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2020-08-25 | Stability results of coupled wave models with locally memory in a past history framework via non smooth coefficients on the interface | In this paper, we investigate the stabilization of a locally coupled wave
equations with local viscoelastic damping of past history type acting only in
one equation via non smooth coefficients. First, using a general criteria of
Arendt-Batty, we prove the strong stability of our system. Second, using a
frequency domain approach combined with the multiplier method, we establish the
exponential stability of the solution if and only if the two waves have the
same speed of propagation. In case of different speed propagation, we prove
that the energy of our system decays polynomially with rate 1/t. Finally, we
show the lack of exponential stability if the speeds of wave propagation are
different. | 2008.11596v1 |
2021-04-24 | Convex optimization via inertial algorithms with vanishing Tikhonov regularization: fast convergence to the minimum norm solution | In a Hilbertian framework, for the minimization of a general convex
differentiable function $f$, we introduce new inertial dynamics and algorithms
that generate trajectories and iterates that converge fastly towards the
minimizer of $f$ with minimum norm. Our study is based on the non-autonomous
version of the Polyak heavy ball method, which, at time $t$, is associated with
the strongly convex function obtained by adding to $f$ a Tikhonov
regularization term with vanishing coefficient $\epsilon(t)$. In this dynamic,
the damping coefficient is proportional to the square root of the Tikhonov
regularization parameter $\epsilon(t)$. By adjusting the speed of convergence
of $\epsilon(t)$ towards zero, we will obtain both rapid convergence towards
the infimal value of $f$, and the strong convergence of the trajectories
towards the element of minimum norm of the set of minimizers of $f$. In
particular, we obtain an improved version of the dynamic of Su-Boyd-Cand\`es
for the accelerated gradient method of Nesterov. This study naturally leads to
corresponding first-order algorithms obtained by temporal discretization. In
the case of a proper lower semicontinuous and convex function $f$, we study the
proximal algorithms in detail, and show that they benefit from similar
properties. | 2104.11987v1 |
2021-08-13 | Topology optimization for acoustic structures considering viscous and thermal boundary layers using a sequential linearized Navier-Stokes model | This study proposes a level set-based topology optimization method for
designing acoustic structures with viscous and thermal boundary layers in
perspective. Acoustic waves propagating in a narrow channel are damped by
viscous and thermal boundary layers. To estimate these viscothermal effects, we
first introduce a sequential linearized Navier-Stokes model based on three
weakly coupled Helmholtz equations for viscous, thermal, and acoustic pressure
fields. Then, the optimization problem is formulated, where a sound-absorbing
structure comprising air and an isothermal rigid medium is targeted, and its
sound absorption coefficient is set as an objective function. The adjoint
variable method and the concept of the topological derivative are used to
approximately obtain design sensitivity. A level set-based topology
optimization method is used to solve the optimization problem. Two-dimensional
numerical examples are provided to support the validity of the proposed method.
Moreover, the mechanisms that lead to the high absorption coefficient of the
optimized design are discussed. | 2108.06116v2 |
2021-10-12 | Computing semigroups with error control | We develop an algorithm that computes strongly continuous semigroups on
infinite-dimensional Hilbert spaces with explicit error control. Given a
generator $A$, a time $t>0$, an arbitrary initial vector $u_0$ and an error
tolerance $\epsilon>0$, the algorithm computes $\exp(tA)u_0$ with error bounded
by $\epsilon$. The algorithm is based on a combination of a regularized
functional calculus, suitable contour quadrature rules, and the adaptive
computation of resolvents in infinite dimensions. As a particular case, we show
that it is possible, even when only allowing pointwise evaluation of
coefficients, to compute, with error control, semigroups on the unbounded
domain $L^2(\mathbb{R}^d)$ that are generated by partial differential operators
with polynomially bounded coefficients of locally bounded total variation. For
analytic semigroups (and more general Laplace transform inversion), we provide
a quadrature rule whose error decreases like $\exp(-cN/\log(N))$ for $N$
quadrature points, that remains stable as $N\rightarrow\infty$, and which is
also suitable for infinite-dimensional operators. Numerical examples are given,
including: Schr\"odinger and wave equations on the aperiodic Ammann--Beenker
tiling, complex perturbed fractional diffusion equations on $L^2(\mathbb{R})$,
and damped Euler--Bernoulli beam equations. | 2110.06350v1 |
2021-10-16 | Global well-posedness, stability and instability for the non-viscous Oldroyd-B model | In this paper we consider the 3-dimensional incompressible Oldroyd-B model.
First, we establish two results of the global existence for different kinds of
the coupling coefficient $k$. Then, we prove that the solutions $(u,\tau)$ are
globally steady when $k^m\rightarrow k>0$, though $(u,\tau)$ corresponds to
different decays for different kinds of $k>0~$. Finally, we show that the
energy of $u(t,x)$ will have a jump when $k\rightarrow 0$ in large time, which
implies a non-steady phenomenon. In a word, we find an interesting physical
phenomenon of \eqref{1} such that smaller coupling coefficient $k$ will have a
better impact for the energy dissipation of $(u,\tau)$, but $k$ can't be too
small to zero, or the dissipation will vanish instantly. While the damping term
$\tau$ and $\mathbb{D}u$ always bring the well impact for the energy
dissipation. | 2110.08475v1 |
2021-11-01 | Dissipative superfluid relativistic magnetohydrodynamics of a multicomponent fluid: the combined effect of particle diffusion and vortices | We formulate dissipative magnetohydrodynamic equations for finite-temperature
superfluid and superconducting charged relativistic mixtures, taking into
account the effects of particle diffusion and possible presence of
Feynman-Onsager and/or Abrikosov vortices in the system. The equations depend
on a number of phenomenological transport coefficients, which describe, in
particular, relative motions of different particle species and their
interaction with vortices. We demonstrate how to relate these transport
coefficients to the mutual friction parameters and momentum transfer rates
arising in the microscopic theory. The resulting equations can be used to
study, in a unified and coherent way, a very wide range of phenomena associated
with dynamical processes in neutron stars, e.g., the magnetothermal evolution,
stellar oscillations and damping, as well as development and suppression of
various hydrodynamic instabilities in neutron stars. | 2111.00999v1 |
2021-11-11 | Quasinormal modes of charged black holes with corrections from nonlinear electrodynamics | We study quasinormal modes related to gravitational and electromagnetic
perturbations of spherically symmetric charged black holes in nonlinear
electrodynamics. Beyond the linear Maxwell electrodynamics, we consider a class
of Lagrangian with higher-order corrections written by the electromagnetic
field strength and its Hodge dual with arbitrary coefficients, and we
parametrize the corrections for quasinormal frequencies in terms of the
coefficients. It is confirmed that the isospectrality of quasinormal modes
under parity is generally violated due to nonlinear electrodynamics. As
applications, the corrections for quasinormal frequencies in Euler-Heisenberg
and Born-Infeld electrodynamics are calculated, then it is clarified that the
nonlinear effects act to lengthen the oscillation period and enhance the
damping rate of the quasinormal modes. | 2111.06273v2 |
2022-06-29 | Strongly coupled quantum Otto cycle with single qubit bath | We discuss a model of a closed quantum evolution of two-qubits where the
joint Hamiltonian is so chosen that one of the qubits acts as a bath and
thermalize the other qubit which is acting as the system. The corresponding
exact master equation for the system is derived. Interestingly, for a specific
choice of parameters the master equation takes the
Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form with constant coefficients,
representing pumping and damping of a single qubit system. Based on this model
we construct an Otto cycle connected to a single qubit bath and study its
thermodynamic properties. Our analysis goes beyond the conventional weak
coupling scenario and illustrates the effects of finite bath including
non-Markovianity. We find closed form expressions for efficiency (coefficient
of performance), power (cooling power) for heat engine regime (refrigerator
regime) for different modifications of the joint Hamiltonian. | 2206.14751v1 |
2022-08-29 | Benchmarking magnetized three-wave coupling for laser backscattering: Analytic solutions and kinetic simulations | Understanding magnetized laser-plasma interactions is important for
controlling magneto-inertial fusion experiments and developing magnetically
assisted radiation and particle sources. In the long-pulse regime, interactions
are dominated by coherent three-wave interactions, whose nonlinear coupling
coefficients become known only recently when waves propagate at oblique angles
with the magnetic field. In this paper, backscattering coupling coefficients
predicted by warm-fluid theory is benchmarked using particle-in-cell
simulations in one spatial dimension, and excellent agreements are found for a
wide range of plasma temperatures, magnetic field strengths, and laser
propagation angles, when the interactions are mediated by electron-dominant
hybrid waves. Systematic comparisons between theory and simulations are made
possible by a rigorous protocol: On the theory side, the initial boundary value
problem of linearized three-wave equations is solved, and the transient-time
solutions allow effects of growth and damping to be distinguished. On the
simulation side, parameters are carefully chosen and calibration runs are
performed to ensure that stimulated runs are well controlled. Fitting
simulation data to analytical solutions yields numerical growth rates, which
match theory predictions within error bars. Although warm-fluid theory is found
to be valid for a wide parameter range, genuine kinetic effects have also been
observed. | 2208.13832v2 |
2022-09-07 | Acoustic attenuation in magnetic insulator films: effects of magnon polaron formation | A magnon and a phonon are the quanta of spin wave and lattice wave,
respectively, and they can hybridize into a magnon polaron when their
frequencies and wavenumbers match close enough the values at the exceptional
point. Guided by an analytically calculated magnon polaron dispersion,
dynamical phase-field simulations are performed to investigate the effects of
magnon polaron formation on the attenuation of a bulk acoustic wave in a
magnetic insulator film. It is shown that a stronger magnon-phonon coupling
leads to a larger attenuation. The simulations also demonstrate the existence
of a minimum magnon-phonon interaction time required for the magnon polaron
formation, which is found to decrease with the magnetoelastic coupling
coefficient but increase with the magnetic damping coefficient. These results
deepen the understanding of the mechanisms of acoustic attenuation in magnetic
crystals and provide insights into the design of new-concept spin interconnects
that operate based on acoustically driven magnon propagation. | 2209.03481v2 |
2023-02-27 | Diagonal State Space Augmented Transformers for Speech Recognition | We improve on the popular conformer architecture by replacing the depthwise
temporal convolutions with diagonal state space (DSS) models. DSS is a recently
introduced variant of linear RNNs obtained by discretizing a linear dynamical
system with a diagonal state transition matrix. DSS layers project the input
sequence onto a space of orthogonal polynomials where the choice of basis
functions, metric and support is controlled by the eigenvalues of the
transition matrix. We compare neural transducers with either conformer or our
proposed DSS-augmented transformer (DSSformer) encoders on three public
corpora: Switchboard English conversational telephone speech 300 hours,
Switchboard+Fisher 2000 hours, and a spoken archive of holocaust survivor
testimonials called MALACH 176 hours. On Switchboard 300/2000 hours, we reach a
single model performance of 8.9%/6.7% WER on the combined test set of the Hub5
2000 evaluation, respectively, and on MALACH we improve the WER by 7% relative
over the previous best published result. In addition, we present empirical
evidence suggesting that DSS layers learn damped Fourier basis functions where
