Related papers: On the Loss of Compactness in the Vectorial Hetero…

We investigate planar piecewise-smooth vector fields with a discontinuity line, focusing on the bifurcation of crossing limit cycles that arise when one of the vector fields is translated along the discontinuity set. We establish…

In this article, the time-discretization of the fluid structure interaction model in the three-dimensional boundary domain is taken into account, which explains the mechanical interaction between the blood flow and the Hookean elasticity.…

In this paper, we study the existence and multiplicity of homoclinic solutions for following Hamiltonian systems with asymptotically quadratic nonlinearities at infinity \begin{eqnarray*} \ddot{u}(t)-L(t)u+\nabla W(t,u)=0. {eqnarray*} We…

We study the deconfinement phase transition of compact $U(1)$ pure lattice gauge theory with the Wilson action on {\em closed topology} lattices. In contrast to studies of compact QED on {\em hypercubic lattices with periodic boundary…

The aim of this work is to prove the global-in-time existence of weak solutions for a viscoelastic phase separation model in three space dimensions. To this end we apply the relative energy concept provided by [3]. We consider the case of…

We consider the minimal action problem min \int\_R 1/2 |$\gamma$'|^2 + W($\gamma$) dt among curves lying in a non-locally-compact metric space and connecting two given zeros of W $\ge$ 0. For this problem, the optimal curves are usually…

We prove the existence of minimal heteroclinic orbits for a class of fourth order O.D.E. systems with variational structure. In our general set-up, the set of equilibria of these systems is a union of manifolds, and the heteroclinic orbits…

In earlier works on Shape Dynamics (SD), a linear method of solving a particular set of Lichnerowicz-type equations through the implicit function theorem was developed in order to implicitly construct SD's global Hamiltonian and eliminate…

We present a systematic downfolding many-body approach for extended systems. Many-body calculations operate on a simpler Hamiltonian which retains material-specific properties. The Hamiltonian is systematically improvable and allows one to…

After a brief comprehensive review of old and new results on the well known Fermi-Pasta-Ulam (FPU) conservative system of $N$ nonlinearly coupled oscillators, we present a compact linear mode representation of the Hamiltonian of the FPU…

We propose a fourth--order compact finite--difference (HOC--FD) scheme for the transformed Bates partial integro--differential equation (PIDE). The method employs an implicit--explicit (IMEX) Crank--Nicolson framework for local terms and…

Hamilton's equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories…

A detailed Dirac's canonical analysis for a topological four dimensional $BF$-like theory with a compact dimension is developed. By performing the compactification process we find out the relevant symmetries of the theory, namely, the full…

The main result is the identification of the orthogonal complement of the subalgebra of conformal vector field inside the algebra of all vector fields of a compact flat 2-manifold. As a fundamental tool, the complete Hodge decomposition for…

We consider a potential $W:R^m\rightarrow R$ with two different global minima $a_-, a_+$ and, under a symmetry assumption, we use a variational approach to show that the Hamiltonian system \begin{equation} \ddot{u}=W_u(u), \hskip 2cm (1)…

We establish the existence of homoclinic solutions for suitable systems of nonlocal equations whose forcing term is of gradient type. The elliptic operator under consideration is the fractional Laplacian and the potentials that we take into…

Using a variational method, we prove the existence of heteroclinic solutions for a 6dimensional system of ordinary differential equations. We derive this system from the classical B{\'e}nard-Rayleigh problem near the convective instability…

We investigate a quasi-static-antiplane contact problem, examining a thermo-electro-visco-elastic material with a friction law dependent on the slip rate, assuming that the foundation is electrically conductive. The mechanical problem is…

This paper has been inspired by ideas presented by V. V. Kozlov in his works [19, 20]. In this paper our goal is to carry out a thorough analysis of some geometric problems of the dynamics of affinely-rigid bodies. We present two ways to…

We propose a new approach to the numerical solution of ergodic problems arising in the homogenization of Hamilton-Jacobi (HJ) equations. It is based on a Newton-like method for solving inconsistent systems of nonlinear equations, coming…