The Quantum Stationary HJ Equation (QSHJE) that we derived from the equivalence principle, gives rise to initial conditions which cannot be seen in the Schrödinger equation. Existence of the classical limit leads to a dependence of the integration constant l = l1 + il2 on the Planck length. Solutions of the QSHJE provide a trajectory representation of quantum mechanics, which, unlike Bohm’s the...

In this paper, a new dynamic developable surface model is proposed. The proposed model represents developable surfaces using triangle meshes. A novel algorithm is proposed to introduce the Hamilton principle into these meshes such that the resulting developable model is dynamic, i.e., it can offer a time-dependent continuous path to deform the model. Applications with examples are presented; th...

This paper develops a reduction theory for Dirac structures that includes in a unified way, reduction of both Lagrangian and Hamiltonian systems. It includes the reduction of variational principles and in particular, the Hamilton–Pontryagin variational principle. It also includes reduction theory for implicit Lagrangian systems that could be degenerate and have constraints. In this paper we foc...

– For binary mixtures of fluids without chemical reactions, but with components having different temperatures, the Hamilton principle of least action is able to produce the equation of motion for each component and a balance equation of the total heat exchange between components. In this nonconservative case, a Gibbs dynamical identity connecting the equations of momenta, masses, energy and hea...

Hamilton-Jacobi theory for general relativity provides an elegant covariant formulation of the gravitational field. A general ‘coordinate-free’ method of integrating the functional Hamilton-Jacobi equation for gravity and matter is described. This series approximation method represents a large generalization of the spatial gradient expansion that had been employed earlier. Additional solutions ...

We review the classical Principle of the Least Action in a general context where the Hamilton function H is possibly non convex. We show how van Groesen [6] principle follow as particular cases where H is hyperregular and of homogeneous type. Homogeneous scalar field spacetimes in spherical symmetry are derived as an application. 2000 Mathematics Subject Classification. 70H03, 70H05, 70H30, 37J05.

Topics considered here include: examples of optimal control problems; dynamic programming and the Hamilton-Jacobi-Bellman equation; verification theorems; the Pontryagin Maximum Principle Principle. The examples include many with an economic flavor, but others too (including the Hopf-Lax solution formula for ut + H(Du) = 0 with H convex). There’s much more here than we’ll have time to do in lec...

This paper deals with dynamic Stability of single walled carbon nanotube. Strain gradient theory and Euler-Bernouli beam theory are implemented to investigate the dynamic stability of SWCNT embedded in an elastic medium. The equations of motion were derived by Hamilton principle and non-local elasticity approach. The nonlocal parameter accounts for the small-size effects when dealing with nano-...

In this paper, the buckling and vibration behaviour of functionally graded flexoelectric nanobeam is examined. The vibration and buckling formulations of functionally graded nanobeam are developed by using a new theory that’s presented exclusively for flexoelecteric nano-materials. So by considering Von-Karman strain and forming enthalpy equation based on displacement, polarization and electric...

A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...