Coarse-graining stiff bonds

The method of constraints in molecular dynamics is useful because it avoids the resolution of high frequency motions with very small time steps. However, the price to pay is that both the dynamics and the statistics of a constrained system differ from those of the unconstrained one. Instead of using constraints, we propose to dispose of high frequency motions by a coarse-graining procedure in which fast variables are eliminated. These fast variables are thus modeled as friction and thermal fluctuations. We illustrate the methodology with a simple model case, a diatomic molecule in a monoatomic solvent, in which the bond between the atoms of a diatomic molecule is stiff. Although the example is very simple and does not display the interesting effects of “wrong” statistics of the constrained system (i.e. the well-known issue connected to the Fixman potential), it is well suited to give the proof of concept of the whole procedure.     

Coarse-graining scale and effectiveness of hydrodynamic modeling

We review our work on the application of the renormalization-group method to obtain first- and second-order relativistic hydrodynamics from the relativistic Boltzmann equation (RBE) as a dynamical system, with some corrections and new unpublished results. For the first-order equation, we explicitly obtain the distribution function in the asymptotic regime as the invariant manifold of the dynamical system, which turns out to be nothing but the matching condition defining the energy frame, i.e., the Landau-Lifshitz one. It is argued that the frame on which the flow of the relativistic hydrodynamic equation is defined must be the energy frame, if the dynamics should be consistent with the underlying RBE. A sketch is also given for derivation of the second-order hydrodynamic equation, i.e., extended thermodynamics, which is accomplished by extending the invariant manifold so that it is spanned by excited modes as well as the zero modes (hydrodynamic modes) of the linearized collision operator. On the basis of thus constructed resummed distribution function, we propose a novel ansatz for the functional form to be used in Grad moment method; it is shown that our theory gives the same expressions for the transport coefficients as those given in the Chapman-Enskog theory as well as the novel expressions for the relaxation times and lengths allowing natural interpretation.     

Coarse-graining approach to first-order phase transitions

On an example of a simple spin system with two ground states and no symmetry, we show how to control low-temperature systems near first-order phase transitions by a straightforward renormalization group argument. The method, as opposed to the Pirogov-Sinai approach, also works for complex Hamiltonians.     

Coarse-graining of diffusion processes with a multistable drift

Some recent results about the reduction to a Markovian jump process, including a formula for the transition rates, are reviewed and also extended.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Coarse-graining the computations of surface reactions: Nonlinear dynamics from atomistic simulators

We review and discuss the use of equation-free computation in extracting coarse-grained, nonlinear dynamics information from atomistic (lattice-gas) models of surface reactions. The approach is based on circumventing the explicit derivation of macroscopic equations for the system statistics (e.g., average coverage). Short bursts of appropriately initialized computational experimentation with the lattice-gas simulator are designed “on demand” and processed in the spirit of the coarse timestepper introduced in Theodoropoulos et al. (2000) (K. Theodoropoulos, Y.-H. Qian, I.G. Kevrekidis, Proc. Natl. Acad. Sci. USA 97 (2000) 9840). The information derived from these computational experiments, processed through traditional, continuum numerical methods is used to solve the macroscopic equations without ever deriving them in closed form. The approach is illustrated through two computational examples: the CO oxidation reaction, and the NO + CO/Pt(1 0 0) reaction.     

Entanglement energetics at zero temperature

We show how many-body ground state entanglement information may be extracted from subsystem energy measurements at zero temperature. Generically, the larger the measured energy fluctuations are, the larger the entanglement is. Examples are given with the two-state system and the harmonic oscillator. Comparisons made with recent qubit experiments show that this type of measurement provides another method to quantify entanglement with the environment.     

The energetics of the isomeric anthrols

We report the results of geometry optimized MP2(FULL)/6-31G(d) quantum chemical calculations with zero-point vibrational energies and thermal corrections of the isomeric 1-, 2- and 9-anthrols and the tautomeric anthrone. We find that 1- and 2-anthrols have nearly the same enthalpy of formation and are some 6?kJ?mol^?1 more stable than their 9-isomer in accord with intuition based on steric hindrance. We find that anthrone is more stable than 9-anthrol by 13.7 ± 6.4?kJ?mol^?1, in satisfactory agreement with the value of 23 ± 8?kJ?mol^?1 suggested elsewhere by experiment and its associated analysis.     

Unified framework for dislocation-based defect energetics

We present a unified framework for the calculation of dislocation-based defect energetics, and then validate this approach by considering both the self and interaction energies of combinations of grain boundaries and cracks. We obtain in a straightforward manner well-known quantities, such as the energy of a low-angle tilt boundary, as well as other lesser known results, including boundary/boundary and crack/boundary interaction energies, from a common formalism based on linear elasticity. This approach, in combination with simple dimensional analysis, permits the rapid calculation of defect energetics.     

Atomistic configurations and energetics of crack extension in silicon

We report the first atomistic determination of the minimum energy path for a series of bond ruptures to advance a crack front. Saddle-point configurations on (111) cleavage planes in Si reveal a steplike distribution of atomic displacements, implying a kink mechanism which is known to control dislocation mobility. Manifestations of lattice trapping and directional cleavage anisotropy are further elucidated.     

The structure and energetics of defects in liquid crystals

The study of defects in ordered media has become a subject of considerable interest to condensed matter physicists in recent years. This article presents a systematic account of the structures, energies and interactions of defects in the nematic, smectic, cholesteric and discotic phases of liquid crystals. Relevant experimental observations are also described.     

Configurational energetics in ice ih probed by compton scattering

Temperature-induced changes in the ground-state electron momentum density of polycrystalline ice Ih are studied with high accuracy by Compton scattering utilizing synchrotron radiation. A unique feasibility of the technique to provide direct experimental information on configurational enthalpies and heat capacities is demonstrated. The configurational enthalpy, obtained with an accuracy of 1.5 meV, evolves linearly with temperature above T=100 K. Consequently the configurational heat capacity is found to be constant, c{p}{config}=(0.44+/-0.11) J g{-1} K-1, in this temperature regime. Obtaining these quantities experimentally is fundamentally important for evaluating the accuracy of molecular-dynamics simulations schemes.     

Degeneracy in loop variables

The small algebra of loop functionals, defined by Rovelli and Smolin, on the Ashtekar phase space of general relativity is studied. Regarded as coordinates on the phase space, the loop functionals become degenerate at certain points. All the degenerate points are found and the corresponding degeneracy is discussed. The intersection of the set of degenerate points with the real slice of the constraint surface is shown to correspond precisely the Goldberg-Kerr solutions. The evolution of the holonomy group of Ashtekar's connection is examined, and the complexification of the holonomy group is shown to be preserved under it. Thus, an observable of the gravitational field is constructed.