On the analytical expression of the multicompacton and some exact compact solutions of a nonlinear diffusive Burgers’type equation

International audienceWe consider the nonlinear diffusive Burgers' equation as a model equation for signals propagation on the nonlinear electrical transmission line with intersite nonlinearities. By applying the extend sine-cosine method and using an appropriate modification of the Double-Exp function method, we successfully derived on one hand the exact analytical solutions of two types of solitary waves with strictly finite extension or compact support: kinks and pulses, and on the other hand the exact solution for two interacting pulse solitary waves with compact support. These analytical results indicate that the speed of the pulse compactons doesn't depends explicitly on the pulse amplitude as has been expected for long, but rather on the dc-component associated to this trigonometric solution. More interesting, the interactions between the two pulse compactons induce only a phase shift even though they are close together. These analytical solutions are checked by means of numerical simulations. (c) 2018 Elsevier B.V. All rights reserved

Angular dependence of atomic friction with deformable substrate

The atomic stick-slip behavior of Prandtl-Tomlinson model sliding on 2D deformable substrate is studied. The influence of the shape of the interaction potential is investigated in details in the well-known phenomenon of the two-dimensional stick-slip friction. Numerical simulations are built to observe the influence of the geometry and orientation. The results show that the friction force has a maximum at r = − 0.6, this value of the shape parameter indicates a transition from a clear stick-slip at r> − 0.6 to a distorted stick-slip at r< − 0.6. We find a remarkable transition of the frictional force image pattern depending on the shape of the substrate

Discrete energy transport in the perturbed Ablowitz-Ladik equation for Davydov model of

The modulational instability of a plane wave for the perturbed non-integrable Ablowitz-Ladik equation for α-helix proteins is analyzed. Through the linear stability analysis, we observe that the presence of additional terms in the Ablowitz-Ladik equation tends to suppress modulational instability. Numerical simulations are performed in order to verify our analytical predictions. The presence of extended terms in the Ablowitz-Ladik equation tends to compactify and split the emerging localized structures. Particular attention is paid to the emergence of multi-hump structures, and the biological relevance of the latter is discussed

Dry friction: motions – map, characterization and control

We consider a simple model of spring-mass block placed over a constant velocity v rolling plate. The map of the dynamic is presented in the (v,r) space where r accounts for the possible variation of the periodic shape profile of the rolling carpet. In order to characterize each type of motion, we found that evaluating the area of the phase space trajectories is more relevant than attempting on one hand, to solve analytically the asymptotic behavior, or on the other hand, to obtain an equivalent of the entropy and the free energy. First-order transition reveals to be the characteristic route from one type of motion to another. Later, we investigate the influence of the classical TMD1 and TLCD2 on the dynamic of this mass. Moreover, we numerically study the effects of a modified TMD. Reduced order parameter provides a quick overview of the whole system than phase space representations and bifurcation diagrams. Comparison of performances in the (v,r) space is made. It reveals the efficiency of the modified TMD. It comes out that the new TMD we designed stabilizes the system better than the two above control systems

Threshold field in nucleation process for an inhomogeneous deformable nonlinear Klein-Gordon system

82.40.Ck Pattern formation in reactions with diffusion, flow and heat transfer, 45.05.+x General theory of classical mechanics of discrete systems, 87.10.+e General theory and mathematical aspects,