the attenuation coefficients are layer specific whereas the frequency
coefficients converge to almost identical linearly-spaced values across all
layers. | 2302.14120v1 |
2023-03-22 | Invariants for time-dependent Hamiltonian systems | An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems
with general time-dependent potentials. The invariant is worked out in two
equivalent ways. In the first approach, we define a special {\it Ansatz\/} for
the invariant and determine its time-dependent coefficients. In the second
approach, we perform a two-step canonical transformation of the initially
time-dependent Hamiltonian to a time-independent one. The invariant is found to
contain a function of time $f_{2}(t)$, defined as a solution of a linear
third-order differential equation whose coefficients depend in general on the
explicitly known configuration space trajectory that follows from the system's
time evolution. It is shown that the invariant can be interpreted as the time
integral of an energy balance equation. Our result is applied to a
one-dimensional, time-dependent, damped non-linear oscillator, and to a
three-dimensional system of Coulomb-interacting particles that are confined in
a time-dependent quadratic external potential. We finally show that our results
can be used to assess the accuracy of numerical simulations of time-dependent
Hamiltonian systems. | 2303.12746v1 |
2023-04-25 | Room dimensions and absorption inference from room transfer function via machine learning | The inference of the absorption configuration of an existing room solely
using acoustic signals can be challenging. This research presents two methods
for estimating the room dimensions and frequency-dependent absorption
coefficients using room transfer functions. The first method, a knowledge-based
approach, calculates the room dimensions through damped resonant frequencies of
the room. The second method, a machine learning approach, employs multi-task
convolutional neural networks for inferring the room dimensions and
frequency-dependent absorption coefficients of each surface. The study shows
that accurate wave-based simulation data can be used to train neural networks
for real-world measurements and demonstrates a potential for this algorithm to
be used to estimate the boundary input data for room acoustic simulations. The
proposed methods can be a valuable tool for room acoustic simulations during
acoustic renovation or intervention projects, as they enable to infer the room
geometry and absorption conditions with reasonably small data requirements. | 2304.12993v1 |
2023-06-19 | Reciprocal hydrodynamic response estimation in a random spreading sea | Direct estimation of the hydrodynamic response of an offshore structure in a
random spreading sea can lead to large computational costs. In this paper the
actual spreading sea is replaced by an idealised diffuse wave field and the
diffuse field reciprocity (DFR) relationship is derived analytically and
verified against diffraction analysis for offshore application. The DFR
approach provides an analytical expression for the estimation of the wave
loading spectrum in a spreading sea. It is very efficient because only the
added damping coefficients are required. Furthermore, if normalised to the peak
amplitude of a spreading sea, an upper bound response can be obtained using the
reciprocal approach. And this is demonstrated using a spar type floating wind
turbine. Given that the hydrodynamic coefficients are routine outputs for
offshore structural design, engineers would obtain the upper bound response
without additional computational cost using this new approach. | 2306.11058v1 |
2023-09-11 | Design of a Freely Rotating Wind Tunnel Test Bench for Measurements of Dynamic Coefficients | The needs to improve performances of artillery projectiles require accurate
aerodynamic investigation methods. The aerodynamic design of a projectile
usually starts from numerical analyses, mostly including semiempirical methods
and/or Computational Fluid Dynamics (CFD), up to experimental techniques
composed of wind-tunnel measurements or free-flight validations. In the frame,
the present paper proposes a dedicated measurement methodology able to
simultaneously determine the stability derivative C m$\alpha$ and the pitch
damping coefficient sum Cmq + Cm$\alpha$ in a wind tunnel by means of a single
and almost non-intrusive metrological setup called MiRo. This method is based
on the stereovision principle and a three-axis freely-rotating mechanical test
bench. In order to assess the reliability, repeatability and accuracy of this
technique, the MiRo wind tunnel measurements are compared to other sources like
aerodynamic balance measurements, alternative wind tunnel measurements, Ludwieg
tube measurements, free-flight measurements and CFD simulations. | 2309.05302v1 |
2006-02-20 | Fluctuation theorem applied to the Nosé-Hoover thermostated Lorentz gas | We present numerical evidence supporting the validity of the Gallavotti-Cohen
Fluctuation Theorem applied to the driven Lorentz gas with Nos\'e-Hoover
thermostating. It is moreover argued that the asymptotic form of the
fluctuation formula is independent of the amplitude of the driving force, in
the limit where it is small. | 0602458v1 |
1997-12-28 | Model-independent $\tan β$ bounds in the MSSM | We demonstrate, through the study of the one-loop effective potential in the
MSSM, the existence of fully model-independent lower and upper theoretical
bounds on $\tan \beta$. We give their general analytic form and illustrate some
of their implications. | 9712529v1 |
2006-12-26 | Very Light Gravitino Dark Matter | We address the question of dark matter in the context of gauge mediated
supersymmetry breaking models. In contrast with mSUGRA scenarios, the messenger
of the susy breaking to the visible sector can play an important role allowing
a relic gravitino in the $\sim {keV}$ to $10 {MeV}$ mass range to account for
the cold dark matter in the Universe. | 0612331v1 |
2004-09-15 | Characterizing rigid simplicial actions on trees | We extend Forester's rigidity theorem so as to give a complete
characterization of rigid group actions on trees (an action is rigid if it is
the only reduced action in its deformation space, in particular it is invariant
under automorphisms preserving the set of elliptic subgroups). | 0409245v1 |
2005-12-14 | Efficient Construction of Photonic Quantum Computational Clusters | We demonstrate a method of creating photonic two-dimensional cluster states
that is considerably more efficient than previously proposed approaches. Our
method uses only local unitaries and type-I fusion operations. The increased
efficiency of our method compared to previously proposed constructions is
obtained by identifying and exploiting local equivalence properties inherent in
cluster states. | 0512110v1 |
2007-10-26 | The dark matter as a light gravitino | We address the question of gravitino dark matter in the context of gauge
mediated supersymmetry breaking models. A special emphasis is put on the role
played by the MSSM singlet messenger in the case of SO(10) grand unification. | 0710.5121v1 |
2008-03-05 | Innovative Weak Formulation for The Landau-Lifshitz-Gilbert Equations | A non-conventional finite element formalism is proposed to solve the dynamic
Landau-Lifshitz-Gilbert micromagnetic equations. Two bidimensional test
problems are treated to estimate the validity and the accuracy of this finite
element approach | 0803.0599v1 |
2008-10-27 | The profile of bubbling solutions of a class of fourth order geometric equations on 4-manifolds | We study a class of fourth order geometric equations defined on a
4-dimensional compact Riemannian manifold which includes the Q-curvature
equation. We obtain sharp estimates on the difference near the blow-up points
between a bubbling sequence of solutions and the standard bubble. | 0810.4879v1 |
2009-03-02 | Asymptotic Improvement of the Binary Gilbert-Varshamov Bound on the Code Rate | We compute the code parameters for binary linear codes obtained by greedy
constructing the parity check matrix. Then we show that these codes improve the
Gilbert-Varshamov (GV) bound on the code size and rate. This result counter
proves the conjecture on the asymptotical exactness of the binary GV bound. | 0903.0302v2 |
2009-11-16 | The Independent Chip Model and Risk Aversion | We consider the Independent Chip Model (ICM) for expected value in poker
tournaments. Our first result is that participating in a fair bet with one
other player will always lower one's expected value under this model. Our
second result is that the expected value for players not participating in a
fair bet between two players always increases. We show that neither result
necessarily holds for a fair bet among three or more players. | 0911.3100v1 |
2011-03-29 | Statistical properties of $r$-adic processes and their connections to families of popular fractal curves | Results concerning the statists of $r$-adic processes and their fractal
properties are reviewed. The connection between singular eigenstates of the
statistical evolution of such processes and popular fractal curves is
emphasized. | 1103.5683v1 |
2011-05-09 | Global Solvability of the Cauchy Problem for the Landau-Lifshitz-Gilbert Equation in Higher Dimensions | We prove existence, uniqueness and asymptotics of global smooth solutions for
the Landau-Lifshitz-Gilbert equation in dimension $n \ge 3$, valid under a
smallness condition of initial gradients in the $L^n$ norm. The argument is
based on the method of moving frames that produces a covariant complex
Ginzburg-Landau equation, and a priori estimates that we obtain by the method
of weighted-in-time norms as introduced by Fujita and Kato. | 1105.1597v1 |
2012-03-28 | Fibonacci numbers in phyllotaxis : a simple model | A simple model is presented which explains the occurrence of high order
Fibonacci number parastichies in asteracae flowers by two distinct steps. First
low order parastichies result from the fact that a new floret, at its
appearance is repelled by two former ones, then, in order to accommodate for
the increase of the radius, parastichies numbers have to evolve and can do it
only by applying the Fibonacci recurrence formula. | 1203.6257v1 |
2014-02-19 | Ordered groupoids and the holomorph of an inverse semigroup | We present a construction for the holomorph of an inverse semigroup, derived
from the cartesian closed structure of the category of ordered groupoids. We
compare the holomorph with the monoid of mappings that preserve the ternary
heap operation on an inverse semigroup: for groups these two constructions
coincide. We present detailed calculations for semilattices of groups and for
the polycyclic monoids. | 1402.4592v1 |
2014-11-01 | Functorial Zeta Integrals | The functional equation for nonarchimedean Rankin-Selberg local Euler factors
was proved by Jacquet, Piatetski-Shapiro, and Shalika in 1983. In this
expository note we translate the original proof into the purely functorial
language of parabolic induction-restriction of Bernstein-Zelevinsky. This new
language gives a clearer presentation of the ideas, and works over arbitrary
fields with characteristic not equal to the residue characteristic. | 1411.0148v1 |
2016-02-17 | Dispersion and Scaling Law of Dynamic Hysteresis Based on the Landau-Lifshitz-Gilbert Model | Hysteresis dispersion under a varying external field Hex is investigated
through numerical simulations based on the Landau-Lifshitz-Gilbert (LLG)
equation, indicating the energy dissipation can be determined by W({\eta}) = A
(f, H0). A linear relation between area of hysteresis and magnitude of external
field is discovered. Evolution of hysteresis is also investigated under
oscillating external field. | 1602.05375v1 |
2016-06-06 | Proof of tightness of Varshamov - Gilbert bound for binary codes | We prove tightness of right logarithmic asymptotic of Varshamov- Gilbert
bound for linear binary codes We find general asymptotic coding bound for
linear codes | 1606.01592v5 |
2017-02-21 | Cohomology and extensions of ordered groupoids | We adapt and generalise results of Loganathan on the cohomology of inverse
semigroups to the cohomology of ordered groupoids. We then derive a five-term
exact sequence in cohomology from an extension of ordered groupoids, and show
that this sequence leads to a classification of extensions by a second
cohomology group. Our methods use structural ideas in cohomology as far as
possible, rather than computation with cocycles. | 1702.06333v1 |
2017-05-11 | Two Gilbert-Varshamov Type Existential Bounds for Asymmetric Quantum Error-Correcting Codes | In this note we report two versions of Gilbert-Varshamov type existential
bounds for asymmetric quantum error-correcting codes. | 1705.04087v2 |
2017-09-21 | Self-Dual Codes better than the Gilbert--Varshamov bound | We show that every self-orthogonal code over $\mathbb F_q$ of length $n$ can
be extended to a self-dual code, if there exists self-dual codes of length $n$.
