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2022-07-27 | Subsonic time-periodic solution to compressible Euler equations with damping in a bounded domain | In this paper, we consider the one-dimensional isentropic compressible Euler
equations with linear damping $\beta(t,x)\rho u$ in a bounded domain, which can
be used to describe the process of compressible flows through a porous
medium.~And the model is imposed a dissipative subsonic time-periodic boundary
condition.~Our main results reveal that the time-periodic boundary can trigger
a unique subsonic time-periodic smooth solution which is stable under small
perturbations on initial data. Moreover, the time-periodic solution possesses
higher regularity and stability provided a higher regular boundary condition. | 2207.13433v1 |
2022-09-10 | Landau damping on the torus for the Vlasov-Poisson system with massless electrons | This paper studies the nonlinear Landau damping on the torus $\mathbb{T}^d$
for the Vlasov-Poisson system with massless electrons (VPME). We consider
solutions with analytic or Gevrey ($\gamma > 1/3$) initial data, close to a
homogeneous equilibrium satisfying a Penrose stability condition. We show that
for such solutions, the corresponding density and force field decay
exponentially fast as time goes to infinity. This work extends the results for
Vlasov-Poisson on the torus to the case of ions and, more generally, to
arbitrary analytic nonlinear couplings. | 2209.04676v2 |
2022-09-25 | Polynomial mixing of a stochastic wave equation with dissipative damping | We study the long time statistics of a class of semi--linear wave equations
modeling the motions of a particle suspended in continuous media while being
subjected to random perturbations via an additive Gaussian noise. By comparison
with the nonlinear reaction settings, of which the solutions are known to
possess geometric ergodicity, we find that, under the impact of nonlinear
dissipative damping, the mixing rate is at least polynomial of any order. This
relies on a combination of Lyapunov conditions, the contracting property of the
Markov transition semigroup as well as the notion of $d$--small sets. | 2209.12151v2 |
2022-09-30 | A Lyapunov approach for the exponential stability of a damped Timoshenko beam | In this technical note, we consider the stability properties of a viscously
damped Timoshenko beam equation with spatially varying parameters. With the
help of the port-Hamiltonian framework, we first prove the existence of
solutions and show, by an appropriate Lyapunov function, that the system is
exponentially stable and has an explicit decay rate. The explicit exponential
bound is computed for an illustrative example of which we provide some
numerical simulations. | 2209.15281v1 |
2022-11-01 | Well-posedness and strong attractors for a beam model with degenerate nonlocal strong damping | This paper is devoted to initial-boundary value problem of an extensible beam
equation with degenerate nonlocal energy damping in
$\Omega\subset\mathbb{R}^n$: $u_{tt}-\kappa\Delta u+\Delta^2u-\gamma(\Vert
\Delta u\Vert^2+\Vert u_t\Vert^2)^q\Delta u_t+f(u)=0$. We prove the global
existence and uniqueness of weak solutions, which gives a positive answer to an
open question in [24]. Moreover, we establish the existence of a strong
attractor for the corresponding weak solution semigroup, where the ``strong"
means that the compactness and attractiveness of the attractor are in the
topology of a stronger space $\mathcal{H}_{\frac{1}{q}}$. | 2211.00287v3 |
2022-11-18 | Energy decay estimates for an axially travelling string damped at one end | We study the small vibrations of an axially travelling string with a
dashpoint damping at one end. The string is modelled by a wave equation in a
time-dependent interval with two endpoints moving at a constant speed $v$. For
the undamped case, we obtain a conserved functional equivalent to the energy of
the solution. We derive precise upper and lower estimates for the exponential
decay of the energy with explicit constants. These estimates do not seem to be
reported in the literature even for the non-travelling case $v=0$. | 2211.10537v1 |
2022-12-01 | The viscous damping of three dimensional spherical gas bubble inside unbounded compressible liquid | The present paper considers a homogeneous bubble inside an unbounded
polytropic compressible liquid with viscosity. The system is governed by the
Navier-Stokes equation with free boundary which is determined by the kinematic
and dynamic boundary conditions on the bubble-liquid interface. The global
existence of solution is proved, and the $\dot{H}^1$ asymptotic stability of
the spherical equilibrium in terms of viscous damping together with a explicit
decay rate is given in bare energy methods. | 2212.00299v1 |
2022-12-27 | Stabilization of the Kawahara-Kadomtsev-Petviashvili equation with time-delayed feedback | Results of stabilization for the higher order of the Kadomtsev-Petviashvili
equation are presented in this manuscript. Precisely, we prove with two
different approaches that under the presence of a damping mechanism and an
internal delay term (anti-damping) the solutions of the
Kawahara-Kadomtsev-Petviashvili equation are locally and globally exponentially
stable. The main novelty is that we present the optimal constant, as well as
the minimal time, that ensures that the energy associated with this system goes
to zero exponentially. | 2212.13552v1 |
2023-03-11 | Control estimates for 0th order pseudodifferential operators | We introduce the control conditions for 0th order pseudodifferential
operators $\mathbf{P}$ whose real parts satisfy the Morse--Smale dynamical
condition. We obtain microlocal control estimates under the control conditions.
As a result, we show that there are no singular profiles in the solution to the
evolution equation $(i\partial_t-\mathbf{P})u=f$ when $\mathbf{P}$ has a
damping term that satisfies the control condition and $f\in C^{\infty}$. This
is motivated by the study of a microlocal model for the damped internal waves. | 2303.06443v2 |
2023-03-25 | Existence and regularity of global attractors for a Kirchhoff wave equation with strong damping and memory | This paper is concerned with the existence and regularity of global attractor
$\mathcal A$ for a Kirchhoff wave equation with strong damping and memory in
the weighted time-dependent spaces $\mathcal H$ and $\mathcal H^{1}$,
respectively. In order to obtain the existence of $\mathcal A$, we mainly use
the energy method in the priori estimations, and then verify the asymptotic
compactness of the semigroup by the method of contraction function. Finally, by
decomposing the weak solutions into two parts and some elaborate calculations,
we prove the regularity of $\mathcal A$. | 2303.14387v1 |
2023-03-27 | Linear Landau damping for a two-species Vlasov-Poisson system for electrons and ions | This paper concerns the linear Landau damping for the two species
Vlasov-Poisson system for ions and electrons near Penrose stable equilibria.
The result is an extension of the result on the one species Vlasov-Poisson
equation by Mouhout and Villani. Different from their work we do not describe
the ions as a background species but as a species which is also described by a
separate Vlasov equation. We show an exponential decay of the electric energy
for the linearised system near Penrose stable equilibria. | 2303.14981v2 |
2023-03-28 | Role of intersublattice exchange interaction on ultrafast longitudinal and transverse magnetization dynamics in Permalloy | We report about element specific measurements of ultrafast demagnetization
and magnetization precession damping in Permalloy (Py) thin films.
Magnetization dynamics induced by optical pump at $1.5$eV is probed
simultaneously at the $M_{2,3}$ edges of Ni and Fe with High order Harmonics
for moderate demagnetization rates (less than $50$%). The role of the
intersublattice exchange interaction on both longitudinal and transverse
dynamics is analyzed with a Landau Lifshitz Bloch description of
ferromagnetically coupled Fe and Ni sublattices. It is shown that the
intersublattice exchange interaction governs the dissipation during
demagnetization as well as precession damping of the magnetization vector. | 2303.15837v1 |
2023-03-31 | Polynomial Mixing for a Weakly Damped Stochastic Nonlinear Schrödinger Equation | This paper is devoted to proving the polynomial mixing for a weakly damped
stochastic nonlinear Schr\"{o}dinger equation with additive noise on a 1D
bounded domain. The noise is white in time and smooth in space. We consider
both focusing and defocusing nonlinearities, respectively, with exponents of
the nonlinearity $\sigma\in[0,2)$ and $\sigma\in[0,\infty)$ and prove the
polynomial mixing which implies the uniqueness of the invariant measure by
using a coupling method. | 2303.18082v1 |
2023-04-19 | Inviscid damping of monotone shear flows for 2D inhomogeneous Euler equation with non-constant density in a finite channel | We prove the nonlinear inviscid damping for a class of monotone shear flows
with non-constant background density for the two-dimensional ideal
inhomogeneous fluids in $\mathbb{T}\times [0,1]$ when the initial perturbation
is in Gevrey-$\frac{1}{s}$ ($\frac{1}{2}<s<1$) class with compact support. | 2304.09841v2 |
2023-05-07 | Nonexistence of global weak solutions to semilinear wave equations involving time-dependent structural damping terms | We consider a semilinear wave equation involving a time-dependent structural
damping term of the form
$\displaystyle\frac{1}{{(1+t)}^{\beta}}(-\Delta)^{\sigma/2} u_t$. Our results
show the influence of the parameters $\beta,\sigma$ on the nonexistence of
global weak solutions under assumptions on the given system data. | 2305.04278v1 |
2023-05-15 | Blow-up phenomena for a class of extensible beam equations | In this paper, we investigate the initial boundary value problem of the
following nonlinear extensible beam equation with nonlinear damping term $$u_{t
t}+\Delta^2 u-M\left(\|\nabla u\|^2\right) \Delta u-\Delta
u_t+\left|u_t\right|^{r-1} u_t=|u|^{p-1} u$$ which was considered by Yang et
al. (Advanced Nonlinear Studies 2022; 22:436-468). We consider the problem with
the nonlinear damping and establish the finite time blow-up of the solution for
the initial data at arbitrary high energy level, including the estimate lower
and upper bounds of the blowup time. The result provides some affirmative
answer to the open problems given in (Advanced Nonlinear Studies 2022;
22:436-468). | 2305.08398v1 |
2023-06-08 | Vanishing of long time average p-enstrophy dissipation rate in the inviscid limit of the 2D damped Navier-Stokes equations | In 2007, Constantin and Ramos proved a result on the vanishing long time
average enstrophy dissipation rate in the inviscid limit of the 2D damped
Navier-Stokes equations. In this work, we prove a generalization of this for
the p-enstrophy, sequences of distributions of initial data and sequences of
strongly converging right-hand sides. We simplify their approach by working
with invariant measures on the global attractors which can be characterized via
bounded complete solution trajectories. Then, working on the level of
trajectories allows us to directly employ some recent results on strong
convergence of the vorticity in the inviscid limit. | 2306.05081v1 |
2023-06-16 | Algorithm MGB to solve highly nonlinear elliptic PDEs in $\tilde{O}(n)$ FLOPS | We introduce Algorithm MGB (Multi Grid Barrier) for solving highly nonlinear
convex Euler-Lagrange equations. This class of problems includes many highly
nonlinear partial differential equations, such as $p$-Laplacians. We prove
that, if certain regularity hypotheses are satisfied, then our algorithm
converges in $\tilde{O}(1)$ damped Newton iterations, or $\tilde{O}(n)$ FLOPS,
where the tilde indicates that we neglect some polylogarithmic terms. This the
first algorithm whose running time is proven optimal in the big-$\tilde{O}$
sense. Previous algorithms for the $p$-Laplacian required $\tilde{O}(\sqrt{n})$
damped Newton iterations or more. | 2306.10183v1 |
2023-07-24 | On the stability of a double porous elastic system with visco-porous dampings | In this paper we consider a one dimensional elastic system with double
porosity structure and with frictional damping in both porous equations. We
introduce two stability numbers $\chi_{0}$ and $\chi_{1}$ and prove that the
solution of the system decays exponentially provided that $\chi_{0}=0$ and
$\chi_{1}\neq0.$ Otherwise, we prove the lack of exponential decay. Our results
improve the results of \cite{Bazarra} and \cite{Nemsi}. | 2307.12690v1 |
2023-08-02 | Blow-up and lifespan estimate for the generalized tricomi equation with the scale-invariant damping and time derivative nonlinearity on exterior domain | The article is devoted to investigating the initial boundary value problem
for the damped wave equation in the scale-invariant case with time-dependent
speed of propagation on the exterior domain. By presenting suitable multipliers
and applying the test-function technique, we study the blow-up and the lifespan
of the solutions to the problem with derivative-type nonlinearity
$ \d u_{tt}-t^{2m}\Delta u+\frac{\mu}{t}u_t=|u_t|^p, \quad \mbox{in}\
\Omega^{c}\times[1,\infty),$ that we associate with appropriate small initial
data. | 2308.01272v2 |
2023-08-03 | Gravitational Wave Heating | It was shown in previous work that when a gravitational wave (GW) passes
through a viscous shell of matter the magnitude of the GW will be damped and
there are astrohysical circumstances in which the damping is almost complete.
