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In this paper we analyze the global existence of classical solutions to the initial boundary-value problem for a nonlinear parabolic equation describing the collective behavior of an ensemble of neurons. These equations were obtained as a…
We study which and how a periodic orbit in phase space links to both the largest Lyapunov exponent and the expectation values of macroscopic variables in a Hamiltonian system with many degrees of freedom. The model which we use in this…
We extend to the fermionic spin-1/2 case earlier work on quantum amplitudes arising from gravitational collapse to a black hole. Boundary data are specified on initial and final asymptotically-flat space-like hypersurfaces $\Sigma_{I,F}$,…
The spontaneous symmetry breaking in noncommutative $\lambda\Phi^4$ theory has been analyzed by using the formalism of the effective action for composite operators in the Hartree-Fock approximation. It turns out that there is no phase…
Analytical approximations for $< \phi^2 >$ of a quantized scalar field in ultrastatic asymptotically flat spacetimes are obtained. The field is assumed to be both massive and massless, with an arbitrary coupling $\xi$ to the scalar…
We examine the nonequilibrium dynamics of a self-interacting $\lambda\phi^4$ scalar field theory. Using a real time formulation of finite temperature field theory we derive, up to two loops and $O(\lambda^2)$, the effective equation of…
We discuss the equations for the bound one-active electron states based on the analytic solutions of the Schrodinger and Pauli equations for a uniform magnetic field and a single attractive $\delta({\bf r})$-potential. It is vary important…
We compute the critical exponents for nonextensive $\lambda\phi^{3}$ scalar field theory for all loop orders and $|q - 1| < 1$. We apply the results for both nonextensive percolation and Lee-Yang edge singularity problems. The corresponding…
The purpose of this paper is to study nonlinear singular parabolic equations with $p(x)$- Laplacian. Precisely, we consider the following problem and discuss the existence of a non-negative weak solution. \begin{align*} \frac{\partial…
We prove global existence and uniqueness of solutions of some important nonlinear lattices which include the Fermi-Pasta-Ulam (FPU) lattice. Our result shows (on a particular example) that the FPU lattice with high nonlinearity and its…
Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a…
Classical $\phi^4$ theory in weak and strong thermal gradients is studied on the lattice in (1+1) dimensions. Classical $\phi^4$ theory in weak and strong thermal gradients is studied on the lattice in (1+1) dimensions. The steady state…
In this letter we introduce the non-linear partial differential equation (PDE) $\partial^2_{\tau} \pi \propto (\vec\nabla \pi)^2$ showing a new type of instability. Such equations appear in the effective field theory (EFT) of dark energy…
In this paper we study non-linear noise excitation for the following class of space-time fractional stochastic equations in bounded domains: $$\partial^\beta_tu_t(x)=-\nu(-\Delta)^{\alpha/2} u_t(x)+I^{1-\beta}_t[\lambda…
We investigate stable solutions of elliptic equations of the type \begin{equation*} \left \{ \begin{aligned} (-\Delta)^s u&=\lambda f(u) \qquad {\mbox{ in $B_1 \subset \R^{n}$}} \\ u&= 0 \qquad{\mbox{ on $\partial B_1$,}}\end{aligned}\right…
We consider a class of fully-nonlinear Fermi-Pasta-Ulam (FPU) lattices, consisting of a chain of particles coupled by fractional power nonlinearities of order $\alpha >1$. This class of systems incorporates a classical Hertzian model…
In this paper we show that under general resonance the classical piecewise linear Fermi-Ulam accelerator behaves substantially different from its quantization in the sense that the classical accelerator exhibits typical recurrence and…
The non-perturbative autonomous renormalization of the scalar $\Phi^4$-model is applied in the framework of stochastic quantization. I show that this requires a selective, momentum-dependent renormalization of the Onsager coefficient…
The integrability properties of the field equation $L_{xx} = F(x)L^2$ of a spherically symmetric shear--free fluid are investigated. A first integral, subject to an integrability condition on $F(x)$, is found, giving a new class of…
We consider the wave equation $(\partial_t^2-\Delta)u=0$ on a planar triangular domain $\Omega\subset\mathbb{R}^2$ with Dirichlet boundary conditions. We use a commutator and integration by parts argument similar to that in…