Using a family of Galois towers of algebraic function fields we show that over
any nonprime field $\mathbb F_q$, with $q\geq 64$, except possibly $q=125$,
there are self-dual codes better than the asymptotic Gilbert--Varshamov bound. | 1709.07221v1 |
2018-10-12 | A convex approach to the Gilbert-Steiner problem | We describe a convex relaxation for the Gilbert-Steiner problem both in $R^d$
and on manifolds, extending the framework proposed in [9], and we discuss its
sharpness by means of calibration type arguments. The minimization of the
resulting problem is then tackled numerically and we present results for an
extensive set of examples. In particular we are able to address the Steiner
tree problem on surfaces. | 1810.05417v1 |
2018-11-09 | Finslerian metrics locally conformally $R$-Einstein | Let $R$ be the $hh$-curvature associated with the Chern connection or the
Cartan connection. Adopting the pulled-back tangent bundle approach to the
Finslerian Geometry, an intrinsic characterization of $R$-Einstein metrics is
given. Finslerian metrics which are locally conformally $R$-Einstein are
classified. | 1811.04077v3 |
2019-02-05 | Harmonic maps with prescribed singularities and applications in general relativity | This paper presents a general existence and uniqueness result for harmonic
maps with prescribed singularities into non-positively curved targets, and
surveys a number of applications to general relativity. It is based on a talk
delivered by the author at The 11th Mathematical Society of Japan Seasonal
Institute, The Role of Metrics in the Theory of Partial Differential Equations. | 1902.01576v2 |
2020-03-13 | 3D Stochastic Landau-Lifshitz-Gilbert Equations coupled with Maxwell's Equations with full energy | We consider 3D stochastic Landau-Lifshitz-Gilbert equations coupled with the
Maxwell equations with the full energy. We have proved the existence and some
further regularities of the weak solution. | 2003.06091v4 |
2021-12-09 | Induced Semi-Riemannian structures on null submanifolds | In this paper, we induce a semi-Riemannian metric on the $r$-null
submanifold. We establish the links between the null geometry and basics
invariants of the associated semi-Riemannian geometry on $r$-null submanifold
and semi-Riemannian constructed from a semi-Riemannian ambient. | 2112.07348v1 |
2022-04-12 | How to design a network architecture using capacity planning | Building a network architecture must answer to organization needs, but also
to two major elements which are the need for dependability and performance. By
performance, we must understand the ability to meet an immediate need and the
ability to scale without reducing the performance of the whole as new elements
are added to the network infrastructure. This last point is covered by Capacity
Planning domain. | 2204.05916v2 |
2022-07-31 | Moduli of Representations of Skewed-Gentle Algebras | We prove irreducible components of moduli spaces of semistable
representations of skewed-gentle algebras, and more generally, clannish
algebras, are isomorphic to products of projective spaces. This is achieved by
showing irreducible components of varieties of representations of clannish
algebras can be viewed as irreducible components of skewed-gentle algebras,
which we show are always normal. The main theorem generalizes an analogous
result for moduli of representations of special biserial algebras proven by
Carroll-Chindris-Kinser-Weyman. | 2208.00336v1 |
2022-08-01 | iOCR: Informed Optical Character Recognition for Election Ballot Tallies | The purpose of this study is to explore the performance of Informed OCR or
iOCR. iOCR was developed with a spell correction algorithm to fix errors
introduced by conventional OCR for vote tabulation. The results found that the
iOCR system outperforms conventional OCR techniques. | 2208.00865v1 |
2023-03-13 | Adaptive mesh refinement for the Landau-Lifshitz-Gilbert equation | We propose a new adaptive algorithm for the approximation of the
Landau-Lifshitz-Gilbert equation via a higher-order tangent plane scheme. We
show that the adaptive approximation satisfies an energy inequality and
demonstrate numerically, that the adaptive algorithm outperforms uniform
approaches. | 2303.07463v1 |
2023-05-08 | Evaluation of the Gilbert-Varshamov Bound using Multivariate Analytic Combinatorics | Analytic combinatorics in several variables refers to a suite of tools that
provide sharp asymptotic estimates for certain combinatorial quantities. In
this paper, we apply these tools to determine the Gilbert-Varshamov (GV) bound
for the sticky insertion and the constrained-synthesis channel. | 2305.04439v1 |
2023-12-11 | Matrix Formulae and Skein Relations for Quasi-cluster Algebras | In this paper, we give matrix formulae for non-orientable surfaces that
provide the Laurent expansion for quasi-cluster variables, generalizing the
orientable surface matrix formulae by Musiker-Williams. We additionally use our
matrix formulas to prove the skein relations for the elements in the
quasi-cluster algebra associated to curves on the non-orientable surface. | 2312.06148v1 |
2009-08-12 | Linear Fractionally Damped Oscillator | In this paper the linearly damped oscillator equation is considered with the
damping term generalized to a Caputo fractional derivative. The order of the
derivative being considered is 0 less than or equal to nu which is less than or
equal to 1 . At the lower end, nu = 0, the equation represents an un-damped
oscillator and at the upper end, nu = 1, the ordinary linearly damped
oscillator equation is recovered. A solution is found analytically and a
comparison with the ordinary linearly damped oscillator is made. It is found
that there are nine distinct cases as opposed to the usual three for the
ordinary equation (damped, over-damped, and critically damped). For three of
these cases it is shown that the frequency of oscillation actually increases
with increasing damping order before eventually falling to the limiting value
given by the ordinary damped oscillator equation. For the other six cases the
behavior is as expected, the frequency of oscillation decreases with increasing
order of the derivative (damping term). | 0908.1683v1 |
1997-10-02 | Dust and elemental abundances in Damped Ly alpha absorbers | The effects of the dust on the determination of elemental abundances in
damped Ly alpha (DLA) absorbers are investigated. Relations between the
observed abundances measured in the gas phase and the overall abundances (gas
plus dust) are derived as a function of dust-to-gas ratio, metallicity,
element-to-element abundance pattern, average extinction coefficient of dust
grains, and chemical composition of dust grains. A method is presented for
determining dust-to-gas ratios, dust-to-metals ratios, and dust-corrected
relative abundances in DLA absorbers by assuming dust of Galactic type and
constant abundance ratios between iron-peak elements. The method is applied to
a sample of 17 DLA absorbers with available Zn, Cr and/or Fe measurements. The
resulting dust-to-gas ratios are mostly distributed between 2% and 25% of the
Galactic value, in good quantitative agreement with the results from reddening
studies of QSOs with foreground DLA absorption. A correlation is found between
dust-to-gas ratio and metallicity in DLA galaxies, with a typical
dust-to-metals ratio of ~ 60% the Galactic value. The derived dust-to-metals
ratios are then used to correct from the effects of dust the abundance ratios
[Si/Fe], [S/Fe], [Ti/Fe], [Mn/Fe], [Ni/Fe] available for a sub-sample of 9
absorbers. The [alpha/Fe] ratios corrected from dust do not show the
enhancement characteristic of metal-poor Galactic stars, but instead have
essentially solar values, within +/- 0.2 dex. This suggests that the chemical
history of DLA absorbers is different from that experienced by the Milky Way.
Evidences that point to dwarf galaxies, rather than to spiral galaxies, as
important contributors to the DLA phenomenon are summarized. | 9710026v1 |
2002-11-26 | R-modes of neutron stars with the superfluid core | We investigate the modal properties of the $r$-modes of rotating neutron
stars with the core filled with neutron and proton superfluids, taking account
of entrainment effects between the superfluids. The stability of the $r$-modes
against gravitational radiation reaction is also examined considering viscous
dissipation due to shear and a damping mechanism called mutual friction between
the superfluids in the core. We find the $r$-modes in the superfluid core are
split into ordinary $r$-modes and superfluid $r$-modes, which we call,
respectively, $r^o$- and $r^s$-modes. The two superfluids in the core flow
together for the $r^o$-modes, while they counter-move for the $r^s$-modes. For
the $r^o$-modes, the coefficient $\kappa_0\equiv\lim_{\Omega\to
0}\omega/\Omega$ is equal to $2m/[l^\prime(l^\prime+1)]$, almost independent of
the parameter $\eta$ that parameterizes the entrainment effects between the
superfluids, where $\Omega$ is the angular frequency of rotation, $\omega$ the
oscillation frequency observed in the corotating frame of the star, and
$l^\prime$ and $m$ are the indices of the spherical harmonic function
representing the angular dependence of the $r$-modes. For the $r^s$-modes, on
the other hand, $\kappa_0$ is equal to $2m/[l^\prime(l^\prime+1)]$ at $\eta=0$
(no entrainment), and it almost linearly increases as $\eta$ is increased from
$\eta=0$. The mutual friction in the superfluid core is found ineffective to
stabilize the $r$-mode instability caused by the $r^o$-mode except in a few
narrow regions of $\eta$. The $r$-mode instability caused by the $r^s$-modes,
on the other hand, is extremely weak and easily damped by dissipative processes
in the star. | 0211580v1 |
2006-02-06 | Voigt Profile Fitting to Quasar Absorption Lines: An Analytic Approximation to the Voigt-Hjerting Function | The Voigt-Hjerting function is fundamental in order to correctly model the
profiles of absorption lines imprinted in the spectra of bright background
sources by intervening absorbing systems. In this work we present a simple
analytic approximation to this function in the context of absorption line
profiles of intergalactic HI absorbers. Using basic calculus tools, we derive
an analytic expression for the Voigt-Hjerting function that contains only
fourth order polynomial and Gaussian functions. In connection with the
absorption coefficient of intergalactic neutral hydrogen, this approximation is
suitable for modeling Voigt profiles with an accuracy of $10^{-4}$ or better
for an arbitrary wavelength baseline, for column densities up to $N_{HI} =
10^{22} cm^{-2}$, and for damping parameters $a \lesssim 10^{-4}$, i.e. the
entire range of parameters characteristic to all Lyman transitions arising in a
variety of HI absorbing systems such as Lyman Alpha Forest clouds, Lyman Limit
systems and Damped Lyman Alpha systems. We hence present an approximation to
the Voigt-Hjerting function that is both accurate and flexible to implement in
various types of programming languages and machines, and with which Voigt
profiles can be calculated in a reliable and very simple manner. | 0602124v2 |
2003-10-29 | Superparamagnetism and Spin Glass Dynamics of Interacting Magnetic Nanoparticle Systems | The physical properties of magnetic nanoparticles have been investigated with
focus on the influence of dipolar interparticle interaction. For weakly coupled
nanoparticles, thermodynamic perturbation theory is employed to derive
analytical expressions for the linear equilibrium susceptibility, the
zero-field specific heat and averages of the local dipolar fields. By
introducing the averages of the dipolar fields in an expression for the
relaxation rate of a single particle, a nontrivial dependence of the
superparamagnetic blocking on the damping coefficient is evidenced. This
damping dependence is interpreted in terms of the nonaxially symmetric
potential created by the transverse component of the dipolar field.
Strongly interacting nanoparticle systems are investigated experimentally in
terms of spin glass behavior. Disorder and frustration arise in samples
consisting of frozen ferrofluids from the randomness in particle position and
anisotropy axis orientation. A strongly interacting FeC system is shown to
exhibit critical dynamics characteristic of a spin glass phase transition.
Aging, memory and rejuvenation phenomena similar to those of conventional spin
glasses are observed, albeit with much weaker rejuvenation effects than in both
a Ag(11 at% Mn) Heisenberg and an Fe_{0.5}Mn_{0.5}TiO_3 Ising spin glass.
