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2015-09-15 | Resonance vibration of impact oscillator with biharmonic excitation | We consider a damped impact oscillator subject to the action of a biharmonic
force. The conditions for the existence and stability of almost periodic
resonance solutions are investigated. | 1509.05381v1 |
2015-11-08 | On 2d incompressible Euler equations with partial damping | We consider various questions about the 2d incompressible Navier-Stokes and
Euler equations on a torus when dissipation is removed from or added to some of
the Fourier modes. | 1511.02530v1 |
2015-12-11 | The Ping Pong Pendulum | Many damped mechanical systems oscillate with increasing frequency as the
amplitude decreases. One popular example is Euler's Disk, where the point of
contact rotates with increasing rapidity as the energy is dissipated. We study
a simple mechanical pendulum that exhibits this behaviour. | 1512.03700v1 |
2016-01-26 | Fast convex optimization via inertial dynamics with Hessian driven damping | We first study the fast minimization properties of the trajectories of the
second-order evolution equation $$\ddot{x}(t) + \frac{\alpha}{t} \dot{x}(t) +
\beta \nabla^2 \Phi (x(t))\dot{x} (t) + \nabla \Phi (x(t)) = 0,$$ where
$\Phi:\mathcal H\to\mathbb R$ is a smooth convex function acting on a real
Hilbert space $\mathcal H$, and $\alpha$, $\beta$ are positive parameters. This
inertial system combines an isotropic viscous damping which vanishes
asymptotically, and a geometrical Hessian driven damping, which makes it
naturally related to Newton's and Levenberg-Marquardt methods. For $\alpha\geq
3$, $\beta >0$, along any trajectory, fast convergence of the values
$$\Phi(x(t))- \min_{\mathcal H}\Phi =\mathcal O\left(t^{-2}\right)$$ is
obtained, together with rapid convergence of the gradients $\nabla\Phi(x(t))$
to zero. For $\alpha>3$, just assuming that $\Phi$ has minimizers, we show that
any trajectory converges weakly to a minimizer of $\Phi$, and $
\Phi(x(t))-\min_{\mathcal H}\Phi = o(t^{-2})$. Strong convergence is
established in various practical situations. For the strongly convex case,
convergence can be arbitrarily fast depending on the choice of $\alpha$. More
precisely, we have $\Phi(x(t))- \min_{\mathcal H}\Phi = \mathcal
O(t^{-\frac{2}{3}\alpha})$. We extend the results to the case of a general
proper lower-semicontinuous convex function $\Phi : \mathcal H \rightarrow
\mathbb R \cup \{+\infty \}$. This is based on the fact that the inertial
dynamic with Hessian driven damping can be written as a first-order system in
time and space. By explicit-implicit time discretization, this opens a gate to
new $-$ possibly more rapid $-$ inertial algorithms, expanding the field of
FISTA methods for convex structured optimization problems. | 1601.07113v1 |
2016-03-28 | Stabilization of gravity water waves | This paper is devoted to the stabilization of the incompressible Euler
equation with free surface. We study the damping of two-dimensional gravity
waves by an absorbing beach where the water-wave energy is dissipated by using
the variations of the external pressure. | 1603.08541v1 |
2016-06-14 | Precession Relaxation of Viscoelastic Oblate Rotators | Perturbations of all sorts destabilise the rotation of a small body and leave
it in a non-principal spin state. In such a state, the body experiences
alternating stresses generated by the inertial forces. This yields nutation
relaxation, i.e., evolution of the spin towards the principal rotation about
the maximal-inertia axis. Knowledge of the timescales needed to damp the
nutation is crucial in studies of small bodies' dynamics. In the literature
hitherto, nutation relaxation has always been described with aid of an
empirical quality factor $\,Q\,$ introduced to parameterise the energy
dissipation rate.
Among the drawbacks of this approach was its inability to describe the
dependence of the relaxation rate upon the current nutation angle. This
inability stemmed from our lack of knowledge of the quality factor's dependence
on the forcing frequency. In this article, we derive our description of
nutation damping directly from the rheological law obeyed by the material. This
renders us the nutation damping rate as a function of the current nutation
angle, as well as of the shape and the rheological parameters of the body. In
contradistinction from the approach based on an empirical $\,Q\,$-factor, our
development gives a zero damping rate in the spherical-shape limit. Our method
is generic and applicable to any shape and to any linear rheological law.
However, to simplify the developments, here we consider a dynamically oblate
rotator with a Maxwell rheology. | 1606.04559v3 |
2016-09-07 | Quasi-stability and Exponential Attractors for A Non-Gradient System---Applications to Piston-Theoretic Plates with Internal Damping | We consider a nonlinear (Berger or Von Karman) clamped plate model with a
{\em piston-theoretic} right hand side---which include non-dissipative,
non-conservative lower order terms. The model arises in aeroelasticity when a
panel is immersed in a high velocity linear potential flow; in this case the
effect of the flow can be captured by a dynamic pressure term written in terms
of the material derivative of the plate's displacement. The effect of
fully-supported internal damping is studied for both Berger and von Karman
dynamics. The non-dissipative nature of the dynamics preclude the use of strong
tools such as backward-in-time smallness of velocities and finiteness of the
dissipation integral. Modern quasi-stability techniques are utilized to show
the existence of compact global attractors and generalized fractal exponential
attractors. Specific results depending on the size of the damping parameter and
the nonlinearity in force. For the Berger plate, in the presence of large
damping, the existence of a proper global attractor (whose fractal dimension is
finite in the state space) is shown via a decomposition of the nonlinear
dynamics. This leads to the construction of a compact set upon which
quasi-stability theory can be implemented. Numerical investigations for
appropriate 1-D models are presented which explore and support the abstract
results presented herein. | 1609.02211v1 |
2016-10-26 | On the region of attraction of phase-locked states for swing equations on connected graphs with inhomogeneous dampings | We consider the synchronization problem of swing equations, a second-order
Kuramoto-type model, on connected networks with inhomogeneous dampings. This
was largely motivated by its relevance to the dynamics of power grids. We focus
on the estimate of the region of attraction of synchronous states which is a
central problem in the transient stability of power grids. In the recent
literature, D\"{o}rfler, Chertkov, and Bullo [Proc. Natl. Acad. Sci. USA, 110
(2013), pp. 2005-2010] found a condition for the synchronization in smart
grids. They pointed out that the region of attraction is an important unsolved
problem. In [SIAM J. Control Optim., 52 (2014), pp. 2482-2511], only a special
case was considered where the oscillators have homogeneous dampings and the
underlying graph has a diameter less than or equal to 2. There the analysis
heavily relies on these assumptions; however, they are too strict compared to
the real power networks. In this paper, we continue the study and derive an
estimate on the region of attraction of phase-locked states for lossless power
grids on connected graphs with inhomogeneous dampings. Our main strategy is
based on the gradient-like formulation and energy estimate. We refine the
assumptions by constructing a new energy functional which enables us to
consider such general settings. | 1610.08437v1 |
2016-10-31 | A quest for new physics inside the neutron | The lecture presents an overview of the quest for the new physics in low
energy neutron phenomena. In addition to the traditional topics the quantum
damping of $n$ $\bar{n}$ oscillations is discussed. | 1610.10046v1 |
2016-12-19 | Improving the efficiency of joint remote state preparation in noisy environment with weak measurement | Quantum secure communication provides a new way for protecting the security
of information. As an important component of quantum secure communication,
remote state preparation (RSP) can securely transmit a quantum state from a
sender to a remote receiver. The existence of quantum noise severely affects
the security and reliability of quantum communication system. In this paper, we
study the method for improving the efficiency of joint RSP (JRSP) subjected to
noise with the help of weak measurement and its reversal measurement. Taking a
GHZ based deterministic JRSP as an example, we utilize the technique of weak
measurement and its reversal to suppress the effect of the amplitude-damping
noise firstly. Our study shows that the fidelity of the output state can be
improved in the amplitude-damping noise. We also study the effect of weak
measurement and its reversal in other three types of noise usually encountered
in real-world, namely, the bit-flip, phase-flip (phase-damping) and
depolarizing noise. Our results show that the weak measurement has no effect
for suppressing the bit-flip and phase-flip (phase-damping) noise, while has
slight effect for suppressing the depolarizing noise. Our study is suitable for
JRSP and RSP, and will be helpful for improving the efficiency of multiparticle
entanglement based quantum secure communication in real implementation. | 1612.06020v1 |
2017-03-21 | Evidence for structural damping in a high-stress silicon nitride nanobeam and its implications for quantum optomechanics | We resolve the thermal motion of a high-stress silicon nitride nanobeam at
frequencies far below its fundamental flexural resonance (3.4 MHz) using
cavity-enhanced optical interferometry. Over two decades, the displacement
spectrum is well-modeled by that of a damped harmonic oscillator driven by a
$1/f$ thermal force, suggesting that the loss angle of the beam material is
frequency-independent. The inferred loss angle at 3.4 MHz, $\phi = 4.5\cdot
10^{-6}$, agrees well with the quality factor ($Q$) of the fundamental beam
mode ($\phi = Q^{-1}$). In conjunction with $Q$ measurements made on higher
order flexural modes, and accounting for the mode dependence of stress-induced
loss dilution, we find that the intrinsic (undiluted) loss angle of the beam
changes by less than a factor of 2 between 50 kHz and 50 MHz. We discuss the
impact of such "structural damping" on experiments in quantum optomechanics, in
which the thermal force acting on a mechanical oscillator coupled to an optical
cavity is overwhelmed by radiation pressure shot noise. As an illustration, we
show that structural damping reduces the bandwidth of ponderomotive squeezing. | 1703.07134v2 |
2017-03-29 | Comment on "Spreading widths of giant resonances in spherical nuclei: damped transient response" by Severyukhin et al. [arXiv:1703.05710] | We argue whether physics of universal approach of Severyukhin et al.
[arXiv:1703.05710] is approved. | 1703.10003v1 |
2017-05-16 | Propagation of transition fronts in nonlinear chains with non-degenerate on-site potentials | We address the problem of a front propagation in chains with a bi-stable
nondegenerate on-site potential and a nonlinear gradient coupling. For a
generic nonlinear coupling, one encounters a special regime of transitions,
characterized by extremely narrow fronts, far supersonic velocities of
propagation and long waves in the oscillatory tail. This regime can be
qualitatively associated with a shock wave. The front propagation can be
described with the help of a simple reduced-order model; the latter delivers a
kinetic law, which is almost not sensitive to fine details of the on-site
potential. Besides, it is possible to predict all main characteristics of the
transition front, including its shape and frequency and amplitude of the
oscillatory tail. The numerical results are in a good agreement with the
analytical predictions. The suggested approach allows one to consider the
effects of an external pre-load and on-site damping. When the damping is
moderate, the analysis remains in the frame of the reduced-order model. It is
possible to consider the solution for the front propagating in the damped chain
as a perturbation of the undamped dynamics. This approach yield reasonable
predictions. When the damping is high, the transition front enters a completely
different asymptotic regime. The gradient nonlinearity generically turns
negligible, and the propagating front converges to the exact solution obtained
from a simple linear continuous model. | 1705.05555v1 |
2017-08-16 | The Frequency-dependent Damping of Slow Magnetoacoustic Waves in a Sunspot Umbral Atmosphere | High spatial and temporal resolution images of a sunspot, obtained
simultaneously in multiple optical and UV wavelengths, are employed to study
the propagation and damping characteristics of slow magnetoacoustic waves up to
transition region heights. Power spectra are generated from intensity
oscillations in sunspot umbra, across multiple atmospheric heights, for
frequencies up to a few hundred mHz. It is observed that the power spectra
display a power-law dependence over the entire frequency range, with a
significant enhancement around 5.5 mHz found for the chromospheric channels.
The phase-difference spectra reveal a cutoff frequency near 3 mHz, up to which
the oscillations are evanescent, while those with higher frequencies propagate
upwards. The power-law index appears to increase with atmospheric height. Also,
shorter damping lengths are observed for oscillations with higher frequencies
suggesting frequency-dependent damping. Using the relative amplitudes of the
5.5 mHz (3 minute) oscillations, we estimate the energy flux at different
heights, which seems to decay gradually from the photosphere, in agreement with
recent numerical simulations. Furthermore, a comparison of power spectra across
the umbral radius highlights an enhancement of high-frequency waves near the
umbral center, which does not seem to be related to magnetic field inclination
angle effects. | 1708.04835v1 |
2017-08-29 | Spin wave damping arising from phase coexistence below $T_c$ in colossal magnetoresistive La$_{0.7}$Ca$_{0.3}$MnO$_3$ | While the spin dynamics of La$_{0.7}$Ca$_{0.3}$MnO$_3$ in the ferromagnetic
phase are known to be unconventional, previous measurements have yielded
contradictory results regarding the damping of spin wave excitations. Neutron
spectroscopy measurements on a sample with a transition temperature of
$T_c$=257 K, higher than most single crystals, unambiguously reveal an
anomalous increase in spin wave damping for excitations approaching the
Brillouin zone boundary along the [$100$] direction that cannot be explained as
an artifact due to a noninteracting phonon branch. Spin waves throughout the
($HK0$) plane display a common trend where the spin wave damping is dependent
upon the excitation energy, increasing for energies above roughly 15 meV and
reaching a full width at half maximum of at least 20 meV. The results are
consistent with a model of intrinsic spatial inhomogeneity with phase separated
regions approximately 18 {\AA} in size persisting over a large range of
temperatures below $T_c$. | 1708.08960v2 |
2017-09-08 | Topological and Graph-coloring Conditions on the Parameter-independent Stability of Second-order Networked Systems | In this paper, we study parameter-independent stability in qualitatively
heterogeneous passive networked systems containing damped and undamped nodes.
Given the graph topology and a set of damped nodes, we ask if output consensus
is achieved for all system parameter values. For given parameter values, an
eigenspace analysis is used to determine output consensus. The extension to
parameter-independent stability is characterized by a coloring problem, named
the richly balanced coloring (RBC) problem. The RBC problem asks if all nodes
of the graph can be colored red, blue and black in such a way that (i) every
damped node is black, (ii) every black node has blue neighbors if and only if
it has red neighbors, and (iii) not all nodes in the graph are black. Such a
colored graph is referred to as a richly balanced colored graph.
Parameter-independent stability is guaranteed if there does not exist a richly
balanced coloring. The RBC problem is shown to cover another well-known graph
coloring scheme known as zero forcing sets. That is, if the damped nodes form a
zero forcing set in the graph, then a richly balanced coloring does not exist
and thus, parameter-independent stability is guaranteed. However, the full
equivalence of zero forcing sets and parameter-independent stability holds only
true for tree graphs. For more general graphs with few fundamental cycles an
algorithm, named chord node coloring, is proposed that significantly
outperforms a brute-force search for solving the NP-complete RBC problem. | 1709.02629v1 |
2017-10-11 | Collisional damping rates for plasma waves | The distinction between the plasma dynamics dominated by collisional
transport versus collective processes has never been rigorously addressed until
recently. A recent paper [Yoon et al., Phys. Rev. E 93, 033203 (2016)]
formulates for the first time, a unified kinetic theory in which collective
processes and collisional dynamics are systematically incorporated from first
principles. One of the outcomes of such a formalism is the rigorous derivation
of collisional damping rates for Langmuir and ion-acoustic waves, which can be
contrasted to the heuristic customary approach. However, the results are given
only in formal mathematical expressions. The present Brief Communication
numerically evaluates the rigorous collisional damping rates by considering the
case of plasma particles with Maxwellian velocity distribution function so as
to assess the consequence of the rigorous formalism in a quantitative manner.
