143 research outputs found
On the influence of reflective boundary conditions on the statistics of Poisson-Kac diffusion processes
We analyze the influence of reflective boundary conditions on the statistics
of Poisson-Kac diffusion processes, and specifically how they modify the
Poissonian switching-time statistics. After addressing simple cases such as
diffusion in a channel, and the switching statistics in the presence of a
polarization potential, we thoroughly study Poisson-Kac diffusion in fractal
domains. Diffusion in fractal spaces highlights neatly how the modification in
the switching-time statistics associated with reflections against a complex and
fractal boundary induces new emergent features of Poisson-Kac diffusion leading
to a transition from a regular behavior at shorter timescales to emerging
anomalous diffusion properties controlled by walk dimensionality of the fractal
set
Stochastic foundations of undulatory transport phenomena: Generalized Poisson-Kac processes - Part II Irreversibility, Norms and Entropies
In this second part, we analyze the dissipation properties of Generalized
Poisson-Kac (GPK) processes, considering the decay of suitable -norms and
the definition of entropy functions. In both cases, consistent energy
dissipation and entropy functions depend on the whole system of primitive
statistical variables, the partial probability density functions , while the corresponding energy
dissipation and entropy functions based on the overall probability density
do not satisfy monotonicity requirements as a function of time.
Examples from chaotic advection (standard map coupled to stochastic GPK
processes) illustrate this phenomenon. Some complementary physical issues are
also addressed: the ergodicity breaking in the presence of attractive
potentials, and the use of GPK perturbations to mollify stochastic field
equations
Markovian nature, completeness, regularity and correlation properties of Generalized Poisson-Kac processes
We analyze some basic issues associated with Generalized Poisson-Kac (GPK)
stochastic processes, starting from the extended notion of the Markovian
condition. The extended Markovian nature of GPK processes is established, and
the implications of this property derived: the associated adjoint formalism for
GPK processes is developed essentially in an analogous way as for the
Fokker-Planck operator associated with Langevin equations driven by Wiener
processes. Subsequently, the regularity of trajectories is addressed: the
occurrence of fractality in the realizations of GPK is a long-term emergent
property, and its implication in thermodynamics is discussed. The concept of
completeness in the stochastic description of GPK is also introduced. Finally,
some observations on the role of correlation properties of noise sources and
their influence on the dynamic properties of transport phenomena are addressed,
using a Wiener model for comparison
Stochastic foundations of undulatory transport phenomena: Generalized Poisson-Kac processes - Part I Basic theory
This article introduces the notion of Generalized Poisson-Kac (GPK) processes
which generalize the class of "telegrapher's noise dynamics" introduced by Marc
Kac in 1974, usingPoissonian stochastic perturbations. In GPK processes the
stochastic perturbation acts as a switching amongst a set of stochastic
velocity vectors controlled by a Markov-chain dynamics. GPK processes possess
trajectory regularity (almost everywhere) and asymptotic Kac limit, namely the
convergence towards Brownian motion (and to stochastic dynamics driven by
Wiener perturbations), which characterizes also the long-term/long-distance
properties of these processes. In this article we introduce the structural
properties of GPK processes, leaving all the physical implications to part II
and part III
A multiscale approach to triglycerides simulations: from atomistic to coarse-grained models and back
The aim of this paper is to provide a simulation strategy to study the liquid-solid transition of triglycerides. The strategy is based on a multiscale approach. A coarse-grained model, parameterized on the basis of reference atomistic simulations, has been used to model the liquid-solid transition. A reverse mapping procedure has been proposed to reconstruct atomistic models from coarse-grained configurations and validated against experimental structural properties. The nucleation and growth of the crystalline order have been analysed in terms of several properties
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