411 research outputs found
Asymptotic analysis of mode-coupling theory of active nonlinear microrheology
We discuss a schematic model of mode-coupling theory for force-driven active
nonlinear microrheology, where a single probe particle is pulled by a constant
external force through a dense host medium. The model exhibits both a glass
transition for the host, and a force-induced delocalization transition, where
an initially localized probe inside the glassy host attains a nonvanishing
steady-state velocity by locally melting the glass. Asymptotic expressions for
the transient density correlation functions of the schematic model are derived,
valid close to the transition points. There appear several nontrivial time
scales relevant for the decay laws of the correlators. For the nonlinear
friction coeffcient of the probe, the asymptotic expressions cause various
regimes of power-law variation with the external force, and two-parameter
scaling laws.Comment: 17 pages, 12 figure
Cones of material response functions in 1D and anisotropic linear viscoelasticity
Viscoelastic materials have non-negative relaxation spectra. This property
implies that viscoelastic response functions satisfy certain necessary and
sufficient conditions. It is shown that these conditions can be expressed in
terms of each viscoelastic response function ranging over a cone. The elements
of each cone are completely characterized by an integral representation. The
1:1 correspondences between the viscoelastic response functions are expressed
in terms of cone-preserving mappings and their inverses. The theory covers
scalar and tensor-valued viscoelastic response functionsComment: submitted to Proc. Roy. Soc.
Fast and Accurate Computation of Orbital Collision Probability for Short-Term Encounters
International audienceThis article provides a new method for computing the probability of collision between two spherical space objects involved in a short-term encounter under Gaussian-distributed uncertainty. In this model of conjunction, classical assumptions reduce the probability of collision to the integral of a two-dimensional Gaussian probability density function over a disk. The computational method presented here is based on an analytic expression for the integral, derived by use of Laplace transform and D-finite functions properties. The formula has the form of a product between an exponential term and a convergent power series with positive coefficients. Analytic bounds on the truncation error are also derived and are used to obtain a very accurate algorithm. Another contribution is the derivation of analytic bounds on the probability of collision itself, allowing for a very fast and - in most cases - very precise evaluation of the risk. The only other analytical method of the literature - based on an approximation - is shown to be a special case of the new formula. A numerical study illustrates the efficiency of the proposed algorithms on a broad variety of examples and favorably compares the approach to the other methods of the literature
Stochastic Transition States: Reaction Geometry amidst Noise
Classical transition state theory (TST) is the cornerstone of reaction rate
theory. It postulates a partition of phase space into reactant and product
regions, which are separated by a dividing surface that reactive trajectories
must cross. In order not to overestimate the reaction rate, the dynamics must
be free of recrossings of the dividing surface. This no-recrossing rule is
difficult (and sometimes impossible) to enforce, however, when a chemical
reaction takes place in a fluctuating environment such as a liquid.
High-accuracy approximations to the rate are well known when the solvent forces
are treated using stochastic representations, though again, exact no-recrossing
surfaces have not been available. To generalize the exact limit of TST to
reactive systems driven by noise, we introduce a time-dependent dividing
surface that is stochastically moving in phase space such that it is crossed
once and only once by each transition path
The spectral action for Moyal planes
Extending a result of D.V. Vassilevich, we obtain the asymptotic expansion
for the trace of a "spatially" regularized heat operator associated with a
generalized Laplacian defined with integral Moyal products. The Moyal
hyperplanes corresponding to any skewsymmetric matrix being spectral
triples, the spectral action introduced in noncommutative geometry by A.
Chamseddine and A. Connes is computed. This result generalizes the Connes-Lott
action previously computed by Gayral for symplectic .Comment: 20 pages, no figure, few improvment
Full counting statistics of energy fluctuations in a driven quantum resonator
We consider the statistics of time-integrated energy fluctuations of a driven
bosonic resonator (as measured by a QND detector), using the standard Keldysh
prescription to define higher moments. We find that due to an effective
cascading of fluctuations, these statistics are surprisingly non-classical: the
low-temperature, quantum probability distribution is not equivalent to the
high-temperature classical distribution evaluated at some effective
temperature. Moreover, for a sufficiently large drive detuning and low
temperatures, the Keldysh-ordered quasi-probability distribution characterizing
these fluctuations fails to be positive-definite; this is similar to the full
counting statistics of charge in superconducting systems. We argue that this
indicates a kind of non-classical behaviour akin to that tested by Leggett-Garg
inequalities.Comment: 10 pages, 2 figure
Uniqueness of nontrivially complete monotonicity for a class of functions involving polygamma functions
For , let
on . In the
present paper, we prove using two methods that, among all for
, only is nontrivially completely monotonic on
. Accurately, the functions and are
completely monotonic on , but the functions for
are not monotonic and does not keep the same sign on
.Comment: 9 page
Operator solutions for fractional Fokker-Planck equations
We obtain exact results for fractional equations of Fokker-Planck type using
evolution operator method. We employ exact forms of one-sided Levy stable
distributions to generate a set of self-reproducing solutions. Explicit cases
are reported and studied for various fractional order of derivatives, different
initial conditions, and for different versions of Fokker-Planck operators.Comment: 4 pages, 3 figure
An exact analytical solution for generalized growth models driven by a Markovian dichotomic noise
Logistic growth models are recurrent in biology, epidemiology, market models,
and neural and social networks. They find important applications in many other
fields including laser modelling. In numerous realistic cases the growth rate
undergoes stochastic fluctuations and we consider a growth model with a
stochastic growth rate modelled via an asymmetric Markovian dichotomic noise.
We find an exact analytical solution for the probability distribution providing
a powerful tool with applications ranging from biology to astrophysics and
laser physics
The Tychonoff uniqueness theorem for the G-heat equation
In this paper, we obtain the Tychonoff uniqueness theorem for the G-heat
equation
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