37,734 research outputs found
The Vortex Kinetics of Conserved and Non-conserved O(n) Models
We study the motion of vortices in the conserved and non-conserved
phase-ordering models. We give an analytical method for computing the speed and
position distribution functions for pairs of annihilating point vortices based
on heuristic scaling arguments. In the non-conserved case this method produces
a speed distribution function consistent with previous analytic results. As two
special examples, we simulate the conserved and non-conserved O(2) model in two
dimensional space numerically. The numerical results for the non-conserved case
are consistent with the theoretical predictions. The speed distribution of the
vortices in the conserved case is measured for the first time. Our theory
produces a distribution function with the correct large speed tail but does not
accurately describe the numerical data at small speeds. The position
distribution functions for both models are measured for the first time and we
find good agreement with our analytic results. We are also able to extend this
method to models with a scalar order parameter.Comment: 21 pages, 9 figure
Nonlinear Stochastic Dynamics of Complex Systems, II: Potential of Entropic Force in Markov Systems with Nonequilibrium Steady State, Generalized Gibbs Function and Criticality
In this paper we revisit the notion of the "minus logarithm of stationary
probability" as a generalized potential in nonequilibrium systems and attempt
to illustrate its central role in an axiomatic approach to stochastic
nonequilibrium thermodynamics of complex systems. It is demonstrated that this
quantity arises naturally through both monotonicity results of Markov processes
and as the rate function when a stochastic process approaches a deterministic
limit. We then undertake a more detailed mathematical analysis of the
consequences of this quantity, culminating in a necessary and sufficient
condition for the criticality of stochastic systems. This condition is then
discussed in the context of recent results about criticality in biological
systemsComment: 28 page
Global dynamic modeling of a transmission system
The work performed on global dynamic simulation and noise correlation of gear transmission systems at the University of Akron is outlined. The objective is to develop a comprehensive procedure to simulate the dynamics of the gear transmission system coupled with the effects of gear box vibrations. The developed numerical model is benchmarked with results from experimental tests at NASA Lewis Research Center. The modal synthesis approach is used to develop the global transient vibration analysis procedure used in the model. Modal dynamic characteristics of the rotor-gear-bearing system are calculated by the matrix transfer method while those of the gear box are evaluated by the finite element method (NASTRAN). A three-dimensional, axial-lateral coupled bearing model is used to couple the rotor vibrations with the gear box motion. The vibrations between the individual rotor systems are coupled through the nonlinear gear mesh interactions. The global equations of motion are solved in modal coordinates and the transient vibration of the system is evaluated by a variable time-stepping integration scheme. The relationship between housing vibration and resulting noise of the gear transmission system is generated by linear transfer functions using experimental data. A nonlinear relationship of the noise components to the fundamental mesh frequency is developed using the hypercoherence function. The numerically simulated vibrations and predicted noise of the gear transmission system are compared with the experimental results from the gear noise test rig at NASA Lewis Research Center. Results of the comparison indicate that the global dynamic model developed can accurately simulate the dynamics of a gear transmission system
Subelliptic Li-Yau estimates on three dimensional model spaces
We describe three elementary models in three dimensional subelliptic geometry
which correspond to the three models of the Riemannian geometry (spheres,
Euclidean spaces and Hyperbolic spaces) which are respectively the SU(2),
Heisenberg and SL(2) groups. On those models, we prove parabolic Li-Yau
inequalities on positive solutions of the heat equation. We use for that the
techniques that we adapt to those elementary model spaces. The
important feature developed here is that although the usual notion of Ricci
curvature is meaningless (or more precisely leads to bounds of the form
for the Ricci curvature), we describe a parameter which plays
the same role as the lower bound on the Ricci curvature, and from which one
deduces the same kind of results as one does in Riemannian geometry, like heat
kernel upper bounds, Sobolev inequalities and diameter estimates
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