The canonical ensemble via symplectic integrators using Nosé and Nosé-Poincaré chains

Simulations that sample from the canonical ensemble can be generated by the addition of a single degree of freedom, provided that the system is ergodic, as described by Nosé with subsequent modifications by Hoover to allow sampling in real time. Nosé-Hoover dynamics is not ergodic for small or stiff systems and the addition of auxiliary thermostats is needed to overcome this deficiency. Nosé-Hoover dynamics, like its derivatives, does not have a Hamiltonian structure, precluding the use of symplectic integrators which are noted for their long term stability and structure preservation. As an alternative to Nosé-Hoover, the Hamiltonian Nosé-Poincaré method was proposed by Bond, Laird, and Leimkuhler [J. Comput. Phys. 151, 114 (1999)], but the straightforward addition of thermostatting chains does not sample from the canonical ensemble. In this paper a method is proposed whereby additional thermostats can be applied to a Hamiltonian system while retaining sampling from the canonical ensemble. This technique has been used to construct thermostatting chains for the Nosé and Nosé-Poincaré methods.     

Some Isoperimetric Inequalities in Electrochemistry and Hele Shaw Flows

Isoperimetric inequalities are applied to a moving-boundaryproblem for doubly-connected domains. This problem occurs forexample in electrochemistry, in which case the domains in questionare the electrolyte of an electrolytic cell. The two electrodessurrounding the electrolyte are assumed to grow or dissolve,at different rates in general, by electrochemical reaction.We obtain optimal estimates showing, for example, that the leastchange in volume of each electrode always occurs in sphericalsymmetry.     

An Efficient Geometric Integrator for Thermostatted Anti-/Ferromagnetic Models

(Anti)-/ferromagnetic Heisenberg spin models arise from discretization of Landau–Lifshitz models in micromagnetic modelling. In many applications it is essential to study the behavior of the system at a fixed temperature. A formulation for thermostatted spin dynamics was given by Bulgac and Kusnetsov, which incorporates a complicated nonlinear dissipation/driving term while preserving spin length. It is essential to properly model this term in simulation, and simplified schemes give poor numerical performance, e.g., requiring an excessively small timestep for stable integration. In this paper we present an efficient, structure-preserving method for thermostatted spin dynamics.     

A temperature control technique for nonequilibrium molecular simulation

We describe a dynamical approach to thermal regulation in molecular dynamics. Temperature is moderated by a control law and an additional variable, as in Nose dynamics, but whose influence on the system decreases as the system approaches equilibrium. This device enables approximation of microcanonical averages and autocorrelation functions consistent with a given target temperature. Moreover, we demonstrate that the suggested technique is effective for the control of heat dissipation in a nonequilibrium setting, first by showing that the temperature control correctly regulates heat introduced by a rapid change to the system, and then by studying the slow relaxation of vibrational degrees of freedom (e.g., due to bonded atoms) in a solvent bath.     

Degradation and reconstruction of moenomycin A and derivatives: dissecting the function of the isoprenoid chain

Moenomycin A is the only known natural product that inhibits peptidoglycan biosynthesis by binding the bacterial transglycosylases. We describe a degradation/reconstruction route to manipulate the reducing end of moenomycin A. A comparison of the biological and enzyme inhibitory activity of moenomycin A and an analogue containing a nerol lipid in place of the natural C25 lipid chain provides insight into the role of the moenocinol unit. Our results show that a lipid chain having ten carbons in moenocinol is sufficient for enzyme inhibition, but a longer chain is required for biological acitivity, apparently because the molecule must partition into biological membranes to reach its target in bacterial cells.