Comparison with the heuristic ("Spitzer") formula shows that the accurate
damping rates are much lower in magnitude than the conventional expression,
which implies that the traditional approach over-estimates the importance of
attenuation of plasma waves by collisional relaxation process. Such a finding
may have a wide applicability ranging from laboratory to space and
astrophysical plasmas. | 1710.03874v1 |
2017-10-20 | Tidal dissipation in rotating fluid bodies: the presence of a magnetic field | We investigate effects of the presence of a magnetic field on tidal
dissipation in rotating fluid bodies. We consider a simplified model consisting
of a rigid core and a fluid envelope, permeated by a background magnetic field
(either a dipolar field or a uniform axial field). The wavelike tidal responses
in the fluid layer are in the form of magnetic-Coriolis waves, which are
restored by both the Coriolis force and the Lorentz force. Energy dissipation
occurs through viscous damping and Ohmic damping of these waves. Our numerical
results show that the tidal dissipation can be dominated by Ohmic damping even
with a weak magnetic field. The presence of a magnetic field smooths out the
complicated frequency-dependence of the dissipation rate, and broadens the
frequency spectrum of the dissipation rate, depending on the strength of the
background magnetic field. However, the frequency-averaged dissipation is
independent of the strength and structure of the magnetic field, and of the
dissipative parameters, in the approximation that the wave-like response is
driven only by the Coriolis force acting on the non-wavelike tidal flow.
Indeed, the frequency-averaged dissipation quantity is in good agreement with
previous analytical results in the absence of magnetic fields. Our results
suggest that the frequency-averaged tidal dissipation of the wavelike
perturbations is insensitive to detailed damping mechanisms and dissipative
properties. | 1710.07690v2 |
2017-11-30 | Implications of dark matter cascade decay from DAMPE, HESS, Fermi-LAT and AMS02 data | Recent high-energy cosmic $e^\pm$ measurement from the DArk Matter Particle
Explorer (DAMPE) satellite confirms the deviation of total cosmic ray electron
spectrum above 700-900 GeV from a simple power law. In this paper we
demonstrate that the cascade decay of dark matter (DM) can account for DAMPE's
TeV $e^+e^-$ spectrum. We select the least constraint DM decay channel into
four muons as the benchmark scenario, and perform an analysis with propagation
variance in both DM signal and the Milky Way's electron background. The
best-fit of the model is obtained for joint DAMPE, Fermi-Large Area Telescope
(Fermi-LAT), High Energy Stereoscopic System (HESS), high energy electron data
sets, and with an $\mathcal{O}(10^{26})$ second decay lifetime, which is
consistent with existing gamma ray and cosmic microwave background limits. We
compare the spectral difference between the cascade decay of typical
final-state channels. The least constrained $4\mu$ channels give good fits to
the electron spectrum's TeV scale down-turn, yet their low energy spectrum has
tension with sub-TeV positron data from AMS02. We also consider a three-step
cascade decay into eight muons, and also a gamma-ray constrained $4\mu,4b$
mixed channel, to demonstrate that a further softened cascade decay signal
would be required for the agreement with all the data sets. | 1712.00370v3 |
2017-12-04 | Scalar dark matter, Type II Seesaw and the DAMPE cosmic ray $e^+ + e^-$ excess | The DArk Matter Particle Explorer (DAMPE) has reported a measurement of the
flux of high energy cosmic ray electrons plus positrons (CREs) in the energy
range between $25$ GeV and $4.6$ TeV. With unprecedented high energy
resolution, the DAMPE data exhibit an excess of the CREs flux at an energy of
around $1.4$ TeV. In this letter, we discuss how the observed excess can be
understood in a minimal framework where the Standard Model (SM) is supplemented
by a stable SM singlet scalar as dark matter (DM) and type II seesaw for
generating the neutrino mass matrix. In our framework, a pair of DM particles
annihilates into a pair of the SM SU(2) triplet scalars ($\Delta$s) in type II
seesaw, and the subsequent $\Delta$ decays create the primary source of the
excessive CREs around $1.4$ TeV. The lepton flavor structure of the primary
source of CREs has a direct relationship with the neutrino oscillation data. We
find that the DM interpretation of the DAMPE excess determines the pattern of
neutrino mass spectrum to be the inverted hierarchy type, taking into account
the constraints from the Fermi-LAT observations of dwarf spheroidal galaxies. | 1712.00869v2 |
2017-12-07 | Nonlinear growth of structure in cosmologies with damped matter fluctuations | We investigate the nonlinear evolution of structure in variants of the
standard cosmological model which display damped density fluctuations relative
to cold dark matter (e.g. in which cold dark matter is replaced by warm or
interacting DM). Using N-body simulations, we address the question of how much
information is retained from different scales in the initial linear power
spectrum following the nonlinear growth of structure. We run a suite of N-body
simulations with different initial linear matter power spectra to show that,
once the system undergoes nonlinear evolution, the shape of the linear power
spectrum at high wavenumbers does not affect the non-linear power spectrum,
while it still matters for the halo mass function. Indeed, we find that linear
power spectra which differ from one another only at wavenumbers larger than
their half-mode wavenumber give rise to (almost) identical nonlinear power
spectra at late times, regardless of the fact that they originate from
different models with damped fluctuations. On the other hand, the halo mass
function is more sensitive to the form of the linear power spectrum. Exploiting
this result, we propose a two parameter model of the transfer function in
generic damped scenarios, and show that this parametrisation works as well as
the standard three parameter models for the scales on which the linear spectrum
is relevant. | 1712.02742v2 |
2017-12-11 | DAMPE excess from decaying right-handed neutrino dark matter | The flux of high-energy cosmic-ray electrons plus positrons recently measured
by the DArk Matter Particle Explorer (DAMPE) exhibits a tentative peak excess
at an energy of around $1.4$ TeV. In this paper, we consider the minimal gauged
$U(1)_{B-L}$ model with a right-handed neutrino (RHN) dark matter (DM) and
interpret the DAMPE peak with a late-time decay of the RHN DM into $e^\pm
W^\mp$. We find that a DM lifetime $\tau_{DM} \sim 10^{28}$ s can fit the DAMPE
peak with a DM mass $m_{DM}=3$ TeV. This favored lifetime is close to the
current bound on it by Fermi-LAT, our decaying RHN DM can be tested once the
measurement of cosmic gamma ray flux is improved. The RHN DM communicates with
the Standard Model particles through the $U(1)_{B-L}$ gauge boson ($Z^\prime$
boson), and its thermal relic abundance is controlled by only three free
parameters: $m_{DM}$, the $U(1)_{B-L}$ gauge coupling ($\alpha_{BL}$), and the
$Z^\prime$ boson mass ($m_{Z^\prime}$). For $m_{DM}=3$ TeV, the rest of the
parameters are restricted to be $m_{Z^\prime}\simeq 6$ TeV and $0.00807 \leq
\alpha_{BL} \leq 0.0149$, in order to reproduce the observed DM relic density
and to avoid the Landau pole for the running $\alpha_{BL}$ below the Planck
scale. This allowed region will be tested by the search for a $Z^\prime$ boson
resonance at the future Large Hadron Collider. | 1712.03652v3 |
2017-12-11 | A Statistical Study on The Frequency-Dependent Damping of Slow-mode Waves in Polar Plumes and Interplumes | We perform a statistical study on the frequency-dependent damping of slow
waves propagating along polar plumes and interplumes in the solar corona.
Analysis of a large sample of extreme ultraviolet (EUV) imaging data with high
spatial and temporal resolutions obtained from AIA/SDO suggests an inverse
power-law dependence of the damping length on the periodicity of slow waves
(i.e., the shorter period oscillations exhibit longer damping lengths), in
agreement with the previous case studies. Similar behavior is observed in both
plume and interplume regions studied in AIA 171 \AA\ and AIA 193 \AA\
passbands. It is found that the short-period (2--6 min) waves are relatively
more abundant than their long period (7--30 min) counterparts in contrast to
the general belief that the polar regions are dominated by the longer-period
slow waves. We also derived the slope of the power spectra ($\mathrm{\alpha}$,
the power-law index) statistically to better understand the characteristics of
turbulence present in the region. It is found that the $\mathrm{\alpha}$ values
and their distributions are similar in both plume and interplume structures
across the two AIA passbands. At the same time, the spread of these
distributions also indicates the complexity of the underlying turbulence
mechanism. | 1712.03673v1 |
2018-08-05 | Dispersion, damping, and intensity of spin excitations in the single-layer (Bi,Pb)$_{2}$(Sr,La)$_{2}$CuO$_{6+δ}$ cuprate superconductor family | Using Cu-$L_3$ edge resonant inelastic x-ray scattering (RIXS) we measured
the dispersion and damping of spin excitations (magnons and paramagnons) in the
high-$T_\mathrm{c}$ superconductor (Bi,Pb)$_{2}$(Sr,La)$_{2}$CuO$_{6+\delta}$
(Bi2201), for a large doping range across the phase diagram ($0.03\lesssim
p\lesssim0.21$). Selected measurements with full polarization analysis
unambiguously demonstrate the spin-flip character of these excitations, even in
the overdoped sample. We find that the undamped frequencies increase slightly
with doping for all accessible momenta, while the damping grows rapidly, faster
in the (0,0)$\rightarrow$(0.5,0.5) nodal direction than in the
(0,0)$\rightarrow$(0.5,0) antinodal direction. We compare the experimental
results to numerically exact determinant quantum Monte Carlo (DQMC)
calculations that provide the spin dynamical structure factor
$S(\textbf{Q},\omega)$ of the three-band Hubbard model. The theory reproduces
well the momentum and doping dependence of the dispersions and spectral weights
of magnetic excitations. These results provide compelling evidence that
paramagnons, although increasingly damped, persist across the superconducting
dome of the cuprate phase diagram; this implies that long range
antiferromagnetic correlations are quickly washed away, while short range
magnetic interactions are little affected by doping. | 1808.01682v1 |
2018-09-19 | Critical exponent for the semilinear wave equations with a damping increasing in the far field | We consider the Cauchy problem of the semilinear wave equation with a damping
term \begin{align*}
u_{tt} - \Delta u + c(t,x) u_t = |u|^p, \quad (t,x)\in (0,\infty)\times
\mathbb{R}^N,\quad
u(0,x) = \varepsilon u_0(x), \ u_t(0,x) = \varepsilon u_1(x), \quad x\in
\mathbb{R}^N, \end{align*} where $p>1$ and the coefficient of the damping term
has the form \begin{align*}
c(t,x) = a_0 (1+|x|^2)^{-\alpha/2} (1+t)^{-\beta} \end{align*} with some $a_0
> 0$, $\alpha < 0$, $\beta \in (-1, 1]$. In particular, we mainly consider the
cases $ \alpha < 0, \beta =0$ or $\alpha < 0, \beta = 1$, which imply $\alpha +
\beta < 1$, namely, the damping is spatially increasing and effective. Our aim
is to prove that the critical exponent is given by $ p = 1+
\frac{2}{N-\alpha}$. This shows that the critical exponent is the same as that
of the corresponding parabolic equation $c(t,x) v_t - \Delta v = |v|^p$. The
global existence part is proved by a weighted energy estimates with an
exponential-type weight function and a special case of the
Caffarelli-Kohn-Nirenberg inequality. The blow-up part is proved by a
test-function method introduced by Ikeda and Sobajima (arXiv:1710.06780v1). We
also give an upper estimate of the lifespan. | 1809.06994v1 |
2018-10-16 | Dark matter gets DAMPE | The DArk Matter Particle Explorer (DAMPE) recently reported an excess of
electrons/positrons above expected background fluxes even when a double
power-law background spectrum is assumed. Several dark matter models that
involve TeV-scale leptophilic WIMPs have been suggested in the literature to
account for this excess. All of these models are associated with the presence
of a nearby dark matter clump/over-density.
In this work we set out to explore how current constraints from observational
data impact the suggested parameter space for a dark matter explanation of the
DAMPE excess, as well as make projections of the capacity of LOFAR and the
up-coming SKA to observe indirect radio emissions from the nearby dark matter
over-density.
We show that LOFAR is incapable of probing the parameter space for DAMPE
excess models, unless the dark matter clump is in the form of an ultra-compact
mini halo. Fermi-LAT limits on dark matter annihilation are unable to probe
these models in all cases. Limits derived from diffuse Coma cluster radio
emission can probe a substantial portion of the parameter space and muon
neutrino limits inferred from galactic centre gamma-ray fluxes heavily restrict
muon coupling for the proposed WIMPs. The SKA is shown to able to fully probe
the parameter space of all the studied models using indirect emissions from the
local dark matter over-density. | 1810.07176v2 |
2018-12-16 | Nonlinear Dynamics of Spherical Shells Buckling under Step Pressure | Dynamic buckling is addressed for complete elastic spherical shells subject
to a rapidly applied step in external pressure. Insights from the perspective
of nonlinear dynamics reveal essential mathematical features of the buckling
phenomena. To capture the strong buckling imperfection-sensitivity, initial
geometric imperfections in the form of an axisymmetric dimple at each pole are
introduced. Dynamic buckling under the step pressure is related to the
quasi-static buckling pressure. Both loadings produce catastrophic collapse of
the shell for conditions in which the pressure is prescribed. Damping plays an
important role in dynamic buckling because of the time-dependent nonlinear
interaction among modes, particularly the interaction between the spherically
symmetric 'breathing' mode and the buckling mode. In this paper we argue that
the precise frequency dependence of the damping does not matter as most of the
damping happens at a single frequency (the breathing frequency). In general,
there is not a unique step pressure threshold separating responses associated
with buckling from those that do not buckle. Instead there exists a cascade of
buckling thresholds, dependent on the damping and level of imperfection,
separating pressures for which buckling occurs from those for which it does not
occur. For shells with small and moderately small imperfections the dynamic
step buckling pressure can be substantially below the quasi-static buckling
pressure. | 1812.06526v2 |
2019-01-09 | Turbulent dynamo in a weakly ionized medium | The small-scale turbulent dynamo is an important process contributing to the
cosmic magnetization. In partially ionized astrophysical plasmas, the dynamo
growth of magnetic energy strongly depends on the coupling state between ions
and neutrals and the ion-neutral collisional damping effect. A new damping
stage of turbulent dynamo in a weakly ionized medium was theoretically
predicted by Xu \& Lazarian (2016). By carrying out a 3D two-fluid dynamo
simulation, here we for the first time numerically confirmed the physical
conditions and the linear-in-time growth of magnetic field strength of the
damping stage of dynamo. The dynamo-amplified magnetic field has a
characteristic length as the damping scale, which increases with time and can
reach the injection scale of turbulence after around eight largest
eddy-turnover times given sufficiently low ionization fraction and weak initial
magnetic field. Due to the weak coupling between ions and neutrals, most
turbulent energy carried by neutrals cannot be converted to the magnetic
energy, resulting in a relatively weak magnetic field at the end of dynamo.
