On practical applicability of the Jarzynski relation in statistical mechanics: a pedagogical example

We suggest and discuss a simple model of an ideal gas under the piston to gain an insight into the workings of the Jarzynski identity connecting the average exponential of the work over the non-equilibrium trajectories with the equilibrium free energy. We show that the Jarzynski identity is valid for our system due to the very rapid molecules belonging to the tail of the Maxwell distribution. For the most interesting extreme, when the system volume is large, while the piston is moving with large speed (compared to thermal velocity) for a very short time, the necessary number of independent experimental runs to obtain a reasonable approximation for the free energy from averaging the non-equilibrium work grows exponentially with the system size.Comment: 15 pages, 7 figures, submitted to JP

Probabilistic fracture finite elements

The Probabilistic Fracture Mechanics (PFM) is a promising method for estimating the fatigue life and inspection cycles for mechanical and structural components. The Probability Finite Element Method (PFEM), which is based on second moment analysis, has proved to be a promising, practical approach to handle problems with uncertainties. As the PFEM provides a powerful computational tool to determine first and second moment of random parameters, the second moment reliability method can be easily combined with PFEM to obtain measures of the reliability of the structural system. The method is also being applied to fatigue crack growth. Uncertainties in the material properties of advanced materials such as polycrystalline alloys, ceramics, and composites are commonly observed from experimental tests. This is mainly attributed to intrinsic microcracks, which are randomly distributed as a result of the applied load and the residual stress

Topologically Driven Swelling of a Polymer Loop

Numerical studies of the average size of trivially knotted polymer loops with no excluded volume are undertaken. Topology is identified by Alexander and Vassiliev degree 2 invariants. Probability of a trivial knot, average gyration radius, and probability density distributions as functions of gyration radius are generated for loops of up to N=3000 segments. Gyration radii of trivially knotted loops are found to follow a power law similar to that of self avoiding walks consistent with earlier theoretical predictions.Comment: 6 pages, 4 figures, submitted to PNAS (USA) in Feb 200

First passage times and asymmetry of DNA translocation

Motivated by experiments in which single-stranded DNA with a short hairpin loop at one end undergoes unforced diffusion through a narrow pore, we study the first passage times for a particle, executing one-dimensional brownian motion in an asymmetric sawtooth potential, to exit one of the boundaries. We consider the first passage times for the case of classical diffusion, characterized by a mean-square displacement of the form $\sim t$, and for the case of anomalous diffusion or subdiffusion, characterized by a mean-square displacement of the form $\sim t^{\gamma}$ with $0<\gamma<1$. In the context of classical diffusion, we obtain an expression for the mean first passage time and show that this quantity changes when the direction of the sawtooth is reversed or, equivalently, when the reflecting and absorbing boundaries are exchanged. We discuss at which numbers of `teeth' $N$ (or number of DNA nucleotides) and at which heights of the sawtooth potential this difference becomes significant. For large $N$, it is well known that the mean first passage time scales as $N^2$. In the context of subdiffusion, the mean first passage time does not exist. Therefore we obtain instead the distribution of first passage times in the limit of long times. We show that the prefactor in the power relation for this distribution is simply the expression for the mean first passage time in classical diffusion. We also describe a hypothetical experiment to calculate the average of the first passage times for a fraction of passage events that each end within some time $t^*$. We show that this average first passage time scales as $N^{2/\gamma}$ in subdiffusion.Comment: 10 pages, 4 figures We incorporated reviewers' suggestions from Physical Review E. We reformulated a few paragraphs in the introduction and further clarified the issue of the (a)symmetry of passage times. In the results section, we re-expressed the results in a form that manifest the important features. We also added a few references concerning anomalous diffusion. The look (but not the content) of figure 1 was also change

Parallel Computing for Probabilistic Response Analysis of High Temperature Composites

The objective of this Phase I research was to establish the required software and hardware strategies to achieve large scale parallelism in solving PCM problems. To meet this objective, several investigations were conducted. First, we identified the multiple levels of parallelism in PCM and the computational strategies to exploit these parallelisms. Next, several software and hardware efficiency investigations were conducted. These involved the use of three different parallel programming paradigms and solution of two example problems on both a shared-memory multiprocessor and a distributed-memory network of workstations

Energetic changes caused by antigenic module insertion in a virus-like particle revealed by experiment and molecular dynamics simulations

The success of recombinant virus-like particles (VLPs) for human papillomavirus and hepatitis B demonstrates the potential of VLPs as safe and efficacious vaccines. With new modular designs emerging, the effects of antigen module insertion on the self-assembly and structural integrity of VLPs should be clarified so as to better enabling improved design. Previous work has revealed insights into the molecular energetics of a VLP subunit, capsomere, comparing energetics within various solution conditions known to drive or inhibit self-assembly. In the present study, molecular dynamics (MD) simulations coupled with the molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) method were performed to examine the molecular interactions and energetics in a modular capsomere of a murine polyomavirus (MPV) VLP designed to protect against influenza. Insertion of an influenza antigenic module is found to lower the binding energy within the capsomere, and a more active state is observed in Assembly Buffer as compared with that in Stabilization Buffer, which has been experimentally validated through measurements using differential scanning calorimetry. Further in-depth analysis based on free-energy decomposition indicates that destabilized binding can be attributed to electrostatic interaction induced by the chosen antigen module. These results provide molecular insights into the conformational stability of capsomeres and their abilities to be exploited for antigen presentation, and are expected to be beneficial for the biomolecular engineering of VLP vaccines.Lin Zhang, Ronghong Tang, Shu Bai, Natalie K. Connors, Linda H.L. Lua, Yap P. Chuan, Anton P.J. Middelberg, Yan Su

GWmodelS: a standalone software to train geographically weighted models

With the recent increase in studies on spatial heterogeneity, geographically weighted (GW) models have become an essential set of local techniques, attracting a wide range of users from different domains. In this study, we demonstrate a newly developed standalone GW software, GWmodelS using a community-level house price data set for Wuhan, China. In detail, a number of fundamental GW models are illustrated, including GW descriptive statistics, basic and multiscale GW regression, and GW principle component analysis. Additionally, functionality in spatial data management and batch mapping are presented as essential supplementary activities for GW modeling. The software provides significant advantages in terms of a user-friendly graphical user interface, operational efficiency, and accessibility, which facilitate its usage for users from a wide range of domains

Abundance of unknots in various models of polymer loops

A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of $N$ segments follows a decaying exponential form, $\sim \exp (-N/N_0)$, where $N_0$ marks the crossover from a mostly unknotted (ie topologically simple) to a mostly knotted (ie topologically complex) ensemble. In the present work we use computational simulation to look closer into the variation of $N_0$ for a variety of polymer models. Among models examined, $N_0$ is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power law tail.Comment: 13 pages, 6 color figure