Differences in the nonequilibrium dynamics of the strongly interacting
nanoparticle system and the two spin glass samples are discussed in terms of
anisotropy and different timescales, due to the much longer microscopic flip
time of a magnetic moment than of an atomic spin. | 0310684v2 |
1996-12-31 | Fluid Models for Kinetic Effects on Coherent Nonlinear Alfven Waves. I. Fundamental Theory | Collisionless regime kinetic models for coherent nonlinear Alfven wave
dynamics are studied using fluid moment equations with an approximate closure
anzatz. Resonant particle effects are modelled by incorporating an additional
term representing dissipation akin to parallel heat conduction. Unlike
collisional dissipation, parallel heat conduction is presented by an integral
operator. The modified derivative nonlinear Schrodinger equation thus has a
spatially nonlocal nonlinear term describing the long-time evolution of the
envelope of parallel-propagating Alfven waves, as well. Coefficients in the
nonlinear terms are free of the 1/(1-beta) singularity usually encountered in
previous analyses, and have very a simple form which clarifies the physical
processes governing the large amplitude Alfvenic nonlinear dynamics. The
nonlinearity appears via coupling of an Alfvenic mode to a kinetic ion-acoustic
mode. Damping of the nonlinear Alfven wave appears via strong Landau damping of
the ion-acoustic wave when the electron-to-ion temperature ratio is close to
unity. For a (slightly) obliquely propagating wave, there are finite Larmor
radius corrections in the dynamical equation. This effect depends on the angle
of wave propagation relative to B_0 and vanishes for the limit of strictly
parallel propagation. Explicit magnetic perturbation envelope equations
amenable to further analysis and numerical solution are obtained. Implications
of these models for collisionless shock dynamics are discussed. | 9612017v1 |
2008-06-01 | Ray-based calculations of backscatter in laser fusion targets | A 1D, steady-state model for Brillouin and Raman backscatter from an
inhomogeneous plasma is presented. The daughter plasma waves are treated in the
strong damping limit, and have amplitudes given by the (linear) kinetic
response to the ponderomotive drive. Pump depletion, inverse-bremsstrahlung
damping, bremsstrahlung emission, Thomson scattering off density fluctuations,
and whole-beam focusing are included. The numerical code DEPLETE, which
implements this model, is described. The model is compared with traditional
linear gain calculations, as well as "plane-wave" simulations with the paraxial
propagation code pF3D. Comparisons with Brillouin-scattering experiments at the
OMEGA Laser Facility [T. R. Boehly et al., Opt. Commun. 133, p. 495 (1997)]
show that laser speckles greatly enhance the reflectivity over the DEPLETE
results. An approximate upper bound on this enhancement, motivated by phase
conjugation, is given by doubling the DEPLETE coupling coefficient. Analysis
with DEPLETE of an ignition design for the National Ignition Facility (NIF) [J.
A. Paisner, E. M. Campbell, and W. J. Hogan, Fusion Technol. 26, p. 755
(1994)], with a peak radiation temperature of 285 eV, shows encouragingly low
reflectivity. Re-absorption of Raman light is seen to be significant in this
design. | 0806.0045v2 |
2015-07-06 | Fast inertial dynamics and FISTA algorithms in convex optimization. Perturbation aspects | In a Hilbert space setting $\mathcal H$, we study the fast convergence
properties as $t \to + \infty$ of the trajectories of the second-order
differential equation $ \ddot{x}(t) + \frac{\alpha}{t} \dot{x}(t) + \nabla \Phi
(x(t)) = g(t)$, where $\nabla\Phi$ is the gradient of a convex continuously
differentiable function $\Phi: \mathcal H \to \mathbb R$, $\alpha$ is a
positive parameter, and $g: [t_0, + \infty[ \rightarrow \mathcal H$ is a
"small" perturbation term. In this damped inertial system, the viscous damping
coefficient $\frac{\alpha}{t}$ vanishes asymptotically, but not too rapidly.
For $\alpha \geq 3$, and $\int_{t_0}^{+\infty} t \|g(t)\| dt < + \infty$,
just assuming that the solution set is non empty, we show that any trajectory
of the above system satisfies the fast convergence property $\Phi(x(t))-
\min_{\mathcal H}\Phi \leq \frac{C}{t^2}$. For $\alpha > 3$, we show that any
trajectory converges weakly to a minimizer of $\Phi$, and we show the strong
convergence property in various practical situations. This complements the
results obtained by Su-Boyd- Cand\`es, and Attouch-Peypouquet-Redont, in the
unperturbed case $g=0$. The parallel study of the time discretized version of
this system provides new insight on the effect of errors, or perturbations on
Nesterov's type algorithms. We obtain fast convergence of the values, and
convergence of the trajectories for a perturbed version of the variant of FISTA
recently considered by Chambolle-Dossal, and Su-Boyd-Cand\`es. | 1507.01367v1 |
2016-02-05 | Combining fast inertial dynamics for convex optimization with Tikhonov regularization | In a Hilbert space setting $\mathcal H$, we study the convergence properties
as $t \to + \infty$ of the trajectories of the second-order differential
equation \begin{equation*}
\mbox{(AVD)}_{\alpha, \epsilon} \quad \quad \ddot{x}(t) + \frac{\alpha}{t}
\dot{x}(t) + \nabla \Phi (x(t)) + \epsilon (t) x(t) =0, \end{equation*} where
$\nabla\Phi$ is the gradient of a convex continuously differentiable function
$\Phi: \mathcal H \to \mathbb R$, $\alpha$ is a positive parameter, and
$\epsilon (t) x(t)$ is a Tikhonov regularization term, with $\lim_{t \to
\infty}\epsilon (t) =0$. In this damped inertial system, the damping
coefficient $\frac{\alpha}{t}$ vanishes asymptotically, but not too quickly, a
key property to obtain rapid convergence of the values. In the case $\epsilon
(\cdot) \equiv 0$, this dynamic has been highlighted recently by Su, Boyd, and
Cand\`es as a continuous version of the Nesterov accelerated method. Depending
on the speed of convergence of $\epsilon (t)$ to zero, we analyze the
convergence properties of the trajectories of $\mbox{(AVD)}_{\alpha,
\epsilon}$. We obtain results ranging from the rapid convergence of $\Phi
(x(t))$ to $\min \Phi$ when $\epsilon (t)$ decreases rapidly to zero, up to the
strong ergodic convergence of the trajectories to the element of minimal norm
of the set of minimizers of $\Phi$, when $\epsilon (t)$ tends slowly to zero. | 1602.01973v1 |
2016-02-19 | Resonant absorption and amplification of circularly-polarized waves in inhomogeneous chiral media | It has been found that in the media where the dielectric permittivity
$\epsilon$ or the magnetic permeability $\mu$ is near zero and in transition
metamaterials where $\epsilon$ or $\mu$ changes from positive to negative
values, there occur a strong absorption or amplification of the electromagnetic
wave energy in the presence of an infinitesimally small damping or gain and a
strong enhancement of the electromagnetic fields. We attribute these phenomena
to the mode conversion of transverse electromagnetic waves into longitudinal
plasma oscillations and its inverse process. In this paper, we study analogous
phenomena occurring in chiral media theoretically using the invariant imbedding
method. In uniform isotropic chiral media, right-circularly-polarized and
left-circularly-polarized waves are the eigenmodes of propagation with
different effective refractive indices $n_+$ and $n_-$, whereas in the chiral
media with a nonuniform impedance variation, they are no longer the eigenmodes
and are coupled to each other. We find that both in uniform chiral slabs where
either $n_+$ or $n_-$ is near zero and in chiral transition metamaterials where
$n_+$ or $n_-$ changes from positive to negative values, a strong absorption or
amplification of circularly-polarized waves occurs in the presence of an
infinitesimally small damping or gain. We present detailed calculations of the
mode conversion coefficient, which measures the fraction of the electromagnetic
wave energy absorbed into the medium, for various configurations of $\epsilon$
and $\mu$ with an emphasis on the influence of a nonuniform impedance. We
propose possible applications of these phenomena to linear and nonlinear
optical devices that react selectively to the helicity of the circular
polarization. | 1602.06022v1 |
2018-06-22 | Overcoming obstacles in nonequilibrium holography | We study universal spatial features of certain non-equilibrium steady states
corresponding to flows of strongly correlated fluids over obstacles. This
allows us to predict universal spatial features of far-from-equilibrium
systems, which in certain interesting cases depend cleanly on the hydrodynamic
transport coefficients of the underlying theory, such as $\eta/s$, the shear
viscosity to entropy density ratio. In this work we give a purely
field-theoretical definition of the spatial collective modes identified earlier
and proceed to demonstrate their usefulness in a set of examples, drawing on
hydrodynamic theory as well as holographic duality. We extend our earlier
treatment by adding a finite chemical potential, which introduces a
qualitatively new feature, namely damped oscillatory behavior in space. We find
interesting transitions between oscillatory and damped regimes and we consider
critical exponents associated with these. We explain in detail the numerical
method and add a host of new examples, including fully analytical ones. Such a
treatment is possible in the large-dimension limit of the bulk theory, as well
as in three dimensions, where we also exhibit a fully analytic non-linear
example that beautifully illustrates the original proposal of spatial
universality. This allows us to explicitly demonstrate how an infinite tower of
discrete modes condenses into a branch cut in the zero-temperature limit,
converting exponential decay into a power law tail. | 1806.08655v1 |
2018-06-28 | Optimizing wave-generation and wave-damping in 3D-flow simulations with implicit relaxation-zones | In finite-volume-based flow-simulations with free-surface waves, wave
reflections at the domain boundaries can cause substantial errors in the
results and must therefore be minimized. This can be achieved via `implicit
relaxation zones', but only if the relaxation zone's case-dependent parameters
are optimized. This work proposes an analytical approach for optimizing these
parameters. The analytical predictions are compared against results from
2D-flow simulations for different water depths, flow solvers, and relaxation
functions, and against results from 3D-flow simulations with strongly
wave-reflecting bodies subjected to nonlinear free-surface waves. The present
results demonstrate that the proposed approach satisfactorily predicts both the
optimum parameter settings and the upper-limit for the corresponding reflection
coefficients $C_{\mathrm{R}}$. Simulation results for $C_{\mathrm{R}}$ were
mostly below or equal to the analytical predictions, but never more than
$3.4\%$ larger. Therefore, the proposed approach can be recommended for
engineering practice. Furthermore, it is shown that implicit relaxation zones
can be considered as a special-case of forcing zones, a family of approaches
which includes among others absorbing layers, damping zones and sponge layers.
The commonalities and differences between these approaches are discussed,
including to what extend the present findings are applicable to these other
approaches and vice versa. | 1806.10995v3 |
2018-07-06 | On the use of circulant matrices for the stability analysis of recent weakly compressible SPH methods | In this study, a linear stability analysis is performed for different Weakly
Compressible Smooth Particle Hydrodynamics (WCSPH) methods on a 1D periodic
domain describing an incompressible base flow. The perturbation equation can be
vectorized and written as an ordinary differential equation where the
coefficients are circulant matrices. The diagonalization of the system is
equivalent to apply a spatial discrete Fourier transform. This leads to
stability conditions expressed by the discrete Fourier transform of the first
and second derivatives of the kernel. Although spurious modes are highlighted,
no tensile nor pairing instabilities are found in the present study, suggesting
that the perturbations of the stresses are always damped if the base flow is
incompressible. The perturbations equation is solved in the Laplace domain,
allowing to derive an analytical solution of the transient state. Also, it is
demonstrated analytically that a positive background pressure combined with the
uncorrected gradient operator leads to a reordering of the particle lattice. It
is also shown that above a critical value, the background pressure leads to
instabilities. Finally, the dispersion curves for inviscid and viscous flows
are plotted for different WCSPH methods and compared to the continuum solution.
It is observed that a background pressure equal to $\rho c^2$ gives the best
fidelity to predict the propagation of a sound wave. When viscosity effects are
taken into account, the damping of pressure fluctuations show the best
agreement with the continuum for $p_{back} \sim \rho c^2/2$. | 1807.02315v2 |
2018-08-15 | Pull-in dynamics of overdamped microbeams | We study the dynamics of MEMS microbeams undergoing electrostatic pull-in. At
DC voltages close to the pull-in voltage, experiments and numerical simulations
have reported `bottleneck' behaviour in which the transient dynamics slow down
considerably. This slowing down is highly sensitive to external forces, and so
has widespread potential for applications that use pull-in time as a sensing
mechanism, including high-resolution accelerometers and pressure sensors.