This result has important implications for the growth of magnetic fields in the
partially ionized interstellar medium and shock acceleration of Galactic cosmic
rays. | 1901.02893v1 |
2019-01-25 | Quantum speed limit time for correlated quantum channel | Memory effects play a fundamental role in the dynamics of open quantum
systems. There exist two different views on memory for quantum noises. In the
first view, the quantum channel has memory when there exist correlations
between successive uses of the channels on a sequence of quantum systems. These
types of channels are also known as correlated quantum channels. In the second
view, memory effects result from correlations which are created during the
quantum evolution. In this work we will consider the first view and study the
quantum speed limit time for a correlated quantum channel. Quantum speed limit
time is the bound on the minimal time which is needed for a quantum system to
evolve from an initial state to desired states. The quantum evolution is fast
if the quantum speed limit time is short. In this work, we will study the
quantum speed limit time for some correlated unital and correlated non-unital
channels. As an example for unital channels we choose correlated dephasing
colored noise. We also consider the correlated amplitude damping and correlated
squeezed generalized amplitude damping channels as the examples for non-unital
channels. It will be shown that the quantum speed limit time for correlated
pure dephasing colored noise is increased by increasing correlation strength,
while for correlated amplitude damping and correlated squeezed generalized
amplitude damping channels quantum speed limit time is decreased by increasing
correlation strength. | 1901.08917v4 |
2019-02-17 | Finite-size effects on sound damping in stable computer glasses | In this brief note we comment on the recent results presented in
arXiv:1812.08736v1 | 1902.06225v1 |
2019-05-04 | A class of second-order geometric quasilinear hyperbolic PDEs and their application in imaging science | In this paper, we study damped second-order dynamics, which are quasilinear
hyperbolic partial differential equations (PDEs). This is inspired by the
recent development of second-order damping systems for accelerating energy
decay of gradient flows. We concentrate on two equations: one is a damped
second-order total variation flow, which is primarily motivated by the
application of image denoising; the other is a damped second-order mean
curvature flow for level sets of scalar functions, which is related to a
non-convex variational model capable of correcting displacement errors in image
data (e.g. dejittering). For the former equation, we prove the existence and
uniqueness of the solution. For the latter, we draw a connection between the
equation and some second-order geometric PDEs evolving the hypersurfaces which
are described by level sets of scalar functions, and show the existence and
uniqueness of the solution for a regularized version of the equation. The
latter is used in our algorithmic development. A general algorithm for
numerical discretization of the two nonlinear PDEs is proposed and analyzed.
Its efficiency is demonstrated by various numerical examples, where simulations
on the behavior of solutions of the new equations and comparisons with
first-order flows are also documented. | 1905.01457v2 |
2019-07-08 | Single-spectrum prediction of kurtosis of water waves in a non-conservative model | We study statistical properties after a sudden episode of wind for water
waves propagating in one direction. A wave with random initial conditions is
propagated using a forced-damped higher order Nonlinear Schr\"odinger equation
(NLS). During the wind episode, the wave action increases, the spectrum
broadens, the spectral mean shifts up and the Benjamin-Feir index (BFI) and the
kurtosis increase. Conversely, after the wind episode, the opposite occurs for
each quantity. The kurtosis of the wave height distribution is considered the
main parameter that can indicate whether rogue waves are likely to occur in a
sea state, and the BFI is often mentioned as a means to predict the kurtosis.
However, we find that while there is indeed a quadratic relation between these
two, this relationship is dependent on the details of the forcing and damping.
Instead, a simple and robust quadratic relation does exist between the kurtosis
and the bandwidth. This could allow for a single-spectrum assessment of the
likelihood of rogue waves in a given sea state. In addition, as the kurtosis
depends strongly on the damping and forcing coefficients, by combining the
bandwidth measurement with the damping coefficient, the evolution of the
kurtosis after the wind episode can be predicted. | 1907.03490v1 |
2019-08-20 | Synthetic Extreme-ultraviolet Emissions Modulated by Leaky Fast Sausage Modes in Solar Active Region Loops | We study the extreme-ultraviolet (EUV) emissions modulated by leaky fast
sausage modes (FSMs) in solar active region loops and examine their
observational signatures via spectrometers like EIS. After computing fluid
variables of leaky FSMs with MHD simulations, we forward-model the intensity
and spectral properties of the Fe X 185~\AA~and Fe XII 195~\AA~lines by
incorporating non-equilibrium ionization (NEI) in the computations of the
relevant ionic fractions. The damping times derived from the intensity
variations are then compared with the wave values, namely the damping times
directly found from our MHD simulations. Our results show that in the
equilibrium ionization cases, the density variations and the intensity
variations can be either in phase or in anti-phase, depending on the loop
temperature. NEI considerably impacts the intensity variations but has only
marginal effects on the derived Doppler velocity or Doppler width. We find that
the damping time derived from the intensity can largely reflect the wave
damping time if the loop temperature is not drastically different from the
nominal formation temperature of the corresponding emission line. These results
are helpful for understanding the modulations to the EUV emissions by leaky
FSMs and hence helpful for identifying FSMs in solar active region loops. | 1908.07131v1 |
2019-10-24 | Frequency criteria for exponential stability | We discuss some frequency-domain criteria for the exponential stability of
nonlinear feedback systems based on dissipativity theory. Applications are
given to convergence rates for certain perturbations of the damped harmonic
oscillator. | 1910.10855v2 |
2019-11-05 | IW And-Type State in IM Eridani | IW And stars are a recently recognized group of dwarf novae which are
characterized by a repeated sequence of brightening from a standstill-like
phase with damping oscillations followed by a deep dip. Kimura et al. (2019)
recently proposed a model based on thermal-viscous disk instability in a tilted
disk to reproduce the IW And-type characteristics. IM Eri experienced the IW
And-type phase in 2018 and we recorded three cycles of the (damping)
oscillation phase terminated by brightening. We identified two periods during
the IW And-type state: 4-5 d small-amplitude (often damping) oscillations and a
34-43 d long cycle. This behavior is typical for an IW And-type star. The
object gradually brightened within the long cycle before the next brightening
which terminated the (damping) oscillation phase. This observation agrees with
the increasing disk mass during the long cycle predicted by a model of
thermal-viscous disk instability in a tilted disk (Kimura et al. 2019). We,
however, did not succeed in detecting negative superhumps, which are considered
to be the signature of a tilted disk. | 1911.01587v1 |
2019-11-28 | Magnon damping in the zigzag phase of the Kitaev-Heisenberg-$Γ$ model on a honeycomb lattice | We calculate magnon dispersions and damping in the Kitaev-Heisenberg model
with an off-diagonal exchange $\Gamma$ and isotropic third-nearest-neighbor
interaction $J_3$ on a honeycomb lattice. This model is relevant to a
description of the magnetic properties of iridium oxides $\alpha$-Li$_2$IrO$_3$
and Na$_2$IrO$_3$, and Ru-based materials such as $\alpha$-RuCl$_3$. We use an
unconventional parametrization of the spin-wave expansion, in which each
Holstein-Primakoff boson is represented by two conjugate hermitian operators.
This approach gives us an advantage over the conventional one in identifying
parameter regimes where calculations can be performed analytically. Focusing on
the parameter regime with the zigzag spin pattern in the ground state that is
consistent with experiments, we demonstrate that one such region is $\Gamma =
K>0$, where $K$ is the Kitaev coupling. Within our approach we are able to
obtain explicit analytical expressions for magnon energies and eigenstates and
go beyond the standard linear spin-wave theory approximation by calculating
magnon damping and demonstrating its role in the dynamical structure factor. We
show that the magnon damping effects in both Born and self-consistent
approximations are very significant, underscoring the importance of non-linear
magnon coupling in interpreting broad features in the neutron-scattering
spectra. | 1911.12829v2 |
2019-12-10 | A Stochastic Quasi-Newton Method for Large-Scale Nonconvex Optimization with Applications | This paper proposes a novel stochastic version of damped and regularized BFGS
method for addressing the above problems. | 1912.04456v1 |
2019-12-27 | Ultralow mechanical damping with Meissner-levitated ferromagnetic microparticles | Levitated nanoparticles and microparticles are excellent candidates for the
realization of extremely isolated mechanical systems, with a huge potential
impact in sensing applications and in quantum physics. Magnetic levitation
based on static fields is a particularly interesting approach, due to the
unique property of being completely passive and compatible with low
temperatures. Here, we show experimentally that micromagnets levitated above
type-I superconductors feature very low damping at low frequency and low
temperature. In our experiment, we detect 5 out of 6 rigid-body mechanical
modes of a levitated ferromagnetic microsphere, using a dc SQUID
(Superconducting Quantum Interference Device) with a single pick-up coil. The
measured frequencies are in agreement with a finite element simulation based on
ideal Meissner effect. For two specific modes we find further substantial
agreement with analytical predictions based on the image method. We measure
damping times $\tau$ exceeding $10^4$ s and quality factors $Q$ beyond $10^7$,
improving by $2-3$ orders of magnitude over previous experiments based on the
same principle. We investigate the possible residual loss mechanisms besides
gas collisions, and argue that much longer damping time can be achieved with
further effort and optimization. Our results open the way towards the
development of ultrasensitive magnetomechanical sensors with potential
applications to magnetometry and gravimetry, as well as to fundamental and
quantum physics. | 1912.12252v3 |
2020-01-22 | Wide Area Measurement System-based Low Frequency Oscillation Damping Control through Reinforcement Learning | Ensuring the stability of power systems is gaining more attraction today than
ever before, due to the rapid growth of uncertainties in load and renewable
energy penetration. Lately, wide area measurement system-based centralized
controlling techniques started providing a more flexible and robust control to
keep the system stable. But, such a modernization of control philosophy faces
pressing challenges due to the irregularities in delays of long-distance
communication channels and response of equipment to control actions. Therefore,
we propose an innovative approach that can revolutionize the control strategy
for damping down low frequency oscillations in transmission systems. Proposed
method is enriched with a potential of overcoming the challenges of
communication delays and other non-linearities in wide area damping control by
leveraging the capability of the reinforcement learning technique. Such a
technique has a unique characteristic to learn on diverse scenarios and
operating conditions by exploring the environment and devising an optimal
control action policy by implementing policy gradient method. Our detailed
analysis and systematically designed numerical validation prove the
feasibility, scalability and interpretability of the carefully modelled
low-frequency oscillation damping controller so that stability is ensured even
with the uncertainties of load and generation are on the rise. | 2001.07829v1 |
2020-02-13 | Semi-realistic tight-binding model for spin-orbit torques | We compute the spin-orbit torque in a transition metal heterostructure using
Slater-Koster parameterization in the two-center tight-binding approximation
and accounting for d-orbitals only. In this method, the spin-orbit coupling is
modeled within Russel-Saunders scheme, which enables us to treat interfacial
and bulk spin-orbit transport on equal footing. The two components of the
spin-orbit torque, dissipative (damping-like) and reactive (field-like), are
computed within Kubo linear response theory. By systematically studying their
thickness and angular dependence, we were able to accurately characterize these
components beyond the traditional "inverse spin galvanic" and "spin Hall"
effects. Whereas the conventional field-like torque is purely interfacial, we
unambiguously demonstrate that the conventional the damping-like torque
possesses both an interfacial and a bulk contribution. In addition, both
field-like and damping-like torques display substantial angular dependence with
strikingly different thickness behavior. While the planar contribution of the
field-like torque decreases smoothly with the nonmagnetic metal thickness, the
planar contribution of the damping-like torque increases dramatically with the
nonmagnetic metal thickness. Finally, we investigate the self-torque exerted on
the ferromagnet when the spin-orbit coupling of the nonmagnetic metal is turned
off. Our results suggest that the spin accumulation that builds up inside the
ferromagnet can be large enough to induce magnetic excitations. | 2002.05533v1 |
2020-02-14 | One-dimensional wave equation with set-valued boundary damping: well-posedness, asymptotic stability, and decay rates | This paper is concerned with the analysis of a one dimensional wave equation
$z_{tt}-z_{xx}=0$ on $[0,1]$ with a Dirichlet condition at $x=0$ and a damping
acting at $x=1$ which takes the form $(z_t(t,1),-z_x(t,1))\in\Sigma$ for every
$t\geq 0$, where $\Sigma$ is a given subset of $\mathbb R^2$. The study is
performed within an $L^p$ functional framework, $p\in [1, +\infty]$. We aim at
determining conditions on $\Sigma$ ensuring existence and uniqueness of
solutions of that wave equation as well as strong stability and uniform global
asymptotic stability of its solutions. In the latter case, we also study the
decay rates of the solutions and their optimality. We first establish a
one-to-one correspondence between the solutions of that wave equation and the
iterated sequences of a discrete-time dynamical system in terms of which we
investigate the above mentioned issues. This enables us to provide a simple
necessary and sufficient condition on $\Sigma$ ensuring existence and
uniqueness of solutions of the wave equation as well as an efficient strategy
for determining optimal decay rates when $\Sigma$ verifies a generalized sector
condition. As an application, we solve two conjectures stated in the
literature, the first one seeking a specific optimal decay rate and the second
one associated with a saturation type of damping. In case the boundary damping
is subject to perturbations, we derive sharp results regarding asymptotic
perturbation rejection and input-to-state issues. | 2002.06186v3 |
2020-03-30 | Optimal absorption of acoustical waves by a boundary | In the aim to find the simplest and most efficient shape of a noise absorbing
wall to dissipate the acoustical energy of a sound wave, we consider a
frequency model described by the Helmholtz equation with a damping on the
boundary. The well-posedness of the model is shown in a class of domains with
d-set boundaries (N -- 1 $\le$ d < N). We introduce a class of admissible
Lipschitz boundaries, in which an optimal shape of the wall exists in the
following sense: We prove the existence of a Radon measure on this shape,
greater than or equal to the usual Lebesgue measure, for which the
corresponding solution of the Helmholtz problem realizes the infimum of the
acoustic energy defined with the Lebesgue measure on the boundary. If this
Radon measure coincides with the Lebesgue measure, the corresponding solution
realizes the minimum of the energy. For a fixed porous material, considered as
an acoustic absorbent, we derive the damping parameters of its boundary from
the corresponding time-dependent problem described by the damped wave equation
(damping in volume). | 2003.13250v2 |
2020-04-24 | Suppression of the longitudinal coupled bunch instability in DA$Φ$NE in collisions with a crossing angle | In DAFNE, the Frascati $e^+e^-$ collider operating since 1998, an innovative
collision scheme, the crab waist, has been successfully implemented during the
years 2008-09. During operations for the Siddharta experiment an unusual
synchrotron oscillation damping effect induced by beam-beam collisions has been
observed. Indeed, when the longitudinal feedback is off, the positron beam
becomes unstable with currents above 200-300 mA due to coupled bunch
instability. The longitudinal instability is damped by colliding the positron
beam with a high current electron beam (of the order of 2 A). A shift of about
-600 Hz in the residual synchrotron sidebands is observed. Precise measurements
have been performed by using both a commercial spectrum analyzer and the
diagnostic capabilities of the longitudinal bunch-by-bunch feedback. The
damping effect has been observed in DAFNE for the first time during collisions
with the crab waist scheme. Our explanation, based both on theoretical
consideration and modeling simulation, is that beam collisions with a large
crossing angle produce longitudinal tune shift and spread, providing Landau
damping of synchrotron oscillations. | 2004.11902v1 |
2020-05-08 | Separatrix crossing and symmetry breaking in NLSE-like systems due to forcing and damping | We theoretically and experimentally examine the effect of forcing and damping
on systems that can be described by the nonlinear Schr\"odinger equation
(NLSE), by making use of the phase-space predictions of the three-wave
truncation of the spectrum. In the latter, only the fundamental frequency and
the upper and lower sidebands are retained. Plane wave solutions to the NLSE
exhibit modulation instability (MI) within a frequency band determined by a
linear stability analysis. For modulation frequencies inside the MI-band, we
experimentally demonstrate that forcing and damping cause a separatrix crossing
during the evolution. Our experiments are performed on deep water waves, which
are better described by the higher-order NLSE, the Dysthe equation. We
therefore extend our analysis to this system. However, our conclusions are
general. When the system is damped by the viscosity of the water, it is pulled
outside the separatrix, which in the real space corresponds to a phase-shift of
the envelope and therefore doubles the period of the Fermi-Pasta-Ulam-Tsingou
recurrence cycle. When the system is forced by the wind, it is pulled inside
the separatrix. Furthermore, for modulation frequencies outside the
conventional MI-band, we experimentally demonstrate that contrary to the linear
prediction, we do observe a growth and decay cycle of the plane-wave
modulation. Finally, we give a theoretical demonstration that forcing the NLSE
system can induce symmetry breaking during the evolution. | 2005.03931v1 |
2020-05-13 | Damping of a micro-electromechanical oscillator in turbulent superfluid $^4$He: A novel probe of quantized vorticity in the ultra-low temperature regime | We report a comprehensive investigation of the effects of quantum turbulence
and quantized vorticity in superfluid $^4$He on the motion of a
micro-electromechanical systems (MEMS) resonator. We find that the MEMS is
uniquely sensitive to quantum turbulence present in the fluid. To generate
turbulence in the fluid, a quartz tuning fork (TF) is placed in proximity to
the MEMS and driven at large amplitude. We observe that at low velocity, the
MEMS is damped by the turbulence, and that above a critical velocity, $v_c
\simeq 5\,$mm\,s$^{-1}$, the turbulent damping is greatly reduced. We find that
above $v_c$, the damping of the MEMS is reduced further for increasing
velocity, indicating a velocity dependent coupling between the surface of the
MEMS and the quantized vortices constituting the turbulence. We propose a model
of the interaction between vortices in the fluid and the surface of the MEMS.
