$ where $G$ has order $n$ then $G$ contains every tree of
order $k+1$ as a subgraph. | 0709.3590v5 |
2008-06-13 | Heat conduction and Fourier's law by consecutive local mixing and thermalization | We present a first-principles study of heat conduction in a class of models
which exhibit a new multi-step local thermalization mechanism which gives rise
to Fourier's law. Local thermalization in our models occurs as the result of
binary collisions among locally confined gas particles. We explore the
conditions under which relaxation to local equilibrium, which involves no
energy exchange, takes place on time scales shorter than that of the binary
collisions which induce local thermalization. The role of this mechanism in
multi-phase material systems such as aerogels is discussed. | 0806.2193v1 |
2009-08-05 | Persistence effects in deterministic diffusion | In systems which exhibit deterministic diffusion, the gross parameter
dependence of the diffusion coefficient can often be understood in terms of
random walk models. Provided the decay of correlations is fast enough, one can
ignore memory effects and approximate the diffusion coefficient according to
dimensional arguments. By successively including the effects of one and two
steps of memory on this approximation, we examine the effects of
``persistence'' on the diffusion coefficients of extended two-dimensional
billiard tables and show how to properly account for these effects, using walks
in which a particle undergoes jumps in different directions with probabilities
that depend on where they came from. | 0908.0600v1 |
2009-08-10 | Diffusion coefficients for multi-step persistent random walks on lattices | We calculate the diffusion coefficients of persistent random walks on
lattices, where the direction of a walker at a given step depends on the memory
of a certain number of previous steps. In particular, we describe a simple
method which enables us to obtain explicit expressions for the diffusion
coefficients of walks with two-step memory on different classes of one-, two-
and higher-dimensional lattices. | 0908.1271v1 |
2010-06-24 | Periodic solutions for the Landau-Lifshitz-Gilbert equation | Ferromagnetic materials tend to develop very complex magnetization patterns
whose time evolution is modeled by the so-called Landau-Lifshitz-Gilbert
equation (LLG). In this paper, we construct time-periodic solutions for LLG in
the regime of soft and small ferromagnetic particles which satisfy a certain
shape condition. Roughly speaking, it is assumed that the length of the
particle is greater than its hight and its width. The approach is based on a
perturbation argument and the spectral analysis of the corresponding linearized
problem as well as the theory of sectorial operators. | 1006.4765v1 |
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