Previously, the bottleneck phenomenon has only been understood using lumped
mass-spring models that do not account for effects such as variable residual
stress and different boundary conditions. We extend these studies to
incorporate the beam geometry, developing an asymptotic method to analyse the
pull-in dynamics. We attribute bottleneck behaviour to critical slowing down
near the pull-in transition, and we obtain a simple expression for the pull-in
time in terms of the beam parameters and external damping coefficient. This
expression is found to agree well with previous experiments and numerical
simulations that incorporate more realistic models of squeeze film damping, and
so provides a useful design rule for sensing applications. We also consider the
accuracy of a single-mode approximation of the microbeam equations --- an
approach that is commonly used to make analytical progress, without systematic
investigation of its accuracy. By comparing to our bottleneck analysis, we
identify the factors that control the error of this approach, and we
demonstrate that this error can indeed be very small. | 1808.05237v1 |
2019-07-05 | Response solutions to quasi-periodically forced systems, even to possibly ill-posed PDEs, with strong dissipation and any frequency vectors | We consider several models (including both multidimensional ordinary
differential equations (ODEs) and partial differential equations (PDEs),
possibly ill-posed), subject to very strong damping and quasi-periodic external
forcing. We study the existence of response solutions (i.e., quasi-periodic
solutions with the same frequency as the forcing). Under some regularity
assumptions on the nonlinearity and forcing, without any arithmetic condition
on the forcing frequency $\omega$, we show that the response solutions indeed
exist. Moreover, the solutions we obtained possess optimal regularity in
$\varepsilon$ (where $\varepsilon$ is the inverse of the coefficients
multiplying the damping) when we consider $\varepsilon$ in a domain that does
not include the origin $\varepsilon=0$ but has the origin on its boundary. We
get that the response solutions depend continuously on $\varepsilon$ when we
consider $\varepsilon $ tends to $0$. However, in general, they may not be
differentiable at $\varepsilon=0$. In this paper, we allow multidimensional
systems and we do not require that the unperturbed equations under
consideration are Hamiltonian. One advantage of the method in the present paper
is that it gives results for analytic, finitely differentiable and low
regularity forcing and nonlinearity, respectively. As a matter of fact, we do
not even need that the forcing is continuous. Notably, we obtain results when
the forcing is in $L^2$ space and the nonlinearity is just Lipschitz as well as
in the case that the forcing is in $H^1$ space and the nonlinearity is $C^{1 +
\text{Lip}}$. In the proof of our results, we reformulate the existence of
response solutions as a fixed point problem in appropriate spaces of smooth
functions. | 1907.02835v1 |
2020-06-23 | Unexpected convergence of lattice Boltzmann schemes | In this work, we study numerically the convergence of the scalar D2Q9 lattice
Boltzmann scheme with multiple relaxation times when the time step is
proportional to the space step and tends to zero. We do this by a combination
of theory and numerical experiment. The classical formal analysis when all the
relaxation parameters are fixed and the time step tends to zero shows that the
numerical solution converges to solutions of the heat equation, with a
constraint connecting the diffusivity, the space step and the coefficient of
relaxation of the momentum. If the diffusivity is fixed and the space step
tends to zero, the relaxation parameter for the momentum is very small, causing
a discrepency between the previous analysis and the numerical results. We
propose a new analysis of the method for this specific situation of evanescent
relaxation, based on the dispersion equation of the lattice Boltzmann scheme. A
new asymptotic partial differential equation, the damped acoustic system, is
emergent as a result of this formal analysis. Complementary numerical
experiments establish the convergence of the scalar D2Q9 lattice Boltzmann
scheme with multiple relaxation times and acoustic scaling in this specific
case of evanescent relaxation towards the numerical solution of the damped
acoustic system. | 2006.12947v1 |
2020-09-13 | Inertia and feedback parameters adaptive control of virtual synchronous generator | The virtual synchronous generator technology analogs the characteristics of
the synchronous generator via the controller design. It improved the stability
of the grid systems which include the new energy. At the same time, according
to the adjustable characteristics of the virtual synchronous generator
parameters, the parameter adaptive adjustment is used to improve the dynamic
performance of the system. However, the traditional virtual synchronous
generator adaptive control technology still has two drawbacks: on the one hand,
the large-scale adjustment of the damping droop coefficient and the virtual
moment of inertia requires the system having a high energy storage margin; On
the other hand, there is a power overshoot phenomenon in the transient
regulation process, which is disadvantageous to the power equipment. First,
this paper provides a convenient adjustment method for improving the transient
stability of the system, the system damping is adjusted by introducing the
output speed feedback. Second, according to the transient power-angle
characteristics of the system, a parameter adaptive control strategy is
proposed, which shortens the transient adjustment time and ensures that the
deviation of the system frequency in the transient adjustment process is within
the allowable range, and improves the transient performance of the grid
frequency adjustment, at the same time, the power overshoot is suppressed.
Finally, the experimental results show that the proposed control strategy is
superior to the existing adaptive control strategy. | 2009.05916v1 |
2021-02-03 | Jerky active matter: a phase field crystal model with translational and orientational memory | Most field theories for active matter neglect effects of memory and inertia.
However, recent experiments have found inertial delay to be important for the
motion of self-propelled particles. A major challenge in the theoretical
description of these effects, which makes the application of standard methods
very difficult, is the fact that orientable particles have both translational
and orientational degrees of freedom which do not necessarily relax on the same
time scale. In this work, we derive the general mathematical form of a field
theory for soft matter systems with two different time scales. This allows to
obtain a phase field crystal model for polar (i.e., nonspherical or active)
particles with translational and orientational memory. Notably, this theory is
of third order in temporal derivatives and can thus be seen as a spatiotemporal
jerky dynamics. We obtain the phase diagram of this model, which shows that,
unlike in the passive case, the linear stability of the liquid state depends on
the damping coefficients. Moreover, we investigate sound waves in active
matter. It is found that, in active fluids, there are two different mechanisms
for sound propagation. For certain parameter values and sufficiently high
frequencies, sound mediated by polarization waves experiences less damping than
usual passive sound mediated by pressure waves of the same frequency. By
combining the different modes, acoustic frequency filters based on active
fluids could be realized. | 2102.02169v1 |
2021-04-23 | Development of Advanced Linearized Gyrokinetic Collision Operators Using a Moment Approach | The derivation and numerical implementation of a linearized version of the
gyrokinetic (GK) Coulomb collision operator (Jorge R. et al., J. Plasma Phys.
85, 905850604 (2019)) and of the widely-used linearized GK Sugama collision
operator (Sugama H. et al., Phys. Plasmas 16, 112503 (2009)) is reported. An
approach based on a Hermite-Laguerre moment expansion of the perturbed
gyrocenter distribution function is used, referred to as gyro-moment expansion.
This approach allows considering arbitrary perpendicular wavenumber and
expressing the two linearized GK operators as a linear combination of
gyro-moments where the expansion coefficients are given by closed analytical
expressions that depend on the perpendicular wavenumber and on the temperature
and mass ratios of the colliding species. The drift-kinetic (DK) limits of the
GK linearized Coulomb and Sugama operators are also obtained. Comparisons
between the gyro-moment approach with the GK continuum code GENE are reported
focusing on the ion-temperature-gradient (ITG) instability and zonal flow (ZF)
damping, finding an excellent agreement. In particular, we demonstrate that the
GK linearized Sugama yields a stronger collisional damping of the ZF residual
compared to the GK linearized Coulomb. Finally, we show that the numerical
efficiency of the gyro-moment approach increases with collisionality, a desired
property for boundary plasma applications. | 2104.11480v2 |
2021-05-19 | Viscoelasticity and elastocapillarity effects in the impact of drops on a repellent surface | We investigate freely expanding viscoelastic sheets. The sheets are produced
by the impact of drops on a quartz plate covered with a thin layer of liquid
nitrogen that suppresses shear viscous dissipation as a result of the cold
Leidenfrost effect. The time evolution of the sheet is simultaneously recorded
from top and side views using high-speed cameras. The investigated viscoelastic
fluids are Maxwell fluids, which are characterized by low elastic moduli, and
relaxation times that vary over almost two orders of magnitude, thus giving
access to a large spectrum of viscoelastic and elastocapillary effects. For the
purposes of comparison, Newtonian fluids, with viscosity varying over three
orders of magnitude, are also investigated. In this study, $d_{\mathrm{max}}$,
the maximal expansion of the sheets, and $t_{\mathrm{max}}$ the time to reach
this maximal expansion from the time at impact, are measured as a function of
the impact velocity. By using a generalized damped harmonic oscillator model,
we rationalize the role of capillarity, bulk elasticity and viscous dissipation
in the expansion dynamics of all investigated samples. In the model, the spring
constant is a combination of the surface tension and the bulk dynamic elastic
modulus. The time-varying damping coefficient is associated to biaxial
extensional viscous dissipation and is proportional to the dynamic loss
modulus. For all samples, we find that the model reproduces accurately the
experimental data for $d_{\mathrm{max}}$ and $t_{\mathrm{max}}$. | 2105.09244v1 |
2021-12-29 | Towards First-principle Characterization of Cosmic-ray Transport Coefficients from Multi-scale Kinetic Simulations | A major uncertainty in understanding the transport and feedback of
cosmic-rays (CRs) within and beyond our Galaxy lies in the unknown CR
scattering rates, which are primarily determined by wave-particle interaction
at microscopic gyro-resonant scales. The source of the waves for the bulk CR
population is believed to be self-driven by the CR streaming instability
(CRSI), resulting from the streaming of CRs downward a CR pressure gradient.
While a balance between driving by the CRSI and wave damping is expected to
determine wave amplitudes and hence the CR scattering rates, the problem
involves significant scale separation with substantial ambiguities based on
quasi-linear theory (QLT). Here we propose a novel "streaming box" framework to
study the CRSI with an imposed CR pressure gradient, enabling first-principle
measurement of the CR scattering rates as a function of environmental
parameters. By employing the magnetohydrodynamic-particle-in-cell (MHD-PIC)
method with ion-neutral damping, we conduct a series of simulations with
different resolutions and CR pressure gradients and precisely measure the
resulting CR scattering rates in steady state. The measured rates show scalings
consistent with QLT, but with a normalization smaller by a factor of several
than typical estimates based on single-fluid treatment of CRs. A
momentum-by-momentum treatment provides better estimates when integrated over
momentum, but is also subject substantial deviations especially at small
momentum. Our framework thus opens up the path towards providing comprehensive
subgrid physics for macroscopic studies of CR transport and feedback in broad
astrophysical contexts. | 2112.14782v2 |
2022-01-17 | Sizing of Energy Storage System for Virtual Inertia Emulation | The infusion of renewable energy sources into the conventional synchronous
generation system decreases the overall system inertia and negatively impacts
the stability of its primary frequency response. The lowered inertia is due to
the absence of inertia in some of the renewable energy-based systems. To
maintain the stability of the system, we need to keep the frequency in the
permissible limits and maintain low rotational inertia. Some authors in the
literature have used the virtual synchronous generators (VSG) as a solution to
this problem. Although the VSG based distributed recourses (DER) exhibits the
characteristics and behavior of synchronous generators (SG) such as inertia,
frequency droop functions and damping but it does not optimally solve the
question of frequency stability. This paper presents a solution for these
problems via an empirical model that sizes the Battery Energy Storage System
(BESS) required for the inertia emulation and damping control. The tested
system consists of a Photovoltaic (PV) based VSG that is connected to a 9-Bus
grid and the simulation experiments are carried out using EMTP software. The
VSG transient response is initiated by a symmetric fault on the grid side. Our
simulations show the battery energy sizing required to emulate the virtual
inertia corresponding to several design parameters, i.e., the droop gain,
K{\omega}, the droop coefficient, Kd, and the VSG time constant Ta. | 2201.06566v2 |
2022-04-12 | The drag exerted by weakly dissipative trapped lee waves on the atmosphere: application to Scorer's two-layer model | While it is known that trapped lee waves propagating at low levels in a
stratified atmosphere exert a drag on the mountains that generate them, the
distribution of the corresponding reaction force exerted on the atmospheric
mean circulation, defined by the wave momentum flux profiles, has not been
established, because for inviscid trapped lee waves these profiles oscillate
indefinitely downstream. A framework is developed here for the unambiguous
calculation of momentum flux profiles produced by trapped lee waves, which
circumvents the difficulties plaguing the inviscid trapped lee wave theory.
