Supersymmetry approach to the random heteropolymer theory

The effective equation of motion that describes the different monomer alternation along the heteropolymer chain is proposed. On this basis the supersymmetry field scheme is built up to analyze memory and ergodicity breaking effects.     

Quenched disorder in a hierarchical Coulomb gas model

The effects of quenched disorder on the two-dimensional Coulomb gas are studied in the hierarchical approximation. The quenched random variables interact with the charges via a potential that decays as an inverse power () of the distance. Recursion relations for the single block charge activities are derived in which the quenched variables explicitly appear. In a linear approximation, for all1, with some restrictions on the variance of the normally distributed random variables, it is shown that the charge activities converge to the Kosterlitz-Thouless fixed point for all sufficiently low temperatures and sufficiently large blocks. The annealed system is also examined. This model is shown to have a Kosterlitz-Thouless phase only for an intermediate range of temperatures. At low temperatures the activities can diverge, and large charges can exist on all length scales.     

An efficient numerical approach to electrostatic microelectromechanical system simulation

Computational analysis of electrostatic microelectromechanical systems (MEMS) requires an electrostatic analysis to compute the electrostatic forces acting on micromechanical structures and a mechanical analysis to compute the deformation of micromechanical structures. Typically, the mechanical analysis is performed on an undeformed geometry. However, the electrostatic analysis is performed on the deformed position of microstructures. In this paper, a new efficient approach to self-consistent analysis of electrostatic MEMS in the small deformation case is presented. In this approach, when the microstructures undergo small deformations, the surface charge densities on the deformed geometry can be computed without updating the geometry of the microstructures. This algorithm is based on the linear mode shapes of a microstructure as basis functions. A boundary integral equation for the electrostatic problem is expanded into a Taylor series around the undeformed configuration, and a new coupled-field equation is presented. This approach is validated by comparing its results with the results available in the literature and ANSYS solutions, and shows attractive features comparable to ANSYS.     

A generic computer model for amphiphilic systems

The European Physical Journal E - We present a simple but versatile off-lattice model for computer simulation studies of amphiphilic systems, constructed mainly for the purpose of computational...     

Numerical evidence for critical behavior of the two-dimensional nonequilibrium zero-temperature random field Ising model

We give numerical evidence that the two-dimensional nonequilibrium zero-temperature random field Ising model exhibits critical behavior. Our findings are based on the results of scaling analysis and collapsing of data, obtained in extensive simulations of systems with sizes sufficiently large to clearly display the critical behavior.     

Phase transitions and critical phenomena in a three-dimensional site-diluted Potts model

The phase transitions and critical phenomena in the three-dimensional (3D) site-diluted q-state Potts models on a simple cubic lattice are explored. We systematically study the phase transitions of the models for q=3 and q=4 on the basis of Wolff high-effective algorithm by the Monte–Carlo (MC) method. The calculations are carried out for systems with periodic boundary conditions and spin concentrations p=1.00–0.65. It is shown that introducing of weak disorder (p∼0.95) into the system is sufficient to change the first order phase transition into a second order one for the 3D 3-state Potts model, while for the 3D 4-state Potts model, such a phase transformation occurs when introducing strong disorder (p∼0.65). Results for 3D pure 3-state and 4-state Potts models (p=1.00) agree with conclusions of mean field theory. The static critical exponents of the specific heat α, susceptibility γ, magnetization β, and the exponent of the correlation radius ν are calculated for the samples on the basis of finite-size scaling theory.     

Spherical/gyroid phase diagram of the diblock copolymer in the median selective solvent

The effect of the median selective solution on the lamellar, spherical and gyroid structures is studied. The self-consistent field equations of the diblock copolymer solution are solved by using the reciprocal space method. It is shown that the spherical and gyroid phases have the lowest free energy in the certain range of the solution concentration. Furthermore, the phase diagram of the ordered structures in the diblock copolymer solution with the median selective solvent is calculated, which is consistent with the experimental results. Supported by the National Natural Science Foundation of China (Grant Nos. 10834014, 10674173, and 30770517) and the National Basic Research Program of China (Grant No. 2009CB930704)     

A hierarchical model for random walks in random media

We show that the random walk generated by a hierarchical Laplacian in ^d has standard diffusive behavior. Moreover, we show that this behavior is stable under a class of random perturbations that resemble an off-diagonal disordered lattice Laplacian. The density of states and its asymptotic behavior around zero energy are computed: singularities appear in one and two dimensions.     

