On the "generalized Generalized Langevin Equation"

In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble ("bundle") of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. In contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation, but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows to relate the Taylor expansion of the memory kernel to data that is accessible in MD simulations and experiments, thus allowing to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions, and is shown to be consistent with direct measurements from simulations

Numerical solution of the two-dimensional time-dependent multigroup equations

Also issued as a Ph. D. thesis in the Dept. of Nuclear Engineering, MIT, 1969"MIT-3903-1."Includes bibliographical references (leaves 60-61)Contract AT(30-1)-390

Cofinement, entropy, and single-particle dynamics of equilibrium hard-sphere mixtures

We use discontinuous molecular dynamics and grand-canonical transition-matrix Monte Carlo simulations to explore how confinement between parallel hard walls modifies the relationships between packing fraction, self-diffusivity, partial molar excess entropy, and total excess entropy for binary hard-sphere mixtures. To accomplish this, we introduce an efficient algorithm to calculate partial molar excess entropies from the transition-matrix Monte Carlo simulation data. We find that the species-dependent self-diffusivities of confined fluids are very similar to those of the bulk mixture if compared at the same, appropriately defined, packing fraction up to intermediate values, but then deviate negatively from the bulk behavior at higher packing fractions. On the other hand, the relationships between self-diffusivity and partial molar excess entropy (or total excess entropy) observed in the bulk fluid are preserved under confinement even at relatively high packing fractions and for different mixture compositions. This suggests that the partial molar excess entropy, calculable from classical density functional theories of inhomogeneous fluids, can be used to predict some of the nontrivial dynamical behaviors of fluid mixtures in confined environments.Comment: submitted to JC

The Origin of Primordial Dwarf Stars and Baryonic Dark Matter

I present a scenario for the production of low mass, degenerate dwarfs of mass $>0.1 M_{\odot}$ via the mechanism of Lenzuni, Chernoff & Salpeter (1992). Such objects meet the mass limit requirements for halo dark matter from microlensing surveys while circumventing the chemical evolution constraints on normal white dwarf stars. I describe methods to observationally constrain this scenario and suggest that such objects may originate in small clusters formed from the thermal instability of shocked, heated gas in dark matter haloes, such as suggested by Fall & Rees (1985) for globular clusters.Comment: TeX, 4 pages plus 2 postscript figures. To appear in Astrophysical Journal Letter

Correction to: Accuracy of surface strain measurements from transmission electron microscopy images of nanoparticles

Abstract Unfortunately, after publication of this article [1], it was noticed that the name of the fifth author was incorrectly displayed as Jakob Schiøz. The correct name is Jakob Schiøtz and can be seen in the corrected author list above. The original article has also been updated to correct this error

Accuracy of surface strain measurements from transmission electron microscopy images of nanoparticles

Additional file 1. Section S1. Measuring the center of mass. Figure S1. Definition of integration regions for center of mass calculations. Figure S2. Comparison of center of mass positions with peak positions. Figure S3. Magnitudes of thermal vibrations. Figure S4. Comparison of our method with GPA. Figure S5. Negative defocus measurements. Figure S6. Planar strain errors for increasing tilt. Figure S7. Surface strain errors for increasing tilt

Correction to: Accuracy of surface strain measurements from transmission electron microscopy images of nanoparticles

Unfortunately, after publication of this article [1], it was noticed that the name of the fifth author was incorrectly displayed as Jakob Schiøz. The correct name is Jakob Schiøtz and can be seen in the corrected author list above. The original article has also been updated to correct this error