The sensitivity of these devices to a small number of vortices and the almost
unlimited customization of MEMS open the door to a more complete understanding
of the interaction between quantized vortices and oscillating structures, which
in turn provides a new route for the investigation of the dynamics of single
vortices. | 2005.06570v1 |
2020-06-10 | Online PMU-Based Wide-Area Damping Control for Multiple Inter-Area Modes | This paper presents a new phasor measurement unit (PMU)-based wide-area
damping control (WADC) method to suppress the critical inter-area modes of
large-scale power systems. Modal participation factors, estimated by a
practically model-free system identification approach, are used to select the
most suitable synchronous generators for control through the proposed WADC
algorithm. It is shown that multiple inter-area modes can be sufficiently
damped by the proposed approach without affecting the rest of the modes, while
only a few machines are needed to perform the control. The proposed technique
is applied to the IEEE 68-bus and the IEEE 145-bus systems, including the test
cases with PMU measurement noise and with missing PMUs. The simulation results
clearly demonstrate the good adaptivity of the control strategy subjected to
network model changes, its effective damping performance comparing to power
system stabilizers (PSSs), and its great potential for near real-time
implementation. | 2006.05651v1 |
2020-06-14 | A general formulation for the magnetic oscillations in two dimensional systems | We develop a general formalism for the magnetic oscillations (MO) in two
dimensional (2D) systems. We consider general 2D Landau levels, which may
depend on other variable or indices, besides the perpendicular magnetic field.
In the ground state, we obtain expressions for the MO phase and amplitude. From
this we use a Fourier expansion to write the MO, with the first term being a
sawtooth oscillation. We also consider the effects of finite temperature,
impurities or lattice imperfections, assuming a general broadening of the
Landau levels. We develop two methods for describing these damping effects in
the MO. One in terms of the occupancy of the Landau levels, the other in terms
of reduction factors, which results in a generalization of the
Lifshits-Kosevich (LK) formula. We show that the first approach is particularly
useful at very low damping, when only the states close to the Fermi energy are
excited. In contrast, the LK formula may be more convenient at higher damping,
when only few terms are needed in its harmonic expansion. We compare different
damping situations, showing how the MO are broadened in each case. The general
formulation presented allows to relate the properties of the MO with those of
the 2D systems. | 2006.07944v2 |
2020-08-03 | Improvement on the blow-up of the wave equation with the scale-invariant damping and combined nonlinearities | We consider in this article the damped wave equation, in the
\textit{scale-invariant case} with combined two nonlinearities, which reads as
follows: \begin{displaymath} \d (E) \hspace{1cm} u_{tt}-\Delta
u+\frac{\mu}{1+t}u_t=|u_t|^p+|u|^q, \quad \mbox{in}\ \R^N\times[0,\infty),
\end{displaymath} with small initial data.\\ Compared to our previous work
\cite{Our}, we show in this article that the first hypothesis on the damping
coefficient $\mu$, namely $\mu < \frac{N(q-1)}{2}$, can be removed, and the
second one can be extended from $(0, \mu_*/2)$ to $(0, \mu_*)$ where $\mu_*>0$
is solution of $(q-1)\left((N+\mu_*-1)p-2\right) = 4$. Indeed, owing to a
better understanding of the influence of the damping term in the global
dynamics of the solution, we think that this new interval for $\mu$ describe
better the threshold between the blow-up and the global existence regions.
Moreover, taking advantage of the techniques employed in the problem $(E)$, we
also improve the result in \cite{LT2,Palmieri} in relationship with the Glassey
conjecture for the solution of $(E)$ but without the nonlinear term $|u|^q$.
More precisely, we extend the blow-up region from $p \in (1, p_G(N+\sigma)]$,
where $\sigma$ is given by \eqref{sigma} below, to $p \in (1, p_G(N+\mu)]$
giving thus a better estimate of the lifespan in this case. | 2008.02109v3 |
2020-08-26 | Quantum Lifshitz points and fluctuation-induced first-order phase transitions in imbalanced Fermi mixtures | We perform a detailed analysis of the phase transition between the uniform
superfluid and normal phases in spin- and mass-imbalanced Fermi mixtures. At
mean-field level we demonstrate that at temperature $T\to 0$ the gradient term
in the effective action can be tuned to zero for experimentally relevant sets
of parameters, thus providing an avenue to realize a quantum Lifshitz point. We
subsequently analyze damping processes affecting the order-parameter field
across the phase transition. We show that, in the low energy limit, Landau
damping occurs only in the symmetry-broken phase and affects exclusively the
longitudinal component of the order-parameter field. It is however unavoidably
present in the immediate vicinity of the phase transition at temperature $T=0$.
We subsequently perform a renormalization-group analysis of the system in a
situation, where, at mean-field level, the quantum phase transition is second
order (and not multicritical). We find that, at $T$ sufficiently low, including
the Landau damping term in a form derived from the microscopic action
destabilizes the renormalization group flow towards the Wilson-Fisher fixed
point. This signals a possible tendency to drive the transition weakly
first-order by the coupling between the order-parameter fluctuations and
fermionic excitations effectively captured by the Landau damping contribution
to the order-parameter action. | 2008.11782v1 |
2020-09-10 | Electron Landau Damping of Kinetic Alfvén Waves in Simulated Magnetosheath Turbulence | Turbulence is thought to play a role in the heating of the solar wind plasma,
though many questions remain to be solved regarding the exact nature of the
mechanisms driving this process in the heliosphere. In particular, the physics
of the collisionless interactions between particles and turbulent
electromagnetic fields in the kinetic dissipation range of the turbulent
cascade remains incompletely understood. A recent analysis of an interval of
Magnetosphere Multiscale (MMS) observations has used the field-particle
correlation technique to demonstrate that electron Landau damping is involved
in the dissipation of turbulence in the Earth's magnetosheath. Motivated by
this discovery, we perform a high-resolution gyrokinetic numerical simulation
of the turbulence in the MMS interval to investigate the role of electron
Landau damping in the dissipation of turbulent energy. We employ the
field-particle correlation technique on our simulation data, compare our
results to the known velocity-space signatures of Landau damping outside the
dissipation range, and evaluate the net electron energization. We find
qualitative agreement between the numerical and observational results for some
key aspects of the energization and speculate on the nature of disagreements in
light of experimental factors, such as differences in resolution, and of
developing insights into the nature of field-particle interactions in the
presence of dispersive kinetic Alfv\'en waves. | 2009.05010v1 |
2020-11-09 | Plasmon energy losses in shear bands of metallic glass | Shear bands resulting from plastic deformation in cold-rolled
Al$_{88}$Y$_{7}$Fe$_{5}$ metallic glass were observed to display alternating
density changes along their propagation direction. Electron-energy loss
spectroscopy (EELS) was used to investigate the volume plasmon energy losses in
and around shear bands. Energy shifts of the peak centre and changes in the
peak width (FWHM) reflecting the damping were precisely determined within an
accuracy of a few meV using an open source python module (Hyperspy) to fit the
shapes of the plasmon and zero-loss peaks with Lorentzian functions. The
maximum bulk plasmon energy shifts were calculated for the bright and dark
shear band segments relative to the matrix to be about 38 and 14 meV,
respectively. The damping was observed to be larger for the denser regions. The
analysis presented here suggests that the changes in the plasmons are caused by
two contributions: (i) Variable damping in the shear band segments due to
changes in the medium-range order (MRO). This affects the static structure
factor S(k), which, in turn, leads to either reduced or increased damping
according to the Ziman-Baym formula. (ii) The ionic density and the effective
electron mass appearing in the zero-momentum plasmon frequency formula
$E_p(q=0)$ are coupled and give rise to small variations in the plasmon energy.
The model predicts plasmon energy shifts in the order of meV. | 2011.04396v3 |
2020-12-04 | Quantum Circuits for Collective Amplitude Damping in Two-Qubit Systems | Quantum computers have now appeared in our society and are utilized for the
investigation of science and engineering. At present, they have been built as
intermediate-size computers containing about fifty qubits and are weak against
noise effects. Hence, they are called noisy-intermediate scale quantum devices.
In order to accomplish efficient quantum computation with using these machines,
a key issue is going to be the coherent control of individual and collective
quantum noises. In this work, we focus on a latter type and investigate
formulations of the collective quantum noises represented as quantum circuits.
To simplify our discussions and make them concrete, we analyze collective
amplitude damping processes in two-qubit systems. As verifications of our
formalisms and the quantum circuits, we demonstrate digital quantum simulations
of the collective amplitude damping by examining six different initial
conditions with varying the number of execution of an overall operation for our
quantum simulations. We observe that our results show good numerical matching
with the solution of quantum master equation for the two-qubit systems as we
increase such a number. In addition, we explain the essence of the way to
extend our formalisms to analyze the collective amplitude damping in larger
qubit systems. These results pave the way for establishing systematic
approaches to control the quantum noises and designing large-scale quantum
computers. | 2012.02410v1 |
2020-12-10 | Dimensional analysis of spring-wing systems reveals performance metrics for resonant flapping-wing flight | Flapping-wing insects, birds, and robots are thought to offset the high power
cost of oscillatory wing motion by using elastic elements for energy storage
and return. Insects possess highly resilient elastic regions in their flight
anatomy that may enable high dynamic efficiency. However, recent experiments
highlight losses due to damping in the insect thorax that could reduce the
benefit of those elastic elements. We performed experiments on, and simulations
of a dynamically-scaled robophysical flapping model with an elastic element and
biologically-relevant structural damping to elucidate the roles of body
mechanics, aerodynamics, and actuation in spring-wing energetics. We measured
oscillatory flapping wing dynamics and energetics subject to a range of
actuation parameters, system inertia, and spring elasticity. To generalize
these results, we derive the non-dimensional spring-wing equation of motion and
present variables that describe the resonance properties of flapping systems:
$N$, a measure of the relative influence of inertia and aerodynamics, and
$\hat{K}$, the reduced stiffness. We show that internal damping scales with
$N$, revealing that dynamic efficiency monotonically decreases with increasing
$N$. Based on these results, we introduce a general framework for understanding
the roles of internal damping, aerodynamic and inertial forces, and elastic
structures within all spring-wing systems. | 2012.05428v1 |
2021-01-22 | Measurements and analysis of response function of cold atoms in optical molasses | We report our experimental measurements and theoretical analysis of the
position response function of a cloud of cold atoms residing in the viscous
medium of an optical molasses and confined by a magneto-optical trap (MOT). We
measure the position response function by applying a transient homogeneous
magnetic field as a perturbing force. We observe a transition from a damped
oscillatory motion to an over-damped relaxation, stemming from a competition
between the viscous drag provided by the optical molasses and the restoring
force of the MOT. Our observations are in both qualitative and quantitative
agreement with the predictions of a theoretical model based on the Langevin
equation. As a consistency check, and as a prototype for future experiments, we
also study the free diffusive spreading of the atomic cloud in our optical
molasses with the confining magnetic field of the MOT turned off. We find that
the measured value of the diffusion coefficient agrees with the value predicted
by our Langevin model, using the damping coefficient. The damping coefficient
was deduced from our measurements of the position response function at the same
temperature. | 2101.09118v2 |
2021-03-11 | Nontrivial damping of quantum many-body dynamics | Understanding how the dynamics of a given quantum system with many degrees of
freedom is altered by the presence of a generic perturbation is a notoriously
difficult question. Recent works predict that, in the overwhelming majority of
cases, the unperturbed dynamics is just damped by a simple function, e.g.,
exponentially as expected from Fermi's golden rule. While these predictions
rely on random-matrix arguments and typicality, they can only be verified for a
specific physical situation by comparing to the actual solution or measurement.