The energy transfer from the GWs to the fluid will increase its temperature. We
construct a model for this process and obtain an expression for the temperature
distribution inside the shell in terms of spherical harmonics. Further, it is
shown that this effect is astrophysically significant: a model problem is
constructed for which the temperature increase is of order $10^6{}^\circ$K. | 2308.01615v2 |
2023-08-08 | Stabilization of piezoelectric beam with Coleman-Gurtin or Gurtin-Pipkin thermal law and under Lorenz gauge condition | In this paper, we present the analysis of stability for a piezoelectric beam
subject to a thermal law (Coleman-Gurtin or Gurtin-Pipkin thermal law) adding
some viscous damping mechanism to the electric field in $x-$direction and
$z-$direction, and we discuss several cases. Then, there is no need to control
the electrical field components in $x$-direction and $z-$ direction to
establish an exponential decay of solutions when the beam is subjected to a
Coleman-Gurtin law, otherwise a polynomial stability is established with
Gurtin-Pipkin thermal law in case when the electrical field components are
damped. | 2308.04231v2 |
2023-08-11 | Well-posedness and global attractor for wave equation with nonlinear damping and super-cubic nonlinearity | In the paper, we study the semilinear wave equation involving the nonlinear
damping $g(u_t) $ and nonlinearity $f(u)$. Under the wider ranges of exponents
of $g$ and $f$, the well-posedness of the weak solution is achieved by
establishing a priori space-time estimates. Then, the existence of the global
attractor in the naturally phase space $H^1_0(\Omega)\times L^2(\Omega)$ is
obtained. Moreover, we prove that the global attrator is regular, that is, the
global attractor is a bounded subset of $(H^2(\Omega)\cap H^1_0(\Omega))\times
H^1_0(\Omega)$. | 2308.06208v1 |
2023-08-16 | Stability for degenerate wave equations with drift under simultaneous degenerate damping | In this paper we study the stability of two different problems. The first one
is a one-dimensional degenerate wave equation with degenerate damping,
incorporating a drift term and a leading operator in non-divergence form. In
the second problem we consider a system that couples degenerate and
non-degenerate wave equations, connected through transmission, and subject to a
single dissipation law at the boundary of the non-degenerate equation. In both
scenarios, we derive exponential stability results. | 2308.08645v3 |
2023-09-02 | Existence and nonexistence of global solutions for time-dependent damped NLS equations | We investigate the Cauchy problem for the nonlinear Schr\"odinger equation
with a time-dependent linear damping term. Under non standard assumptions on
the loss dissipation, we prove the blow-up in the inter-critical regime, and
the global existence in the energy subcritical case. Our results generalize and
improve the ones in [9, 11, 21]. | 2309.00849v1 |
2023-09-09 | Finite-dimensionality of attractors for wave equations with degenerate nonlocal damping | In this paper we study the fractal dimension of global attractors for a class
of wave equations with (single-point) degenerate nonlocal damping. Both the
equation and its linearization degenerate into linear wave equations at the
degenerate point and the usual approaches to bound the dimension of the
entirety of attractors do not work directly. Instead, we develop a new process
concerning the dimension near the degenerate point individually and show the
finite dimensionality of the attractor. | 2309.04712v2 |
2023-09-19 | The Raman gap and collisional absorption | One of the long-standing puzzles observed in many laser-plasma experiments is
the gap in the Raman backscattering spectrum. This gap is characterized by the
absence of backscattered light between some critical wavelength and twice the
incident laser wavelength. The latter is associated with the absolute Raman
instability from the quarter-critical density surface. Supported by
particle-in-cell (PIC) simulations, it is suggested that the gap can result
from the collisional damping of the backscattered light. A linear analysis of
the competition between the Raman growth rate and the damping rate in a
non-homogenous plasma predicts the gap's existence and width as a function of
the system's parameters. The theory is compared with the PIC simulations and
past experiments. | 2309.10366v1 |
2023-09-28 | On inverse problems for a strongly damped wave equation on compact manifolds | We consider a strongly damped wave equation on compact manifolds, both with
and without boundaries, and formulate the corresponding inverse problems. For
closed manifolds, we prove that the metric can be uniquely determined, up to an
isometry, from the knowledge of the source-to-solution map. Similarly, for
manifolds with boundaries, we prove that the metric can be uniquely determined,
up to an isometry, from partial knowledge of the Dirichlet-to-Neumann map. The
key point is to retrieve the spectral information of the Laplace-Beltrami
operator, from the Laplace transform of the measurements. Further we show that
the metric can be determined up to an isometry, using a single measurement in
both scenarios. | 2309.16182v1 |
2023-10-10 | Emerging Spin-Orbit Torques in Low Dimensional Dirac Materials | We report a theoretical description of novel spin-orbit torque components
emerging in two-dimensional Dirac materials with broken inversion symmetry. In
contrast to usual metallic interfaces where field-like and damping-like torque
components are competing, we find that an intrinsic damping-like torque which
derives from all Fermi-sea electrons can be simultaneously enhanced along with
the field-like component. Additionally, hitherto overlooked torque components
unique to Dirac materials, emerge from the coupling between spin and pseudospin
degrees of freedom. These torques are found to be resilient to disorder and
could enhance the magnetic switching performance of nearby magnets. | 2310.06447v1 |
2023-10-22 | The residual flow in well-optimized stellarators | The gyrokinetic theory of the residual flow, in the electrostatic limit, is
revisited, with optimized stellarators in mind. We consider general initial
conditions for the problem, and identify cases that lead to a non-zonal
residual electrostatic potential, i.e. one having a significant component that
varies within a flux surface. We investigate the behavior of the ``intermediate
residual'' in stellarators, a measure of the flow that remains after geodesic
acoustic modes have damped away, but before the action of the slower damping
that is caused by unconfined particle orbits. The case of a quasi-isodynamic
stellarator is identified as having a particularly large such residual, owing
to the small orbit width achieved by optimization. | 2310.14218v1 |
2023-10-26 | Efficient Numerical Algorithm for Large-Scale Damped Natural Gradient Descent | We propose a new algorithm for efficiently solving the damped Fisher matrix
in large-scale scenarios where the number of parameters significantly exceeds
the number of available samples. This problem is fundamental for natural
gradient descent and stochastic reconfiguration. Our algorithm is based on
Cholesky decomposition and is generally applicable. Benchmark results show that
the algorithm is significantly faster than existing methods. | 2310.17556v1 |
2023-11-09 | Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings | We study the global well-posedness and asymptotic behavior for a semilinear
damped wave equation with Neumann boundary conditions, modelling a
one-dimensional linearly elastic body interacting with a rigid substrate
through an adhesive material. The key feature of of the problem is that the
interplay between the nonlinear force and the boundary conditions allows for a
continuous set of equilibrium points. We prove an exponential rate of
convergence for the solution towards a (uniquely determined) equilibrium point. | 2311.05295v1 |
2023-11-29 | On the exponential stability of uniformly damped wave equations | We study damped wave propagation problems phrased as abstract evolution
equations in Hilbert spaces. Under some general assumptions, including a
natural compatibility condition for initial values, we establish exponential
decay estimates for all mild solutions using the language and tools of Hilbert
complexes. This framework turns out strong enough to conduct our analysis but
also general enough to include a number of interesting examples. Some of these
are briefly discussed. By a slight modification of the main arguments, we also
obtain corresponding decay results for numerical approximations obtained by
compatible discretization strategies. | 2311.18084v1 |
2023-12-01 | Semilinear wave inequalities with double damping and potential terms on Riemannian Manifolds | We study a semilinear wave inequality with double damping on a complete
noncompact Riemannian manifold. The considered problem involves a potential
function $V$ depending on the space variable in front of the power nonlinearity
and an inhomogeneous term $W$ depending on both time and space variables.
Namely, we establish sufficient conditions for the nonexistence of weak
solutions in both cases: $W\equiv 0$ and $W\not\equiv 0$. The obtained
conditions depend on the parameters of the problem as well as the geometry of
the manifold. Some special cases of manifolds, and of $V$ and $W$ are discussed
in detail. | 2312.00617v1 |
2024-01-23 | Revisit on global existence of solutions for semilinear damped wave equations in $\mathbb{R}^N$ with noncompactly supported initial data | In this note, we study the Cauchy problem of the semilinear damped wave
equation and our aim is the small data global existence for noncompactly
supported initial data. For this problem, Ikehata and Tanizawa [5] introduced
the energy method with the exponential-type weight function $e^{|x|^2/(1+t)}$,
which is the so-called Ikehata--Todorova--Yordanov type weight. In this note,
we suggest another weight function of the form $(1+|x|^2/(1+t))^{\lambda}$,
which allows us to treat polynomially decaying initial data and give a simpler
proof than the previous studies treating such initial data. | 2401.12530v1 |
2024-01-24 | Eigenmode analysis of the damped Jaynes-Cummings model | The generating functions for density matrix elements of the Jaynes-Cummings
model with cavity damping are analysed in terms of their eigenmodes, which are
characterised by a specific temporal behaviour. These eigenmodes are shown to
be proportional to particular generalised hypergeometric functions. The
relative weights of these eigenmodes in the generating functions are determined
by the initial conditions of the model. These weights are found by deriving
orthogonality relations involving adjoint modes. In an example it is shown how
the time-dependent density matrix elements and the related factorial moments
can be extracted from the eigenmode decompositions of the generating functions. | 2401.13348v1 |
2024-02-15 | A comprehensive modelling and experimental approach for damped oscillations in U-tubes via Easy JavaScript Simulations | In recent years, science simulations have become popular among educators due
to their educational usefulness, availability, and potential for increasing the
students' knowledge on scientific topics. In this paper, we introduce the
implementation of a user-friendly simulation based on Easy Java/JavaScript
Simulations (EJS) to study the problem of damped oscillations in U-tubes.
Furthermore, we illustrate various advantages associated with the capabilities
of EJS in terms of design and usability in order to encourage teachers to use
it as an educational supplement to physics laboratories. | 2402.09866v1 |
2024-02-21 | Hybrid Multi-Directional Quantum Communication Protocol | The way a new type of state called a hybrid state, which contains more than
one degree of freedom, is used in many practical applications of quantum
communication tasks with lesser amount of resources. Similarly, our aim is here
to perform multi-quantum communication tasks in a protocol to approach quantum
information in multipurpose and multi-directional. We propose a hybrid
multi-directional six-party scheme of implementing quantum teleportation and
joint remote state preparation under the supervision of a controller via a
multi-qubit entangled state as a quantum channel with 100% success probability.