Using linear theory, and taking Scorer's two-layer atmosphere as an example,
the waves are assumed to be subject to a small dissipation, expressed as a
Rayleigh damping. The resulting wave pattern decays downstream, so the momentum
flux profile integrated over the area occupied by the waves converges to a
well-defined form. Remarkably, for weak dissipation, this form is independent
of the value of Rayleigh damping coefficient, and the inviscid drag, determined
in previous studies, is recovered as the momentum flux at the surface. The
divergence of this momentum flux profile accounts for the areally-integrated
drag exerted by the waves on the atmosphere. The application of this framework
to this and other types of trapped lee waves potentially enables the
development of physically-based parametrizations of the effects of trapped lee
waves on the atmosphere. | 2204.05858v1 |
2022-08-30 | Hyperon bulk viscosity and $r$-modes of neutron stars | We propose and apply a new parameterization of the modified chiral effective
model to study rotating neutron stars with hyperon cores in the framework of
the relativistic mean-field theory. The inclusion of mesonic cross couplings in
the model has improved the density content of the symmetry energy slope
parameters, which are in agreement with the findings from recent terrestrial
experiments. The bulk viscosity of the hyperonic medium is analyzed to
investigate its role in the suppression of gravitationally driven $r$-modes.
The hyperonic bulk viscosity coefficient caused by non-leptonic weak
interactions and the corresponding damping timescales are calculated and the
$r$-mode instability windows are obtained. The present model predicts a
significant reduction of the unstable region due to a more effective damping of
oscillations. We find that from $\sim 10^8$ K to $\sim 10^{9}$ K, hyperonic
bulk viscosity completely suppresses the $r$-modes leading to a stable region
between the instability windows. Our analysis indicates that the instability
can reduce the angular velocity of the star up to $\sim$0.3~$\Omega_K$, where
$\Omega_K$ is the Kepler frequency of the star. | 2208.14436v1 |
2023-02-19 | Non-separable Covariance Kernels for Spatiotemporal Gaussian Processes based on a Hybrid Spectral Method and the Harmonic Oscillator | Gaussian processes provide a flexible, non-parametric framework for the
approximation of functions in high-dimensional spaces. The covariance kernel is
the main engine of Gaussian processes, incorporating correlations that underpin
the predictive distribution. For applications with spatiotemporal datasets,
suitable kernels should model joint spatial and temporal dependence. Separable
space-time covariance kernels offer simplicity and computational efficiency.
However, non-separable kernels include space-time interactions that better
capture observed correlations. Most non-separable kernels that admit explicit
expressions are based on mathematical considerations (admissibility conditions)
rather than first-principles derivations. We present a hybrid spectral approach
for generating covariance kernels which is based on physical arguments. We use
this approach to derive a new class of physically motivated, non-separable
covariance kernels which have their roots in the stochastic, linear, damped,
harmonic oscillator (LDHO). The new kernels incorporate functions with both
monotonic and oscillatory decay of space-time correlations. The LDHO covariance
kernels involve space-time interactions which are introduced by dispersion
relations that modulate the oscillator coefficients. We derive explicit
relations for the spatiotemporal covariance kernels in the three oscillator
regimes (underdamping, critical damping, overdamping) and investigate their
properties. We further illustrate the hybrid spectral method by deriving
covariance kernels that are based on the Ornstein-Uhlenbeck model. | 2302.09580v3 |
2023-11-28 | Energy diffusion in weakly interacting chains with fermionic dissipation-assisted operator evolution | Interacting lattice Hamiltonians at high temperature generically give rise to
energy transport governed by the classical diffusion equation; however,
predicting the rate of diffusion requires numerical simulation of the
microscopic quantum dynamics. For the purpose of predicting such transport
properties, computational time evolution methods must be paired with schemes to
control the growth of entanglement to tractably simulate for sufficiently long
times. One such truncation scheme -- dissipation-assisted operator evolution
(DAOE) -- controls entanglement by damping out components of operators with
large Pauli weight. In this paper, we generalize DAOE to treat fermionic
systems. Our method instead damps out components of operators with large
fermionic weight. We investigate the performance of DAOE, the new fermionic
DAOE (FDAOE), and another simulation method, density matrix truncation (DMT),
in simulating energy transport in an interacting one-dimensional Majorana
chain. The chain is found to have a diffusion coefficient scaling like
interaction strength to the fourth power, contrary to naive expectations based
on Fermi's Golden rule -- but consistent with recent predictions based on the
theory of \emph{weak integrability breaking}. In the weak interaction regime
where the fermionic nature of the system is most relevant, FDAOE is found to
simulate the system more efficiently than DAOE. | 2311.17148v2 |
2005-03-08 | Electron-Ion Recombination Rate Coefficients and Photoionization Cross Sections for Astrophysically Abundant Elements. IX. Ni XXVI and Ni XXVII for UV and X-ray modeling | The inverse processes of photoionization and electron-ion recombination of
(hnu + Ni XXVI --> Ni XXVII + e and (hnu + Ni XXVII --> Ni XXVIII + e) are
studied using the unified method for the total recombination. The method
subsumes both the radiative and di-electronic recombination processes and
enables self-consistent sets of results for photoionization and electron-ion
recombination by using the same wavefunction expansion. Photoionization cross
sections (sigma_PI), recombination cross sections (sigma_{RC}), recombination
collision strengths (Omega_{RC}), and recombination rate coefficients
(alpha_{RC}) are obtained for ionization balance and spectral analysis of UV
and X-ray lines. Level-specific photoionization cross sections and
recombination rates are presented to enable accurate computation of
recombination-cascade matrices for all fine structure levels n(SLJ) up to n <=
10: 98 bound fine structure levels of Ni XXVI with 0 <= l <= 9, 0 <= L <= 11,
1/2 <= J <= 17/2, and 198 levels of Ni XXVII with 0 <= l <= 9, 0 <= L <= 14, 0
<= J <= 10. Total alpha_{RC} for Ni XXVI and Ni XXVII are compared with the
existing values with very good agreement. Total recombination rate coefficients
for the hydrogen-like recombined ion, Ni XXVIII, are also presented. The
calculations are carried out in relativistic Breit-Pauli R-matrix (BPRM)
approximation with inclusion of radiation damping of resonances. With
consideration of all details of the processes, the results, which include the
level specific sigma_{PI} and alpha_{R} calculated for the first time, should
be the most accurate for these ions. | 0503197v1 |
2013-09-12 | Diffusive transport in Weyl semimetals | Diffusion, a ubiquitous phenomenon in nature, is a consequence of particle
number conservation and locality, in systems with sufficient damping. In this
paper we consider diffusive processes in the bulk of Weyl semimetals, which are
exotic quantum materials, recently of considerable interest. In order to do
this, we first explicitly implement the analytical scheme by which disorder
with anisotropic scattering amplitude is incorporated into the diagrammatic
response-function formalism for calculating the `diffuson'. The result thus
obtained is consistent with transport coefficients evaluated from the Boltzmann
transport equation or the renormalized uniform current vertex calculation, as
it should be. We thus demonstrate that the computation of the diffusion
coefficient should involve the transport lifetime, and not the quasiparticle
lifetime. Using this method, we then calculate the density response function in
Weyl semimetals and discover an unconventional diffusion process that is
significantly slower than conventional diffusion. This gives rise to relaxation
processes that exhibit stretched exponential decay, instead of the usual
exponential diffusive relaxation. This result is then explained using a model
of thermally excited quasiparticles diffusing with diffusion coefficients which
are strongly dependent on their energies. We elucidate the roles of the various
energy and time scales involved in this novel process and propose an experiment
by which this process may be observed. | 1309.3278v1 |
2018-01-03 | Gravitational Waves in Locally Rotationally Symmetric (LRS) Class II Cosmologies | In this work we consider perturbations of homogeneous and hypersurface
orthogonal cosmological backgrounds with local rotational symmetry (LRS), using
a method based on the 1 + 1 + 2 covariant split of spacetime. The backgrounds,
of LRS class II, are characterised by that the vorticity, the twist of the
2-sheets, and the magnetic part of the Weyl tensor all vanish. They include the
flat Friedmann universe as a special case. The matter contents of the perturbed
spacetimes are given by vorticity-free perfect fluids, but otherwise the
perturbations are arbitrary and describe gravitational, shear, and density
waves. All the perturbation variables can be given in terms of the time
evolution of a set of six harmonic coefficients. This set decouples into one
set of four coefficients with the density perturbations acting as source terms,
and another set of two coefficients describing damped source-free gravitational
waves with odd parity. We also consider the flat Friedmann universe, which~has
been considered by several others using the 1 + 3 covariant split, as a check
of the isotropic limit. In agreement with earlier results we find a
second-order wavelike equation for the magnetic part of the Weyl tensor which
decouples from the density gradient for the flat Friedmann universes. Assuming
vanishing vector perturbations, including the density gradient, we find a
similar equation for the electric part of the Weyl tensor, which was previously
unnoticed. | 1801.01147v1 |
2019-04-12 | Phonon hydrodynamics, thermal conductivity and second sound in 2D crystals | Starting from our previous work where we have obtained a system of coupled
integro-differential equations for acoustic sound waves and phonon density
fluctuations in 2D crystals, we derive here the corresponding hydrodynamic
equations and study their consequences as function of temperature and
frequency. These phenomena encompass propagation and damping of acoustic sound
waves, diffusive heat conduction, second sound and Poiseuille heat flow, all of
which are characterized by specific transport coefficients. We calculate these
coefficients by means of correlation functions without using the concept of
relaxation time. Numerical calculations are performed as well in order to show
the temperature dependence of the transport coefficients and of the thermal
conductivity. As a consequence of thermal tension mechanical and thermal
phenomena are coupled. We calculate the dynamic susceptibilities for
displacement and temperature fluctuations and study their resonances. Due to
the thermo-mechanical coupling the thermal resonances such as Landau-Placzek
peak and second sound doublet appear in the displacement susceptibility and
conversely the acoustic sound wave doublet appears in the temperature
susceptibility, Our analytical results do not only apply to graphene but are
also valid for arbitrary 2D crystals with hexagonal symmetry like 2D h-BN,
2H-transition metal dichalcogenides and oxides. | 1904.06327v1 |
2020-12-17 | Surface wave scattering by multiple flexible fishing cage system | A study of the wave dynamics around a multiple fishing cage system is carried
out under the assumption of the linear water wave theory and small-amplitude
wave response. The Fourier--Bessel series expansion of the velocity potential
is derived for regions enclosed under the open-water and cage systems and in
the immediate vicinity. Further, the scattering between the cages is accounted
for by employing Graf's addition theorem. The porous flexible cage system is
modelled using Darcy's law and the three-dimensional membrane equation. The
edges of the cages are moored along its circumferences to balance its position
in the deep sea. The unknown coefficients in the potentials are obtained by
employing the matched eigenfunction method in conjunction with the
least-squares approximation method. In addition, the far-field scattering
coefficients for the entire system are obtained by expanding the Bessel and
Hankel functions in the plane wave representation form. Numerical results such
as the hydrodynamic forces, scattering coefficients, and power dissipation are
investigated for various cage and wave parameters. The wave loading on the cage
system can be significantly damped by the spatial arrangement, membrane
tension, and porous-effect parameter. Moreover, the far-field results suggest
that the cage system can also be used as a breakwater. | 2012.09522v1 |
2021-01-19 | Role of nucleon-nucleon correlation in transport coefficients and gravitational-wave-driven $r$-mode instability of neutron stars | The thermal conductivity and shear viscosity of dense nuclear matter, along
