This paper adopts Rotem and Shinnar?s modification of the Rabinowitsch fluid model for one-dimensional non-Newtonian lubrication problem, a variational principle is established by semi-inverse method, generalized Reynolds-type equation obtained. article opens new avenue establishment complex problems.

Assume that A is a bounded self-adjoint operator in a Hilbert space H. Then, the variational principle max v |(Au, v)|2 (Av, v) = (Au, u) (*) holds if and only if A ≥ 0, that is, if (Av, v) ≥ 0 for all v ∈ H. We define the quotient on the left-hand side in (*) to be zero if (Av, v) = 0. As an application of this principle a variational principle for the electrical capacitance of a conductor of ...

We show that the minimal speed for the existence of monotonic fronts of the equation ut = (u )xx + f(u) with f(0) = f(1) = 0, m > 1 and f > 0 in (0, 1), derives from a variational principle. The variational principle allows to calculate, in principle, the exact speed for general f . The case m = 1 when f (0) = 0 is included as an extension of the results.

We consider the localized entropy of a point w ∈ R which is computed by considering only those (n, ε)-separated sets whose statistical sums with respect to an m-dimensional potential Φ are ”close” to a given value w. Previously, a local version of the variational principle was established for systems on non-Besicovitch compact metric spaces. We extend this result to all compact metric spaces.

We reexamine the problem of having nonconservative equations of motion arise from the use of a variational principle. In particular, a formalism is developed that allows the inclusion of fractional derivatives. This is done within the Lagrangian framework by treating the action as a Volterra series. It is then possible to derive two equations of motion, one of these is an advanced equation and ...

nonequilibrium statistical mechanics we focus on nonequilibrium corrections Δs to entropy and energy of the fluid in terms of the nonequilibrium density distribution function, f. We also evaluate coefficients of wave model of heat such as: relaxation time, propagation speed and thermal inertia. With these data a quadratic Lagrangian and a variational principle of Hamilton's type follows for a f...

The log-aesthetic curves include the logarithmic (equiangular) spiral, clothoid, and involute curves. Although most of them are expressed only by an integral form of the tangent vector, it is possible to interactively generate and deform them and they are expected to be utilized for practical use of industrial and graphical design. The discrete log-aesthetic filter based on the formulation of t...

We study the speed of propagating fronts of the convection reaction diffusion equation ut + μuux = uxx + f(u) for reaction terms f(u) such that in the non convective case fronts joining two equilibrium states exist. A variational principle for the wave speed is constructed from which upper and lower bounds are obtained. We find that, in general, there is a transition value μc below which advect...

The variational principle (VP) has been used to capture the metastable states of a glass-forming molecular system without quenched disorder. It has been shown that VP naturally leads to a self-consistent random field Ginzburg-Landau model (RFGLM). In the framework of one-step replica symmetry breaking (1-RSB) the general solution of RFGLM is discussed in the vicinity of the spinodal temperature...

A variational principle is obtained for the Burridge–Knopoff model for earthquake faults, and this paper considers an analytic approach that does not require linearization or perturbation. 2002 Elsevier Science Inc. All rights reserved.