Narrow-band model for nonequilibrium air plasma radiation

A band model is developed for the prediction of radiative transfer in air plasma applications under equilibrium and non-equilibrium conditions. For non-equilibrium applications, the medium is described by rotational–translational and vibrational temperatures but the populations of electronic states can be arbitrary. A specific formulation of the statistical narrow-band (SNB) model is developed for optically thick electronic systems of diatomic molecules when their populations are described by an electronic temperature. Model parameters, deduced from line by line calculations in the Voigt regime, are shown to be also convenient for arbitrary distribution of molecular electronic populations. This model is then complemented to include optically thin electronic systems and the continuum radiation through the simple box model, and line by line calculations for atomic lines. Several tests including equilibrium, non-equilibrium, uniform, and non-uniform conditions show the ability of this hybrid model to provide accurate and efficient solutions for radiative transfer problems in air plasmas.     

Exact results for a random frustrated Ising model on the Kagomé lattice

We perform a slight modification of the decoration-decimation transformation which allows us to map the homogeneous Ising model on the honeycomb lattice on an inhomogeneous Ising model on the Kagomé lattice. Then, we obtain exact results for a class of random bond Ising model on the Kagomé lattice with competing interactions and show that the different types of frustration make the critical point of the pure model disappear.     

Effective field investigation of dynamic phase transitions for site diluted Ising ferromagnets driven by a periodically oscillating magnetic field

Dynamic behavior of a site diluted Ising ferromagnet in the presence of a periodically oscillating magnetic field has been analyzed by means of the effective field theory (EFT). The dynamic equation of motion has been solved for a honeycomb lattice (z=3$z=3$) with the help of a Glauber type stochastic process. The global phase diagrams and the variation of the corresponding dynamic order parameter as a function of the Hamiltonian parameters and temperature has been investigated in detail and it has been shown that the system exhibits reentrant phenomena, as well as a dynamic tricritical point which disappears for sufficiently weak dilution.     

Multiple temperature model for the information preservation method and its application to nonequilibrium gas flows

The information preservation (IP) method has been successfully applied to various nonequilibrium gas flows. Comparing with the direct simulation Monte Carlo (DSMC) method, the IP method dramatically reduces the statistical scatter by preserving collective information of simulation molecules. In this paper, a multiple temperature model is proposed to extend the IP method to strongly translational nonequilibrium gas flows. The governing equations for the IP quantities have been derived from the Boltzmann equation based on an assumption that each simulation molecule represents a Gaussian distribution function with a second-order temperature tensor. According to the governing equations, the implementation of IP method is divided into three steps: molecular movement, molecular collision, and update step. With a reasonable multiple temperature collision model and the flux splitting method in the update step, the transport of IP quantities can be accurately modeled. We apply the IP method with the multiple temperature model to shear-driven Couette flow, external force-driven Poiseuille flow and thermal creep flow, respectively. In the former two cases, the separation of different temperature components is clearly observed in the transition regime, and the velocity, temperature and pressure distributions are also well captured. The thermal creep flow, resulting from the presence of temperature gradients along boundary walls, is properly simulated. All of the IP results compare well with the corresponding DSMC results, whereas the IP method uses much smaller sampling sizes than the DSMC method. This paper shows that the IP method with the multiple temperature model is an accurate and efficient tool to simulate strongly translational nonequilibrium gas flows.     

A random covering interpretation for the phase transition of the random energy model

The random energy model is related to a random covering of the real line. The phase transition is interpreted as the passage from a regime where a family of random intervals covers the line (high temperature) to a noncovering regime (low temperature).     

Synthesis of multivariate random vibration systems: A two-stage least squares AR-MA model approach

A parametric time series model procedure for the synthesis of multivariate stationary time series random vibrations is shown. The vibrations are assumed to be the outputs of a regularly sampled, random noise excited, differential equation model of a vivration system. The procedure is a two-stage least squares method for realizing a multivariate disrcrete time mixed autoregressive-moving average (AR-MA) model from a given stationary process matrix covariance function. The synthesis procedure and the problem of the minimal representation of multivariate output systems and the overparameterization of AR-MA models are discussed and illustrated.     

