Nonlinear vibrations of symmetric cross-ply laminates via thermomechanically coupled reduced order models

Thermomechanically coupled, geometrically nonlinear, laminated plates are addressed through a unified 2D formulation, by considering classical and third-order shear-deformable von Karman models, along with correspondingly consistent linear and cubic variations of the temperature along the thickness. Minimal dimension reduction of the mechanical problem is accomplished for symmetric cross-ply laminates, ending up for both models to a coupled three-mode reduced model with terms and coefficients of variable nature depending on the variety of mechanical and/or thermal excitations. Nonlinear vibrations of the classical model are investigated in conditions of thermal dynamics either passively entrained by the harmonically varying transverse load via the existing coupling terms, or also playing some active role owed to a temperature difference with respect to the surrounding medium

Group classification of variable coefficient quasilinear reaction-diffusion equations

The group classification of variable coefficient quasilinear reaction-diffusion equations $u_t=u_{xx}+h(x)B(u)$ is carried out exhaustively. This became possible due to usage of a conditional equivalence group found in the course of the study of admissible point transformation within the class.Comment: 10 pages, submitted to the Proceedings of the XVII Geometrical Seminar (September 3-8, 2012, Zlatibor, Serbia

Reaction-diffusion systems with constant diffusivities: conditional symmetries and form-preserving transformations

Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first type (R. Cherniha J. Phys. A: Math. Theor., 2010. vol. 43., 405207), an exhaustive list of reaction-diffusion systems admitting such symmetry is derived. The form-preserving transformations for this class of systems are constructed and it is shown that this list contains only non-equivalent systems. The obtained symmetries permit to reduce the reaction-diffusion systems under study to two-dimensional systems of ordinary differential equations and to find exact solutions. As a non-trivial example, multiparameter families of exact solutions are explicitly constructed for two nonlinear reaction-diffusion systems. A possible interpretation to a biologically motivated model is presented

HD Physiology Project-Japanese efforts to promote multilevel integrative systems biology and physiome research.

The HD Physiology Project is a Japanese research consortium that aimed to develop methods and a computational platform in which physiological and pathological information can be described in high-level definitions across multiple scales of time and size. During the 5 years of this project, an appropriate software platform for multilevel functional simulation was developed and a whole-heart model including pharmacokinetics for the assessment of the proarrhythmic risk of drugs was developed. In this article, we outline the description and scientific strategy of this project and present the achievements and influence on multilevel integrative systems biology and physiome research

On Transformations of the Rabelo Equations

We study four distinct second-order nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constant-characteristic form we relate them to some well-studied integrable equations. Two of the Rabelo equations are found to be related to the sine-Gordon equation. The other two are transformed into a linear equation and the Liouville equation, and in this way their general solutions are obtained.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Recent history of fractional calculus

This survey intends to report some of the major documents and events in the area of fractional calculus that took place since 1974 up to the present date