Crucially, it also remains unclear how frequent and under which conditions
counterexamples to the typical behavior occur. In this work, we discuss this
question from the perspective of projection-operator techniques, where
exponential damping of a density matrix occurs in the interaction picture but
not necessarily in the Schr\"odinger picture. We show that a nontrivial damping
in the Schr\"odinger picture can emerge if the dynamics in the unperturbed
system possesses rich features, for instance due to the presence of strong
interactions. This suggestion has consequences for the time dependence of
correlation functions. We substantiate our theoretical arguments by large-scale
numerical simulations of charge transport in the extended Fermi-Hubbard chain,
where the nearest-neighbor interactions are treated as a perturbation to the
integrable reference system. | 2103.06646v2 |
2021-03-24 | Multimode piezoelectric shunt damping of thin plates with arrays of separately shunted patches, method, and experimental validation | Two-dimensional thin plates are widely used in many applications. Shunt
damping is a promising way for the attenuation of vibration of these
electromechanical systems. It enables a compact vibration damping method
without adding significant mass and volumetric occupancy. Analyzing the
dynamics of such electromechanical systems requires precise modeling tools that
properly consider the coupling between the piezoelectric elements and the host
structure. Although the concept of shunt damping has been studied extensively
in the literature, most of the studies do not provide a formulation for
modeling the multiple piezoelectric patches that are scattered on the host
structure and shunted separately. This paper presents a methodology and a
formulation for separately shunted piezoelectric patches for achieving higher
performance on vibration attenuation. The Rayleigh-Ritz method is used for
performing modal analysis and obtaining the frequency response functions of the
electro-mechanical system. The developed model includes mass and stiffness
contribution of the piezoelectric patches as well as the electromechanical
coupling effect. In this study, the piezoelectric patches are shunted via
separate electrical circuits and compared with the ones those are shunted via
interconnected electrical circuits. For verification, system-level finite
element simulations are performed in ANSYS software and compared with the
analytical model results. An experimental setup is also built to validate the
performance of the separately shunted piezoelectric patches. The effectiveness
of the method is investigated for a broader range of frequencies and it was
shown that separately shunted piezoelectric patches are more effective compared
to connected for a wide range of frequencies. | 2103.13179v1 |
2021-03-29 | Nonequilibrium Dynamics of the Chiral Quark Condensate under a Strong Magnetic Field | Strong magnetic fields impact quantum-chromodynamics (QCD) properties in
several situations; examples include the early universe, magnetars, and
heavy-ion collisions. These examples share a common trait: time evolution. A
prominent QCD property impacted by a strong magnetic field is the quark
condensate, an approximate order parameter of the QCD transition between a
high-temperature quark-gluon phase and a low-temperature hadronic phase. We use
the linear sigma model with quarks to address the quark condensate time
evolution under a strong magnetic field. We use the closed time path formalism
of nonequilibrium quantum field theory to integrate out the quarks and obtain a
mean-field Langevin equation for the condensate. The Langevin equation features
dissipation and noise kernels controlled by a damping coefficient. We compute
the damping coefficient for magnetic field and temperature values achieved in
peripheral relativistic heavy-ion collisions and solve the Langevin equation
for a temperature quench scenario. The magnetic field changes the dissipation
and noise pattern by increasing the damping coefficient compared to the
zero-field case. An increased damping coefficient increases fluctuations and
time scales controlling condensate's short-time evolution, a feature that can
impact hadron formation at the QCD transition. The formalism developed here can
be extended to include other order parameters, hydrodynamic modes, and system's
expansion to address magnetic field effects in complex settings as heavy-ion
collisions, the early universe, and magnetars. | 2103.15665v1 |
2021-04-09 | Taming the pinch singularities in the two-loop neutrino self-energy in a medium | We consider the calculation of the thermal self-energy of a neutrino that
propagates in a medium composed of fermions and scalars interacting via a
Yukawa-type coupling, in the case that the neutri no energy is much larger than
the fermion and scalar masses, as well as the temperature and chemical
potentials of the background. In this kinematic regime the one-loop
contribution to the imaginary part of the self-energy is negligible. We
consider the two-loop contribution and we encounter the so-called pinch
singularities which are known to arise in higher loop self-energy calculations
in Thermal Field Theory. With a judicious use of the properties and
parametrizations of the thermal propagators the singularities are treated
effectively and actually disappear. From the imaginary part of the self-energy,
we obtain a precise formula for the damping matrix expressed in terms of
integrals over the background particle distributions. The formulas predict a
specific dependence of the damping terms on the neutrino energy, depending on
the background conditions. For guidance to estimating the effects in specific
contexts, we compute the damping terms for several limiting cases of the
momentum distribution functions of the background particles. We discuss briefly
the connection between the results of our calculations for the damping matrix
and the decoherence effects described in terms of the Lindblad equation. | 2104.04459v2 |
2021-06-20 | Life-cycle assessment for flutter probability of a long-span suspension bridge based on field monitoring data | Assessment of structural safety status is of paramount importance for
existing bridges, where accurate evaluation of flutter probability is essential
for long-span bridges. In current engineering practice, at the design stage,
flutter critical wind speed is usually estimated by the wind tunnel test, which
is sensitive to modal frequencies and damping ratios. After construction,
structural properties of existing structures will change with time due to
various factors, such as structural deteriorations and periodic environments.
The structural dynamic properties, such as modal frequencies and damping
ratios, cannot be considered as the same values as the initial ones, and the
deteriorations should be included when estimating the life-cycle flutter
probability. This paper proposes an evaluation framework to assess the
life-cycle flutter probability of long-span bridges considering the
deteriorations of structural properties, based on field monitoring data. The
Bayesian approach is employed for modal identification of a suspension bridge
with the main span of 1650 m, and the field monitoring data during 2010-2015 is
analyzed to determine the deterioration functions of modal frequencies and
damping ratios, as well as their inter-seasonal fluctuations. According to the
historical trend, the long-term structural properties can be predicted, and the
probability distributions of flutter critical wind speed for each year in the
long term are calculated. Consequently, the life-cycle flutter probability is
estimated, based on the predicted modal frequencies and damping ratios. | 2106.10694v1 |
2021-07-17 | Theoretical and numerical study of vibrational resonance in a damped softening Duffing oscillator | We study the possibility of occurrence of vibrational resonance in a
softening Duffing oscillator in the underdamped and overdamped cases both
theoretically as well as numerically. The oscillator is driven by two periodic
forces. Numerically we find that in the underdamped case two oscillatory
solutions are obtained in a limited range of the parameters considered (damping
coefficient and amplitude of the high frequency force) for a fixed frequency
and amplitude of the low frequency periodic force depending on the initial
conditions. These solutions have distinct response amplitude to the low
frequency force. When damping is gradually increased, only one oscillatory
solution is observed. Vibrational resonance is observed in both the regions of
oscillation. The analytical approximation yields only one oscillatory solution
for all damping values. Analytically, the peak in the area bounded by the phase
portrait as a function of the amplitude of the high frequency force is
connected to vibrational resonance. Also, the values of the frequency of the
low frequency forcing and the amplitude of the high frequency forcing at which
vibrational resonance is found to occur are obtained. In the overdamped case,
vibrational resonance is not observed for the softening Duffing oscillator thus
showing a marked contrast to the overdamped bistable oscillator | 2107.08302v1 |
2021-07-28 | Optimal gamma-ray selections for monochromatic line searches with DAMPE | The DArk Matter Particle Explorer (DAMPE) is a space high-energy cosmic-ray
detector covering a wide energy band with a high energy resolution. One of the
key scientific goals of DAMPE is to carry out indirect detection of dark matter
by searching for high-energy gamma-ray line structure. To promote the
sensitivity of gamma-ray line search with DAMPE, it is crucial to improve the
acceptance and energy resolution of gamma-ray photons. In this paper, we
quantitatively prove that the photon sample with the largest ratio of
acceptance to energy resolution is optimal for line search. We therefore
develop a line-search sample specifically optimized for the line search.
Meanwhile, in order to increase the statistics, we also selected the so called
BGO-only photons that convert into $e^+e^-$ pairs only in the BGO calorimeter.
The standard, the line-search, and the BGO-only photon samples are then tested
for line search individually and collectively. The results show that a
significantly improved limit could be obtained from an appropriate combination
of the date sets, and the increase is about 20\% for the highest case compared
with using the standard sample only. | 2107.13208v2 |
2021-07-28 | Magnetic field induced asymmetric splitting of the output signal | In this paper we have investigated the dynamics of a damped harmonic
oscillator in the presence of an electromagnetic field. The transients for the
two dimensional harmonic oscillator imply about the modulation of the frequency
of the oscillator by the velocity dependent non conservative force from an
applied magnetic field. Except a special condition, the motion is in general
quasi periodic nature even in the absence of damping. Another interesting
finding is that the magnetic field may induce an asymmetric splitting of the
spectrum of the output signal with two peaks in the case of a driven damped two
dimensional harmonic oscillator. One more additional peak may appear for the
three dimensional case. In some cases the spectrum may have similarity with the
Normal Zeeman Effect. At the same time one may observe to appear the anti
resonance phenomenon even for the driven damped cyclotron motion where the
system with the purely non conservative force fields is driven by an electric
field. Finally, our calculation exhibits how the magnetic field can modulate
the phase difference (between input and output signals) and the efficiency like
quantity of the energy storing process. Thus the present study might be
applicable in the areas related to the refractive index, the barrier crossing
dynamics and autonomous stochastic resonance, respectively. | 2107.13305v1 |
2021-07-31 | Oscillating scalar dissipating in a medium | We study how oscillations of a scalar field condensate are damped due to
dissipative effects in a thermal medium. Our starting point is a non-linear and
non-local condensate equation of motion descending from a 2PI-resummed
effective action derived in the Schwinger-Keldysh formalism appropriate for
non-equilibrium quantum field theory. We solve this non-local equation by means
of multiple-scale perturbation theory appropriate for time-dependent systems,
obtaining approximate analytic solutions valid for very long times. The
non-linear effects lead to power-law damping of oscillations, that at late
times transition to exponentially damped ones characteristic for linear
systems. These solutions describe the evolution very well, as we demonstrate
numerically in a number of examples. We then approximate the non-local equation
of motion by a Markovianised one, resolving the ambiguities appearing in the
process, and solve it utilizing the same methods to find the very same leading
approximate solution. This comparison justifies the use of Markovian equations
at leading order. The standard time-dependent perturbation theory in comparison
is not capable of describing the non-linear condensate evolution beyond the
early time regime of negligible damping. The macroscopic evolution of the
condensate is interpreted in terms of microphysical particle processes. Our
results have implications for the quantitative description of the decay of
cosmological scalar fields in the early Universe, and may also be applied to
other physical systems. | 2108.00254v1 |
2021-08-02 | Large-amplitude longitudinal oscillations in solar prominences simulated with different resolutions | Large-amplitude longitudinal oscillations (LALOs) in solar prominences have
been widely studied in the last decades. However, their damping and
amplification mechanisms are not well understood. In this study, we investigate
the attenuation and amplification of LALOs using high-resolution numerical
simulations with progressively increasing spatial resolutions. We performed
time-dependent numerical simulations of LALOs using the 2D magnetic
configuration that contains a dipped region. After the prominence mass loading
in the magnetic dips, we triggered LALOs by perturbing the prominence mass
along the magnetic field. We performed the experiments with four values of
spatial resolution. In the simulations with the highest resolution, the period
shows a good agreement with the pendulum model. The convergence experiment
revealed that the damping time saturates at the bottom prominence region with
improving the resolution, indicating the existence of a physical reason for the
damping of oscillations. At the prominence top, the oscillations are amplified
during the first minutes and then are slowly attenuated. The characteristic
time suggests more significant amplification in the experiments with the
highest spatial resolution. The analysis revealed that the energy exchange
between the bottom and top prominence regions is responsible for the
attenuation and amplification of LALOs. The high-resolution experiments are
crucial for the study of the periods and the damping mechanism of LALOs. The
period agrees with the pendulum model only when using high enough spatial
resolution. The results suggest that numerical diffusion in simulations with
insufficient spatial resolution can hide important physical mechanisms, such as
amplification of oscillations. | 2108.01143v1 |
2021-08-05 | Complexity analysis of quantum teleportation via different entangled channels in the presence of noise | Quantum communication is one of the hot topics in quantum computing, where
teleportation of a quantum state has a slight edge and gained significant
attention from researchers. A large number of teleportation schemes have
already been introduced so far. Here, we compare the teleportation of a single
qubit message among different entangled channels such as the two-qubit Bell
channel, three-qubit GHZ channel, two- and three-qubit cluster states, the
highly entangled five-qubit Brown \emph{et al.} state and the six-qubit Borras
\emph{et al.} state. We calculate and compare the quantum costs in each of the
cases. Furthermore, we study the effects of six noise models, namely bit-flip
noise, phase-flip noise, bit-phase flip noise, amplitude damping, phase damping
and the depolarizing error that may affect the communication channel used for
the teleportation. An investigation on the variation of the initial state's
fidelity with respect to the teleported state in the presence of the noise
model is performed. A visual representation of the variation of fidelity for
various values of the noise parameter $\eta$ is done through a graph plot. It
is observed that as the value of noise parameter in the range $\eta \in
[0,0.5]$, the fidelity decreases in all the entangled channels under all the
noise models. After that, in the Bell channel, GHZ channel and three-qubit
cluster state channel, the fidelity shows an upward trend under all the noise
models. However, in the other three channels, the fidelity substantially
decreases in the case of amplitude damping, phase damping and depolarizing
noise, and even it reaches zero for $\eta = 1$ in Brown \emph{et al.} and
Borras \emph{et al.} channels. | 2108.02641v1 |
2021-08-06 | Noncontact friction: Role of phonon damping and its nonuniversality | While obtaining theoretical predictions for dissipation during sliding motion
is a difficult task, one regime that allows for analytical results is the
so-called noncontact regime, where a probe is weakly interacting with the
surface over which it moves. Studying this regime for a model crystal, we
extend previously obtained analytical results and confirm them quantitatively
via particle based computer simulations. Accessing the subtle regime of weak
coupling in simulations is possible via use of Green-Kubo relations. The
analysis allows to extract and compare the two paradigmatic mechanisms that
have been found to lead to dissipation: phonon radiation, prevailing even in a
purely elastic solid, and phonon damping, e.g., caused by viscous motion of
crystal atoms. While phonon radiation is dominant at large probe-surface
distances, phonon damping dominates at small distances. Phonon radiation is
furthermore a pairwise additive phenomenon so that the dissipation due to
interaction with different parts (areas) of the surface adds up. This additive
scaling results from a general one-to-one mapping between the mean
probe-surface force and the friction due to phonon radiation, irrespective of
the nature of the underlying pair interaction. In contrast, phonon damping is
strongly nonadditive, and no such general relation exists. We show that for
certain cases, the dissipation can even {\it decrease} with increasing surface
area the probe interacts with. The above properties, which are rooted in the
spatial correlations of surface fluctuations, are expected to have important
consequences when interpreting experimental measurements, as well as scaling
with system size. | 2108.03025v3 |
2021-09-14 | Design of a HOM-Damped 166.6 MHz Compact Quarter-Wave beta=1 Superconducting Cavity for High Energy Photon Source | Superconducting cavities with low RF frequencies and heavy damping of higher
order modes (HOM) are desired for the main accelerator of High Energy Photon
Source (HEPS), a 6 GeV synchrotron light source promising ultralow emittance
currently under construction in Beijing. A compact 166.6 MHz superconducting
cavity was proposed adopting a quarter-wave beta=1 geometry. Based on the
successful development of a proof-of-principle cavity, a HOM-damped 166.6 MHz
compact superconducting cavity was subsequently designed. A ferrite damper was
installed on the beam pipe to reduce HOM impedance below the stringent
threshold of coupled-bunch instabilities. Being compact, RF field heating on
the cavity vacuum seal was carefully examined against quenching the NbTi
flange. The cavity was later dressed with a helium vessel and the tuning
mechanism was also realized. Excellent RF and mechanical properties were
eventually achieved. Finally, the two-cavity string was designed to ensure
smooth transitions among components and proper shielding of synchrotron light.
