Study of Critical Dynamics in Fluid via Molecular Dynamics in Canonical Ensemble

With the objective of demonstrating usefulness of thermostats in the study of dynamic critical phenomena in fluids, we present results for transport properties in a binary Lennard-Jones fluid that exhibits liquid-liquid phase transition. Results from the molecular dynamics simulations in canonical ensemble, with various thermostats, are compared with those from microcanonical ensemble. It is observed that the Nos\'{e}-Hoover and dissipative particle dynamics thermostats are useful for the calculations of mutual diffusivity and shear viscosity. The Nos\'{e}-Hoover thermostat, however, appears inadequate for the study of bulk viscosity.Comment: 5 pages, 4 figures in European Physical Journal E 201

Finite-size Scaling Study of Shear Viscosity Anomaly at Liquid-Liquid Criticality

We study equilibrium dynamics of a symmetrical binary Lennard-Jones fluid mixture near its consolute criticality. Molecular dynamics simulation results for shear viscosity, $\eta$, from microcanonical ensemble are compared with those from canonical ensemble with various thermostats. It is observed that Nos\'{e}-Hoover thermostat is a good candidate for this purpose and so, is adopted for the quantification of critical singularity of $\eta$, to avoid temperature fluctuation (or even drift) that is often encountered in microcanonical simulations. Via finite-size scaling analysis of our simulation data, thus obtained, we have been able to quantify even the weakest anomaly, of all transport properties, that shear viscosity exhibits and confirm the corresponding theoretical prediction.Comment: 6 pages, 6 figure

Four-connected triangulations of planar point sets

In this paper, we consider the problem of determining in polynomial time whether a given planar point set $P$ of $n$ points admits 4-connected triangulation. We propose a necessary and sufficient condition for recognizing $P$, and present an $O(n^3)$ algorithm of constructing a 4-connected triangulation of $P$. Thus, our algorithm solves a longstanding open problem in computational geometry and geometric graph theory. We also provide a simple method for constructing a noncomplex triangulation of $P$ which requires $O(n^2)$ steps. This method provides a new insight to the structure of 4-connected triangulation of point sets.Comment: 35 pages, 35 figures, 5 reference

On the Spatial Pattern of Input-Output Metrics for a Network Synchronization Process

A graph-theoretic analysis is undertaken for a compendium of input-output (transfer) metrics of a standard discrete-time linear synchronization model, including lp gains, frequency responses, frequency-band energy, and Markov parameters. We show that these transfer metrics exhibit a spatial degradation, such that they are monotonically nonincreasing along vertex cutsets away from an exogenous input. We use this spatial analysis to characterize signal-to-noise ratios (SNRs) in diffusive networks driven by process noise, and to develop a notion of propagation stability for dynamical networks. Finally, the formal results are illustrated through an example