Moreover, we analytically derive the average fidelities of this hybrid scheme
under the amplitude-damping and the phase-damping noise. | 2402.14043v1 |
2024-03-19 | Damped energy-norm a posteriori error estimates for fully discrete approximations of the wave equation using C2-reconstructions | We derive a posteriori error estimates for the the scalar wave equation
discretized in space by continuous finite elements and in time by the explicit
leapfrog scheme. Our analysis combines the idea of invoking extra
time-regularity for the right-hand side, as previously introduced in the space
semi-discrete setting, with a novel, piecewise quartic, globally
twice-differentiable time-reconstruction of the fully discrete solution. Our
main results show that the proposed estimator is reliable and efficient in a
damped energy norm. These properties are illustrated in a series of numerical
examples. | 2403.12954v1 |
2004-04-16 | Transport coefficients for inelastic Maxwell mixtures | The Boltzmann equation for inelastic Maxwell models is used to determine the
Navier-Stokes transport coefficients of a granular binary mixture in $d$
dimensions. The Chapman-Enskog method is applied to solve the Boltzmann
equation for states near the (local) homogeneous cooling state. The mass, heat,
and momentum fluxes are obtained to first order in the spatial gradients of the
hydrodynamic fields, and the corresponding transport coefficients are
identified. There are seven relevant transport coefficients: the mutual
diffusion, the pressure diffusion, the thermal diffusion, the shear viscosity,
the Dufour coefficient, the pressure energy coefficient, and the thermal
conductivity. All these coefficients are {\em exactly} obtained in terms of the
coefficients of restitution and the ratios of mass, concentration, and particle
sizes. The results are compared with known transport coefficients of inelastic
hard spheres obtained analytically in the leading Sonine approximation and by
means of Monte Carlo simulations. The comparison shows a reasonably good
agreement between both interaction models for not too strong dissipation,
especially in the case of the transport coefficients associated with the mass
flux. | 0404386v2 |
2006-12-12 | Investigating Diffusion Coefficient Using Dynamic Light Scattering Technique | In this work, the Z-average, effective, apparent diffusion coefficients and
their poly-dispersity indexes were investigated for dilute poly-disperse
homogeneous spherical particles in dispersion where the Rayleigh-Gans-Debye
approximation is valid. The results reveal that the values of the apparent and
effective diffusion coefficients at a scattering angle investigated are
consistent and the difference between the effective and Z-average diffusion
coefficients is a function of the mean particle size, size distribution and
scattering angle. For the small particles with narrow size distributions, the
Z-average diffusion coefficient can be got directly at any scattering angle.
For the small particles with wide size distributions, the Z-average diffusion
coefficient should be measured at a small scattering angle. For large
particles, in order to obtain a good approximate value of Z-average diffusion
coefficient, the wider the particle size distribution, the smaller the
scattering angle that the DLS data are measured. The poly-dispersity index of
the effective diffusion coefficient at a scattering angle investigated is
consistent with that of the Z-average diffusion coefficient and without
considering the influences of noises, the difference between the
poly-dispersity indexes of the Z-average and apparent diffusion coefficients is
determined by the mean particle size, size distribution and scattering angle
together. | 0612101v1 |
2013-06-19 | Conditional Stability for Single Interior Measurement | An inverse problem to identify unknown coefficients of a partial differential
equation by a single interior measurement is considered. The equation
considered in this paper is a strongly elliptic second order scalar equation
which can have complex coefficients in a bounded domain with $C^2$ boundary and
single interior measurement means that we know a given solution of the equation
in this domain. The equation includes some model equations arising from
acoustics, viscoelasticity and hydrology. We assume that the coefficients are
piecewise analytic. Our major result is the local H\"older stability estimate
for identifying the unknown coefficients. If the unknown coefficients is a
complex coefficient in the principal part of the equation, we assumed a
condition which we named admissibility assumption for the real part and
imaginary part of the difference of the two complex coefficients. This
admissibility assumption is automatically satisfied if the complex coefficients
are real valued. For identifying either the real coefficient in the principal
part or the coefficient of the 0-th order of the equation, the major result
implies the global uniqueness for the identification. | 1306.4433v2 |
2016-04-04 | Combinatorics on several families of Kronecker coefficients related to plane partitions | We present a study of three families of Kronecker coefficients, which we
describe in terms of reduced Kronecker coefficients. This study is grounded on
the generating function of the coefficients, proved by a bijection between two
combinatorial objects. This study includes the connection between plane
partitions and these three families of reduced Kronecker coefficients,
providing us their combinatorial interpretation. As an application, we verify
that the saturation hypothesis holds for our three families of reduced
Kronecker coefficients. The study also includes other interpretation in terms
of the quasipolynomials that govern these families. We specify the degree and
the period of these quasipolynomials. Finally, the direct relation between
Kronecker coefficients and reduced Kronecker coefficients allows us to give
some observations about the rate of growth of the Kronecker coefficients
associated to the reduced Kronecker coefficients of the study. | 1604.00803v1 |
2022-06-29 | Complexity of representations of coefficients of power series in classical statistical mechanics. Their classification and complexity criteria | It is declared that the aim of simplifying representations of coefficients of
power series of classical statistical mechanics is to simplify a process of
obtaining estimates of the coefficients using their simplified representations.
The aim of the article is: to formulate criteria for the complexity (from the
above point of view) of these representations and to demonstrate their
application by examples of comparing Ree-Hoover representations of virial
coefficients and such representations of power series coefficients that are
based on the conception of the frame classification of labeled graphs.
To solve these problems, mathematical notions were introduced (such as a base
product, a base integral, a base linear combination of integrals, a base linear
combination of integrals with coefficients of negligible complexity, a base set
of base linear combinations of integrals with coefficients of negligible
complexity); and a classification of representations of coefficients of power
series of classical statistical mechanics is proposed. In this classification
the class of base linear combinations of integrals with coefficients of
negligible complexity is the most important class. It includes the most
well-known representations of the coefficients of power series of classical
statistical mechanics.
Three criteria are formulated to estimate the comparative complexity of base
linear combinations of integrals with coefficients of negligible complexity and
their extensions to the totality of base sets of base linear combinations of
integrals with coefficients of negligible complexity are constructed. The
application of all the constructed criteria is demonstrated by examples of
comparing with each other of the above power series coefficients
representations. The obtained results are presented in the tables and
commented. | 2207.07583v1 |
2023-09-15 | Doeblin Coefficients and Related Measures | Doeblin coefficients are a classical tool for analyzing the ergodicity and
exponential convergence rates of Markov chains. Propelled by recent works on
contraction coefficients of strong data processing inequalities, we investigate
whether Doeblin coefficients also exhibit some of the notable properties of
canonical contraction coefficients. In this paper, we present several new
structural and geometric properties of Doeblin coefficients. Specifically, we
show that Doeblin coefficients form a multi-way divergence, exhibit
tensorization, and possess an extremal trace characterization. We then show
that they also have extremal coupling and simultaneously maximal coupling
characterizations. By leveraging these characterizations, we demonstrate that
Doeblin coefficients act as a nice generalization of the well-known total
variation (TV) distance to a multi-way divergence, enabling us to measure the
"distance" between multiple distributions rather than just two. We then prove
that Doeblin coefficients exhibit contraction properties over Bayesian networks
similar to other canonical contraction coefficients. We additionally derive
some other results and discuss an application of Doeblin coefficients to
distribution fusion. Finally, in a complementary vein, we introduce and discuss
three new quantities: max-Doeblin coefficient, max-DeGroot distance, and
min-DeGroot distance. The max-Doeblin coefficient shares a connection with the
concept of maximal leakage in information security; we explore its properties
and provide a coupling characterization. On the other hand, the max-DeGroot and
min-DeGroot measures extend the concept of DeGroot distance to multiple
distributions. | 2309.08475v1 |
1995-02-09 | A linear thermohaline oscillator driven by stochastic atmospheric forcing | The interdecadal variability of a stochastically forced four-box model of the
oceanic meridional thermohaline circulation (THC) is described and compared to
the THC variability in the coupled ocean-atmosphere GCM of Delworth, Manabe,
and Stouffer (1993). The box model is placed in a linearly stable thermally
dominant mean state under mixed boundary conditions. A linear stability
analysis of this state reveals one damped oscillatory THC mode in addition to
purely damped modes. The variability of the model under a moderate amount of
stochastic forcing, meant to emulate the random variability of the atmosphere
affecting the coupled model's interdecadal THC variability, is studied. A
linear interpretation, in which the damped oscillatory mode is of primary
importance, is sufficient for understanding the mechanism accounting for the
stochastically forced variability. Direct comparison of the variability in the
box model and coupled GCM reveals common qualitative aspects. Such a comparison
supports, although does not verify, the hypothesis that the coupled model's THC
variability can be interpreted as the result of atmospheric weather exciting a
linear damped oscillatory THC mode. | 9502002v2 |
1993-09-30 | The metal systems in Q0000--2619 at high resolution | We have obtained high, 11 and 14 \kms, and medium, 40 and 53 \kms, resolution
spectra of the $z_{em} = 4.11$ quasar Q0000--2619 covering the range 4400 \AA\
to 9265 \AA . We identify nine metal absorption systems, of which four were
previously known. A fifth previously suggested system at $z_{abs} \approx
3.409$ (Turnshek et al~ 1991) is ruled out by our data. Two of the eight
systems for which the \lya~ line is in the observable range have a damped \lya~
line. Six of the nine systems show evidence for complex sub--component
structure. At our resolution and S/N we identify a total of 21 sub--components
in the nine systems. Five of the nine systems (11 of the 21 components) fall
within the $\pm 5000$ \kms~ range of the emission redshift, and are hence
classified as \zae~ absorbers. For the two damped systems we find metal
abundances of $\leq 1$% and $\leq 8$% of solar values at redshifts of 3.0541
and 3.3901 respectively. These upper limits are consistent with what would be
expected from previous determinations at lower redshifts, and our data are
hence compatible with earlier conclusions that no evidence is yet found for
chemical evolution of intervening damped and Lyman limit absorbers. For the
\zae~ systems we found indications of metallicities comparable to, and even in
excess of solar values. These much higher values compared to the damped
systems, are in favour of the intrinsic hypothesis for these systems. | 9309053v1 |
1994-12-27 | The z=0.8596 Damped Lyman Alpha Absorbing Galaxy Toward PKS 0454+039 | We present {\it Hubble Space Telescope} and ground--based data on the
$z_{abs}=0.8596$ metal line absorption system along the line of sight to PKS
0454+0356. The system is a moderate redshift damped Lyman alpha system, with
${\rm N(HI)}=(5.7\pm0.3)\times10^{20}$~cm$^{-2}$ as measured from the {\it
Faint Object Spectrograph} spectrum. We also present ground--based images which
we use to identify the galaxy which most probably gives rise to the damped
system; the most likely candidate is relatively underluminous by QSO absorber
standards ($M_B \sim -19.0$ for $q_0=0.5$ and $H_0=50$ \kms Mpc$^{-1}$), and
lies $\sim 8.5h^{-1}$ kpc in projection from the QSO sightline. Ground--based
measurements of Zn~II, Cr~II, and Fe~II absorption lines from this system allow
us to infer abundances of [Zn/H]=$-1.1$, [Cr/H]=$-1.2$, and [Fe/H]=$-1.2$,
indicating overall metallicity similar to damped systems at $z >2$, and that
the depletion of Cr and Fe onto dust grains may be even {\it less} important
than in many of the high redshift systems of comparable metallicity. Limits
previously placed on the 21-cm optical depth in the $z=0.8596$ system, together
with our new N(H~I) measurement, suggest a very high spin temperature for the
H~I, $T_S >> 580$ K. | 9412093v2 |
1995-05-17 | GRAVITATIONAL LENSING OF QUASARS BY THEIR DAMPED LYMAN-ALPHA ABSORBERS | Damped Lyman-alpha absorbers are believed to be associated with galactic
disks. We show that gravitational lensing can therefore affect the statistics
of these systems. First, the magnification bias due to lensing raises faint
QSOs above a given magnitude threshold and thereby enhances the probability for
observing damped absorption systems. Second, the bending of light rays from the
source effectively limits the minimum impact parameter of the line-of-sight
relative to the center of the absorber, thus providing an upper cut-off to the
observed neutral hydrogen (HI) column density. The combination of these effects
yields a pronounced peak in the observed abundance of absorbers with high
column densities (>2*10^{21} cm^{-2}) and low redshifts (z<1). The inferred
value of the cosmological density parameter of neutral hydrogen, Omega_{HI},
increases with increasing redshift and luminosity of the sources even if the
true HI density remains constant. This trend resembles the observed evolution
of Omega_{HI}(z). Damped Lyman-alpha absorbers with column densities >10^{21}
cm^{-2} and redshifts 0.5<z<1 are reliable flags for lensed QSOs with a close
pair of images separated by 0.3 arcsec. Detection of these gravitational
lensing signatures with the Hubble Space Telescope can be used to constrain the
depth of the absorber potential-wells and the cosmological constant. | 9505078v1 |
1996-08-22 | APM z>4 QSO Survey: Distribution and Evolution of High Column Density HI Absorbers | Eleven candidate damped Lya absorption systems were identified in 27 spectra
of the quasars from the APM z>4 survey covering the redshift range
2.8<z(abs)<4.4 (8 with z(abs)>3.5). High resolution echelle spectra (0.8A FWHM)
have been obtained for three quasars, including 2 of the highest redshift
objects in the survey. Two damped systems have confirmed HI column densities of
N(HI) >= 10^20.3 atoms cm^-2, with a third falling just below this threshold.