This paper presents a complete design of a fully dressed HOM-damped
low-frequency beta=1 superconducting cavity for HEPS. | 2109.06560v1 |
2021-11-13 | Effects of microplastics and surfactants on surface roughness of water waves | In this paper, we study the flow physics underlying the recently developed
remote sensing capability of detecting oceanic microplastics, which is based on
the measurable surface roughness reduction induced by the presence of
microplastics on the ocean surface. In particular, we are interested in whether
this roughness reduction is caused by the microplastics as floating particles,
or by the surfactants which follow similar transport paths as microplastics.
For this purpose, we experimentally test the effects of floating particles and
surfactants on surface roughness, quantified by the mean square slope (MSS),
with waves generated by a mechanical wave maker or by wind. For microplastics,
we find that their effect on wave energy and MSS critically depends on the
surface area fraction of coverage, irrespective of the particle sizes in the
test range. The damping by particles is observed only for fractions above
$O(5-10\%)$, which is much higher than the realistic ocean condition. For
surfactants, their damping effect on mechanically generated irregular waves
generally increases with the concentration of surfactants, but no optimal
concentration corresponding to maximum damping is observed, in contrast to
previous studies based on monochromatic waves. In wind-wave experiments, the
presence of surfactants suppresses the wave generation, due to the combined
effects of reduced wind shear stress and increased wave damping. For the same
wind speed, the wind stress is identified to depend on the concentration of
surfactants with a power-law relation. The implications of these findings to
remote sensing are discussed. | 2111.07021v1 |
2021-11-17 | United Nation Security Council in Quantum World: Experimental Realization of Quantum Anonymous Veto Protocols using IBM Quantum Computer | United Nation (UN) security council has fifteen members, out of which five
permanent members of the council can use their veto power against any
unfavorable decision taken by the council. In certain situation, a member using
right to veto may prefer to remain anonymous. This need leads to the
requirement of the protocols for anonymous veto which can be viewed as a
special type of voting. Recently, a few protocols for quantum anonymous veto
have been designed which clearly show quantum advantages in ensuring anonymity
of the veto. However, none of the efficient protocols for quantum anonymous
veto have yet been experimentally realized. Here, we implement 2 of those
protocols for quantum anonymous veto using an IBM quantum computer named IBMQ
Casablanca and different quantum resources like Bell, GHZ and cluster states.
In this set of proof-of-principle experiments, it's observed that using the
present technology, a protocol for quantum anonymous veto can be realized
experimentally if the number of people who can veto remains small as in the
case of UN council. Further, it's observed that Bell state based protocol
implemented here performs better than the GHZ/cluster state based
implementation of the other protocol in an ideal scenario as well as in
presence of different types of noise (amplitude damping, phase damping,
depolarizing and bit-flip noise). In addition, it's observed that based on
diminishing impact on fidelity, different noise models studied here can be
ordered in ascending order as phase damping, amplitude damping, depolarizing,
bit-flip. | 2111.09028v1 |
2021-12-03 | The Importance of Electron Landau Damping for the Dissipation of Turbulent Energy in Terrestrial Magnetosheath Plasma | Heliospheric plasma turbulence plays a key role in transferring the energy of
large-scale magnetic field and plasma flow fluctuations to smaller scales where
the energy can be dissipated, ultimately leading to plasma heating.
High-quality measurements of electromagnetic fields and electron velocity
distributions by the Magnetospheric Multiscale (MMS) mission in Earth's
magnetosheath present a unique opportunity to characterize plasma turbulence
and to determine the mechanisms responsible for its dissipation. We apply the
field-particle correlation technique to a set of twenty MMS magnetosheath
intervals to identify the dissipation mechanism and quantify the dissipation
rate. It is found that 95% of the intervals have velocity-space signatures of
electron Landau damping that are quantitatively consistent with linear kinetic
theory for the collisionless damping of kinetic Alfv\'en waves. About 75% of
the intervals contain asymmetric signatures, indicating a local imbalance of
kinetic Alfv\'en wave energy flux in one direction along the magnetic field
than the other. About one third of the intervals have an electron energization
rate with the same order-of-magnitude as the estimated turbulent cascade rate,
suggesting that electron Landau damping plays a significant, and sometimes
dominant, role in the dissipation of the turbulent energy in these
magnetosheath intervals. | 2112.02171v1 |
2022-01-01 | Extremely strong DLAs at high redshift: Gas cooling and H$_2$ formation | We present a spectroscopic investigation with VLT/X-shooter of seven
candidate extremely strong damped Lyman-$\alpha$ absorption systems (ESDLAs,
$N(\text{HI})\ge 5\times 10^{21}$ cm$^{-2}$) observed along quasar sightlines.
We confirm the extremely high column densities, albeit slightly (0.1~dex) lower
than the original ESDLA definition for four systems. We measured low-ionisation
metal abundances and dust extinction for all systems. For two systems we also
found strong associated H$_2$ absorption $\log
N(\text{H$_2$)[cm$^{-2}$]}=18.16\pm0.03$ and $19.28\pm0.06$ at $z=3.26$ and
$2.25$ towards J2205+1021 and J2359+1354, respectively), while for the
remaining five we measured conservative upper limits on the H$_2$ column
densities of typically $\log N(\text{H$_2$)[cm$^{-2}$]}<17.3$. The increased
H$_2$ detection rate ($10-55$% at 68% confidence level) at high HI column
density compared to the overall damped Lyman-$\alpha$ population ($\sim 5-10$%)
confirms previous works. We find that these seven ESDLAs have similar observed
properties as those previously studied towards quasars and gamma-ray burst
afterglows, suggesting they probe inner regions of galaxies. We use the
abundance of ionised carbon in excited fine-structure level to calculate the
cooling rates through the CII $\lambda$158$\mu$m emission, and compare them
with the cooling rates from damped Lyman-$\alpha$ systems in the literature. We
find that the cooling rates distribution of ESDLAs also presents the same
bimodality as previously observed for the general (mostly lower HI column
density) damped Lyman-$\alpha$ population. | 2201.00245v1 |
2022-01-05 | Stability of the discrete time-crystalline order in spin-optomechanical and open cavity QED systems | Discrete time crystals (DTC) have been demonstrated experimentally in several
different quantum systems in the past few years. Spin couplings and cavity
losses have been shown to play crucial roles for realizing DTC order in open
many-body systems out of equilibrium. Recently, it has been proposed that
eternal and transient DTC can be present with an open Floquet setup in the
thermodynamic limit and in the deep quantum regime with few qubits,
respectively. In this work, we consider the effects of spin damping and spin
dephasing on the DTC order in spin-optomechanical and open cavity systems in
which the spins can be all-to-all coupled. In the thermodynamic limit, it is
shown that the existence of dephasing can destroy the coherence of the system
and finally lead the system to its trivial steady state. Without dephasing,
eternal DTC is displayed in the weak damping regime, which may be destroyed by
increasing the all-to-all spin coupling or the spin damping. By contrast, the
all-to-all coupling is constructive to the DTC in the moderate damping regime.
We also focus on a model which can be experimentally realized by a suspended
hexagonal boron nitride (hBN) membrane with a few spin color centers under
microwave drive and Floquet magnetic field. Signatures of transient DTC
behavior are demonstrated in both weak and moderate dissipation regimes without
spin dephasing. Relevant experimental parameters are also discussed for
realizing transient DTC order in such an hBN optomechanical system. | 2201.01568v2 |
2022-01-20 | Sharp resolvent estimate for the Baouendi-Grushin operator and applications | In this article we study the semiclassical resolvent estimate for the
non-selfadjoint Baouendi-Grushin operator on the two-dimensional torus
$\mathbb{T}^2=\mathbb{R}^2/(2\pi\mathbb{Z})^2$ with H\"older dampings. The
operator is subelliptic degenerating along the vertical direction at $x=0$. We
exhibit three different situations:
(i) the damping region verifies the geometric control condition with respect
to both the non-degenerate Hamiltonian flow and the vertical subelliptic flow;
(ii) the undamped region contains a horizontal strip;
(iii) the undamped part is a line. In all of these situations, we obtain
sharp resolvent estimates. Consequently, we prove the optimal energy decay rate
for the associated damped waved equations. For (i) and (iii), our results are
in sharp contrast to the Laplace resolvent since the optimal bound is governed
by the quasimodes in the subelliptic regime. While for (ii), the optimality is
governed by the quasimodes in the elliptic regime, and the optimal energy decay
rate is the same as for the classical damped wave equation on $\mathbb{T}^2$.
Our analysis contains the study of adapted two-microlocal semiclassical
measures, construction of quasimodes and refined Birkhoff normal-form
reductions in different regions of the phase-space. Of independent interest, we
also obtain the propagation theorem for semiclassical measures of quasimodes
microlocalized in the subelliptic regime. | 2201.08189v2 |
2022-02-24 | Coherence of ion cyclotron resonance for damping ion cyclotron waves in space plasmas | Ion cyclotron resonance is one of the fundamental energy conversion processes
through field-particle interaction in collisionless plasmas. However, the key
evidence for ion cyclotron resonance (i.e., the coherence between
electromagnetic fields and the ion phase space density) and the resulting
damping of ion cyclotron waves (ICWs) has not yet been directly observed.
Investigating the high-quality measurements of space plasmas by the
Magnetospheric Multiscale (MMS) satellites, we find that both the wave
electromagnetic field vectors and the bulk velocity of the disturbed ion
velocity distribution rotate around the background magnetic field. Moreover, we
find that the absolute gyro-phase angle difference between the center of the
fluctuations in the ion velocity distribution functions and the wave electric
field vectors falls in the range of (0, 90) degrees, consistent with the
ongoing energy conversion from wave-fields to particles. By invoking plasma
kinetic theory, we demonstrate that the field-particle correlation for the
damping ion cyclotron waves in our theoretical model matches well with our
observations. Furthermore, the wave electric field vectors ($\delta
\mathbf{E'}_{\mathrm {wave,\perp}}$), the ion current density ($\delta
\mathbf{J}_\mathrm {i,\perp}$) and the energy transfer rate ($\delta
\mathbf{J}_\mathrm {i,\perp}\cdot \delta \mathbf{E'}_{\mathrm {wave,\perp}}$)
exhibit quasi-periodic oscillations, and the integrated work done by the
electromagnetic field on the ions are positive, indicates that ions are mainly
energized by the perpendicular component of the electric field via cyclotron
resonance. Therefore, our combined analysis of MMS observations and kinetic
theory provides direct, thorough, and comprehensive evidence for ICW damping in
space plasmas. | 2202.11967v1 |
2022-03-15 | Search for gamma-ray line signals around the black hole at the galactic center with DAMPE observation | The adiabatic growth of a black hole (BH) may enhance the dark matter (DM)
density surrounding it, causing a spike in the DM density profile. The spike
around the supermassive BH at the center of the Milky Way may lead to a
dramatic enhancement of the gamma-ray flux of DM annihilation from the galactic
center (GC). In this work, we analyze the gamma-ray data of the innermost
region (i.e., the inner 1$^\circ$) of the GC to search for potential line-like
signals from the BH spike. Such line-like signals could be generated in the
process of DM particles annihilating into double photons. We adopt the
gamma-ray data from the Dark Matter Particle Explorer (DAMPE). Although the
DAMPE has a much smaller effective area than the Fermi-LAT, the gamma-ray line
search can benefit from its unprecedented high energy resolution. No
significant line-like signals are found in our analysis. We derive upper limits
on the cross section of the annihilation based on this non-detection. We find
that despite the DAMPE's small effective area for photon detection, we can
still place strong constraints on the cross section ($\left<\sigma
v\right>\lesssim10^{-27}\,{\rm cm^3\,s^{-1}}$) in the spike scenario due to the
very bright model-expected flux from the spike. Our results indicate that
either DM does not annihilate primarily through the $\gamma\gamma$ channel in
the mass range we considered or no sharp density spike is present at the GC. | 2203.08078v1 |
2022-03-15 | Optimal Damping with Hierarchical Adaptive Quadrature for Efficient Fourier Pricing of Multi-Asset Options in Lévy Models | Efficiently pricing multi-asset options is a challenging problem in
quantitative finance. When the characteristic function is available,
Fourier-based methods are competitive compared to alternative techniques
because the integrand in the frequency space often has a higher regularity than
that in the physical space. However, when designing a numerical quadrature
method for most Fourier pricing approaches, two key aspects affecting the
numerical complexity should be carefully considered: (i) the choice of damping
parameters that ensure integrability and control the regularity class of the
integrand and (ii) the effective treatment of high dimensionality. We propose
an efficient numerical method for pricing European multi-asset options based on
two complementary ideas to address these challenges. First, we smooth the
Fourier integrand via an optimized choice of the damping parameters based on a
proposed optimization rule. Second, we employ sparsification and
dimension-adaptivity techniques to accelerate the convergence of the quadrature
in high dimensions. The extensive numerical study on basket and rainbow options
under the multivariate geometric Brownian motion and some L\'evy models
demonstrates the advantages of adaptivity and the damping rule on the numerical
complexity of quadrature methods. Moreover, for the tested two-asset examples,
the proposed approach outperforms the COS method in terms of computational
time. Finally, we show significant speed-up compared to the Monte Carlo method
for up to six dimensions. | 2203.08196v4 |
2022-03-25 | Nonlinear damped spatially periodic breathers and the emergence of soliton-like rogue waves | The spatially periodic breather solutions (SPBs) of the nonlinear
Schr\"odinger equation, prominent in modeling rogue waves, are unstable. In
this paper we numerically investigate the effects of nonlinear dissipation and
higher order nonlinearities on the routes to stability of the SPBs in the
framework of the nonlinear damped higher order nonlinear Schr\"odinger
(NLD-HONLS) equation. The initial data used in the experiments are generated by
evaluating exact SPB solutions at time $T_0$. The number of instabilities of
the background Stokes wave and the damping strength are varied. The Floquet
spectral theory of the NLS equation is used to interpret and provide a
characterization of the perturbed dynamics in terms of nearby solutions of the
NLS equation. Significantly, as $T_0$ is varied, tiny bands of complex spectrum
are observed to pinch off in the Floquet decomposition of the NLD-HONLS data,
reflecting the breakup of the SPB into a waveform that is close to either a one
or two "soliton-like" structure. For wide ranges of $T_0$, i.e. for solutions
initialized in the early to middle stage of the development of the MI, all
rogue waves are observed to occur when the spectrum is close to a one or two
soliton-like state. When the solutions are initialized as the MI is saturating,
rogue waves also can occur after the spectrum has left a soliton-like state.