A double random phase encoding approach for cancelable iris recognition

In a cancelable iris recognition technique, all enrollment patterns are masked using a transformation function, and the invertibility process for obtaining the original data should not be possible. A novel cancelable iris authentication approach in the encrypted domain is presented in this paper. The double random phase encoding (DRPE) algorithm in the Fractional Fourier Transform (FrFT) Domain is utilized to generate the optical masked IrisCodes. For the transmitter side, two encryption keys (RPM1 and RPM2) are utilized, while the second phase mask is proposed to be the right iris feature vector of the same user. As a result, mixing the feature vectors of the left and right iris patterns of the same subject to an encrypted IrisCode results in enhancing the privacy and preserving the system performance. This proposed system success is attributed to the fact that the iris authentication issue is transformed to a key authentication process. Experimental results conducted on CASIA-IrisV3-Interval dataset achieve a significant gain for both privacy and performance proving the superiority of the proposed approach.     

A CSP and tabulation-based adaptive chemistry model

We demonstrate the feasibility of a new strategy for the construction of an adaptive chemistry model that is based on an explicit integrator stabilized by an approximation of the Computational Singular Perturbation (CSP)-slow-manifold projector. We examine the effectiveness and accuracy of this technique first using a model problem with variable stiffness. We assess the effect of using an approximation of the CSP-slow-manifold by either reusing the CSP vectors calculated in previous steps or from a pre-built tabulation. We find that while accuracy is preserved, the associated CPU cost was reduced substantially by this method. We used two ignition simulations – hydrogen–air and heptane–air mixtures – to demonstrate the feasibility of using the new method to handle realistic kinetic mechanisms. We test the effect of utilizing an approximation of the CSP-slow-manifold and find that its use preserves the order of the explicit integrator, produces no degradation in accuracy, and results in a scheme that is competitive with traditional implicit integration. Further analysis on the performance data demonstrates that the tabulation of the CSP-slow-manifold provides an increasing level of efficiency as the size of the mechanism increases. From the software engineering perspective, all the machinery developed is Common Component Architecture compliant, giving the software a distinct advantage in the ease of maintainability and flexibility in its utilization. Extension of this algorithm is underway to implement an automated tabulation of the CSP-slow-manifold for a detailed chemical kinetic system either off-line, or on-line with a reactive flow simulation code.     

A nonequilibrium entropy for dynamical systems

It is proposed to define entropy for nonequilibrium ensembles using a method of coarse graining which partitions phase space into sets which typically have zero measure. These are chosen by considering the totality of future possibilities for observation on the system. It is shown that this entropy is necessarily a nondecreasing function of the timet. There is no contradiction with the reversibility of the laws of motion because this method of coarse graining is asymmetric under time reversal. Under suitable conditions (which are stated explicitly) this entropy approaches the equilibrium entropy ast+ and the fine-grained entropy ast–. In particular, the conditions can always be satisfied if the system is aK-system, as in the Sinai billiard models. Some theorems are given which give information about whether it is possible to generate the partition used here for coarse graining from time translates of a finite partition, and at the same time elucidate the connection between our concept of entropy and the entropy invariant of Kolmogorov and Sinai.Research supported in part by NSF grants PHY78-03816 and PHY78-15920.     

A BEM approach to validate a model for predicting sound propagation over non-flat terrain

A two-dimensional boundary element model for sound propagation in a homogeneous atmosphere above non-flat terrain has been constructed. An infinite impedance plane is taken into account in the Green's function in the underlying integral equation, so that only the non-flat parts of the terrain need to be discretised in the boundary element model. This Green's function is undefined for points below the impedance plane, and therefore valleys and hollows are taken into account by coupling the exterior domain above the ground with one or several interior domains below the ground, as suggested in a recent paper [J. Sound Vibrat. 223 (1999) 355]. The resulting BEM model, which can handle arbitrary combinations of barriers and hollows, has been used for validating a ray model for various difficult configurations, including combinations of valleys and barriers.