Computer simulation of two continuous spin models using Wang-Landau-Transition-Matrix Monte Carlo Algorithm

Monte Carlo simulation using a combination of Wang Landau (WL) and Transition Matrix (TM) Monte Carlo algorithms to simulate two lattice spin models with continuous energy is described. One of the models, the one dimensional Lebwohl-Lasher model has an exact solution and we have used this to test the performance of the mixed algorithm (WLTM). The other system we have worked on is the two dimensional XY-model. The purpose of the present work is to test the performance of the WLTM algorithm in continuous models and to suggest methods for obtaining best results in such systems using this algorithm.Comment: 29 pages, 15 figure

Convergence and Refinement of the Wang-Landau Algorithm

Recently, Wang and Landau proposed a new random walk algorithm that can be very efficiently applied to many problems. Subsequently, there has been numerous studies on the algorithm itself and many proposals for improvements were put forward. However, fundamental questions such as what determines the rate of convergence has not been answered. To understand the mechanism behind the Wang-Landau method, we did an error analysis and found that a steady state is reached where the fluctuations in the accumulated energy histogram saturate at values proportional to $[\log(f)]^{-1/2}$. This value is closely related to the error corrections to the Wang-Landau method. We also study the rate of convergence using different "tuning" parameters in the algorithm.Comment: 6 pages, submitted to Comp. Phys. Com

On the Wang-Landau Method for Off-Lattice Simulations in the "Uniform" Ensemble

We present a rigorous derivation for off-lattice implementations of the so-called "random-walk" algorithm recently introduced by Wang and Landau [PRL 86, 2050 (2001)]. Originally developed for discrete systems, the algorithm samples configurations according to their inverse density of states using Monte-Carlo moves; the estimate for the density of states is refined at each simulation step and is ultimately used to calculate thermodynamic properties. We present an implementation for atomic systems based on a rigorous separation of kinetic and configurational contributions to the density of states. By constructing a "uniform" ensemble for configurational degrees of freedom--in which all potential energies, volumes, and numbers of particles are equally probable--we establish a framework for the correct implementation of simulation acceptance criteria and calculation of thermodynamic averages in the continuum case. To demonstrate the generality of our approach, we perform sample calculations for the Lennard-Jones fluid using two implementation variants and in both cases find good agreement with established literature values for the vapor-liquid coexistence locus.Comment: 21 pages, 4 figure

Effect of Volume and Temperature on the Global and Segmental Dynamics in Polypropylene Glycol and 1,4-polyisoprene

Published dielectric relaxation measurements on polypropylene glycol and 1,4-polyisoprene are analyzed to determine the relative effect that thermal energy and volume have on the temperature dependence of the normal mode relaxation times, and compare this to their effect on the temperature dependence of the local segmental relaxation times. We find that for both polymers at temperatures well above Tg, both relaxation modes are governed more by thermal energy than by volume, although the latter's contribution is not negligible. Such a result is consistent with an assumption underlying models for polymer viscoelasticity, such as the Rouse and tube models, that the friction coefficient governing motions over large length scales can be identified with the local segmental friction coefficient. We also show that relaxation data for both the segmental and the normal mode superimpose, when expressed as a function of the product of the temperature and the volume, the latter raised to a power. This scaling form arises from an inverse power form for the intermolecular potential. The value of the exponent on the volume for these two polymers indicates a relatively "soft" potential.Comment: 15 pages, 3 figure

Brief communication: Chronic undernutrition is associated with higher mucosal antibody levels among ariaal infants of northern kenya

The immune activation that occurs with infection diverts energy from growth and can contribute to poor nutritional outcomes in developing infants and children. This study investigates the association between salivary immunoglobulin A (IgA) levels and growth outcomes among Ariaal infants of northern Kenya. The Ariaal are a group of settled northern Kenyan pastoralists who are under considerable nutritional stress. Two hundred and thirty‐nine breastfeeding Ariaal infants were recruited into the study and underwent anthropometric measurement and saliva collection, with mothers providing individual and household characteristics for them via questionnaire. Infant saliva samples were analyzed with an ELISA for IgA in the United States. Infant anthropometric measurements were converted to height‐for‐age z ‐scores (HAZ) using the WHO Child Growth Standards. Based on multivariate models performed in SAS 9.2 two main results emerge: 1) low HAZ, an indicator of chronic undernutrition, was significantly associated with higher IgA concentration (β = −0.12, P = 0.050) and 2) boys had significantly higher IgA levels than girls (β = 0.25, P = 0.039). Although there was not a significant interactive effect between HAZ and sex, the two variables confound each other, with boys having significantly lower HAZ values than girls do. In addition, maternal breastmilk IgA was significantly associated with infant salivary IgA, indicating that maternal effects play a role in infant IgA development. Future research will unravel the three‐way association between sex, stunting, and immune function in the Ariaal community. Am J PhyAnthropol 2012. © Wiley Periodicals, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/93535/1/22108_ftp.pd