We have discovered the highest redshift damped Lya absorber known at z=4.383 in
QSO BR1202-0725. The APM QSOs provide a substantial increase in the redshift
path available for damped surveys for z>3. We combine this high redshift sample
with other quasar samples covering the redshift range 0.008 < z < 4.7 to study
the redshift evolution and the column density distribution function for
absorbers with log N(HI)>=17.2. In the HI column density distribution
f(N)=kN^-beta we find evidence for breaks in the power law, flattening for
17.2< log N(HI)<21 and steepening for log N(HI)>21.2. The column density
distribution function for the data with log N(HI)>=20.3 is better fit with the
form f(N)=(f*/N*)(N/N*)^-beta exp(-N/N*). Significant redshift evolution in the
number density per unit redshift is evident in the higher column density
systems with an apparent decline in N(z) for z>3.5. | 9608146v1 |
1997-05-16 | Testing Cosmological Models Against the Abundance of Damped Lyman-Alpha Absorbers | We calculate the number of damped Lyman-alpha absorbers expected in various
popular cosmological models as a function of redshift and compare our
predictions with observed abundances. The Press-Schechter formalism is used to
obtain the distribution of halos with circular velocity in different
cosmologies, and we calibrate the relation between circular velocity and
absorption cross-section using detailed gas dynamical simulations of a
``standard'' cold dark matter (CDM) model. Because of this calibration, our
approach makes more realistic assumptions about the absorption properties of
collapsed objects than previous, analytic calculations of the damped
Lyman-alpha abundance. CDM models with Omega_0=1, H_0=50, baryon density
Omega_b=0.05, and scale-invariant primeval fluctuations reproduce the observed
incidence and redshift evolution of damped Lyman-alpha absorption to within
observational uncertainty, for both COBE normalization (sigma_8=1.2) and a
lower normalization (sigma_8=0.7) that better matches the observed cluster
abundance at z=0. A tilted (n=0.8, sigma_8=0.7) CDM model tends to underproduce
absorption, especially at z=4. With COBE normalization, a CDM model with
Omega_0=0.4, Omega_{Lambda}=0.6 gives an acceptable fit to the observed
absorption; an open CDM model is marginally acceptable if Omega_0 is at least
0.4 and strongly inconsistent with the z=4 data if Omega_0=0.3. Mixed dark
matter models tend not to produce sufficient absorption, being roughly
comparable to tilted CDM models if Omega_{nu} = 0.2 and failing drastically if
Omega_{nu} = 0.3. | 9705118v1 |
1997-05-28 | Zinc and Chromium Abundances in a Third Damped Lyman alpha System at Intermediate Redshift | We have determined the metallicity of the $z_{abs} = 1.0093$ damped Lyman
alpha system in the bright QSO EX 0302-223; this is only the third such
measurement at redshifts $z \simlt 1$. Unlike the previous two cases, we find
that the abundance of Zn is only a factor of $\sim 2$ lower than in the
Galactic interstellar medium today and is entirely compatible with the typical
metallicity of stars in the Milky Way disk at a look-back time of 9.5 Gyrs.
Although the galaxy responsible for producing the absorption system has yet to
be positively identified, our observations show that galaxies on a chemical
evolution path similar to that of the Milky Way do contribute to the damped
Lyman alpha population at intermediate redshifts. Cr is 2.5 times less abundant
than Zn, presumably because of depletion onto dust; however, the degree of
depletion is less severe than in diffuse interstellar clouds in the disk of our
Galaxy and in the Magellanic Clouds. Evidently, the interstellar environment in
damped Lyman alpha galaxies is less conducive to the formation and survival of
dust grains (and molecular hydrogen), but the physical processes at the root of
this effect have yet to be clarified. | 9705222v1 |
1998-11-18 | The Closest Damped Lyman Alpha System | A difficulty of studying damped Lyman alpha systems is that they are distant,
so one knows little about the interstellar medium of the galaxy. Here we report
upon a damped Lyman alpha system in the nearby galaxy NGC 4203, which is so
close (v_helio = 1117 km/s) and bright (B_o = 11.62) that its HI disk has been
mapped. The absorption lines are detected against Ton 1480, which lies only
1.9' (12 h_50 kpc) from the center of NGC 4203. Observations were obtained with
the Faint Object Spectrograph on HST (G270H grating) over the 2222-3277
Angstrom region with 200 km/s resolution. Low ionization lines of Fe, Mn, and
Mg were detected, leading to metallicities of -2.29, < -0.68, and > -2.4, which
are typical of other damped Lyman alpha systems, but well below the stellar
metallicity of this type of galaxy. Most notably, the velocity of the lines is
1160 +- 10 km/s, which is identical to the HI rotational velocity of 1170 km/s
at that location in NGC 4203, supporting the view that these absorption line
systems can be associated with the rotating disks of galaxies. In addition, the
line widths of the Mg lines give an upper limit to the velocity dispersion of
167 km/s, to the 99% confidence level. | 9811274v1 |
1999-07-29 | Ionized Gas in Damped Lyman-alpha Systems and Its Effects on Elemental Abundance Studies | Recent high-resolution observations of metal absorption lines in
high-redshift damped Ly-alpha systems have shown that Al III, a tracer of
moderately-ionized gas, very often has a velocity structure indistinguishable
from that of low-ionization gas. Regions of ionized and neutral hydrogen in
these systems are likely cospatial. The higher-ionization Si IV and C IV
absorption shows a much weaker or non-existent correlation with the low
ionization material, implying that the regions traced by Al III are
photoionized by a soft (stellar) spectrum, by a hard (power law) spectrum with
a very low ionization parameter, or a combination of both. We discuss the
ionization of the damped Ly-alpha systems and use photoionization equilibrium
models to make quantitative estimates of its effects on abundance studies in
these systems. We show that ionization effects may be large enough to account
for the observed dispersion in absolute metal abundances in damped Ly-alpha
systems, causing systematically higher abundances in lower column density
systems. The observed Si^+/Fe^+ and Zn^+/Cr^+ ratios may systematically
overestimate the intrinsic Si/Fe and Zn/Cr ratios, respectively, if ionized gas
is present in these systems, thereby mimicking the effects of alpha-element
enrichment or dust depletion. | 9907428v1 |
1999-11-09 | Detection of Warm and Cold Phases of the Neutral ISM in a Damped Ly-alpha Absorber | We present a detailed study of the HI 21cm absorption system at z=0.0912
towards the radio quasar B0738+313. The uncommonly narrow main absorption line
and weak secondary line are resolved for the first time. In addition we find it
necessary to add a third, broader shallow component to obtain a good fit to the
spectrum. Although the harmonic mean spin temperature calculated by comparison
of the 21cm lines to the damped Ly-alpha line is T_s = 775 K, the thermal
kinetic temperatures of the two narrow components, calculated from their
widths, are much lower: T_k \leq 297 and \leq 103 K respectively. This is the
first case of a redshifted absorption system for which T_k is measured to be
less than T_s. We discuss this result in the context of a two phase gas model,
in which the damped Ly-alpha gas is sensitive to a significant neutral column
density of warm phase gas as well as the cold phase gas of the narrow 21cm
lines. The third component is interpreted as representing the warm phase gas
with with T_k \leq 5050 K. The combined column density of the three 21cm
components is approximately equal to that derived from fits to the damped
Ly-alpha line. | 9911142v1 |
2000-06-01 | Crust-core coupling and r-mode damping in neutron stars: a toy model | R-modes in neutron stars with crusts are damped by viscous friction at the
crust-core boundary. The magnitude of this damping, evaluated by Bildsten and
Ushomirsky (BU) under the assumption of a perfectly rigid crust, sets the
maximum spin frequency for a neutron star spun up by accretion in a Low-Mass
X-ray binary (LMXB). In this paper we explore the mechanical coupling between
the core r-modes and the elastic crust, using a toy model of a constant density
neutron star with a constant shear modulus crust. We find that, at spin
frequencies in excess of ~50 Hz, the r-modes strongly penetrate the crust. This
reduces the relative motion (slippage) between the crust and the core compared
to the rigid crust limit. We therefore revise down, by as much as a factor of
10^2-10^3, the damping rate computed by BU, significantly reducing the maximal
possible spin frequency of neutron star with a solid crust. The dependence of
the crust-core slippage on the spin frequency is complicated, and is very
sensitive to the physical thickness of the crust. If the crust is sufficiently
thick, the curve of the critical spin frequency for the onset of the r-mode
instability becomes multi-valued for some temperatures; this is related to the
avoided crossings between the r-mode and the higher-order torsional modes in
the crust. The critical frequencies are comparable to the observed spins of
neutron stars in LMXBs and millisecond pulsars. | 0006028v1 |
2001-03-23 | First Investigation of the Clustering Environment of Damped Lyman Alpha Absorbers at z=4 | We report the first observations of the clustering environment of damped
Lyman alpha absorption systems at z=4. Color selection and photometric
redshifts were used to select 44 candidate Lyman-break galaxies brighter than
I_AB=25.5 from deep BRI images of the 35 sq. arcmin field containing the quasar
BR 0951-04. Multislit spectroscopy of 35 candidate galaxies was performed and 8
of these candidates have been confirmed as z>3.5 Lyman-break galaxies. With
only BRI photometry, the photometric redshifts are quite accurate for the
spectroscopically confirmed galaxies but have a high rate of misclassification
due to color degeneracies between Lyman-break galaxies and low-redshift
ellipticals. Both of the z>3.5 galaxies found within 15'' of the quasar
line-of-sight appear to be causing absorption systems in the quasar spectrum.
We use a battery of statistical tests to look for clustering in the redshift
histogram of the z>3.5 galaxies but do not find measurable clustering of these
Lyman-break galaxies with the damped Lyman alpha absorbers. With a larger
sample of galaxies, our method should determine the cross-correlation between
these objects, which probes the bias and hence the mass of the damped Lyman
alpha absorbers. | 0103387v2 |
2002-11-11 | Damped Lyman alpha systems and galaxy formation models - II. High ions and Lyman limit systems | We investigate a model for the high-ionization state gas associated with
observed damped Lyman-alpha systems, based on a semi-analytic model of galaxy
formation set within the paradigm of hierarchical structure formation. In our
model, the hot gas in halos and sub-halos gives rise to CIV absorption, while
the low-ionization state gas is associated with the cold gas in galaxies. The
model matches the distribution of CIV column densities and leads naturally to
kinematic properties that are in good agreement with the data.
We examine the contribution of both hot and cold gas to sub-damped systems
and suggest that the properties of these systems can be used as an important
test of the model. We expect that sub-DLA systems will generally be composed of
a single gas disk and thus predict that they should have markedly different
kinematics than the damped systems.
