1,405 research outputs found
An Elementary Proof of the Existence and Uniqueness Theorem for the Navier-Stokes Equations
We give a geometric approach to proving know regularity and existence
theorems for the 2D Navier-Stokes Equations. We feel this point of view is
instructive in better understanding the dynamics. The technique is inspired by
constructions in the Dynamical Systems.Comment: 15 Page
Remark on the (Non)convergence of Ensemble Densities in Dynamical Systems
We consider a dynamical system with state space , a smooth, compact subset
of some , and evolution given by , , ;
is invertible and the time may be discrete, , , or continuous, . Here we show that starting with a
continuous positive initial probability density , with respect
to , the smooth volume measure induced on by Lebesgue measure on , the expectation value of , with respect to any
stationary (i.e. time invariant) measure , is linear in , . depends only on and vanishes
when is absolutely continuous wrt .Comment: 7 pages, plain TeX; [email protected],
[email protected], [email protected], to appear in Chaos: An
Interdisciplinary Journal of Nonlinear Science, Volume 8, Issue
Naturalistic paradigms for neuroimaging and bedside measures of conscious awareness
Complex, naturalistic stimuli can test for covert awareness in behaviourally non-responsive patients. For patients with poor visual function, this thesis aimed to identify an auditory-only stimulus that could evaluate executive function. Also, it assessed if Galvanic Skin Response could be a suitable bedside testing method. Healthy individuals listened to 4 auditory stimuli in the fMRI scanner. During Galvanic Skin Response recording, an independent group of controls listened to an audio narrative and watched a movie. Behaviourally non-responsive patients were also tested during movie viewing. Using fMRI, an audio narrative was identified that produced widespread brain synchronization between healthy participants, critically in the frontoparietal network. Healthy controls showed highly similar GSR to a suspenseful movie. A locked-in syndrome patient had a similar GSR to controls during movie viewing. The audio narrative can be used for future patient testing, and GSR can be used to test for consciousness at the bedside
A boundary integral formalism for stochastic ray tracing in billiards
Determining the flow of rays or non-interacting particles driven by a force or velocity field is fundamental to modelling many physical processes. These include particle flows arising in fluid mechanics and ray flows arising in the geometrical optics limit of linear wave equations. In many practical applications, the driving field is not known exactly and the dynamics are determined only up to a degree of uncertainty. This paper presents a boundary integral framework for propagating flows including uncertainties, which is shown to systematically interpolate between a deterministic and a completely random description of the trajectory propagation. A simple but efficient discretisation approach is applied to model uncertain billiard dynamics in an integrable rectangular domain
Non-ergodicity of the motion in three dimensional steep repelling dispersing potentials
It is demonstrated numerically that smooth three degrees of freedom
Hamiltonian systems which are arbitrarily close to three dimensional strictly
dispersing billiards (Sinai billiards) have islands of effective stability, and
hence are non-ergodic. The mechanism for creating the islands are corners of
the billiard domain.Comment: 6 pages, 8 figures, submitted to Chao
The largest eigenvalue of rank one deformation of large Wigner matrices
The purpose of this paper is to establish universality of the fluctuations of
the largest eigenvalue of some non necessarily Gaussian complex Deformed Wigner
Ensembles. The real model is also considered. Our approach is close to the one
used by A. Soshnikov in the investigations of classical real or complex Wigner
Ensembles. It is based on the computation of moments of traces of high powers
of the random matrices under consideration
Nonequilibrium, thermostats and thermodynamic limit
The relation between thermostats of "isoenergetic" and "frictionless" kind is
studied and their equivalence in the thermodynamic limit is proved in space
dimension and, for special geometries, .Comment: 22 pages PRA 2-columns format v3: Typos corrected as acknowledge
In-flight dissipation as a mechanism to suppress Fermi acceleration
Some dynamical properties of time-dependent driven elliptical-shaped billiard
are studied. It was shown that for the conservative time-dependent dynamics the
model exhibits the Fermi acceleration [Phys. Rev. Lett. 100, 014103 (2008)]. On
the other hand, it was observed that damping coefficients upon collisions
suppress such phenomenon [Phys. Rev. Lett. 104, 224101 (2010)]. Here, we
consider a dissipative model under the presence of in-flight dissipation due to
a drag force which is assumed to be proportional to the square of the
particle's velocity. Our results reinforce that dissipation leads to a phase
transition from unlimited to limited energy growth. The behaviour of the
average velocity is described using scaling arguments.Comment: 4 pages, 5 figure
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