Isotropic soft-core potentials with two characteristic length scales and anomalous behaviour

Isotropic soft-core potentials with two characteristic length scales have been used since 40 years to describe systems with polymorphism. In the recent years intense research is showing that these potentials also display polyamorphism and several anomalies, including structural, diffusion and density anomaly. These anomalies occur in a hierarchy that resembles the anomalies of water. However, the absence of directional bonding in these isotropic potentials makes them different from water. Other systems, such as colloidal suspensions, protein solutions or liquid metals, can be well described by these family of potentials, opening the possibility of studying the mechanism generating the polyamorphism and anomalies in these complex liquids

First-order transition features of the triangular Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions

We implement a new and accurate numerical entropic scheme to investigate the first-order transition features of the triangular Ising model with nearest-neighbor ($J_{nn}$) and next-nearest-neighbor ($J_{nnn}$) antiferromagnetic interactions in ratio $R=J_{nn}/J_{nnn}=1$. Important aspects of the existing theories of first-order transitions are briefly reviewed, tested on this model, and compared with previous work on the Potts model. Using lattices with linear sizes $L=30,40,...,100,120,140,160,200,240,360$ and 480 we estimate the thermal characteristics of the present weak first-order transition. Our results improve the original estimates of Rastelli et al. and verify all the generally accepted predictions of the finite-size scaling theory of first-order transitions, including transition point shifts, thermal, and magnetic anomalies. However, two of our findings are not compatible with current phenomenological expectations. The behavior of transition points, derived from the number-of-phases parameter, is not in accordance with the theoretically conjectured exponentially small shift behavior and the well-known double Gaussian approximation does not correctly describe higher correction terms of the energy cumulants. It is argued that this discrepancy has its origin in the commonly neglected contributions from domain wall corrections.Comment: 34 pages, 11 figure

An effective all-atom potential for proteins

We describe and test an implicit solvent all-atom potential for simulations of protein folding and aggregation. The potential is developed through studies of structural and thermodynamic properties of 17 peptides with diverse secondary structure. Results obtained using the final form of the potential are presented for all these peptides. The same model, with unchanged parameters, is furthermore applied to a heterodimeric coiled-coil system, a mixed alpha/beta protein and a three-helix-bundle protein, with very good results. The computational efficiency of the potential makes it possible to investigate the free-energy landscape of these 49--67-residue systems with high statistical accuracy, using only modest computational resources by today's standards

Relationship between Structure, Entropy and Diffusivity in Water and Water-like Liquids

Anomalous behaviour of the excess entropy ($S_e$) and the associated scaling relationship with diffusivity are compared in liquids with very different underlying interactions but similar water-like anomalies: water (SPC/E and TIP3P models), tetrahedral ionic melts (SiO$_2$ and BeF$_2$) and a fluid with core-softened, two-scale ramp (2SRP) interactions. We demonstrate the presence of an excess entropy anomaly in the two water models. Using length and energy scales appropriate for onset of anomalous behaviour, the density range of the excess entropy anomaly is shown to be much narrower in water than in ionic melts or the 2SRP fluid. While the reduced diffusivities ($D^*$) conform to the excess entropy scaling relation, $D^* =A\exp (\alpha S_e)$ for all the systems (Y. Rosenfeld, Phys. Rev. A {\bf 1977}, {\it 15}, 2545), the exponential scaling parameter, $\alpha$, shows a small isochore-dependence in the case of water. Replacing $S_e$ by pair correlation-based approximants accentuates the isochore-dependence of the diffusivity scaling. Isochores with similar diffusivity scaling parameters are shown to have the temperature dependence of the corresponding entropic contribution. The relationship between diffusivity, excess entropy and pair correlation approximants to the excess entropy are very similar in all the tetrahedral liquids.Comment: 24 pages, 4 figures, to be published in Journal of Physical Chemistry