with the corresponding shear viscosity timescale of canonical neutron stars
(NSs), are investigated, where the effect of Fermi surface depletion (i.e., the
$Z$-factor effect) induced by the nucleon-nucleon correlation are taken into
account. The factors which are responsible for the transport coefficients,
including the equation of state for building the stellar structure, nucleon
effective masses, in-medium cross sections, and the $Z$-factor at Fermi
surfaces, are all calculated in the framework of the Brueckner theory. The
Fermi surface depletion is found to enhance the transport coefficients by
several times at high densities, which is more favorable to damping the
gravitational-wave-driven $r$-mode instability of NSs. Yet, the onset of the
$Z$-factor-quenched neutron triplet superfluidity provides the opposite
effects, which can be much more significant than the above mentioned $Z$-factor
effect itself. Therefore, different from the previous understanding, the
nucleon shear viscosity is still smaller than the lepton one in the superfluid
NS matter at low temperatures. Accordingly, the shear viscosity cannot stablize
canonical NSs against $r$-mode oscillations even at quite low core temperatures
$10^6$ K. | 2101.07551v1 |
2022-07-12 | Operator growth and Krylov construction in dissipative open quantum systems | Inspired by the universal operator growth hypothesis, we extend the formalism
of Krylov construction in dissipative open quantum systems connected to a
Markovian bath. Our construction is based upon the modification of the
Liouvillian superoperator by the appropriate Lindbladian, thereby following the
vectorized Lanczos algorithm and the Arnoldi iteration. This is well justified
due to the incorporation of non-Hermitian effects due to the environment. We
study the growth of Lanczos coefficients in the transverse field Ising model
(integrable and chaotic limits) for boundary amplitude damping and bulk
dephasing. Although the direct implementation of the Lanczos algorithm fails to
give physically meaningful results, the Arnoldi iteration retains the generic
nature of the integrability and chaos as well as the signature of
non-Hermiticity through separate sets of coefficients (Arnoldi coefficients)
even after including the dissipative environment. Our results suggest that the
Arnoldi iteration is meaningful and more appropriate in dealing with open
systems. | 2207.05347v3 |
2022-09-27 | Inertio-capillary rebound of a droplet impacting a fluid bath | The rebound of droplets impacting a deep fluid bath is studied both
experimentally and theoretically. Millimetric drops are generated using a
piezoelectric droplet-on-demand generator and normally impact a bath of the
same fluid. Measurements of the droplet trajectory and other rebound metrics
are compared directly to the predictions of a linear quasi-potential model, as
well as fully resolved direct numerical simulations (DNS) of the unsteady
Navier-Stokes equations. Both models resolve the time-dependent bath and
droplet shapes in addition to the droplet trajectory. In the quasi-potential
model, the droplet and bath shape are decomposed using orthogonal function
decompositions leading to two sets of coupled damped linear harmonic oscillator
equations solved using an implicit numerical method. The underdamped dynamics
of the drop are directly coupled to the response of the bath through a
single-point kinematic match condition which we demonstrate to be an effective
and efficient model in our parameter regime of interest. Starting from the
inertio-capillary limit in which both gravitational and viscous effects are
negligible, increases in gravity or viscosity lead to a decrease in the
coefficient of restitution and an increase in the contact time. The
inertio-capillary limit defines an upper bound on the possible coefficient of
restitution for droplet-bath impact, depending only on the Weber number. The
quasi-potential model is able to rationalize historical experimental
measurements for the coefficient of restitution, first presented by Jayaratne
and Mason (1964). | 2209.13276v2 |
2017-06-28 | Generating Log-normal Mock Catalog of Galaxies in Redshift Space | We present a public code to generate a mock galaxy catalog in redshift space
assuming a log-normal probability density function (PDF) of galaxy and matter
density fields. We draw galaxies by Poisson-sampling the log-normal field, and
calculate the velocity field from the linearised continuity equation of matter
fields, assuming zero vorticity. This procedure yields a PDF of the pairwise
velocity fields that is qualitatively similar to that of N-body simulations. We
check fidelity of the catalog, showing that the measured two-point correlation
function and power spectrum in real space agree with the input precisely. We
find that a linear bias relation in the power spectrum does not guarantee a
linear bias relation in the density contrasts, leading to a cross-correlation
coefficient of matter and galaxies deviating from unity on small scales. We
also find that linearising the Jacobian of the real-to-redshift space mapping
provides a poor model for the two-point statistics in redshift space. That is,
non-linear redshift-space distortion is dominated by non-linearity in the
Jacobian. The power spectrum in redshift space shows a damping on small scales
that is qualitatively similar to that of the well-known Fingers-of-God (FoG)
effect due to random velocities, except that the log-normal mock does not
include random velocities. This damping is a consequence of non-linearity in
the Jacobian, and thus attributing the damping of the power spectrum solely to
FoG, as commonly done in the literature, is misleading. | 1706.09195v2 |
2021-02-22 | Slow-Mode Magnetoacoustic Waves in Coronal Loops | Rapidly decaying long-period oscillations often occur in hot coronal loops of
active regions associated with small (or micro-) flares. This kind of wave
activity was first discovered with the SOHO/SUMER spectrometer from Doppler
velocity measurements of hot emission lines, thus also often called "SUMER"
oscillations. They were mainly interpreted as global (or fundamental mode)
standing slow magnetoacoustic waves. In addition, increasing evidence has
suggested that the decaying harmonic type of pulsations detected in light
curves of solar and stellar flares are likely caused by standing slow-mode
waves. The study of slow magnetoacoustic waves in coronal loops has become a
topic of particular interest in connection with coronal seismology. We review
recent results from SDO/AIA and Hinode/XRT observations that have detected both
standing and reflected intensity oscillations in hot flaring loops showing the
physical properties (e.g., oscillation periods, decay times, and triggers) in
accord with the SUMER oscillations. We also review recent advances in theory
and numerical modeling of slow-mode waves focusing on the wave excitation and
damping mechanisms. MHD simulations in 1D, 2D and 3D have been dedicated to
understanding the physical conditions for the generation of a reflected
propagating or a standing wave by impulsive heating. Various damping mechanisms
and their analysis methods are summarized. Calculations based on linear theory
suggest that the non-ideal MHD effects such as thermal conduction, compressive
viscosity, and optically thin radiation may dominate in damping of slow-mode
waves in coronal loops of different physical conditions. Finally, an overview
is given of several important seismological applications such as determination
of transport coefficients and heating function. | 2102.11376v1 |
2022-05-29 | Modeling the Dynamics of the Coronavirus SARS-CoV-2 Pandemic using Modified SIR Model with the 'Damped-Oscillator' Dynamics of the Effective Reproduction Number | The COVID-19 pandemic has been a great catastrophe that upended human lives
and caused millions of deaths all over the world. The rapid spread of the
virus, with its early-stage exponential growth and subsequent 'waves', caught
many medical professionals and decision-makers unprepared. Even though
epidemiological models have been known for almost a century (since the 'Spanish
Influenza' pandemic of 1918-20), the real-life spread of the SARS-CoV-2 virus
often confounded the modelers. While the general framework of epidemiological
models like SEIR (susceptible-exposed-infected-recovered) or SIR
(susceptible-exposed-infected) was not in question, the behavior of model
parameters turned out to be unpredictable and complicated. In particular, while
the 'basic' reproduction number, R0, can be considered a constant (for the
original SARS-CoV-2 virus, prior to the emergence of variants, R0 is between
2.5 and 3.0), the 'effective' reproduction number, R(t), was a complex function
of time, influenced by human behavior in response to the pandemic (e.g.,
masking, lockdowns, transition to remote work, etc.) To better understand these
phenomena, we model the first year of the pandemic (between February 2020 and
February 2021) for a number of localities (fifty US states, as well as several
countries) using a simple SIR model. We show that the evolution of the pandemic
can be described quite successfully by assuming that R(t) behaves in a
'viscoelastic' manner, as a sum of two or three 'damped oscillators' with
different natural frequencies and damping coefficients. These oscillators
likely correspond to different sub-populations having different reactions to
proposed mitigation measures. The proposed approach can offer future data
modelers new ways to fit the reproduction number evolution with time (as
compared to the purely data-driven approaches most prevalent today). | 2205.14747v1 |
2023-08-03 | Part I: Rebuttal to "Uniform stabilization for the Timoshenko beam by a locally distributed damping" | A paper, entitled "Uniform stabilization for the Timoshenko beam by a locally
distributed damping" was published in 2003, in the journal Electronic Journal
of Differential Equations. Its title concerns exclusively its Section 3,
devoted to the case of equal speeds of propagation and to its main theorem,
namely Theorem 3.1. It states that the solutions of the Timoshenko system (see
(1.3) in [1]) decays exponentially when the damping coefficient b is locally
distributed. The proof of Theorem 3.1 is crucially based on Lemma 3.6, which
states the existence of a strict Lyapunov function along which the solutions of
(1.3) decay when the speeds of propagation are equal. This rebuttal shows the
major gap and flaws in the proof of Lemma 3.6, which invalidate the proofs of
Lemma 3.6 and Theorem 3.1. Lemma 3.6 is stated at the top of page 12. The main
part of its proof is given in the pages 12 and 13. In the last eight lines of
page 13, eight inequalities are requested to hold together for the proof of
Lemma 3.6. They don't appear in the statements of Lemma 3.6. The subsequent
flaws come from the evidence that several of them are contradictory either
between them or with claims in the title of the article. We also point in this
rebuttal other flaws, or gaps in the proofs of Theorem 2.2 related to strong
stability and non uniform stability for the case of distinct speeds of
propagation. In [3], we correct and complete the proof of strong stability. We
also correct, set up the missing functional frames, fill the gaps in the proof
of non uniform stability in the cases of different speeds of propagation, and
complete a missing argument in the proof of Theorem A in [4] (see Remark 4.3),
the result of Theorem A being used in the paper [1] on which this rebuttal is
mainly devoted. | 2308.01611v1 |
2023-08-05 | Modulating Spin Current Induced Effective Damping in $β-W/Py$ Heterostructures by a Systematic Variation in Resistivity of the Sputtered Deposited $β-W$ films | Utilizing the spin-induced pumping from a ferromagnet (FM) into a heavy metal
(HM) under the ferromagnetic resonance (FMR) condition, we report an
enhancement in effective damping in $\beta$- W/Py bilayers by systematically
varying resistivity ($\rho_{W}$) of $\beta$-W films. Different resistivity
ranging from 100 $\mu\Omega$-cm to 1400 $\mu\Omega$-cm with a thickness of 8 nm
can be achieved by varying the argon pressure ($P_{Ar}$) during the growth by
the method of sputtering. The coefficient of effective damping $\alpha_{eff}$
is observed to increase from 0.010 to 0.025 with $\rho_{W}$, which can be
modulated by $P_{Ar}$. We observe a modest dependence of $\alpha_{eff}$ on the
sputtering power ($p_{S}$) while keeping the $P_{Ar}$ constant. $\alpha_{eff}$
dependence on both $P_{Ar}$ and $p_{S}$ suggests that there exists a strong
correlation between $\alpha_{eff}$ and $\rho_{W}$. It is thus possible to
utilize $\rho_{W}$ as a tuning parameter to regulate the $\alpha_{eff}$, which
can be advantageous for faster magnetization dynamics switching. The thickness
dependence study of Py in the aforementioned bilayers manifests a higher spin
mixing conductance ($g^{\uparrow\downarrow}_{eff}$) which suggests a strong
spin pumping from Py into the $\beta$-W layer. The effective spin current
($J_{S(eff)}$) is also evaluated by considering the spin-back flow in this
process. Intrinsic spin mixing conductance ($g^{\uparrow\downarrow}_{W}$) and
spin diffusion length ($\lambda_{SD}$) of $\beta$-W are additionally
investigated using thickness variations in $\beta$-W. Furthermore, the