Other novel features arise due to nonlinear damping: enhanced asymmetry, two
timescales in the evolution of the spectrum and a delay in the growth of
instabilities due to frequency downshifting. | 2203.13488v2 |
2022-03-25 | Investigating the effect of noise channels on the quality of unitary t-designs | Unitary t-designs have a wide variety of applications in quantum information
theory, such as quantum data encryption and randomised benchmarking. However,
experimental realisations of t-designs are subject to noise. Here we
investigate the effect of noise channels on the quality of single-qubit
t-designs. The noise channels we study are bit flips, phase flips, bit and
phase flips, phase damping, amplitude damping, and depolarising noise. We
consider two noise models: the first has noise applied before the t-design
unitary operations, while the second has noise applied after the unitary
operations. We show that the single-qubit 1-design is affected only by
amplitude damping, while numeric results obtained for the 2-, 3-, 4-, and
5-designs suggest that a 2t-design is significantly more sensitive to noise
than a (2t-1)-design and that, with the exception of amplitude damping, a
(2t+1)-design is as sensitive to noise as a 2t-design. Numeric results also
reveal substantial variations in sensitivity to noise throughout the Bloch
sphere. In particular, t-designs appear to be most sensitive to noise when
acting on pure states and least sensitive to noise for the maximally mixed
state. For depolarising noise, we show that our two noise models are
equivalent, and for the other noise channels, numeric results obtained for the
model where noise is applied after the unitaries reflect the transformation of
the noise channel into a depolarising channel, an effect exploited in
randomised benchmarking with 2-designs. | 2203.13771v2 |
2022-04-25 | Geometrical aspects of contact mechanical systems and field theories | Many important theories in modern physics can be stated using differential
geometry. Symplectic geometry is the natural framework to deal with autonomous
Hamiltonian mechanics. This admits several generalizations for nonautonomous
systems, both regular and singular. Some of these extensions are the subject of
this thesis.
Recently there has been a growing interest in studying dissipative mechanical
systems from a geometric perspective using contact geometry. In this thesis we
review what has been done in this topic and go deeper, studying symmetries and
dissipated quantities of contact systems, and developing the Skinner-Rusk
formalism for these systems.
With regard to classical field theory, we introduce the notion of
k-precosymplectic manifold and use it to give a geometric description of
singular nonautonomous field theories. We also devise a constraint algorithm
for these systems.
Field theories with damping are described through a modification of the De
Donder-Weyl Hamiltonian field theory. This is achieved by combining contact
geometry and k-symplectic structures, resulting in the k-contact formalism. We
introduce two notions of dissipation laws, generalizing the concept of
dissipated quantity. These developments are also applied to Lagrangian field
theory. The Skinner-Rusk formulation for k-contact systems is described in
detail and we show how to recover the Lagrangian and Hamiltonian formalisms
from it.
Throughout the thesis we present several examples in mechanics and field
theory. The most remarkable mechanical examples are the damped harmonic
oscillator, the motion in a gravitational field with friction, the parachute
equation and the damped simple pendulum. In field theory, we study the damped
vibrating string, the Burgers' equation, the Klein-Gordon equation and its
relation with the telegrapher's equation, and the Maxwell's equations with
dissipation. | 2204.11537v1 |
2022-06-20 | Swinging a playground swing: torque controls for inducing sustained oscillations | Models of a playground swing have been studied since the 1960s. However, in
most of them, the position of the swinger is controlled directly. This
simplifies the problem but hides the mechanics of torques applied to keep the
swing moving in a regular pattern. This article studies these mechanics. Two
models of a swing with torques as controls that we consider are identical to
popular models of modern robotics: the Acrobot and reaction wheel pendulum.
However, the control task of sustaining the swing's regular oscillations by a
static feedback control is new and challenging, especially when damping in the
joint connecting the swing to the frame is considered. We develop two types of
controls to accomplish this task. One works for small damping and is based on
linearizing the undamped system by a suitable preliminary feedback control. The
other works for large damping. In the steady state, the resulting closed-loop
system describes a harmonically driven damped pendulum (a simple system known
for its complex behavior), including chaotic motion for some parameter values.
To address such complexities, we build free parameters into the controls, then
adjust them based on simulations to avoid chaos and achieve regular
oscillations that are seen on playgrounds. | 2206.09579v1 |
2022-07-01 | Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate | We study the breathing (monopole) oscillations and their damping in a
harmonically trapped one-dimensional (1D) Bose gas in the quasicondensate
regime using a finite-temperature classical field approach. By characterising
the oscillations via the dynamics of the density profile's rms width over long
time, we find that the rms width displays beating of two distinct frequencies.
This means that 1D Bose gas oscillates not at a single breathing mode
frequency, as found in previous studies, but as a superposition of two distinct
breathing modes, one oscillating at frequency close to $\simeq\!\sqrt{3}\omega$
and the other at $\simeq\!2\omega$, where $\omega$ is the trap frequency. The
breathing mode at $\sim\!\sqrt{3}\omega$ dominates the beating at lower
temperatures, deep in the quasicondensate regime, and can be attributed to the
oscillations of the bulk of the density distribution comprised of particles
populating low-energy, highly-occupied states. The breathing mode at
$\simeq\!2\omega$, on the other hand, dominates the beating at higher
temperatures, close to the nearly ideal, degenerate Bose gas regime, and is
attributed to the oscillations of the tails of the density distribution
comprised of thermal particles in higher energy states. The two breathing modes
have distinct damping rates, with the damping rate of the bulk component being
approximately four times larger than that of the tails component. | 2207.00209v2 |
2022-07-29 | Coordinated control in multi-terminal VSC-HVDC systems to improve transient stability: Impact on electromechanical-oscillation damping | Multi-terminal high-voltage Direct Current technology based on Voltage-Source
Converter stations (VSC-MTDC) is expected to be one of the most important
contributors to the future of electric power systems. In fact, among other
features, it has already been shown how this technology can contribute to
improve transient stability in power systems by the use of supplementary
controllers. Along this line, this paper will investigate in detail how these
supplementary controllers may affect electromechanical oscillations, by means
of small-signal stability analysis. The paper analyses two control strategies
based on the modulation of active-power injections (P-WAF) and reactive-power
injections (Q-WAF) in the VSC stations. Both control strategies use global
signals of the frequencies of the VSC-MTDC system and they presented
significant improvements on transient stability. The paper will provide
guidelines for the design of these type of controllers to improve both, large-
and small-disturbance angle stability. Small-signal stability techniques (in
Matlab) will be used to assess electromechanical-oscillation damping, while
non-linear time domain simulation (in PSS/E) will be used to confirm the
results. Results will be illustrated in Nordic32A test system with an embedded
VSC-MTDC system. The paper analyses the impact of the controller gains and
communication latency on electromechanical-oscillation damping. The main
conclusion of the paper is that transient-stability-tailored supplementary
controllers in VSC-MTDC systems can be tuned to damp inter-area oscillations
too, maintaining their effectiveness for transient-stability improvement. | 2208.00083v1 |
2022-08-04 | Thermoelastic Damping in MEMS Gyroscopes at High Frequencies | Microelectromechanical systems (MEMS) gyroscopes are widely used, e.g. in
modern automotive and consumer applications, and require signal stability and
accuracy in rather harsh environmental conditions. In many use cases, device
reliability must be guaranteed under large external loads at high frequencies.
The sensitivity of the sensor to such external loads depends strongly on the
damping, or rather quality factor, of the high frequency mechanical modes of
the structure. In this paper, we investigate the influence of thermoelastic
damping on several high frequency modes by comparing finite element simulations
with measurements of the quality factor in an application-relevant temperature
range. We measure the quality factors over different temperatures in vacuum, to
extract the relevant thermoelastic material parameters of the polycrystalline
MEMS device. Our simulation results show a good agreement with the measured
quantities, therefore proving the applicability of our method for predictive
purposes in the MEMS design process. Overall, we are able to uniquely identify
the thermoelastic effects and show their significance for the damping of the
high frequency modes of an industrial MEMS gyroscope. Our approach is generic
and therefore easily applicable to any mechanical structure with many possible
applications in nano- and micromechanical systems. | 2208.02591v2 |
2022-08-02 | Motion of a parametrically driven damped coplanar double pendulum | We present the results of linear stability of a damped coplanar double
pendulum and its non-linear motion, when the point of suspension is vibrated
sinusoidally in the vertical direction with amplitude $a$ and frequency $\omega
$. A double pendulum has two pairs of Floquet multipliers, which have been
calculated for various driving parameters. We have considered the stability of
a double pendulum when it is in any of its possible stationary states: (i) both
pendulums are either vertically downward or upward and (ii) one pendulum is
downward, and the other is upward. The damping is considered to be
velocity-dependent, and the driving frequency is taken in a wide range. A
double pendulum excited from its stable state shows both periodic and chaotic
motion. The periodic motion about its pivot may be either oscillatory or
rotational. The periodic swings of a driven double pendulum may be either
harmonic or subharmonic for lower values of $a$. The limit cycles corresponding
to the normal mode oscillations of a double pendulum of two equal masses are
squeezed into a line in its configuration space. For unequal masses, the
pendulum shows multi-period swings for smaller values of $a$ and damping, while
chaotic swings or rotational motion at relatively higher values of $a$. The
parametric driving may lead to stabilization of a partially or fully inverted
double pendulum. | 2208.03292v2 |
2022-08-09 | Simultaneous measurements of unstable and stable Alfvén Eigenmodes in JET | In this paper, we report the novel experimental observation of both unstable
and stable Toroidicity-induced Alfv\'en Eigenmodes (TAEs) measured
simultaneously in a JET tokamak plasma. The three-ion-heating scheme
(D-DNBI-3He) is employed to accelerate deuterons to MeV energies, thereby
destabilizing TAEs with toroidal mode numbers n = 3-5, each decreasing in mode
amplitude. At the same time, the Alfv\'en Eigenmode Active Diagnostic
resonantly excites a stable n = 6 TAE with total normalized damping rate
$-\gamma/\omega_0 \approx$ 1%-4%. Hybrid kinetic-MHD modeling with codes NOVA-K
and MEGA both find eigenmodes with similar frequencies, mode structures, and
radial locations as in experiment. NOVA-K demonstrates good agreement with the
n = 3, 4, and 6 TAEs, matching the damping rate of the n = 6 mode within
uncertainties and identifying radiative damping as the dominant contribution.
Improved agreement is found with MEGA for all modes: the unstable n = 3-5 and
stable n = 2, 6 modes, with the latter two stabilized by higher intrinsic
damping and lower fast ion drive, respectively. While some discrepancies remain
to be resolved, this unique validation effort gives us confidence in TAE
stability predictions for future fusion devices. | 2208.05052v1 |
2022-09-24 | Deep Attentive Belief Propagation: Integrating Reasoning and Learning for Solving Constraint Optimization Problems | Belief Propagation (BP) is an important message-passing algorithm for various
reasoning tasks over graphical models, including solving the Constraint
Optimization Problems (COPs). It has been shown that BP can achieve
state-of-the-art performance on various benchmarks by mixing old and new
messages before sending the new one, i.e., damping. However, existing methods
of tuning a static damping factor for BP not only are laborious but also harm
their performance. Moreover, existing BP algorithms treat each variable node's
neighbors equally when composing a new message, which also limits their
exploration ability. To address these issues, we seamlessly integrate BP, Gated
Recurrent Units (GRUs), and Graph Attention Networks (GATs) within the
message-passing framework to reason about dynamic weights and damping factors
for composing new BP messages. Our model, Deep Attentive Belief Propagation
(DABP), takes the factor graph and the BP messages in each iteration as the
input and infers the optimal weights and damping factors through GRUs and GATs,
followed by a multi-head attention layer. Furthermore, unlike existing
neural-based BP variants, we propose a novel self-supervised learning algorithm
for DABP with a smoothed solution cost, which does not require expensive
training labels and also avoids the common out-of-distribution issue through
efficient online learning. Extensive experiments show that our model
significantly outperforms state-of-the-art baselines. | 2209.12000v1 |
2022-12-01 | Slack-based tunable damping leads to a trade-off between robustness and efficiency in legged locomotion | Animals run robustly in diverse terrain. This locomotion robustness is
puzzling because axon conduction velocity is limited to a few ten meters per
second. If reflex loops deliver sensory information with significant delays,
one would expect a destabilizing effect on sensorimotor control. Hence, an
alternative explanation describes a hierarchical structure of low-level
adaptive mechanics and high-level sensorimotor control to help mitigate the
effects of transmission delays. Motivated by the concept of an adaptive
mechanism triggering an immediate response, we developed a tunable physical
damper system. Our mechanism combines a tendon with adjustable slackness
connected to a physical damper. The slack damper allows adjustment of damping
force, onset timing, effective stroke, and energy dissipation. We characterize
the slack damper mechanism mounted to a legged robot controlled in open-loop
mode. The robot hops vertically and planar over varying terrains and
perturbations. During forward hopping, slack-based damping improves faster
perturbation recovery (up to 170%) at higher energetic cost (27%). The tunable
slack mechanism auto-engages the damper during perturbations, leading to a
perturbation-trigger damping, improving robustness at minimum energetic cost.
With the results from the slack damper mechanism, we propose a new functional
interpretation of animals' redundant muscle tendons as tunable dampers. | 2212.00475v1 |
2022-12-22 | Spin wave dispersion of ultra-low damping hematite ($α\text{-Fe}_2\text{O}_3$) at GHz frequencies | Low magnetic damping and high group velocity of spin waves (SWs) or magnons
are two crucial parameters for functional magnonic devices. Magnonics research
on signal processing and wave-based computation at GHz frequencies focussed on
the artificial ferrimagnetic garnet Y$_3$Fe$_5$O$_{12}$ (YIG) so far. We report
on spin-wave spectroscopy studies performed on the natural mineral hematite
($\alpha\text{-Fe}_2\text{O}_3$) which is a canted antiferromagnet. By means of
broadband GHz spectroscopy and inelastic light scattering, we determine a
damping coefficient of $1.1\times10^{-5}$ and magnon group velocities of a few
10 km/s, respectively, at room temperature. Covering a large regime of wave
vectors up to $k\approx 24~{\rm rad}/\mu$m, we find the exchange stiffness
length to be relatively short and only about 1 \r{A}. In a small magnetic field
of 30 mT, the decay length of SWs is estimated to be 1.1 cm similar to the best
YIG. Still, inelastic light scattering provides surprisingly broad and partly
asymmetric resonance peaks. Their characteristic shape is induced by the large
group velocities, low damping and distribution of incident angles inside the
laser beam. Our results promote hematite as an alternative and sustainable
basis for magnonic devices with fast speeds and low losses based on a stable
natural mineral. | 2212.11887v2 |
2023-01-19 | Magnetoreological spring as element of vibration control system of dynamicly active equipment for biofuel production | The development of vibration protection systems that ensure efficiency and
safety in the operation of process equipment and pipelines is one of the main
tasks of controlling the dynamic state of machines. One of the effective
methods of vibration isolation of the equipment of these installations is the
use of vibration mounts. Today, both passive and active methods of
extinguishing are actively used. The combination of two methods of damping will
ensure the stability and adaptability of vibration protection systems to the
operating conditions of process equipment. The paper presents and investigates
the device of a hybrid vibration support, including a magnetorheological
spring, as an element of vibration damping. A distinctive feature of the
vibration mount is an extended range of performance and reduced wear rate of
the components. An analysis of the damping characteristics of a hybrid
vibration support in passive and active modes of operation is presented. A
simulation model of the vibration support under consideration has been
developed in the MATLAB Simulink simulation environment using the PIB
controller. The simulation results indicate the effectiveness of the use of
vibration damping systems with a magnetorheological spring in conjunction with
various technological equipment. | 2301.07911v1 |
2023-02-19 | Collective Quantum Approach to Surface Plasmon Resonance Effect | In this research we present a theory of the surface plasmon resonance (SPR)
effect based on the dual length-scale driven damped collective quantum
oscillations of the spill-out electrons in plasmonic material surface. The
metallic electron excitations are modeled using the Hermitian effective
Schr\"{o}dinger-Poisson system, whereas, the spill-out electron excitations are
modeled via the damped non-Hermitian effective Schr\"{o}dinger-Poisson system
adapted appropriately at the metal-vacuum interface. It is shows that, when
driven by external field, the system behaves like the driven damped oscillator
in wavenumber domain, quite analogous to the driven damped mechanical
oscillation in frequency domain, leading to the collective surface spill-out
electron excitation resonance. In this model the resonance occurs when the
wavenumber of the driving pseudoforce matches that of the surface plasmon
excitations which can be either due to single-electrons or collective effects.