Finally, we find that hot halo gas produces less than one third of Lyman
limit systems at redshift three. We model the contribution of mini-halos (halos
with virial velocities < 35 km/s) to Lyman limit systems and find that they may
contain as much gas as is observed in these systems. However, if we adopt
realistic models of the gas density distribution we find that these systems are
not a significant source of Lyman limit absorption. Instead we suggest that
uncollapsed gas outside of virialized halos is responsible for most of the
Lyman limit systems at high redshift. | 0211231v1 |
2003-05-16 | The Age-Metallicity Relation of the Universe in Neutral Gas: The First 100 Damped Lya Systems | We present accurate metallicity measurements for 121 damped Lya systems at
0.5<z<5 including ~50 new measurements from our recently published Echellette
Spectrograph and Imager surveys. This dataset is analysed to determine the
age-metallicity relation of neutral gas in the universe. Contrary to previous
datasets this sample shows statistically significant evolution in the mean
metallicity. The best linear fit rate to metallicity vs. redshift is -0.26 +/-
0.07 dex corresponding to approximately a factor of 2 every Gyr at z=3. The DLA
continue to maintain a floor in metallicity of ~1/700 solar independent of
observational effects. This metallicity threshold limits the prevalence of
primordial gas in high redshift galaxies and stresses the correspondence
between damped systems and star formation (i.e. galaxy formation). This floor
is significantly offset from the metallicity of the Lya forest and therefore we
consider it to be more related to active star formation within these galaxies
than scenarios of enrichment in the very early universe. Finally, we comment on
an apparent 'missing metals problem': the mean metallicity of the damped
systems is ~10x lower than the value expected from their observed star
formation history. This problem is evident in current theoretical treatments of
chemical evolution and galaxy formation; it may indicate a serious flaw in our
understanding of the interplay between star formation and metal production. | 0305314v1 |
2003-09-24 | WIMP matter power spectra and small scale power generation | Dark Matter (DM) is generally assumed to be massive, cold and collisionless
from the structure formation point of view. A more correct statement however is
that DM indeed experiences collisional damping, but on a scale which is
supposed to be too small to be relevant for structure formation. The aim of
this paper is to present a Cold (although ``collisional'') Dark Matter particle
whose matter power spectrum is damped and see whether it is distinguishable
from standard candidates. To achieve this purpose, we calculate the collisional
damping and free-streaming scales of neutralinos and non conventional
candidates (say light particles heavier than ~1 MeV but lighter than O(10)
GeV). The latter can be considered as Cold Dark Matter (CDM) particles in the
sense that they become non relativistic before their thermal decoupling epoch.
Unlike neutralinos, however, their linear matter power spectrum can be damped
on scales of ~ 10^3 Msol due to their interactions. Since these scales are of
cosmological interest for structure formation, we perform a series of numerical
simulations to obtain the corresponding non linear matter power spectra
P(k)_{nl} at the present epoch. We show that because of small scale
regeneration, they all resemble each other at low redshifts, i.e. become very
similar to a typical CDM matter power spectrum on all but the smallest scales.
Therefore, even if lensing measurements at redshift below unity were to yield a
P(k)_{nl} consistent with CDM models, this would not constitute a sufficiently
robust evidence in favour of the neutralino to rule out alternative DM
candidates. | 0309652v1 |
2004-03-16 | The SDSS Damped Lya Survey: Data Release 1 | We present the results from an automated search for damped Lya (DLA) systems
in the quasar spectra of Data Release 1 from the Sloan Digital Sky Survey
(SDSS-DR1). At z~2.5, this homogeneous dataset has greater statistical
significance than the previous two decades of research. We derive a statistical
sample of 71 damped Lya systems (>50 previously unpublished) at z>2.1 and
measure HI column densities directly from the SDSS spectra. The number of DLA
systems per unit redshift is consistent with previous measurements and we
expect our survey has >95% completeness. We examine the cosmological baryonic
mass density of neutral gas Omega_g inferred from the damped Lya systems from
the SDSS-DR1 survey and a combined sample drawn from the literature. Contrary
to previous results, the Omega_g values do not require a significant correction
from Lyman limit systems at any redshift. We also find that the Omega_g values
for the SDSS-DR1 sample do not decline at high redshift and the combined sample
shows a (statistically insignificant) decrease only at z>4. Future data
releases from SDSS will provide the definitive survey of DLA systems at z~2.5
and will significantly reduce the uncertainty in Omega_g at higher redshift. | 0403391v2 |
2006-06-28 | Neutral gas density in Damped Lyman Alpha systems | We estimate the intrinsic neutral gas density in Damped Lyman Alpha systems
($\Omega_{HI}^{(DLA)}$) in the redshift range $ 2.2 \lesssim z \lesssim 5$ from
the DLA SDSS DR_3 sample of optically selected quasars. We take into account
self-consistently the obscuration on background quasars due to the dust present
in Damped Lyman Alpha systems. We model the column density and redshift
distribution of these systems by using both a non-parametric and a parametric
approach. Under conservative assumptions on the dust content of Damped Lyman
$\alpha$ systems, we show that selection effects lead to underestimating the
intrinsic neutral gas density by at least $15\%$ with respect to the observed
neutral gas density. Over the redshift range $[2.2;5.5]$ we find
$\Omega_{HI}^{(DLA)}=0.97^{+0.08+0.28}_{-0.06-0.15} \cdot 10^{-3}$, where the
first set of error bars gives the $1\sigma$ random errors and the second set
gives the modeling uncertainty dependent on the fraction of metals in dust -
from 0\% to 50\%. This value compares with
$\Omega_{HI}^{(DLA)}=0.82^{+0.05}_{-0.05}$ ($1\sigma$ error bars), which is
obtained when no correction for dust is introduced. In the model with half of
the metals mass in dust we cannot constraint $\Omega_{HI}^{(DLA)}$ at a
confidence level higher than $90\%$. In this case there is indeed a probability
of about $10\%$ that the intrinsic column density distribution of DLA systems
is a power law $f(N_{HI}) \propto 1/N_{HI}^{~1.95}$. In contrast, with $25 \%$
of the metals in dust - the most realistic estimate - a power law is ruled out
at $99.5\%$ of confidence level. | 0606693v1 |
2006-09-06 | Sun-as-a-star observations: evidence for degree dependence of changes in damping of low-l p modes along the solar cycle | We use 9.5-yr of BiSON Sun-as-a-star data to search for dependence of
solar-cycle parameter changes on the angular degree, l, of the data. The nature
of the Sun-as-a-star observations is such that for changes measured at fixed
frequency, or for changes averaged across the same range in frequency, any l
dependence present carries information on the latitudinal distribution of the
agent (i.e., the activity) responsible for those changes. We split the 9.5-yr
timeseries into contiguous 108-d pieces, and determine mean changes in the
damping of, power in, and energy supplied to the modes through the solar cycle.
We also apply a careful correction to account for the deleterious effects of
the ground-based BiSON window function on the results. From our full analysis
we obtain a marginally significant result for the damping parameter, where the
mean change is found to be weakest at l=0. The other parameters show hints of
some dependence in l. Our main conclusion is that the mean fractional
solar-cycle change in the l=0 damping rates is approximately 50 % smaller than
was previously assumed. It had been common practice to use an average over all
low-l modes; our downward revision of the radial-mode value has implications
for comparisons with models of the global solar cycle changes, which are
usually based on a spherically symmetric geometry. | 0609156v2 |
1997-08-12 | Coherence in the Quasi-Particle 'Scattering' by the Vortex Lattice in Pure Type-II Superconductors | The effect of quasi-particle (QP) 'scattering' by the vortex lattice on the
de-Haas van-Alphen oscillations in a pure type-II superconductor is
investigated within mean field,asymptotic perturbation theory. Using a 2D
electron gas model it is shown that, due to a strict phase coherence in the
many-particle correlation functions, the 'scattering' effect in the asymptotic
limit ($\sqrt{E_F/\hbar\omega_c}\gg 1$) is much weaker than what is predicted
by the random vortex lattice model proposed by Maki and Stephen, which destroys
this coherence . The coherent many particle configuration is a collinear array
of many particle coordinates, localized within a spatial region with size of
the order of the magnetic length. The amplitude of the magnetization
oscillations is sharply damped just below $% H_{c2}$ because of strong
$180^{\circ}$ out of phase magnetic oscillations in the superconducting
condensation energy ,which tend to cancel the normal electron oscillations.
Within the ideal 2D model used it is found, however, that because of the
relative smallness of the quartic and higher order terms in the expansion, the
oscillations amplitude at lower fields does not really damp to zero, but only
reverses sign and remains virtually undamped well below $H_{c2}$. This
conclusion may be changed if disorder in the vortex lattice, or vortex lines
motion will be taken into account. The reduced QP 'scattering' effect may be
responsible for the apparent crossover from a strong damping of the dHvA
oscillations just below $H_{c2}$ to a weaker damping at lower fields observed
experimentally in several 3D superconductors. | 9708088v1 |
1999-08-27 | Electron Correlations in an Electron Bilayer at Finite Temperature: Landau Damping of the Acoustic Plasmon | We report angle-resolved Raman scattering observations of the temperature
dependent Landau damping of the acoustic plasmon in an electron bilayer system
realised in a GaAs double quantum well structure. Corresponding calculations of
the charge-density excitation spectrum of the electron bilayer using forms of
the random phase approximation (RPA), and the static local field formalism of
Singwi, Tosi, Land and Sj\"{o}lander (STLS) extended to incorporate non-zero
electron temperature $T_{\rm e}$ and phenomenological damping, are also
presented. The STLS calculations include details of the temperature dependence
of the intra- and inter-layer local field factors and pair-correlation
functions. Good agreement between experiment and the various theories is
obtained for the acoustic plasmon energy and damping for $T_{\rm e} \lesssim
T_{\rm F}/2$, the Fermi temperature. However, contrary to current expectations,
all of the calculations show significant departures from our experimental data
for $T_{\rm e} \gtrsim T_{\rm F}/2$. From this, we go on to demonstrate
unambiguously that real local field factors fail to provide a physically
accurate description of exchange correlation behaviour in low dimensional
electron gases. Our results suggest instead that one must resort to a
{\em{dynamical}} local field theory, characterised by a {\em{complex}} field
factor to provide a more accurate description. | 9908408v1 |
2000-10-02 | Comment on "Magnetic Breakdown at High Fields: Semiclassical and Quantum Treatments" | We comment on the study of the spin-damping factor on the de Haas-van Alphen
(dHvA) discussed by Han et al. (Phys. Rev. Lett. 85, 1500 (2000)). | 0010018v1 |
2002-03-11 | Shubnikov - de Haas effect in the quantum vortex liquid state of the organic superconductor $κ$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$ | We report the Shubnikov-de Haas (SdH) oscillations observed in the vortex
liquid state of the quasi two dimensional organic superconductor
$\kappa$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$. The SdH oscillations can be observed
down to about 5 T at 0.5 K, where the flux flow resistivity becomes as small as
about 30 % of the normal state value. Below the upper critical field $H_{\rm
c2}$ of about 7 T, the additional damping of the SdH oscillation amplitude
appears, as well as that of the de Haas-van Alphen (dHvA) oscillations, with
respect to the normal state one which is described with the standard
Lifshitz-Kosevich formula. The magnitude of the additional damping near $H_{\rm
c2}$ is the same with that observed in the dHvA oscillations and well explained
by the theoretical predictions in consideration of fluctuations in the thermal
vortex liquid state. In the quantum fluctuation region at lower temperature,
however, only SdH effect shows the stronger damping than that of the dHvA
oscillations. The different magnetic field dependence of the additional damping
of the oscillation amplitude between the SdH and dHvA effects is discussed in
connection with the effect of the transport current on the short-range order of
vortices in the quantum vortex slush state reported at the same temperature and
magnetic field region. | 0203228v2 |
2003-03-13 | Vibrational sidebands and dissipative tunneling in molecular transistors | Transport through molecular devices with strong coupling to a single
vibrational mode is considered in the case where the vibration is damped by
coupling to the environment. We focus on the weak tunneling limit, for which a
rate equation approach is valid. The role of the environment can be
characterized by a frictional damping term $\mysig(\omega)$ and corresponding
frequency shift. We consider a molecule that is attached to a substrate,
leading to frequency-dependent frictional damping of the single oscillator mode
of the molecule, and compare it to a reference model with frequency-independent
damping featuring a constant quality factor $Q$. For large values of $Q$, the
transport is governed by tunneling between displaced oscillator states giving
rise to the well-known series of the Frank-Condon steps, while at small $Q$,
there is a crossover to the classical regime with an energy gap given by the
classical displacement energy. Using realistic values for the elastic
properties of the substrate and the size of the molecule, we calculate $I$-$V$
curves and find qualitative agreement between our theory and recent experiments
on $C_{60}$ single-molecule devices. | 0303236v3 |
2004-09-03 | Weyl equation for temperature fields induced by attosecond laser pulses | In this paper the Weyl equation for temperature field induced by laser beam
interaction with matter is proposed and solved. Depending on the scattering
mechanism the temperature field oscillate or is damped.
