In this paper we present a formulation of the nonlinear stochastic differential equation which allows for systematic approximations. The method is not restricted to the asymptotic, i.e., stationary, regime but can be applied to derive effective equations describing the relaxation of the system from arbitrary initial conditions. The basic idea is to reduce the nonlinear Langevin equation to an e...

We consider a description of membranes by (2, 1)-dimensional field theory, or alternatively a description of irrotational, isentropic fluid motion by a field theory in any dimension. We show that these Galileo-invariant systems, as well as others related to them, admit a peculiar diffeomorphism symmetry, where the transformation rule for coordinates involves the fields. The symmetry algebra coi...

We consider some differential geometric classes of local and nonlocal Poisson and symplectic structures on loop spaces of smooth manifolds which give natural Hamiltonian or multihamiltonian representations for some important nonlinear equations of mathematical physics and field theory such as nonlinear sigma models with torsion, degenerate Lagrangian systems of field theory, systems of hydrodyn...

The influence of an external electric field on the current in charged systems is investigated. The results beyond linear response from the classical hierarchy of density matrices are compared with the results from quantum kinetic theory. It is found that even an infinitesimal friction with the background changes the results in a noncontinuous way. The kinetic theory yields a systematic treatmen...

A short overview of the theory and applications of nonlinear spin wave phenomena in ferrite films at microwave frequencies is given. A method of classical Hamiltonian formalism for spin waves in bulk femmagnets in combination with the theory of spin wave spectrum for thin magnetic films is used for theoretical description of nonlinear spin wave phenomena in films. Comparative roles of three-wav...

(2016). Calcium dependent plasticity applied to repetitive transcranial magnetic stimulation with a neural field model. (2016). Real-time automated EEG tracking of brain states using neural field theory. propensity under forced desynchrony in a model of arousal state dynamics. (2016). The spatiotemporal hemodynamic response function for depth-dependent functional imaging of human cortex. (2015)...

This paper describes a systematic technique for obtaining controllers for Nonlinear Systems using a Continuous Piecewise Linear Approximation (CPWL) of the given Nonlinear vector field. The method proposes the use of a CPWL approximation of the Nonlinear System and then a theory is developed to show that the stabilization of the CPWL aproximation ODE yields stability for the Nonlinear ODE. An e...

We investigate the nonlinearity-assisted quantum tunnelling and formation of nonlinear collective excitations in a matter-wave interferometer, which is realized by the adiabatic transformation of a double-well potential into a singlewell harmonic trap. In contrast to the linear quantum tunnelling induced by the crossing (or avoided crossing) of neighbouring energy levels, the quantum tunnelling...

The SU (N f) L ⊗ SU (N f) R chiral symmetry of QCD is of central importance for the nonpertur-bative low-energy dynamics of light quarks and gluons. Lattice field theory provides a theoretical framework in which these dynamics can be studied from first principles. The implementation of chiral symmetry on the lattice is a nontrivial issue. In particular, local lattice fermion actions with the ch...

An analysis method for electromagnetic field coupling to microstrip line connected with nonlinear components is proposed in this paper. Different from the published work, not only the voltage and current response of the nonlinear component connected to the transmission line (TL) can be obtained, but also the power transmitted from this nonlinear component to the next one at both the fundamental...