2,001 research outputs found
A Micro-CT Analysis of the Hominoid Subnasal Anatomy
This thesis performed a micro-CT analysis of extant hominoid subnasal anatomy and a review of the subnasal anatomy of the Miocene hominoids. This thesis tested the hypothesis that the extant hominoids exhibit diagnostic morphological patterns of the subnasal anatomy that are phylogenetically informative. The terminology of the subnasal anatomy was revised and new measurements were constructed to analyze the morphology of the hominoid subnasal anatomy. It is suggested that previous analyses of the hominoid subnasal anatomy were limited by technological constraints, poorly constructed measurements, and ambiguous terminology. This micro-CT analysis confirmed that the extant hominoids do exhibit diagnostic patterns of their subnasal morphology and that these patterns are indeed phylogenetically informative. A new character state was also discovered that differentiated extant cercopithecoids from extant hominoids. The extant hominids exhibit a shared derived subnasal morphology, while Pongo exhibits the most diagnostic and derived morphological pattern among the extant hominoids
Understanding Anomalous Transport in Intermittent Maps: From Continuous Time Random Walks to Fractals
We show that the generalized diffusion coefficient of a subdiffusive
intermittent map is a fractal function of control parameters. A modified
continuous time random walk theory yields its coarse functional form and
correctly describes a dynamical phase transition from normal to anomalous
diffusion marked by strong suppression of diffusion. Similarly, the probability
density of moving particles is governed by a time-fractional diffusion equation
on coarse scales while exhibiting a specific fine structure. Approximations
beyond stochastic theory are derived from a generalized Taylor-Green-Kubo
formula.Comment: 4 pages, 3 eps figure
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
Logarithmic oscillators: ideal Hamiltonian thermostats
A logarithmic oscillator (in short, log-oscillator) behaves like an ideal
thermostat because of its infinite heat capacity: when it weakly couples to
another system, time averages of the system observables agree with ensemble
averages from a Gibbs distribution with a temperature T that is given by the
strength of the logarithmic potential. The resulting equations of motion are
Hamiltonian and may be implemented not only in a computer but also with
real-world experiments, e.g., with cold atoms.Comment: 5 pages, 3 figures. v4: version accepted in Phys. Rev. Let
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
Random walk approach to the d-dimensional disordered Lorentz gas
A correlated random walk approach to diffusion is applied to the disordered
nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length
distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic
expression for the diffusion constant in arbitrary number of dimensions d is
obtained. The result corresponds to an Enskog-like correction to the Boltzmann
prediction, being exact in the dilute limit, and better or nearly exact in
comparison to renormalized kinetic theory predictions for all allowed densities
in d=2,3. Extensive numerical simulations were also performed to elucidate the
role of the approximations involved.Comment: 5 pages, 5 figure
Separation of trajectories and its Relation to Entropy for Intermittent Systems with a Zero Lyapunov exponent
One dimensional intermittent maps with stretched exponential separation of
nearby trajectories are considered. When time goes infinity the standard
Lyapunov exponent is zero. We investigate the distribution of
,
where is determined by the nonlinearity of the map in the vicinity of
marginally unstable fixed points. The mean of is determined
by the infinite invariant density. Using semi analytical arguments we calculate
the infinite invariant density for the Pomeau-Manneville map, and with it
obtain excellent agreement between numerical simulation and theory. We show
that \alpha \left is equal to Krengel's entropy and
to the complexity calculated by the Lempel-Ziv compression algorithm. This
generalized Pesin's identity shows that \left and
Krengel's entropy are the natural generalizations of usual Lyapunov exponent
and entropy for these systems.Comment: 12 pages, 10 figure
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