Key words: Thermal processes, Weyl equation | 0409076v1 |
2004-12-08 | Spectroscopy of a driven solid-state qubit coupled to a structured environment | We study the asymptotic dynamics of a driven spin-boson system where the
environment is formed by a broadened localized mode. Upon exploiting an exact
mapping, an equivalent formulation of the problem in terms of a quantum
two-state system (qubit) coupled to a harmonic oscillator which is itself
Ohmically damped, is found. We calculate the asymptotic population difference
of the two states in two complementary parameter regimes. For weak damping and
low temperature, a perturbative Floquet-Born-Markovian master equation for the
qubit-oscillator system can be solved. We find multi-photon resonances
corresponding to transitions in the coupled quantum system and calculate their
line-shape analytically. In the complementary parameter regime of strong
damping and/or high temperatures, non-perturbative real-time path integral
techniques yield analytic results for the resonance line shape. In both
regimes, we find very good agreement with exact results obtained from a
numerical real-time path-integral approach. Finally, we show for the case of
strong detuning between qubit and oscillator that the width of the $n$-photon
resonance scales with the $n$-th Bessel function of the driving strength in the
weak-damping regime. | 0412194v2 |
1995-03-08 | A NEW NUMERICAL APPROACH TO THE OSCILLATION MODES OF RELATIVISTIC STARS | The oscillation modes of a simple polytropic stellar model are studied. Using
a new numerical approach (based on integration for complex coordinates) to the
problem for the stellar exterior we have computed the eigenfrequencies of the
highly damped w-modes. The results obtained agree well with recent ones of
Leins, Nollert and Soffel (1993) Specifically, we are able to explain why
several modes in this regime of the complex frequency plane could not be
identified within the WKB approach of Kokkotas and Schutz (1992). Furthermore,
we have established that the ``kink'' that was a prominent feature of the
spectra of Kokkotas and Schutz, but did not appear in the results of Leins {\em
et al.}, was a numerical artefact. Using our new numerical code we are also
able to compute, for the first time, several of the slowly damped (p) modes for
the considered stellar models. For very compact stars we find, somewhat
surprisingly, that the damping of these modes does not decrease monotonically
as one proceeds to higher oscillation frequencies. The existence of low-order
modes that damp away much faster than anticipated may have implications for
questions regarding stellar stability and the lifetime of gravitational-wave
sources. The present results illustrate the accuracy and reliability of the
complex-coordinate method and indicate that the method could prove to be of
great use also in problems involving rotating stars. There is no apparent
reason why the complex-coordinate approach should not extend to rotating stars,
whereas it is accepted that all previous methods will fail to do so. | 9503014v1 |
1998-01-29 | On the gravitational, dilatonic and axionic radiative damping of cosmic strings | We study the radiation reaction on cosmic strings due to the emission of
dilatonic, gravitational and axionic waves. After verifying the (on average)
conservative nature of the time-symmetric self-interactions, we concentrate on
the finite radiation damping force associated with the half-retarded minus
half-advanced ``reactive'' fields. We revisit a recent proposal of using a
``local back reaction approximation'' for the reactive fields. Using
dimensional continuation as convenient technical tool, we find, contrary to
previous claims, that this proposal leads to antidamping in the case of the
axionic field, and to zero (integrated) damping in the case of the
gravitational field. One gets normal positive damping only in the case of the
dilatonic field. We propose to use a suitably modified version of the local
dilatonic radiation reaction as a substitute for the exact (non-local)
gravitational radiation reaction. The incorporation of such a local
approximation to gravitational radiation reaction should allow one to complete,
in a computationally non-intensive way, string network simulations and to give
better estimates of the amount and spectrum of gravitational radiation emitted
by a cosmologically evolving network of massive strings. | 9801105v3 |
2004-10-15 | A Nonlinear Coupling Network to Simulate the Development of the r-mode Instablility in Neutron Stars II. Dynamics | Two mechanisms for nonlinear mode saturation of the r-mode in neutron stars
have been suggested: the parametric instability mechanism involving a small
number of modes and the formation of a nearly continuous Kolmogorov-type
cascade. Using a network of oscillators constructed from the eigenmodes of a
perfect fluid incompressible star, we investigate the transition between the
two regimes numerically. Our network includes the 4995 inertial modes up to n<=
30 with 146,998 direct couplings to the r-mode and 1,306,999 couplings with
detuning< 0.002 (out of a total of approximately 10^9 possible couplings).
The lowest parametric instability thresholds for a range of temperatures are
calculated and it is found that the r-mode becomes unstable to modes with
13<n<15. In the undriven, undamped, Hamiltonian version of the network the rate
to achieve equipartition is found to be amplitude dependent, reminiscent of the
Fermi-Pasta-Ulam problem. More realistic models driven unstable by
gravitational radiation and damped by shear viscosity are explored next. A
range of damping rates, corresponding to temperatures 10^6K to 10^9K, is
considered. Exponential growth of the r-mode is found to cease at small
amplitudes, approximately 10^-4. For strongly damped, low temperature models, a
few modes dominate the dynamics. The behavior of the r-mode is complicated, but
its amplitude is still no larger than about 10^-4 on average. For high
temperature, weakly damped models the r-mode feeds energy into a sea of
oscillators that achieve approximate equipartition. In this case the r-mode
amplitude settles to a value for which the rate to achieve equipartition is
approximately the linear instability growth rate. | 0410072v1 |
1997-02-20 | Numerical study of plasmon properties in the SU(2)-Higgs model | Using the (effective) classical approximation, we compute numerically
time-dependent correlation functions in the SU(2)-Higgs model around the
electroweak phase transition, for $m_H \approx m_W$. The parameters of the
classical model have been determined previously by the dimensional reduction
relations for time-independent correlators. The $H$ and $W$ correlation
functions correspond to gauge invariant fields. They show damped oscillatory
behavior from which we extract frequencies $\om$ and damping rates $\gm$. In
the Higgs phase the damping rates have roughly the values obtained in analytic
calculations in the quantum theory. In the plasma phase (where analytic
estimates for gauge invariant fields are not available), the damping rate
associated with $H$ is an order of magnitude larger than in the Higgs phase,
while the $W$ correlator appears to be overdamped, with a small rate. The
frequency $\om_H$ shows a clear dip at the transition. The results are
approximately independent of the lattice spacing, but this appears to be
compatible with the lattice spacing dependence expected from perturbation
theory. | 9702017v2 |
2001-01-16 | Nonlinear Landau damping of a plasmino in the quark-gluon plasma | On the basis of the Blaizot-Iancu equations, which are a local formulation of
the hard thermal loop (HTL) equations of motion for soft fluctuating quark and
gluon fields and their induced sources, the coupled kinetic equations for
plasminos and plasmons are obtained. The equality of matrix elements for
nonlinear scattering of a plasmino by hard particles in covariant and temporal
gauges is established by using effective Ward identities. The model problem of
the interaction of two infinitely narrow packets with fermion and boson quantum
numbers is considered. The kinematical relations between wave vectors of the
plasmino and plasmon are derived, when the effective pumping over of the plasma
excitation energy from the fermion branch of plasma excitations to the boson
branch and vice versa occur. The expression for the nonlinear Landau damping
rate of a plasmino at rest is found, and a comparison with a plasmino damping
constant obtained within the framework of the hard thermal loop approximation
is made. The nonlinear Landau damping rate for normal quark excitations is
shown to diverge like $1/\sqrt{q^2}$ near the light cone where $q$ is a
four-momentum of excitations, and the improved Blaizot-Iancu equations removing
this divergence are proposed. | 0101167v2 |
2003-12-15 | Nonequilibrium pion dynamics near the critical point in a constituent quark model | We study static and dynamical critical phenomena of chiral symmetry breaking
in a two-flavor Nambu--Jona-Lasinio constituent quark model. We obtain the
low-energy effective action for scalar and pseudoscalar degrees of freedom to
lowest order in quark loops and to quadratic order in the meson fluctuations
around the mean field. The \emph{static} limit of critical phenomena is shown
to be described by a Ginzburg-Landau effective action including \emph{spatial}
gradients. Hence \emph{static} critical phenomena is described by the
universality class of the O(4) Heisenberg ferromagnet. \emph{Dynamical}
critical phenomena is studied by obtaining the equations of motion for pion
fluctuations. We find that for $T<T_c$ the are stable long-wavelength pion
excitations with dispersion relation $\omega_{\pi}(k)=k$ described by isolated
pion poles. The residue of the pion pole vanishes near $T_c$ as $Z \propto
1/|\ln(1-T/T_c)|$ and long-wavelength fluctuations are damped out by Landau
damping on a time scale $t_\mathrm{rel}(k)\propto 1/k$, reflecting
\emph{critical slowing down} of pion fluctuations near the critical point. At
the critical point, the pion propagator features mass shell logarithmic
divergences which we conjecture to be the harbinger of a (large) dynamical
anomalous dimension. We find that while the \emph{classical spinodal} line
coincides with that of the Ginzburg-Landau theory, the growth rate of
long-wavelength spinodal fluctuations has a richer wavelength dependence as a
consequence of Landau damping. We argue that Landau damping prevents a
\emph{local} low energy effective action in terms of a derivative expansion in
real time. | 0312185v2 |
2002-02-01 | Time Domain Computation of a Nonlinear Nonlocal Cochlear Model with Applications to Multitone Interaction in Hearing | A nonlinear nonlocal cochlear model of the transmission line type is studied
in order to capture the multitone interactions and resulting tonal suppression
effects. The model can serve as a module for voice signal processing, it is a
one dimensional (in space) damped dispersive nonlinear PDE based on mechanics
and phenomenology of hearing. It describes the motion of basilar membrane (BM)
in the cochlea driven by input pressure waves. Both elastic damping and
selective longitudinal fluid damping are present. The former is nonlinear and
nonlocal in BM displacement, and plays a key role in capturing tonal
interactions. The latter is active only near the exit boundary (helicotrema),
and is built in to damp out the remaining long waves. The initial boundary
value problem is numerically solved with a semi-implicit second order finite
difference method. Solutions reach a multi-frequency quasi-steady state.
Numerical results are shown on two tone suppression from both high-frequency
and low-frequency sides, consistent with known behavior of two tone
suppression. Suppression effects among three tones are demonstrated by showing
how the response magnitudes of the fixed two tones are reduced as we vary the
third tone in frequency and amplitude. We observe qualitative agreement of our
model solutions with existing cat auditory neural data. The model is thus
simple and efficient as a processing tool for voice signals. | 0202004v3 |
2003-12-22 | Intermittency is a consequence of turbulent transport in nonlinear systems | Intermittent high-amplitude structures emerge in a damped and driven discrete
nonlinear Schroedinger equation whose solutions transport both energy and
particles from sources to sinks. These coherent structures are necessary for
any solution that has statistically stationary transport properties. | 0312059v1 |
2004-06-17 | Multi-frequency control of Faraday wave patterns | We show how pattern formation in Faraday waves may be manipulated by varying
the harmonic content of the periodic forcing function. Our approach relies on
the crucial influence of resonant triad interactions coupling pairs of critical
standing wave modes with damped, spatio-temporally resonant modes. Under the
assumption of weak damping and forcing, we perform a symmetry-based analysis
that reveals the damped modes most relevant for pattern selection, and how the
strength of the corresponding triad interactions depends on the forcing
frequencies, amplitudes, and phases. In many cases, the further assumption of
Hamiltonian structure in the inviscid limit determines whether the given triad
interaction has an enhancing or suppressing effect on related patterns.
