We consider dynamics driven by interaction energies on graphs. introduce graph analogues of the continuum nonlocal-interaction equation and interpret them as gradient flows with respect to a Wasserstein distance. The particular distance we arises from analogue Benamou-Brenier formulation where continuity uses an upwind interpolation define density along edges. While this approach has both theor...

Continuum manipulators are robotic manipulators built using one continuous, elastic, and highly deformable “backbone” instead of multiple rigid links and joints. I n previous work, we illuminated various kinematic and dynamic properties of continuum robots, but the question of controller design remained open. This paper presents a basic result for continuum robots that has long been knoum for r...

The classical approach to linking lattice dynamics properties to continuum equations of motion, the “method of long waves,” is extended to include higher order terms. The additional terms account for non-local and non-linear effects. In the first part of the article, the derivation is made within the harmonic approximation for the perfect lattice response. Higher order terms are included in the...

We describe a model based in continuum mechanics that reduces the study of a significant class of problems of discrete dislocation dynamics to questions of the modern theory of continuum plasticity. As applications, we explore the questions of the existence of a Peierls stress in a continuum theory, dislocation annihilation, dislocation dissociation, finite-speed-of-propagation effects of elast...

in this paper, homotopy perturbation method (hpm) has been applied to investigate the effect of magnetic field on cu-water nanofluid flow in non-parallel walls. the validity of hpm solutions were verified by comparing with numerical results obtained using a fourth order runge–kutta method. effects of active parameters on flow have been presented graphically. the results show that velocity in bo...