low-temperature study in $\beta$-W/Py reveals an intriguing temperature
dependence in $\alpha_{eff}$ which is quite different from $\alpha_{b}$ of
single Py layer and the enhancement in $\alpha_{eff}$ at low temperature can be
attributed to the spin-induced pumping from Py layer into $\beta$-W. | 2308.02939v1 |
2004-05-06 | On a theorem of Kac and Gilbert | We prove a general operator theoretic result that asserts that many
multiplicity two selfadjoint operators have simple singular spectrum. | 0405110v1 |
2011-01-05 | Beating the Gilbert-Varshamov Bound for Online Channels | In the online channel coding model, a sender wishes to communicate a message
to a receiver by transmitting a codeword x =(x_1,...,x_n) in {0,1}^n bit by bit
via a channel limited to at most pn corruptions. The channel is online in the
sense that at the ith step the channel decides whether to flip the ith bit or
not and its decision is based only on the bits transmitted so far, i.e.,
(x_1,...,x_i). This is in contrast to the classical adversarial channel in
which the corruption is chosen by a channel that has full knowledge on the sent
codeword x. The best known lower bound on the capacity of both the online
channel and the classical adversarial channel is the well-known
Gilbert-Varshamov bound. In this paper we prove a lower bound on the capacity
of the online channel which beats the Gilbert-Varshamov bound for any positive
p such that H(2p) < 0.5 (where H is the binary entropy function). To do so, we
prove that for any such p, a code chosen at random combined with the nearest
neighbor decoder achieves with high probability a rate strictly higher than the
Gilbert-Varshamov bound (for the online channel). | 1101.1045v1 |
2014-11-25 | From heavy-tailed Boolean models to scale-free Gilbert graphs | Define the scale-free Gilbert graph based on a Boolean model with
heavy-tailed radius distribution on the $d$-dimensional torus by connecting two
centers of balls by an edge if at least one of the balls contains the center of
the other. We investigate two asymptotic properties of this graph as the size
of the torus tends to infinity. First, we determine the tail index associated
with the asymptotic distribution of the sum of all power-weighted incoming and
outgoing edge lengths at a randomly chosen vertex. Second, we study the
behavior of chemical distances on scale-free Gilbert graphs and show the
existence of different regimes depending on the tail index of the radius
distribution. Despite some similarities to long-range percolation and
ultra-small scale-free geometric networks, scale-free Gilbert graphs are
actually more closely related to fractal percolation and this connection gives
rise to different scaling limits. We also propose a modification of the graph,
where the total number of edges can be reduced substantially at the cost of
introducing a logarithmic factor in the chemical distances. | 1411.6824v1 |
2016-03-16 | Recent Results from SPLASH: Chemical Abundances and Kinematics of Andromeda's Stellar Halo | Large scale surveys of Andromeda's resolved stellar populations have
revolutionized our view of this galaxy over the past decade. The combination of
large-scale, contiguous photometric surveys and pointed spectroscopic surveys
has been particularly powerful for discovering substructure and disentangling
the structural components of Andromeda. The SPLASH (Spectroscopic and
Photometric Landscape of Andromeda's Stellar Halo) survey consists of broad-
and narrow-band imaging and spectroscopy of red giant branch stars in lines of
sight ranging in distance from 2 kpc to more than 200 kpc from Andromeda's
center. The SPLASH data reveal a power-law surface brightness profile extending
to at least two-thirds of Andromeda's virial radius (Gilbert et al. 2012), a
metallicity gradient extending to at least 100 kpc from Andromeda's center
(Gilbert et al. 2014), and evidence of a significant population of heated disk
stars in Andromeda's inner halo (Dorman et al. 2013). We are also using the
velocity distribution of halo stars to measure the tangential motion of
Andromeda (Beaton et al., in prep). | 1603.05160v1 |
2017-05-09 | Gilbert's disc model with geostatistical marking | We study a variant of Gilbert's disc model, in which discs are positioned at
the points of a Poisson process in $\mathbb{R}^2$ with radii determined by an
underlying stationary and ergodic random field
$\varphi:\mathbb{R}^2\to[0,\infty)$, independent of the Poisson process. When
the random field is independent of the point process one often talks about
'geostatistical marking'. We examine how typical properties of interest in
stochastic geometry and percolation theory, such as coverage probabilities and
the existence of long-range connections, differ between Gilbert's model with
radii given by some random field and Gilbert's model with radii assigned
independently, but with the same marginal distribution. Among our main
observations we find that complete coverage of $\mathbb{R}^2$ does not
necessarily happen simultaneously, and that the spatial dependence induced by
the random field may both increase as well as decrease the critical threshold
for percolation. | 1705.03337v2 |
2019-01-30 | Is the mailing Gilbert-Steiner problem convex? | A convexification of the mailing version of the finite Gilbert problem for
optimal networks is introduced. It is ia convex functional on the set of
probability measures subject to the Wasserstein $p-$ metric. The minimizer of
this convex functional is a measure supported in a graph. If this graph is a
tree (i.e contains no cycles) then this tree is also a minimum of the
corresponding mailing Gilbert problem. A numerical algorithm for the
implementation of the convexified Gilbert-mailing problem is also suggested,
based on entropic regularization. | 1901.10924v4 |
2019-11-06 | Phase transitions for chase-escape models on Gilbert graphs | We present results on phase transitions of local and global survival in a
two-species model on Gilbert graphs. At initial time there is an infection at
the origin that propagates on the Gilbert graph according to a continuous-time
nearest-neighbor interacting particle system. The Gilbert graph consists of
susceptible nodes and nodes of a second type, which we call white knights. The
infection can spread on susceptible nodes without restriction. If the infection
reaches a white knight, this white knight starts to spread on the set of
infected nodes according to the same mechanism, with a potentially different
rate, giving rise to a competition of chase and escape. We show
well-definedness of the model, isolate regimes of global survival and
extinction of the infection and present estimates on local survival. The proofs
rest on comparisons to the process on trees, percolation arguments and
finite-degree approximations of the underlying random graphs. | 1911.02622v2 |
2019-12-13 | Distance between Bound Entangled States from Unextendible Product Bases and Separable States | We discuss the use of the Gilbert algorithm to tailor entanglement witnesses
for unextendibleproduct basis bound entangled states (UPB BE states). The
method relies on the fact that an optimalentanglement witness is given by a
plane perpendicular to a line between the reference state, entanglementof which
is to be witnessed, and its closest separable state (CSS). The Gilbert
algorithm finds anapproximation of CSS. In this article, we investigate if this
approximation can be good enough toyield a valid entanglement witness. We
compare witnesses found with Gilbert algorithm and those givenby
Bandyopadhyay-Ghosh-Roychowdhury (BGR) construction. This comparison allows us
to learnabout the amount of entanglement and we find a relationship between it
and a feature of the constructionof UPB BE states, namely the size of their
central tile. We show that in most studied cases, witnessesfound with the
Gilbert algorithm in this work are more optimal than ones obtained by
Bandyopadhyay,Ghosh, and Roychowdhury. This result implies the increased
tolerance to experimental imperfections ina realization of the state. | 1912.06569v2 |
2020-10-16 | Genome organization: experiments and modelling | This is an introduction to the special issue Genome organization: experiments
and simulations, published in Chromosome Research, volume 25, issue 1 (2017). | 2010.08464v1 |
2023-10-17 | Sparse grid approximation of stochastic parabolic PDEs: The Landau--Lifshitz--Gilbert equation | We show convergence rates for a sparse grid approximation of the distribution
of solutions of the stochastic Landau-Lifshitz-Gilbert equation. Beyond being a
frequently studied equation in engineering and physics, the stochastic
Landau-Lifshitz-Gilbert equation poses many interesting challenges that do not
appear simultaneously in previous works on uncertainty quantification: The
equation is strongly non-linear, time-dependent, and has a non-convex side
constraint. Moreover, the parametrization of the stochastic noise features
countably many unbounded parameters and low regularity compared to other
elliptic and parabolic problems studied in uncertainty quantification. We use a
novel technique to establish uniform holomorphic regularity of the
parameter-to-solution map based on a Gronwall-type estimate and the implicit
function theorem. This method is very general and based on a set of abstract
assumptions. Thus, it can be applied beyond the Landau-Lifshitz-Gilbert
equation as well. We demonstrate numerically the feasibility of approximating
with sparse grid and show a clear advantage of a multi-level sparse grid
scheme. | 2310.11225v2 |
2024-04-04 | Resolving Gilbert's Conjecture: Dimensional Dependencies in Hardy Spaces Valued in Clifford Modules | This article provides a thorough investigation into Gilbert's Conjecture,
pertaining to Hardy spaces in the upper half-space valued in Clifford modules.
We explore the conjecture proposed by Gilbert in 1991, which seeks to extend
the classical principle of representing real $L^p$ functions on the real line
as boundary values of Hardy holomorphic functions to higher-dimensional
Euclidean spaces valued in any Clifford module. We present a complete
resolution to this conjecture, demonstrating that its validity is contingent
upon the dimension $n$, specifically holding true when \(n \not\equiv 6, 7 \mod
8\) and failing otherwise. The pivotal discovery that Gilbert's conjecture can
be reformulated as a set of algebraic conditions is underscored in this work.
To navigate these conditions, we employ a novel strategy that leverages the
octonions, revealing their instrumental role in addressing issues related to
Clifford modules and spinors. This innovative approach not only provides
explicit realization through the generalization of the Hilbert transform to the
Riesz transform but also establishes a significant advancement in the
understanding of Hardy spaces within higher dimensions. | 2404.03478v1 |
1998-02-23 | Shell Effects on Rotational Damping in Superdeformed Nuclei | Damping of rotational motion in superdeformed Hg and Dy-region nuclei is
studied by means of cranked shell model diagonalization. It is shown that a
shell oscillation in single-particle alignments affects significantly
properties of rotational damping. Onset properties of damping and damping width
for Hg are quite different from those for Dy-region superdeformed nuclei. | 9802065v1 |
2003-08-29 | Influence of radiative damping on the optical-frequency susceptibility | Motivated by recent discussions concerning the manner in which damping
appears in the electric polarizability, we show that (a) there is a dependence
of the nonresonant contribution on the damping and that (b) the damping enters
according to the "opposite sign prescription." We also discuss the related
question of how the damping rates in the polarizability are related to
energy-level decay rates. | 0309001v1 |
2024-03-19 | Weakly elliptic damping gives sharp decay | We prove that weakly elliptic damping gives sharp energy decay for the
abstract damped wave semigroup, where the damping is not in the functional
calculus. In this case, there is no overdamping. We show applications in
linearised water waves and Kelvin--Voigt damping. | 2403.13067v1 |
2019-02-25 | Resonant absorption as a damping mechanism for the transverse oscillations of the coronal loops observed by SDO/AIA | Solar coronal loops represent the variety of fast, intermediate, and slow
normal mode oscillations. In this study, the transverse oscillations of the
loops with a few-minutes period and also with damping caused by the resonant
absorption were analyzed using extreme ultraviolet (EUV) images of the Sun. We
employed the 171 $\AA$ data recorded by Solar Dynamic Observatory
(SDO)/Atmospheric Imaging Assembly (AIA) to analyze the parameters of coronal
loop oscillations such as period, damping time, loop length, and loop width.
For the loop observed on 11 October 2013, the period and the damping of this
loop are obtained to be 19 and 70 minutes, respectively. The damping quality,
the ratio of the damping time to the period, is computed about 3.6. The period
and damping time for the extracted loop recorded on 22 January 2013 are about
81 and 6.79 minutes, respectively. The damping quality is also computed as 12.
It can be concluded that the damping of the transverse oscillations of the
loops is in the strong damping regime, so resonant absorption would be the main
reason for the damping. | 1902.09649v1 |
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