Mixed mode pattern in Doublefoot mutant mouse limb - Turing reaction-diffusion model on a growing domain during limb development

It has been suggested that the Turing reaction–diffusion model on a growing domain is applicable during limb development, but experimental evidence for this hypothesis has been lacking. In the present study, we found that in Doublefoot mutant mice, which have supernumerary digits due to overexpansion of the limb bud, thin digits exist in the proximal part of the hand or foot, which sometimes become normal abruptly at the distal part. We found that exactly the same behaviour can be reproduced by numerical simulation of the simplest possible Turing reaction–diffusion model on a growing domain. We analytically showed that this pattern is related to the saturation of activator kinetics in the model. Furthermore, we showed that a number of experimentally observed phenomena in this system can be explained within the context of a Turing reaction–diffusion model. Finally, we make some experimentally testable predictions

Stability ordering of cycle expansions

We propose that cycle expansions be ordered with respect to stability rather than orbit length for many chaotic systems, particularly those exhibiting crises. This is illustrated with the strong field Lorentz gas, where we obtain significant improvements over traditional approaches.Comment: Revtex, 5 incorporated figures, total size 200

Microscopic expressions for the thermodynamic temperature

We show that arbitrary phase space vector fields can be used to generate phase functions whose ensemble averages give the thermodynamic temperature. We describe conditions for the validity of these functions in periodic boundary systems and the Molecular Dynamics (MD) ensemble, and test them with a short-ranged potential MD simulation.Comment: 21 pages, 2 figures, Revtex. Submitted to Phys. Rev.

Lyapunov instability for a periodic Lorentz gas thermostated by deterministic scattering

In recent work a deterministic and time-reversible boundary thermostat called thermostating by deterministic scattering has been introduced for the periodic Lorentz gas [Phys. Rev. Lett. {\bf 84}, 4268 (2000)]. Here we assess the nonlinear properties of this new dynamical system by numerically calculating its Lyapunov exponents. Based on a revised method for computing Lyapunov exponents, which employs periodic orthonormalization with a constraint, we present results for the Lyapunov exponents and related quantities in equilibrium and nonequilibrium. Finally, we check whether we obtain the same relations between quantities characterizing the microscopic chaotic dynamics and quantities characterizing macroscopic transport as obtained for conventional deterministic and time-reversible bulk thermostats.Comment: 18 pages (revtex), 7 figures (postscript

Integration through transients for Brownian particles under steady shear

Starting from the microscopic Smoluchowski equation for interacting Brownian particles under stationary shearing, exact expressions for shear-dependent steady-state averages, correlation and structure functions, and susceptibilities are obtained, which take the form of generalized Green-Kubo relations. They require integration of transient dynamics. Equations of motion with memory effects for transient density fluctuation functions are derived from the same microscopic starting point. We argue that the derived formal expressions provide useful starting points for approximations in order to describe the stationary non-equilibrium state of steadily sheared dense colloidal dispersions.Comment: 17 pages, Submitted to J. Phys.: Condens. Matter; revised version with minor correction

A systematically coarse-grained model for DNA, and its predictions for persistence length, stacking, twist, and chirality

We introduce a coarse-grained model of DNA with bases modeled as rigid-body ellipsoids to capture their anisotropic stereochemistry. Interaction potentials are all physicochemical and generated from all-atom simulation/parameterization with minimal phenomenology. Persistence length, degree of stacking, and twist are studied by molecular dynamics simulation as functions of temperature, salt concentration, sequence, interaction potential strength, and local position along the chain, for both single- and double-stranded DNA where appropriate. The model of DNA shows several phase transitions and crossover regimes in addition to dehybridization, including unstacking, untwisting, and collapse which affect mechanical properties such as rigidity and persistence length. The model also exhibits chirality with a stable right-handed and metastable left-handed helix.Comment: 30 pages, 20 figures, Supplementary Material available at http://www.physics.ubc.ca/~steve/publications.htm

Master equation approach to the conjugate pairing rule of Lyapunov spectra for many-particle thermostatted systems

The master equation approach to Lyapunov spectra for many-particle systems is applied to non-equilibrium thermostatted systems to discuss the conjugate pairing rule. We consider iso-kinetic thermostatted systems with a shear flow sustained by an external restriction, in which particle interactions are expressed as a Gaussian white randomness. Positive Lyapunov exponents are calculated by using the Fokker-Planck equation to describe the tangent vector dynamics. We introduce another Fokker-Planck equation to describe the time-reversed tangent vector dynamics, which allows us to calculate the negative Lyapunov exponents. Using the Lyapunov exponents provided by these two Fokker-Planck equations we show the conjugate pairing rule is satisfied for thermostatted systems with a shear flow in the thermodynamic limit. We also give an explicit form to connect the Lyapunov exponents with the time-correlation of the interaction matrix in a thermostatted system with a color field.Comment: 10 page

Lyapunov Mode Dynamics in Hard-Disk Systems

The tangent dynamics of the Lyapunov modes and their dynamics as generated numerically - {\it the numerical dynamics} - is considered. We present a new phenomenological description of the numerical dynamical structure that accurately reproduces the experimental data for the quasi-one-dimensional hard-disk system, and shows that the Lyapunov mode numerical dynamics is linear and separate from the rest of the tangent space. Moreover, we propose a new, detailed structure for the Lyapunov mode tangent dynamics, which implies that the Lyapunov modes have well-defined (in)stability in either direction of time. We test this tangent dynamics and its derivative properties numerically with partial success. The phenomenological description involves a time-modal linear combination of all other Lyapunov modes on the same polarization branch and our proposed Lyapunov mode tangent dynamics is based upon the form of the tangent dynamics for the zero modes

Boundary effects in the stepwise structure of the Lyapunov spectra for quasi-one-dimensional systems

Boundary effects in the stepwise structure of the Lyapunov spectra and the corresponding wavelike structure of the Lyapunov vectors are discussed numerically in quasi-one-dimensional systems consisting of many hard-disks. Four kinds of boundary conditions constructed by combinations of periodic boundary conditions and hard-wall boundary conditions are considered, and lead to different stepwise structures of the Lyapunov spectra in each case. We show that a spatial wavelike structure with a time-oscillation appears in the spatial part of the Lyapunov vectors divided by momenta in some steps of the Lyapunov spectra, while a rather stationary wavelike structure appears in the purely spatial part of the Lyapunov vectors corresponding to the other steps. Using these two kinds of wavelike structure we categorize the sequence and the kinds of steps of the Lyapunov spectra in the four different boundary condition cases.Comment: 33 pages, 25 figures including 10 color figures. Manuscript including the figures of better quality is available from http://newt.phys.unsw.edu.au/~gary/step.pd