412 research outputs found
Extended Poisson-Kac Theory: A Unifying Framework for Stochastic Processes
Stochastic processes play a key role for modeling a huge variety of transport
problems out of equilibrium, with manifold applications throughout the natural
and social sciences. To formulate models of stochastic dynamics the
conventional approach consists in superimposing random fluctuations on a
suitable deterministic evolution. These fluctuations are sampled from
probability distributions that are prescribed a priori, most commonly as
Gaussian or L\'evy. While these distributions are motivated by (generalised)
central limit theorems they are nevertheless \textit{unbounded}, meaning that
arbitrarily large fluctuations can be obtained with finite probability. This
property implies the violation of fundamental physical principles such as
special relativity and may yield divergencies for basic physical quantities
like energy. Here we solve the fundamental problem of unbounded random
fluctuations by constructing a comprehensive theoretical framework of
stochastic processes possessing physically realistic finite propagation
velocity. Our approach is motivated by the theory of L\'evy walks, which we
embed into an extension of conventional Poisson-Kac processes. The resulting
extended theory employs generalised transition rates to model subtle
microscopic dynamics, which reproduces non-trivial spatio-temporal correlations
on macroscopic scales. It thus enables the modelling of many different kinds of
dynamical features, as we demonstrate by three physically and biologically
motivated examples. The corresponding stochastic models capture the whole
spectrum of diffusive dynamics from normal to anomalous diffusion, including
the striking `Brownian yet non Gaussian' diffusion, and more sophisticated
phenomena such as senescence. Extended Poisson-Kac theory can therefore be used
to model a wide range of finite velocity dynamical phenomena that are observed
experimentally.Comment: 26 pages, 5 figure
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Dispersion phenomena in microchannels: Transition from Taylor-Aris to convection-dominated regime
This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.This article addresses the qualitative and quantitative properties of solute transport and dispersion in microchannel of finite-length. As the Peclet number increases a transition from the Taylor-Aris to a new
regime referred as convection dominated dispersion occurs, which is controlled by the velocity profile near the stagnation points at the solid walls. The properties characterizing dispersion dominated regime can be used for analytical purposes as a chromatographic-based velocimetry and for determining the eventual occurrence of slip at the solid walls of microchannels
Spectral Properties of Stochastic Processes Possessing Finite Propagation Velocity.
This article investigates the spectral structure of the evolution operators associated with the statistical description of stochastic processes possessing finite propagation velocity. Generalized Poisson-Kac processes and Lévy walks are explicitly considered as paradigmatic examples of regular and anomalous dynamics. A generic spectral feature of these processes is the lower boundedness of the real part of the eigenvalue spectrum that corresponds to an upper limit of the spectral dispersion curve, physically expressing the relaxation rate of a disturbance as a function of the wave vector. We also analyze Generalized Poisson-Kac processes possessing a continuum of stochastic states parametrized with respect to the velocity. In this case, there is a critical value for the wave vector, above which the point spectrum ceases to exist, and the relaxation dynamics becomes controlled by the essential part of the spectrum. This model can be extended to the quantum case, and in fact, it represents a simple and clear example of a sub-quantum dynamics with hidden variables
Age representation of Levy walks: partial density waves, relaxation and first passage time statistics
Lévy walks (LWs) define a fundamental class of finite velocity stochastic processes that can be introduced as a special case of continuous time random walks. Alternatively, there is a hyperbolic representation of them in terms of partial probability density waves. Using the latter framework we explore the impact of aging on LWs, which can be viewed as a specific initial preparation of the particle ensemble with respect to an age distribution. We show that the hyperbolic age formulation is suitable for a simple integral representation in terms of linear Volterra equations for any initial preparation. On this basis relaxation properties, i.e. the convergence towards equilibrium of a generic thermodynamic function dependent on the spatial particle distribution, and first passage time statistics in bounded domains are studied by connecting the latter problem with solute release kinetics. We find that even normal diffusive LWs, where the long-term mean square displacement increases linearly with time, may display anomalous relaxation properties such as stretched exponential decay. We then discuss the impact of aging on the first passage time statistics of LWs by developing the corresponding Volterra integral representation. As a further natural generalization the concept of LWs with wearing is introduced to account for mobility losses