Surprisingly, even for forcing functions with arbitrarily many frequency
components, there are at most five frequencies that affect each of the
important triad interactions at leading order. The relative phases of those
forcing components play a key role, sometimes making the difference between an
enhancing and suppressing effect. In numerical examples, we examine the
validity of our results for larger values of the damping and forcing. Finally,
we apply our findings to one-dimensional periodic patterns obtained with
impulsive forcing and to two-dimensional superlattice patterns and
quasipatterns obtained with multi-frequency forcing. | 0406034v1 |
1997-01-22 | Shell Model for Warm Rotating Nuclei | In order to provide a microscopic description of levels and E2 transitions in
rapidly rotating nuclei with internal excitation energy up to a few MeV, use is
made of a shell model which combines the cranked Nilsson mean-field and the
residual surface delta two-body force. The damping of collective rotational
motion is investigated in the case of a typical rare-earth nucleus, namely \Yb.
It is found that rotational damping sets in at around 0.8 MeV above the yrast
line, and the levels which form rotational band structures are thus limited. We
predict at a given rotational frequency existence of about 30 rotational bands
of various lengths, in overall agreement with the experimental findings. The
onset of the rotational damping proceeds quite gradually as a function of the
internal excitation energy. The transition region extends up to around 2 MeV
above yrast and it is characterized by the presence of scars of discrete
rotational bands which extend over few spin values and stand out among the
damped transitions, and by a two-component profile in the $E_\gamma -E_\gamma$
correlation. The important role played by the high-multipole components of the
two-body residual interaction is emphasized. | 9701044v1 |
2005-04-21 | Enhanced optical cooling of particle beams in storage rings | The problem of enhanced optical cooling (EOC) of particle beams in storage
rings beyond the Robinson's damping criterion is discussed. | 0504145v1 |
2005-10-21 | Non-contact atomic force microscopy: Stability criterion and dynamical responses of the shift of frequency and damping signal | The aim of this article is to provide a complete analysis of the behavior of
a noncontact atomic force microscope (NC-AFM). We start with a review of the
equations of motion of a tip interacting with a surface in which the stability
conditions are first revisited for tapping mode. Adding the equations of
automatic gain control (AGC), which insures constant amplitude of the
oscillations in the NC-AFM, to the equations of motion of the tip, a new
analytical stability criterion that involves proportional and integral gains of
AGC is deduced. Stationary solutions for the shift of frequency and for the
damping signal are obtained. Special attention is paid to the damping signal in
order to clarify its physical origin. The theoretical results are then compared
to those given by a virtual machine. The virtual machine is a set of equations
solved numerically without any approximation. The virtual machine is of great
help in understanding the dynamical behavior of the NC-AFM as images are
recorded. Transient responses of the shift in frequency and of the damping
signal are discussed in relation to the values of proportional and integral
gains of AGC. | 0510192v1 |
1999-06-09 | Quantum dynamics of a damped deformed oscillator | The interaction of a quantum deformed oscillator with the environment is
studied deriving a master equation whose form strongly depends on the type of
deformation. | 9906031v1 |
2007-04-29 | Long Term Evolution of Magnetic Turbulence in Relativistic Collisionless Shocks: Electron-Positron Plasmas | We study the long term evolution of magnetic fields generated by a
collisionless relativistic $e^+e^-$ shock which is initially unmagnetized. Our
2D particle-in-cell numerical simulations show that downstream of such a
Weibel-mediated shock, particle distributions are close to isotropic,
relativistic Maxwellians, and the magnetic turbulence is highly intermittent
spatially, with the non-propagating magnetic fields forming relatively isolated
regions with transverse dimension $\sim 10-20$ skin depths. These structures
decay in amplitude, with little sign of downstream merging. The fields start
with magnetic energy density $\sim (0.1-0.2)$ of the upstream kinetic energy
within the shock transition, but rapid downstream decay drives the fields to
much smaller values, below $10^{-3}$ of equipartition after $10^3$ skin depths.
In an attempt to construct a theory that follows field decay to these smaller
values, we explore the hypothesis that the observed damping is a variant of
Landau damping in an unmagnetized plasma. The model is based on the small value
of the downstream magnetic energy density, which suggests that particle orbits
are only weakly perturbed from straight line motion, if the turbulence is
homogeneous. Using linear kinetic theory applied to electromagnetic fields in
an isotropic, relativistic Maxwellian plasma, we find a simple analytic form
for the damping rates, $\gamma_k$, in two and three dimensions for small
amplitude, subluminous electromagnetic fields. We find that magnetic energy
does damp due to phase mixing of current carrying particles as $(\omega_p
t)^{-q}$ with $q \sim 1$. (abridged) | 0704.3832v2 |
2007-06-21 | Production of a sterile species via active-sterile mixing: an exactly solvable model | The production of a sterile species via active-sterile mixing in a thermal
medium is studied in an exactly solvable model. The \emph{exact} time evolution
of the sterile distribution function is determined by the dispersion relations
and damping rates $\Gamma_{1,2}$ for the quasiparticle modes. These depend on
$\wtg = \Gamma_{aa}/2\Delta E$, with $\Gamma_{aa}$ the interaction rate of the
active species in absence of mixing and $\Delta E$ the oscillation frequency in
the medium without damping. $\wtg \ll1,\wtg \gg 1$ describe the weak and strong
damping limits respectively. For $\wtg\ll1$, $\Gamma_1 = \Gamma_{aa}\cos^2\tm ;
\Gamma_{2}=\Gamma_{aa}\sin^2\tm$ where $\tm$ is the mixing angle in the medium
and the sterile distribution function \emph{does not} obey a simple rate
equation. For $\wtg \gg 1$, $\Gamma_1= \Gamma_{aa}$ and $\Gamma_2 = \Gamma_{aa}
\sin^22\tm/4\wtg^2$, is the sterile production rate. In this regime sterile
production is suppressed and the oscillation frequency \emph{vanishes} at an
MSW resonance, with a breakdown of adiabaticity. These are consequences of
quantum Zeno suppression. For active neutrinos with standard model interactions
the strong damping limit is \emph{only} available near an MSW resonance
\emph{if} $\sin\theta \lesssim \alpha_w$ with $\theta$ the vacuum mixing angle.
The full set of quantum kinetic equations for sterile production for arbitrary
$\wtg$ are obtained from the quantum master equation. Cosmological resonant
sterile neutrino production is quantum Zeno suppressed relieving potential
uncertainties associated with the QCD phase transition. | 0706.3167v2 |
2007-08-02 | Eccentricity evolution of giant planet orbits due to circumstellar disk torques | The extrasolar planets discovered to date possess unexpected orbital
elements. Most orbit their host stars with larger eccentricities and smaller
semi-major axes than similarly sized planets in our own solar system do. It is
generally agreed that the interaction between giant planets and circumstellar
disks (Type II migration) drives these planets inward to small radii, but the
effect of these same disks on orbital eccentricity, e, is controversial.
Several recent analytic calculations suggest that disk-planet interactions can
excite eccentricity, while numerical studies generally produce eccentricity
damping. This paper addresses this controversy using a quasi-analytic approach,
drawing on several preceding analytic studies. This work refines the current
treatment of eccentricity evolution by removing several approximations from the
calculation of disk torques. We encounter neither uniform damping nor uniform
excitation of orbital eccentricity, but rather a function de/dt that varies in
both sign and magnitude depending on eccentricity and other solar system
properties. Most significantly, we find that for every combination of disk and
planet properties investigated herein, corotation torques produce negative
values of de/dt for some range in e within the interval [0.1, 0.5]. If
corotation torques are saturated, this region of eccentricity damping
disappears, and excitation occurs on a short timescale of less than 0.08 Myr.
Thus, our study does not produce eccentricity excitation on a timescale of a
few Myr -- we obtain either eccentricity excitation on a short time scale, or
eccentricity damping on a longer time scale. Finally, we discuss the
implications of this result for producing the observed range in extrasolar
planet eccentricity. | 0708.0335v1 |
2007-10-10 | HE 0515-4414 - an unusual sub-damped Ly alpha system revisited | Using STIS and VLT UVES observations we have examined the ionization,
abundances, and differential dust depletion of metals, the kinematic structure,
and the physical conditions in the molecular hydrogen-bearing sub-damped Ly
alpha system toward HE 0515-4414 at z = 1.15. The velocity interval of
associated metal lines extends for 700 km/s. In addition, saturated H I
absorption is detected in the blue damping wing of the main component. The
column density ratios of associated Al II, Al III, and Fe II lines indicate
that the absorbing material is ionized. 19 of in total 31 detected metal line
components are formed within peripheral H II regions, while only 12 components
are associated with the predominantly neutral main absorber. For the main
absorber the observed abundance ratios of refractory elements to Zn range from
Galactic warm disk [Si/Zn] = - 0.40, [Fe/Zn] = -1.10 to halo-like and
essentially undepleted patterns. The dust-corrected metal abundances indicate a
nucleosynthetic odd-even effect and might imply an anomalous depletion of Si
relative to Fe for two components, but otherwise do correspond to solar ratios.
