Transition state theory (TST) 1 is the most widely used theory for calculating rates of bimolecular eactions occurring in the gas phase and in condensed phases. TST is also incorporated into the widely used RRKM theory for unimolecular reactions. The popularity of TST is largely due to its simplicity and its usefulness for correlating trends in reaction rates in terms of easily interpreted quan...

In the past the variational theory of mixtures due to Mansoori and Leland has been applied successfully to the calculation of excess properties of mixtures. In the present work the origin of the variational theory is discussed along with the important applications of the theory to pure fluid and mixture properties. The advances of the theory in performing mixture calculations are reviewed and a...

We introduce provably unconditionally stable mixed variational methods for phasefield models. Our formulation is based on a mixed finite element method for space discretization and a new second-order accurate time integration algorithm. The fully-discrete formulation inherits the main characteristics of conserved phase dynamics, namely, mass conservation and nonlinear stability with respect to ...

We propose and analyze a simple variational model for dislocations at semi-coherent interfaces. The energy functional describes the competition between two terms: a surface energy induced by dislocations and a bulk elastic energy, spent to decrease the amount of dislocations needed to compensate the lattice misfit. We prove that, for minimizers, the former scales like the surface area of the in...

Fractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dyn...

In this paper, we deduce a macroscopic strain gradient theory for plasticity from a model of discrete dislocations. We restrict our analysis to the case of a cylindrical symmetry for the crystal in exam, so that the mathematical formulation will involve a two dimensional variational problem. The dislocations are introduced as point topological defects of the strain fields, for which we compute ...

We consider H(curl, Ω)-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume that the underlying tetrahedral mesh has been created by successive local mesh refinement, either by local uniform refinement with hanging nodes or bisection refinement. In this setting we develop a convergence the...

Gelfand and Dikii gave a bosonic formal variational calculus in [5, 6] and Xu gave a fermionic formal variational calculus in [13]. Combining the bosonic theory of Gelfand-Dikii and the fermionic theory, Xu gave in [14] a formal variational calculus of super-variables. Fermionic Novikov algebras are related to the Hamiltonian super-operator in terms of this theory. A fermionic Novikov algebra i...

The purpose of this research project is to develop variational integrators synchronous or asynchronous, which can be used as tools to study complex structures composed of plates and beams subjected to large deformations and stress. We consider the geometrically exact models of beam and plate, whose configuration spaces are Lie groups. These models are suitable for modeling objects subjected to ...