On the Relation of the Principle of Maximum Dissipation to the Principles of Jourdain and Gauss for Rigid Body Systems

A dissipation based definition of the principle of Jourdain is presented for rheonomic (explicitly time dependent) mechanical systems, which evolve under the influence of convex dissipation potentials. It is shown, that the variational condition of the dissipative principle of Jourdain is the necessary condition for the maximization of the total dissipated power with respect to generalized velocities. The principle of maximum dissipation is shown to be the dual principle of the dissipative principle of Jourdain. A dissipative principle of Gauss is formulated by making use of nonsmooth analysis and potential theory and its dual principle is formulated.

Constitutive Equations for a Model of Nonlocal Plasticity which Complies with a Nonlocal Maximum Plastic Dissipation Principle

In the present paper constitutive equations for a nonlocal plasticity model are presented. Elasticity is considered to be governed by local forces so that only the dissipation processes are adopted as nonlocal. Differing from other proposed models in which the isotropic hardening/softening variables are considered as nonlocal, in the present paper the nonlocality is extended in order to include the kinematic hardening behaviour as well, so that both types of hardening (kinematic and isotropic) are considered as nonlocal. The present formulation satisfies a variational condition representing nonlocal maximum plastic dissipation. The proposed constitutive formulation of nonlocal plasticity is thus equipped with a sound variational basis.

NON-PERTURBATIVE VACUUM WAVE-FUNCTIONAL AND CLOSED STRING EQUATIONS OF MOTION

The anomalous conformal dependence of the vacuum wave-functional is studied in the non-perturbative regime of the closed bosonic string theory. It is shown that the vanishing of the vacuum expectation value of the stress-energy tensor trace leads to the implementation of a suitable variational condition on the wave-functional, provided that the dilaton condensate be taken as a conformal compensator for the graviton condensate of the embedding space.

(Non-)rigid motion interpretation : a regularized approach

Determining 3D motion from a time-varying 2D image is an ill-posed problem; unless we impose additional constraints, an infinite number of solutions is possible. The usual constraint is rigidity, but many naturally occurring motions are not rigid and not even piecewise rigid. A more general assumption is that the parameters (or some of the parameters) characterizing the motion are approximately (but not exactly) constant in any sufficiently small region of the image. If we know the shape of a surface we can uniquely recover the smoothest motion consistent with image data and the known structure of the object, through regularization. This paper develops a general paradigm for the analysis of nonrigid motion. The variational condition we obtain includes many previously studied constraints as ‘special cases’. Among them are isometry, rigidity and planarity. If the variational condition is applied at multiple scales of resolution, it can be applied to turbulent motion. Finally, it is worth noting that our theory does not require the computation of correspondence (optic flow or discrete displacements), and it is effective in the presence of motion discontinuities.

Unified field theory in a curvature-free five-dimensional manifold

Instead of identifying fields with the curvature of a metric, the present theory shows that they may be identified with the manner in which the four-way measuring system of the physical observer O is embedded in a flat five-dimensional manifold provided that due accouut is taken of the imperceptibility of the fifth dimension. In this system fields are introduced by treating the direction cosines, k l j , of the four directions of measurement and of the imperceptible direction as variable functions of position in the manifold. The track of an unconstrained body P is taken as a straight line (cosmodesic) in the manifold, but the ‘projection’ of it which O observes in his four-co-ordinate system is in general curved. Thus the equation describing the element ds of P 's cosmodesic in O 's four-co-ordinate system (∆ x µ ) is ds 2 cos 2 λ-2 ds sinλ{(∑ v =1 4 v l 5 v l µ ) ∆ x µ }={ 5 l µ 5 l v -2 5 l v ∑ k =1 5 k l 5 k l µ +∑ k =1 5 k l µ k l v }∆ x µ ∆ x v . When O applies the variational condition to ds which expresses the fact that the cosmodesic is straight, he concludes that it has a space-time curvature with two distinct components, one dependent upon λ which is the angle between the cosmodesic and an universal direction 5 Q and upon v l 5 , the other acting equally on all P bodies whatever the value of λ and depending only on 5 l µ . These ‘accelerations’ are shown to correspond to electromagnetic and gravitational fields respectively, and the inverse square law of force is shown to hold for spherically sym­metrical fields of both types as a consequence of the condition of coherence of the measuring system. When the cause of the positional variation of the k l µ is a heavy body, having a constrained rotation, it is shown to give rise to the magnetic field that a body of charge equal to its gravi­tation mass would have, without the corresponding electrostatic field. The k l j 's are restricted by the requirement that the angles between the absolute fifth direction, the direction imperceptible for O , and the direction orthogonal to O 's four measuring directions, are all null.