Current theory of SPR is based on longitudinal electrostatic excitations of the
surface electrons, instead of the polariton excitation parallel to the
metal-dielectric or metal-vacuum surface. Current theory may also be extended
to use for the localized surface plasmon resonance (LSPR) in nanometer sized
metallic surfaces in non-planar geometry. A new equation of state (EoS) for the
plasmon electron number density in quantum plasmas is obtained which limits the
plasmonic effects in high-density low-temperature electron gas regime, due to
small transition probability of electrons to the plasmon energy band. | 2302.13974v1 |
2023-03-01 | Evolution of the eccentricity and inclination of low-mass planets subjected to thermal forces: a numerical study | By means of three dimensional, high resolution hydrodynamical simulations we
study the orbital evolution of weakly eccentric or inclined low-mass
protoplanets embedded in gaseous discs subject to thermal diffusion. We
consider both non-luminous planets, and planets that also experience the
radiative feedback from their own luminosity. We compare our results to
previous analytical work, and find that thermal forces (the contribution to the
disc's force arising from thermal effects) match those predicted by linear
theory within $\sim 20$%. When the planet's luminosity exceeds a threshold
found to be within $10$% of that predicted by linear theory, its eccentricity
and inclination grow exponentially, whereas these quantities undergo a strong
damping below this threshold. In this regime of low luminosity indeed, thermal
diffusion cools the surroundings of the planet and allows gas to accumulate in
its vicinity. It is the dynamics of this gas excess that contributes to damp
eccentricity and inclination. The damping rates obtained can be up to $h^{-1}$
times larger than those due to the resonant interaction with the disc, where
$h$ is the disc's aspect ratio. This suggests that models that incorporate
planet-disc interactions using well-known formulae based on resonant
wave-launching to describe the evolution of eccentricity and inclination
underestimate the damping action of the disc on the eccentricity and
inclination of low-mass planets by an order of magnitude. | 2303.00867v1 |
2023-03-13 | Discriminative sEMG-based features to assess damping ability and interpret activation patterns in lower-limb muscles of ACLR athletes | Objective: The main goal of the athletes who undergo anterior cruciate
ligament reconstruction (ACLR) surgery is a successful return-to-sport. At this
stage, identifying muscular deficits becomes important. Hence, in this study,
three discriminative features based on surface electromyographic signals (sEMG)
acquired in a dynamic protocol are introduced to assess the damping ability and
interpret activation patterns in lower-limb muscles of ACLR athletes. Methods:
The features include the median frequency of the power spectrum density (PSD),
the relative percentage of the equivalent damping or equivalent stiffness
derived from the median frequency, and the energy of the signals in the
time-frequency plane of the pseudo-Wigner-Ville distribution (PWVD). To
evaluate the features, 11 healthy and 11 ACLR athletes (6 months
post-reconstruction surgery) were recruited to acquire the sEMG signals from
the medial and the lateral parts of the hamstrings, quadriceps, and
gastrocnemius muscles in pre- and post-fatigue single-leg landings. Results: A
significant damping deficiency is observed in the hamstring muscles of ACLR
athletes by evaluating the proposed features. This deficiency indicates that
more attention should be paid to this muscle of ACLR athletes in
pre-return-to-sport rehabilitations. Conclusion: The quality of
electromyography-based pre-return-to-sport assessments on ACLR subjects depends
on the sEMG acquisition protocol, as well as the type and nature of the
extracted features. Hence, combinatorial application of both energy-based
features (derived from the PWVD) and power-based features (derived from the
PSD) could facilitate the assessment process by providing additional
biomechanical information regarding the behavior of the muscles surrounding the
knee. | 2303.06954v1 |
2023-03-28 | Search for damped oscillating structures from charged pion electromagnetic form factor data | The damped oscillating structures recently revealed by a three parametric
formula from the proton ``effective'' form factor data extracted of the
measured total cross section $\sigma^{bare}_{tot}(e^+e^-\to p\bar p)$ still
seem to have an unknown origin. The conjectures of their direct manifestation
of the quark-gluon structure of the proton indicate that they are not specific
only of the proton and neutron, but they have to be one's own, similar to other
hadrons.
Therefore, the oscillatory structures from the charged pion electromagnetic
form factor timelike data, extracted of the process $e^+e^-\to \pi^+ \pi^-$ are
investigated by using the same procedure as in the case of the proton.
The analysis shows the appearance of the oscillating structures in the
description of the charged pion electromagnetic form factor timelike data by
three parametric formula with a rather large value of $\chi^2/ndf$, while the
description of the data by the physically well-founded Unitary and Analytic
model has not revealed any damped oscillating structures.
From the obtained result on the most simple object of strong interactions,
one can conclude that damped oscillating structures received from the
``effective'' proton form factor data are probably generated by a utilization
of the improper three parametric formula which does not describe these data
with sufficient precision. | 2303.16681v1 |
2023-05-15 | Landau damping and the survival threshold | In this paper, we establish the large time asymptotic behavior of solutions
to the linearized Vlasov-Poisson system near general spatially homogenous
equilibria $\mu(\frac12|v|^2)$ with connected support on the whole space
$\RR^3_x \times \RR^3_v$, including those that are non-monotone. The problem
can be solved completely mode by mode for each spatial wave number, and their
longtime dynamics is intimately tied to the ``survival threshold'' of wave
numbers computed by $$\kappa_0^2 = 4\pi \int_0^\Upsilon \frac{u^2\mu(\frac12
u^2)}{\Upsilon^2-u^2} \;du$$ where $\Upsilon$ is the maximal speed of particle
velocities. It is shown that purely oscillatory electric fields exist and obey
a Klein-Gordon's type dispersion relation for wave numbers below the threshold,
thus confirming the existence of Langmuir's oscillatory waves known in the
physical literature. At the threshold, the phase velocity of these oscillatory
waves enters the range of admissible particle velocities, namely there are
particles that move at the same propagation speed of the waves. It is this
exact resonant interaction between particles and the oscillatory fields that
causes the waves to be damped, classically known as Landau damping. Landau's
law of decay is explicitly computed and is sensitive to the decaying rate of
the background equilibria. The faster it decays at the maximal velocity, the
weaker Landau damping is. Beyond the threshold, the electric fields are a
perturbation of those generated by the free transport dynamics and thus decay
rapidly fast due to the phase mixing mechanism. | 2305.08672v1 |
2023-06-04 | Large Dynamical Tide Amplitudes from Small Kicks at Pericenter | The effect of dynamical tide ``kicks" on eccentric binary orbits is
considered using the orbital mapping method. It is demonstrated that when mode
damping is negligible the mode amplitude will generically grow in time for all
values of orbital eccentricity and semi-major axis, even for small kicks
outside the regime exhibiting diffusive growth. The origin of the small-kick
growth is the change in kick size from orbit to orbit, an effect quadratic in
the mode amplitude. When damping of the mode is included, the growth is shut
off when the damping time is shorter than the growth time. Hence, in practice,
kicks of sufficient size and long mode damping times are required for
interesting levels of growth to occur. Application to the circularization of
hot Jupiters is discussed. Previous investigations found that diffusive growth
of the planetary f-mode in the large-kick regime would lead to rapid orbital
shrinkage, but upon exiting the diffusive regime at $e \sim 0.9$ the theory
would predict a large population of highly eccentric orbits. Simulations
presented here show that subsequent orbital evolution relying on the small-kick
regime may further decrease the eccentricity to $e \sim 0.2$ on timescales much
less than the Gyrs ages of these systems. | 2306.02382v1 |
2023-06-16 | Damping of MHD Turbulence in A Partially Ionized Medium | The coupling state between ions and neutrals in the interstellar medium plays
a key role in the dynamics of magnetohydrodynamic (MHD) turbulence, but is
challenging to study numerically. In this work, we investigate the damping of
MHD turbulence in a partially ionized medium using 3D two-fluid (ions+neutrals)
simulations generated with the AthenaK code. Specifically, we examine the
velocity, density, and magnetic field statistics of the two-fluid MHD
turbulence in different regimes of neutral-ion coupling. Our results
demonstrate that when ions and neutrals are strongly coupled, the velocity
statistics resemble those of single-fluid MHD turbulence. Both the velocity
structures and kinetic energy spectra of ions and neutrals are similar, while
their density structures can be significantly different. With an excess of
small-scale sharp density fluctuations in ions, the density spectrum in ions is
shallower than that of neutrals. When ions and neutrals are weakly coupled, the
turbulence in ions is more severely damped due to the ion-neutral collisional
friction than that in neutrals, resulting in a steep kinetic energy spectrum
and density spectrum in ions compared to the Kolmogorov spectrum. We also find
that the magnetic energy spectrum basically follows the shape of the kinetic
energy spectrum of ions, irrespective of the coupling regime. In addition, we
find large density fluctuations in ions and neutrals and thus spatially
inhomogeneous ionization fractions. As a result, the neutral-ion decoupling and
damping of MHD turbulence take place over a range of length scales. | 2306.10010v2 |
2023-07-24 | BGO quenching effect on spectral measurements of cosmic-ray nuclei in DAMPE experiment | The Dark Matter Particle Explorer (DAMPE) is a satellite-borne detector
designed to measure high energy cosmic-rays and $\gamma$-rays. As a key
sub-detector of DAMPE, the Bismuth Germanium Oxide (BGO) imaging calorimeter is
utilized to measure the particle energy with a high resolution. The nonlinear
fluorescence response of BGO for large ionization energy deposition, known as
the quenching effect, results in an under-estimate of the energy measurement
for cosmic-ray nuclei. In this paper, various models are employed to
characterize the BGO quenching factors obtained from the experimental data of
DAMPE. Applying the proper quenching model in the detector simulation process,
we investigate the tuned energy responses for various nuclei and compare the
results based on two different simulation softwares, i.e. GEANT4 and FLUKA. The
BGO quenching effect results in a decrease of the measured energy by
approximately $2.5\%$ ($5.7 \%$) for carbon (iron) at $\sim$10 GeV/n and $<1\%$
above 1 TeV/n, respectively. Accordingly, the correction of the BGO quenching
effect leads to an increase of the low-energy flux measurement of cosmic-ray
nuclei. | 2307.12629v1 |
2023-08-04 | Interplay of space charge, intrabeam scattering and synchrotron radiation in the Compact Linear Collider damping rings | Future ultra-low emittance rings for electron/positron colliders requiring
extremely high beam brightness can be limited by collective effects. In this
paper, the interplay of effects such as synchrotron radiation, intra-beam
scattering (IBS) and space charge in the vicinity of excited betatron
resonances is assessed. In this respect, two algorithms were developed to
simulate IBS and synchrotron radiation effects and integrated in the PyORBIT
tracking code, to be combined with its widely used space charge module. The
impact of these effects on the achievable beam parameters of the Compact Linear
Collider (CLIC) Damping Rings was studied, showing that synchrotron radiation
damping mitigates the adverse effects of IBS and space charge induced resonance
crossing. The studies include also a full dynamic simulation of the CLIC
damping ring cycle starting from the injection beam parameters. It is
demonstrated that a careful working point choice is necessary, in order to
accommodate the transition from a non-linear lattice induced detuning to a
space-charge dominated one and thereby avoid excessive losses and emittance
growth generated in the vicinity of strong resonances. | 2308.02196v3 |
2023-08-04 | Nonlinear wave damping by Kelvin-Helmholtz instability induced turbulence | Magnetohydrodynamic kink waves naturally form as a consequence of
perturbations to a structured medium, for example transverse oscillations of
coronal loops. Linear theory has provided many insights in the evolution of
linear oscillations, and results from these models are often applied to infer
information about the solar corona from observed wave periods and damping
times. However, simulations show that nonlinear kink waves can host the
Kelvin-Helmholtz instability (KHi) which subsequently creates turbulence in the
loop, dynamics which are beyond linear models. In this paper we investigate the
evolution of KHi-induced turbulence on the surface of a flux tube where a
non-linear fundamental kink-mode has been excited. We control our numerical
experiment so that we induce the KHi without exciting resonant absorption. We
find two stages in the KHi turbulence dynamics. In the first stage, we show
that the classic model of a KHi turbulent layer growing $\propto t$is
applicable. We adapt this model to make accurate predictions for damping of the
oscillation and turbulent heating as a consequence of the KHi dynamics. In the
second stage, the now dominant turbulent motions are undergoing decay. We find
that the classic model of energy decay proportional to $t^{-2}$ approximately
holds and provides an accurate prediction of the heating in this phase. Our
results show that we can develop simple models for the turbulent evolution of a
non-linear kink wave, but the damping profiles produced are distinct from those
of linear theory that are commonly used to confront theory and observations. | 2308.02217v2 |
2023-08-10 | JWST observations of galaxy damping wings during reionization interpreted with cosmological simulations | Spectra of the highest redshift galaxies taken with JWST are now allowing us
to see into the heart of the reionization epoch. Many of these observed
galaxies exhibit strong damping wing absorption redward of their Lyman-$\alpha$
emission. These observations have been used to measure the redshift evolution
of the neutral fraction of the intergalactic medium and sizes of ionized
bubbles. However, these estimates have been made using a simple analytic model
for the intergalactic damping wing. We explore the recent observations with
models of inhomogeneous reionization from the Sherwood-Relics simulation suite.
We carry out a comparison between the damping wings calculated from the
simulations and from the analytic model. We find that although the agreement is
good on the red side of the Lyman-$\alpha$ emission, there is a discrepancy on
the blue side due to residual neutral hydrogen present in the simulations,
which saturates the intergalactic absorption. For this reason, we find that it
is difficult to reproduce the claimed observations of large bubble sizes at z ~
7, which are driven by a detection of transmitted flux blueward of the
Lyman-$\alpha$ emission. We suggest instead that the observations can be
explained by a model with smaller ionized bubbles and larger intrinsic
Lyman-$\alpha$ emission from the host galaxy. | 2308.05800v1 |
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