A renormalisation approach to excitable reaction-diffusion waves in fractal media
Of fundamental importance to wave propagation in a wide range of physical phenomena is the structural geometry of the supporting medium. Recently, there have been several investigations on wave propagation in fractal media. We present here a renormalization approach to the study of reaction-diffusion (RD) wave propagation on finitely ramified fractal structures. In particular we will study a Rinzel-Keller (RK) type model, supporting travelling waves on a Sierpinski gasket (SG), lattice
Long-term efficacy and safety results of taliglucerase alfa through 5years in adult treatment-naïve patients with Gaucher disease
Taliglucerase alfa, the first available plant cell-expressed recombinant therapeutic protein, is an enzyme replacement therapy approved for Gaucher disease (GD). PB-06-001, a pivotal phase 3, multicenter, randomized, double-blind, parallel-dose study investigated taliglucerase alfa 30 or 60U/kg every other week through 9months in treatment-naïve adults with GD; 30-month extension study PB-06-003 followed. Patients completing PB-06-001 and PB-06-003 could continue treatment in PB-06-007. Nineteen patients enrolled in PB-06-007 (30U/kg, n=8; 60U/kg, n=9; dose adjusted, n=2); 17 completed 5 total years of treatment. In these 3 groups, respectively, taliglucerase alfa resulted in mean decreases in spleen volume (-8.7, -6.9, -12.4 multiples of normal), liver volume (-0.6, -0.4, -0.5 multiples of normal), chitotriosidase activity (-83.1%, -93.4%, -87.9%), and chemokine (CC motif) ligand 18 concentration (-66.7%, -83.3%, -78.9%), as well as mean increases in hemoglobin concentration (+2.1, +2.1, +1.8mg/dL) and platelet count (+31,871, +106,800, +34,000/mm3). The most common adverse events were nasopharyngitis and arthralgia. Most adverse events were mild/moderate; no serious adverse events were considered treatment-related. These results demonstrate continued improvement of disease parameters during 5years of taliglucerase alfa therapy in 17 treatment-naive patients with no new safety concerns, extending the taliglucerase alfa clinical efficacy and safety dataset. This study was registered at www.clinicaltrials.gov as NCT01422187
Critical dimensions for random walks on random-walk chains
The probability distribution of random walks on linear structures generated
by random walks in -dimensional space, , is analytically studied
for the case . It is shown to obey the scaling form
, where is
the density of the chain. Expanding in powers of , we find that
there exists an infinite hierarchy of critical dimensions, ,
each one characterized by a logarithmic correction in . Namely, for
, ; for ,
; for , ; for , ; for , , {\it etc.\/} In particular, for
, this implies that the temporal dependence of the probability density of
being close to the origin .Comment: LATeX, 10 pages, no figures submitted for publication in PR
A preliminary investigation of a novel method to manipulate penis length to measure female sexual satisfaction: a single-case experimental design
Precision Measurements of Stretching and Compression in Fluid Mixing
The mixing of an impurity into a flowing fluid is an important process in
many areas of science, including geophysical processes, chemical reactors, and
microfluidic devices. In some cases, for example periodic flows, the concepts
of nonlinear dynamics provide a deep theoretical basis for understanding
mixing. Unfortunately, the building blocks of this theory, i.e. the fixed
points and invariant manifolds of the associated Poincare map, have remained
inaccessible to direct experimental study, thus limiting the insight that could
be obtained. Using precision measurements of tracer particle trajectories in a
two-dimensional fluid flow producing chaotic mixing, we directly measure the
time-dependent stretching and compression fields. These quantities, previously
available only numerically, attain local maxima along lines coinciding with the
stable and unstable manifolds, thus revealing the dynamical structures that
control mixing. Contours or level sets of a passive impurity field are found to
be aligned parallel to the lines of large compression (unstable manifolds) at
each instant. This connection appears to persist as the onset of turbulence is
approached.Comment: 5 pages, 5 figure
Fractional differentiability of nowhere differentiable functions and dimensions
Weierstrass's everywhere continuous but nowhere differentiable function is
shown to be locally continuously fractionally differentiable everywhere for all
orders below the `critical order' 2-s and not so for orders between 2-s and 1,
where s, 1<s<2 is the box dimension of the graph of the function. This
observation is consolidated in the general result showing a direct connection
between local fractional differentiability and the box dimension/ local Holder
exponent. Levy index for one dimensional Levy flights is shown to be the
critical order of its characteristic function. Local fractional derivatives of
multifractal signals (non-random functions) are shown to provide the local
Holder exponent. It is argued that Local fractional derivatives provide a
powerful tool to analyze pointwise behavior of irregular signals.Comment: minor changes, 19 pages, Late
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