We describe the theory of reciprocal diffusions in flat space. A reciprocal process is a Markov random field on a one dimensional parameter space. Every Markov process is reciprocal but not vice versa. We descibe the first and second order mean differential characteristics of reciprocal diffusions. This includes a new definition of stochastic acceleration. We show that reciprocal diffusions sat...

in this paper, a numerical solution procedure is presented for the forced vibration of a piezoelectric nanowire under thermo-electro-mechanical loads based on the nonlocal elasticity theory within the framework of timoshenko beam theory. using hamilton’s principle, the nonlocal governing differential equations are derived. the governing equations and the related boundary conditions are discreti...

Two similar Minkowskian diffusions have been considered, on one hand by Barbachoux, Debbasch, Malik and Rivet ([BDR1], [BDR2], [BDR3], [DMR], [DR]), and on the other hand by Dunkel and Hänggi ([DH1], [DH2]). We address here two questions, asked in [DR] and in ([DH1], [DH2]) respectively, about the asymptotic behaviour of such diffusions. More generally, we establish a central limit theorem for ...

Many situations of physical and biological interest involve diffusions on manifolds. It is usually assumed that irregularities in the geometry of these manifolds do not influence diffusions. The validity of this assumption is put to the test by studying Brownian motions on nearly flat 2D surfaces. It is found by perturbative calculations that irregularities in the geometry have a cumulative and...

We show that there is a one-to-one correspondence between diffusions and the solutions of the Skorokhod Embedding Problem due to Bertoin and Le-Jan. In particular, the minimal embedding corresponds to a ‘minimal local martingale diffusion’, which is a notion we introduce in this article. Minimality is closely related to the martingale property. A diffusion is minimal if it it minimises the expe...

In mathematical modeling of the non-squared frequency-dependent diffusions, also known as the anomalous diffusions, it is desirable to have a positive real Fourier transform for the time derivative of arbitrary fractional or odd integer order. The Fourier transform of the fractional time derivative in the Riemann-Liouville and Caputo senses, however, involves a complex power function of the fra...

this paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. the characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal mindlin plate. this theory is considering both the small length scale effects and transverse shear deformation ef...

Torsional dynamic analysis of carbon nanotubes under the effect of longitudinal magnetic field is carried out in the present study. Torque effect of an axial magnetic field on a carbon nanotube has been defined using Maxwell’s relation. Nonlocal governing equation and boundary conditions for carbon nanotubes are obtained by using Hamilton’s minimum energy principle. Eringen’s nonlocal stress gr...

We compare the spectral gaps and thus the exponential rates of convergence to equilibrium for ergodic one-dimensional diffusions on an interval. One of the results may be thought of as the diffusion analog of a recent result for the spectral gap of one-dimensional Schrödinger operators. We also discuss the similarities and differences between spectral gap results for diffusions and for Schrödin...

Abstract We study convergence to non-minimal quasi-stationary distributions for one-dimensional diffusions. give a method reducing the tail behavior of lifetime via property we call first hitting uniqueness. apply results Kummer diffusions with negative drift and class initial converging each distribution.