Relationship between entropy and diffusion: A statistical mechanical derivation of Rosenfeld expression for a rugged energy landscape

Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by studying diffusion of a point Brownian particle on a model potential energy surface characterized by ruggedness. If we assume that the ruggedness has a Gaussian distribution, then for this model, one can obtain the excess entropy exactly for any dimension. By using the expression for the mean first passage time, we present a statistical mechanical derivation of the well-known and well-tested scaling relation proposed by Rosenfeld between diffusion and excess entropy. In anticipation that Rosenfeld diffusion-entropy scaling (RDES) relation may continue to be valid in higher dimensions (where the mean first passage time approach is not available), we carry out an effective medium approximation (EMA) based analysis of the effective transition rate and hence of the effective diffusion coefficient. We show that the EMA expression can be used to derive the RDES scaling relation for any dimension higher than unity. However, RDES is shown to break down in the presence of spatial correlation among the energy landscape values. (C) 2015 AIP Publishing LLC.

On the Equivalence of Acoustic Impedance and Squeeze Film Impedance in Micromechanical Resonators

In this work, we address the issue of modeling squeeze film damping in nontrivial geometries that are not amenable to analytical solutions. The design and analysis of microelectromechanical systems (MEMS) resonators, especially those that use platelike two-dimensional structures, require structural dynamic response over the entire range of frequencies of interest. This response calculation typically involves the analysis of squeeze film effects and acoustic radiation losses. The acoustic analysis of vibrating plates is a very well understood problem that is routinely carried out using the equivalent electrical circuits that employ lumped parameters (LP) for acoustic impedance. Here, we present a method to use the same circuit with the same elements to account for the squeeze film effects as well by establishing an equivalence between the parameters of the two domains through a rescaled equivalent relationship between the acoustic impedance and the squeeze film impedance. Our analysis is based on a simple observation that the squeeze film impedance rescaled by a factor of jx, where x is the frequency of oscillation, qualitatively mimics the acoustic impedance over a large frequency range. We present a method to curvefit the numerically simulated stiffness and damping coefficients which are obtained using finite element analysis (FEA) analysis. A significant advantage of the proposed method is that it is applicable to any trivial/nontrivial geometry. It requires very limited finite element method (FEM) runs within the frequency range of interest, hence reducing the computational cost, yet modeling the behavior in the entire range accurately. We demonstrate the method using one trivial and one nontrivial geometry.

Continuum in the X-Z-Y Weak Bonds: Z= Main Group Elements

The Continuum in the variation of the X-Z bond length change from blue-shifting to red-shifting through zero-shifting in the X-Z---Y complex is inevitable. This has been analyzed by ab-initio molecular orbital calculations using Z= Hydrogen, Halogens, Chalcogens, and Pnicogens as prototypical examples. Our analysis revealed that, the competition between negative hyperconjugation within the donor (X-Z) molecule and Charge Transfer (CT) from the acceptor (Y) molecule is the primary reason for the X-Z bond length change. Here, we report that, the proper tuning of X-and Y-group for a particular Z-can change the blue-shifting nature of X-Z bond to zero-shifting and further to red-shifting. This observation led to the proposal of a continuum in the variation of the X-Z bond length during the formation of X-Z---Y complex. The varying number of orbitals and electrons available around the Z-atom differentiates various classes of weak interactions and leads to interactions dramatically different from the H-Bond. Our explanations based on the model of anti-bonding orbitals can be transferred from one class of weak interactions to another. We further take the idea of continuum to the nature of chemical bonding in general. (C) 2015 Wiley Periodicals, Inc.

Exceptional resistance to grain growth in nanocrystalline CoCrFeNi high entropy alloy at high homologous temperatures

Nanocrystalline CoCrFeNi high entropy alloy, synthesized by mechanical alloying followed by spark plasma sintering, demonstrated extremely sluggish grain growth even at very high homologous temperature of 0.68 T-m (900 degrees C) for annealing duration of 600 h. Mechanically alloyed powder had carbon and oxygen as impurities, which in turn led to the formation of two-phase mixture of FCC and Cr-rich carbide with fine distribution of Cr-rich oxide during spark plasma sintering. Sluggish grain growth is attributed to the Zener pinning effect from the fine dispersion of oxide, mutual retardation of grain boundaries in the presence of two phases, and sluggish diffusivity because of cooperative diffusion of multi-principle elements. (C) 2015 Elsevier B.V. All rights reserved.

A hybrid finite element formulation for flexible multibody dynamics

This work deals with the transient analysis of flexible multibody systems within a hybrid finite element framework. Hybrid finite elements are based on a two-field variational formulation in which the displacements and stresses are interpolated separately yielding very good coarse mesh accuracy. Most of the literature on flexible multibody systems uses beam-theory-based formulations. In contrast, the use of hybrid finite elements uses continuum-based elements, thus avoiding the problems associated with rotational degrees of freedom. In particular, any given three-dimensional constitutive relations can be directly used within the framework of this formulation. Since the coarse mesh accuracy as compared to a conventional displacement-based formulation is very high, the scheme is cost effective as well. A general formulation is developed for the constrained motion of a given point on a line manifold, using a total Lagrangian method. The multipoint constraint equations are implemented using Lagrange multipliers. Various kinds of joints such as cylindrical, prismatic, and screw joints are implemented within this general framework. Hinge joints such as spherical, universal, and revolute joints are obtained simply by using shared nodes between the bodies. In addition to joints, the formulation and implementation details for a DC motor actuator and for prescribed relative rotation are also presented. Several example problems illustrate the efficacy of the developed formulation.