(Adiabatic) phase boundaries in a bistable chain with twist and stretch

Mass–spring chains with only extensional degrees of freedom have provided insights into the behavior of crystalline solids, including those capable of phase transitions. Here we add rotational degrees of freedom to the masses in a chain and study the dynamics of phase boundaries across which both the twist and stretch can jump. We solve impact and Riemann problems in the chain by numerical integration of the equations of motion and show that the solutions are analogous to those in a phase transforming rod whose stored energy function depends on both twist and stretch. From the dynamics of phase boundaries in the chain we extract a kinetic relation whose form is familiar from earlier studies involving chains with only extensional degrees of freedom. However, for some combinations of parameters characterizing the energy landscape of our springs we find propagating phase boundaries for which the rate of dissipation, as calculated using isothermal expressions for the driving force, is negative. This suggests that we cannot neglect the energy stored in the oscillations of the masses in the interpretation of the dynamics of mass–spring chains. Keeping this in mind we define a local temperature of our chain and show that it jumps across phase boundaries, but not across sonic waves. Hence, impact problems in our mass–spring chains are analogous to those on continuum thermoelastic bars with Mie–Gruneisen type constitutive laws. At the end of the paper we use our chain to shed some light on experiments involving yarns that couple twist and stretch to perform useful work in response to various stimuli.     

Using adjoint error estimation techniques for elastohydrodynamic lubrication line contact problems

The use of an adjoint technique for goal‐based error estimation described by Hartit et al. (Int. J. Numer. Meth. Fluids 2005; 47 :1069–1074) is extended to the numerical solution of free boundary problems that arise in elastohydrodynamic lubrication (EHL). EHL systems are highly nonlinear and consist of a thin‐film approximation of the flow of a non‐Newtonian lubricant which separates two bodies that are forced together by an applied load, coupled with a linear elastic model for the deformation of the bodies. A finite difference discretization of the line contact flow problem is presented, along with the numerical evaluation of an exact solution for the elastic deformation, and a moving grid representation of the free boundary that models cavitation at the outflow in this one‐dimensional case. The application of a goal‐based error estimate for this problem is then described. This estimate relies on the solution of an adjoint problem; its effectiveness is demonstrated for the physically important goal of the total friction through the contact. Finally, the application of this error estimate to drive local mesh refinement is demonstrated. Copyright © 2010 John Wiley & Sons, Ltd.     

Thermomechanical modeling of the thermo-order-mechanical coupling behaviors in liquid crystal elastomers

Liquid crystal elastomer is a kind of anisotropic polymeric material, with complicated micro-structures and thermo-order-mechanical coupling behaviors. In this paper, we propose a method to systematically model these coupling behaviors. We derive the constitutive model in full tensor structure according to the Clausius-Duhem inequality. Two of the constitutive equations represent the mechanical equilibrium and the other two represent the phase equilibrium. Choosing the total free energy as the combination of the neo-classical free energy and the Landau-de Gennes nematic free energy, we obtain the Cauchy stress-deformation gradient relation and the order-mechanical coupling equations. We find the analytical homogeneous solutions of the deformation for the typical mechanical loadings, such as uniaxial stretch, and simple shear in any directions. We also compare the compression behavior of prolate liquid crystal elastomers with the stretch behavior of oblate liquid crystal elastomers. As a result, the stress, strain, temperature, order parameter, biaxiality and the direction of the director of liquid crystal elastomers couple with each other. When the prolate liquid crystal elastomer sample is stretched in the direction parallel to its director, the deviatoric stress makes the mesogens more order and increase the transition temperature. When the sample is sheared or stretched in the direction non-parallel to the director, the director of the liquid crystal elastomer will rotate, and the biaxiality will be induced. Because of the order-mechanical coupling, under infinitesimal deformation, liquid crystal elastomer has anisotropic Young’s modulus and zero shear modulus in the direction parallel or perpendicular to the director. While for the oblate liquid crystal elastomers, the stretch parallel to the director will cause the rotation of the director and induce the biaxiality.     

A Stokes model with cavitation for the numerical simulation of hydrodynamic lubrication

We present a cavitation model based on the Stokes equation and formulate adaptive finite element methods for its numerical solution. A posteriori error estimates and adaptive algorithms are derived, and numerical examples illustrating the theory are supplied, in particular with comparison to the simplified Reynolds model of lubrication. Copyright © 2010 John Wiley & Sons, Ltd.     

Synthesis and Characterization of the Titanium Containing Mesoporous Molecular Sieve MCM-48

Ti-MCM-48 mesoporous materials have been synthesized by sequential addition of alkoxides. The atomic ratio of Si and Ti in the synthesis gel was 40 and 5, respectively. The materials were characterized by means of powder XRD, N₂ adsorption-desorption measurements. HREM, ²⁹Si MAS NMR, diffuse reflectance FT-IR spectroscopy, electrophoretic mobility measurements and electron probe microanalysis.     

Simultaneous differential thermal and volume analysis at high pressure

Abstract

A method for simultaneous measurement of heat and volume changes associated with phase transformations is presented. Examples for melting, polymorphism and structural relaxation illustrate the method.     

Meshing Requirements for Tidal Modeling in the Western North Atlantic

This paper presents an a posteriori approach to unstructured mesh generation via a localized truncation error analysis and applies it to the Western North Atlantic Tidal (WNAT) model domain. The WNAT model domain encompasses the Gulf of Mexico, the Caribbean Sea, and the North Atlantic Ocean east to the 60°W Meridian. Herein, we pay particular attention to the area surrounding the Bahamas.

A bathymetric data set with fine resolution is employed in seven separate linear, harmonic simulations of shallow water tidal flow for seven different tidal-forcing constituents. Each set of simulation results is used to perform a truncation error analysis of a linear, harmonic form of the depth-averaged momentum equations for each of the seven different tidal-forcing frequencies. Truncation error is then driven to a more uniform, domain-wide value by solving for local node spacing requirements. The process is built upon successful research aiming to produce unstructured grids for large-scale domains that can be used in the accurate and efficient modeling of shallow water flow. The methodology described herein can also be transferred to other modeling applications.     

High‐Pressure Synthesis,Crystal Structure,and Properties of GdS2 with Thermodynamic Investigations in the Phase Diagram Gd–S

Gadolinium disulfide was prepared by high‐pressure synthesis at 8 GPa and 1173 K. It crystallizes in the monoclinic space group P12₁/a1 (No. 14) with lattice parameters a = 7.879(1) Å; b = 3.936(1) Å, c = 7.926(1) Å and β = 90.08(1)°. The crystal structure is a twofold superstructure of the aristotype ZrSSi and consists of puckered cationic [GdS]⁺ double slabs that are sandwiched by planar sulfur sheets containing S₂^2– dumbbells. The thermal decomposition of GdS₂ proceeds via the sulfur‐deficient polysulfides GdS_1.9, GdS_1.85 and GdS_1.77 and eventually results in the sesquisulfide Gd₂S₃. GdS₂ is a paramagnetic semiconductor which orders antiferromagnetically at T_N = 7.7(1) K. A metamagnetic transition is observed in the magnetically ordered state.