The intrinsic average metallicity is almost solar [Fe/H] = -0.08, whereas the
uncorrected average is [Zn/H] = -0.38. The ion abundances in the periphery
conform with solar element composition. The detection of H II as well as the
large variation in dust depletion for this sight line raises the question
whether in future studies of damped Ly alpha systems ionization and depletion
effects have to be considered in further detail. Ionization effects, for
instance, may pretend an enrichment of alpha elements. An empirical recipe for
detecting H II regions is provided. | 0710.3560v1 |
2008-06-05 | Viscous damping of r-mode oscillations in compact stars with quark matter | We determine characteristic timescales for the viscous damping of r-mode
oscillations in rapidly rotating compact stars that contain quark matter. We
present results for the color-flavor-locked (CFL) phase of dense quark matter,
in which the up, down and strange quarks are gapped, as well as the normal
(ungapped) quark phase. While the ungapped quark phase supports a temperature
window between 10^8 K and 5x10^9 K where the r-mode is damped even for rapid
rotation, the r-mode in a rapidly rotating pure CFL star is not damped in the
temperature range 10^10 K - 10^11 K. Rotating hybrid stars with quark matter
cores display an instability window whose width is determined by the amount of
quark matter present, and they can have large spin frequencies outside this
window. Except at high temperatures T > 10^10 K, the presence of a quark phase
allows for larger critical frequencies and smaller spin-periods compared to
rotating neutron stars. If low-mass X-ray binaries contain a large amount of
ungapped or CFL quark matter, then our estimates of the r-mode instability
suggest that there should be a population of rapidly rotating binaries at
frequencies greater than 1000 Hz which have not yet been observed. | 0806.1005v2 |
2008-06-09 | Relaxation Time and Relaxation Function of Quark-Gluon Plasma with Lattice QCD | We propose a method which enables a QCD-based calculation of a relaxation
time for a dissipative current in the causal and dissipative hydrodynamic
equation derived by Israel and Stewart. We point out that the Israel-Stewart
equation is not unique as a causal and dissipative hydrodynamic equation, and
the form of the causal and dissipative hydrodynamic equation is determined by
the shape of a spectral function reflecting the properties of elementary
excitations in the system we consider. Our method utilizes a relaxation
function, which can be calculated from QCD using the linear response theory. We
show that the relaxation function can be derived from a spectral function for a
microscopic representation of the dissipative current. We also show that the
Israel-Stewart equation is acceptable only as long as the calculated relaxation
function is approximated well by a exponentially damping function, and the
relaxation time can be obtained as its damping time constant. Taking a
baryon-number dissipative current of a plasma consisting of charm quarks and
gluons as a simple example, we present the first calculation of the relaxation
function with use of the spectral function derived employing the quenched
lattice QCD together with the maximum entropy method. The calculated relaxation
function shows a strongly-oscillation damping behaviour due to the charmed
vector hadron $J/\Psi$ surviving above the deconfinement phase transition
temperature in QCD. This result suggests that the applicability of the
Israel-Stewart equation to the baryon-number dissipative current of the charm
quark-gluon plasma is quite doubtful. We present an idea for the improvement of
the Israel-Stewart equation by deriving the hydrodynamic equation consistent
with the strongly-oscillation damping relaxation function. | 0806.1481v1 |
2008-06-18 | Imaging method for interface rheological characterization | The present work investigates free damped oscillations of an oil drop in
water after its release from a capillary tube. Both pure heptane drops and
diluted crude oil drops are considered (in the second case the interface is
covered by amphiphilic species, natural components of crude oil). Shadowgraph
images of the drops are taken by means of a high speed camera and the drop
contour is detected by image processing. The axisymmetric drop shape is then
decomposed into spherical harmonics, which constitute the eigenmodes of
oscillations predicted by the Rayleigh-Lamb theory. Time evolution of each mode
is then obtained. The frequency and the damping rate of the principal mode
(n=2) are accurately determined and compared with theoretical values for an
immobile clean drop oscillating around spherical shape. For pure heptane drops,
theoretical value of the frequency agrees well with experiments whereas the
damping rate is significantly underestimated by theory. The experimental
results clearly show that the different modes are coupled. Energy is thus
transfered from mode n=2 to n=3, which probably explains the observed
enhancement of the damping rate. The effect of the interface viscoelastic
behaviour, induced by adsorbed amphiphilic species on the free oscillations was
examined. No significant effect was observed in the experiments conditions
(small amplitude oscillations and moderate aging). | 0806.3030v1 |
2008-06-27 | Klein - Gordon equation for market wealth operations | In this paper the modified Klein - Gordon equation for market processes is
proposed and solved. It is argued that the oscillations in market propagate
with the light velocity. The initial pulse in the market is damped and for very
large time diffused according to the Fourier law. | 0806.4466v1 |
2008-10-22 | Mean Motion Resonances in Extrasolar Planetary Systems with Turbulence, Interactions, and Damping | This paper continues previous work on the effects of turbulence on mean
motion resonances in extrasolar planetary systems. Turbulence is expected to
arise in the disks that form planets, and these fluctuations act to compromise
resonant configurations. This paper extends previous work by considering how
interactions between the planets and possible damping effects imposed by the
disk affect the outcomes. These physical processes are studied using three
approaches: numerical integrations of the 3-body problem with additional
forcing due to turbulence, model equations that reduce the problem to
stochastically driven oscillators, and Fokker-Planck equations that describe
the time evolution of an ensemble of systems. With this combined approach, we
elucidate the physics of how turbulence can remove extrasolar planetary systems
from mean motion resonance. As expected, systems with sufficiently large
damping (dissipation) can maintain resonance, in spite of turbulent forcing. In
the absence of strong damping, ensembles of these systems exhibit two regimes
of behavior, where the fraction of the bound states decreases as a power-law or
as an exponential. Both types of behavior can be understood through the model
developed herein. For systems with weak interactions between planets, the model
reduces to a stochastic pendulum, and the fraction of bound states decreases as
a power-law. For highly interactive systems, the dynamics are more complicated
and the fraction of bound states decreases exponentially. We show how planetary
interactions lead to drift terms in the Fokker-Planck equation and account for
this exponential behavior. In addition to clarifying the physical processes
involved, this paper strengthens the finding that turbulence implies that mean
motions resonances should be rare. | 0810.4076v1 |
2009-01-11 | On the derivation of structural models with general thermomechanical prestress | The vibrating behaviour of thin structures is affected by prestress states.
Hence, the effects of thermal prestress are important research subjects in view
of ambient vibration monitoring of civil structures. The interaction between
prestress, geometrically non-linear behaviour, as well as damping and its
coupling with the aforementioned phenomena has to be taken into account for a
comprehensive understanding of the structural behaviour. Since the literature
on this subject lacks a clear procedure to derive models of thin prestressed
and damped structures from 3D continuum mechanics, this paper presents a new
derivation of models for thin structures accounting for generic prestress,
moderate rotations and viscous damping. Although inspired by classical
approaches, the proposed procedure is quite different, because of (i) the
definition of a modified Hu-Washizu (H-W) functional, accounting for stress
constraints associated with Lagrange multipliers, in order to derive
lower-dimensional models in a convenient way; (ii) an original definition of a
(mechanical and thermal) strain measure and a rotation measure enabling one to
identify the main terms in the strain energy and to derive a cascade of
lower-dimensional models (iii) a new definition of "strain-rotation domains"
providing a clear interpretation of the classical assumptions of "small
perturbations" and "small strains and moderate rotations"; (iv) the
introduction of a pseudo-potential with stress constraints to account for
viscous damping. The proposed procedure is applied to thin beams. | 0901.1446v1 |
2009-04-17 | On Landau damping | Going beyond the linearized study has been a longstanding problem in the
theory of Landau damping. In this paper we establish exponential Landau damping
in analytic regularity. The damping phenomenon is reinterpreted in terms of
transfer of regularity between kinetic and spatial variables, rather than
exchanges of energy; phase mixing is the driving mechanism. The analysis
involves new families of analytic norms, measuring regularity by comparison
with solutions of the free transport equation; new functional inequalities; a
control of nonlinear echoes; sharp scattering estimates; and a Newton
approximation scheme. Our results hold for any potential no more singular than
Coulomb or Newton interaction; the limit cases are included with specific
technical effort. As a side result, the stability of homogeneous equilibria of
the nonlinear Vlasov equation is established under sharp assumptions. We point
out the strong analogy with the KAM theory, and discuss physical implications. | 0904.2760v5 |
2009-07-27 | Parameter exploration of optically trapped liquid aerosols | When studying the motion of optically trapped particles on the $\mu s$ time
scale, in low viscous media such as air, inertia cannot be neglected.
Resolution of unusual and interesting behaviour not seen in colloidal trapping
experiments is possible. In attempt to explain the phenomena we use power
spectral methods to perform a parameter study of the Brownian motion of
optically trapped liquid aerosol droplets concentrated around the critically
damped regime. We present evidence that the system is suitably described by a
simple harmonic oscillator model which must include a description of
Fax\'{e}n's correction, but not necessarily frequency dependent hydrodynamic
corrections to Stokes' law. We also provide results describing how the system
behaves under several variables and discuss the difficulty in decoupling the
parameters responsible for the observed behaviour. We show that due to the
relatively low dynamic viscosity and high trap stiffness it is easy to transfer
between over- and under-damped motion by experimentally altering either trap
stiffness or damping. Our results suggest stable aerosol trapping may be
achieved in under-damped conditions, but the onset of deleterious optical
forces at high trapping powers prevents the probing of the upper stability
limits due to Brownian motion. | 0907.4582v2 |
2010-06-19 | On the saturation amplitude of the f-mode instability | We investigate strong nonlinear damping effects which occur during high
amplitude oscillations of neutron stars, and the gravitational waves they
produce. For this, we use a general relativistic nonlinear hydrodynamics code
in conjunction with a fixed spacetime (Cowling approximation) and a polytropic
equation of state (EOS). Gravitational waves are estimated using the quadrupole
formula. Our main interest are l=m=2 f modes subject to the CFS (Chandrasekhar,
Friedman, Schutz) instability, but we also investigate axisymmetric and
quasiradial modes. We study various models to determine the influence of
rotation rate and EOS. We find that axisymmetric oscillations at high
amplitudes are predominantly damped by shock formation, while the
nonaxisymmetric f modes are mainly damped by wave breaking and, for rapidly
rotating models, coupling to nonaxisymmetric inertial modes. From the observed
nonlinear damping, we derive upper limits for the saturation amplitude of
CFS-unstable f modes. Finally, we estimate that the corresponding gravitational
waves for an oscillation amplitude at the upper limit should be detectable with
the advanced LIGO and VIRGO interferometers at distances above 10 MPc. This
strongly depends on the stellar model, in particular on the mode frequency. | 1006.3885v2 |
2010-07-06 | Magneto-elastic oscillations and the damping of crustal shear modes in magnetars | In a realistic model of magneto-elastic oscillations in magnetars, we find
that crustal shear oscillations, often invoked as an explanation of
quasi-periodic oscillations (QPOs) seen after giant flares in soft gamma-ray
repeaters (SGRs), are damped by resonant absorption on timescales of at most
0.2s, for a lower limit on the dipole magnetic field strength of 5 x 10^13 G.
At higher magnetic field strengths (typical in magnetars) the damping timescale
is even shorter, as anticipated by earlier toy-models. We have investigated a
range of equations of state and masses and if magnetars are dominated by a
dipole magnetic field, our findings exclude torsional shear oscillations of the
crust from explaining the observed low-frequency QPOs. In contrast, we find
that the Alfv\'en QPO model is a viable explanation of observed QPOs, if the
dipole magnetic field strength exceeds a minimum strength of about several
times 10^14 G to 10^15 G. Then, Alfv\'en QPOs are no longer confined to the
fluid core, but completely dominate in the crust region and have a maximum
amplitude at the surface of the star. | 1007.0856v2 |
2010-08-16 | Orbital evolution of eccentric planets in radiative discs | With an average eccentricity of about 0.29, the eccentricity distribution of
extrasolar planets is markedly different from the solar system. Among other
scenarios considered, it has been proposed that eccentricity may grow through
planet-disc interaction. Recently, it has been noticed that the thermodynamical
state of the disc can significantly influence the migration properties of
growing protoplanets. However, the evolution of planetary eccentricity in
radiative discs has not been considered yet. In this paper we study the
evolution of planets on eccentric orbits that are embedded in a
three-dimensional viscous disc and analyse the disc's effect on the orbital
evolution of the planet. We use the three-dimensional hydrodynamical code
NIRVANA that includes full tensor viscosity and implicit radiation transport in
the flux-limited diffusion approximation. The code uses the FARGO-algorithm to
speed up the simulations. First we measure the torque and power exerted on the
planet by the disc for fixed orbits, and then we let the planet start with
initial eccentricity and evolve it in the disc. For locally isothermal we
confirm previous results and find eccentricity damping and inward migration for
planetary cores. In the case of radiative discs, the planets experience an
inward migration as long as its eccentricity lies above a certain threshold.
After the damping of eccentricity cores with masses below 33 Earthmasses begin
to migrate outward in radiative discs, while higher mass cores always migrate
inward. For all planetary masses studied (up to 200 Earthmasses) we find
eccentricity damping. In viscous discs the orbital eccentricity of embedded
planets is damped during the evolution independent of the mass. Hence,
planet-disc interaction does not seem to be a viable mechanism to explain the
observed high eccentricity of exoplanets. | 1008.2656v1 |
2010-11-02 | A Carbon-enhanced Metal-poor Damped Lyman alpha System: Probing Gas from Population III Nucleosynthesis? | We present high resolution observations of an extremely metal-poor damped
Lyman-alpha system, at z_abs = 2.3400972 in the spectrum of the QSO J0035-0918,
exhibiting an abundance pattern consistent with model predictions for the
supernova yields of Population III stars. Specifically, this DLA has [Fe/H] =
-3.04, shows a clear `odd-even' effect, and is C-rich with [C/Fe] = +1.53, a
factor of about 20 greater than reported in any other damped Lyman-alpha
system. In analogy to the carbon-enhanced metal-poor stars in the Galactic halo
(with [C/Fe] > +1.0), this is the first reported case of a carbon-enhanced
damped Lyman-alpha system. We determine an upper limit to the mass of 12C,
M(12C) < 200 solar masses, which depends on the unknown gas density n(H); if
n(H) > 1 atom per cubic cm (which is quite likely for this DLA given its low
velocity dispersion), then M(12C) < 2 solar masses, consistent with pollution
by only a few prior supernovae. We speculate that DLAs such as the one reported
here may represent the `missing link' between the yields of Pop III stars and
their later incorporation in the class of carbon-enhanced metal-poor stars
which show no enhancement of neutron-capture elements (CEMP-no stars). | 1011.0733v2 |
2010-11-08 | Exponential stabilization without geometric control | We present examples of exponential stabilization for the damped wave equation
on a compact manifold in situations where the geometric control condition is
not satisfied. This follows from a dynamical argument involving a topological
pressure on a suitable uncontrolled set. | 1011.1699v1 |
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