The present paper is aimed at studying the effects of viscosity and time on the propagation of thermoelastic waves in a homogeneous and isotropic three-dimensional medium whose surface is acted upon by a thermal load under the purview of temperature-rate-dependent thermoelasticity. The normal mode analysis technique has been employed to solve the resulting non-dimensional coupled field equations and hence the exact expressions for displacement component, stress, temperature field and strain are obtained. The problem is further illustrated by computing the numerical values of the field variables for a copper- like material and depicting them graphically. Numerical results predict finite speed of propagation for thermoelastic waves.

The conformational (structural) change of proteins plays an essential role in their functions. Experiments have been conducted to try to understand the conformational change of proteins, but they have not been successful in providing information on the atomic scale. Simulation methods have been developed to understand the conformational change at an atomic scale in detail. Coarse-grained methods have been developed to calculate protein dynamics with computational efficiency when compared with than all-atom models. A structure-based mass-spring model called the elastic network model (ENM) showed excellent performance in various protein studies. Coarse-grained ENM was modified in various ways to improve the computational efficiency, and consequently to reduce required computational cost for studying the large-scale protein structures. Our previous studies report a modified mass-spring model, which was developed based on condensation method applicable to ENM, and show that the model is able to accurately predict the fluctuation behavior of proteins. We applied this modified mass-spring model to analyze the conformational changes in proteins. We consider two model proteins as an example, where these two proteins exhibit different functions and molecular sizes. It is shown that the modified mass-spring model allows for accurately predicting the pathways of conformation changes for proteins. Our model provides structural insights into the conformation change of proteins related to the biological functions of large protein complexes.

The present paper is concerned with an in-depth study of the effects of rotation, two-temperature parameter and voids on the magneto-thermoelastic interactions in a homogeneous, isotropic, generalized half-space with gravity field. The formulation is applied within the frame-work of two-temperature generalized thermoelasticity based on the hyperbolic heat conduction model with one relaxation time. Using normal mode analysis technique for the physical variables appearing in the governing equations, we get the analytical expressions for displacement components, stress, thermodynamic temperature, conductive temperature and change in volume fraction field. The general solution obtained is then applied to a specific problem of an infinite half-space having isothermal boundary subjected to mechanical load. Variations of the considered variables through the vertical distance are illustrated graphically.

In this paper, the generalized thermoelasticity problem for an infinite fiber-reinforced transversely-isotropic thick plate subjected to initial stress is solved. The lower surface of the plate rests on a rigid foundation and temperature while the upper surface is thermally insulated with prescribed surface loading. The normal mode analysis is used to obtain the analytical expressions for the displacements, stresses and temperature distributions. The problem has been solved analytically using the generalized thermoelasticity theory of dual-phase-lags. Effect of phase-lags, reinforcement and initial stress on the field quantities is shown graphically. The results due to the coupled thermoelasticity theory, Lord and Shulman’s theory, and Green and Naghdi’s theory have been derived as limiting cases. The graphs illustrated that the initial stress, the reinforcement and phase-lags have great effects on the distributions of the field quantities.

In multi physics computations where a compressible fluid is coupled with a linearly elastic solid, it is standard to enforce continuity of the normal velocities and of the normal stresses at the interface between the fluid and the solid. In a numerical scheme, there are many ways that velocity- and stress-continuity can be enforced in the discrete approximation. This paper performs a normal mode stability analysis of the linearized problem to investigate the stability of different numerical interface conditions for a model problem approximated by upwind type finite difference schemes. The analysis shows that depending on the ratio of densities between the solid and the fluid, some numerical interface conditions are stable up to the maximal CFL-limit, while other numerical interface conditions suffer from a severe reduction of the stable CFL-limit. The paper also presents a new interface condition, obtained as a simplified characteristic boundary condition, that is proved to not suffer from any reduction of the stable CFL-limit. Numerical experiments in one space dimension show that the new interface condition is stable also for computations with the non-linear Euler equations of compressible fluid flow coupled with a linearly elastic solid.

Linear oscillators are used for modeling a diverse array of natural systems, for instance acoustics, materials science, and chemical spectroscopy. In this paper I describe simple models of structural interactions in biological molecules, known as elastic network models, as a useful topic for undergraduate biology instruction in mathematical modeling. These models use coupled linear oscillators to model the fluctuations of molecular structures around the equilibrium state. I present many learning activities associated with building and understanding these models, ranging from analytical to computational. I provide a number of web resources where students can obtain structural data, perform calculations, and suggest research directions for independent projects.