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We present a covariant formalism for studying nonlinear perturbations of scalar fields. In particular, we consider the case of two scalar fields and introduce the notion of adiabatic and isocurvature covectors. We obtain differential…

The effect of inter-subsystem coupling on the adiabaticity of composite systems and that of its subsystems is investigated. Similar to the adiabatic evolution defined for pure states, non-transitional evolution for mixed states is…

Nonlinearity in many systems is heavily dependent on component variation and environmental factors such as temperature. This is often overcome by keeping signals close enough to the device's operating point that it appears approximately…

We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka-Volterra's classical equations. The novelty of this work is that the interaction terms are non local and the interaction occurs…

In the present paper geometric aspects of relationship between non-Noether symmetries and conservation laws in Hamiltonian systems is discussed. It is shown that integrals of motion associated with continuous non-Noether symmetry are in…

Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological, mechanical, and transportation systems. Thus…

The parabolic N-membranes problem for the p-Laplacian and the complete order constraint on the components of the solution is studied in what concerns the approximation, the regularity and the stability of the variational solutions. We…

The nonlocal world presents an abundance of surprises and wonders to discover. These special properties of the nonlocal world are usually the consequence of long-range interactions, which, especially in presence of geometric structures and…

Understanding how systems respond to external perturbations is fundamental to statistical physics. For systems far from equilibrium, a general framework for response remains elusive. While progress has been made on the linear response of…

Many physical processes we observe in nature involve variations of macroscopic quantities over spatial and temporal scales much larger than microscopic molecular collision scales and can be considered as in local thermal equilibrium. In…

In this work, we study the implications of nonlinearity in general relativistic spherically symmetric inviscid irrotational accretion flow in a stationary non-rotating spacetime. It has been found that the perturbation scheme leads to a…

A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…

Some systems of nonlinear wave equations admit global solutions for all sufficiently small initial data, while others do not. The (classical) null condition guarantees that such a result holds, but it is too strong to capture certain…

The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are…

We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the…

We investigate a system of harmonically coupled identical nonlinear constituents subject to noise in different spatial arrangements. For global coupling we find for infinitely many constituents the coexistence of several ergodic components…

It is well-known that nonlinearity may lead to localization effects and coupling of internally resonant modes. However, research focused primarily on conservative systems commonly assumes that the near-resonant forced response closely…

Density perturbations and their dynamic evolution from early to late times can be used for an improved understanding of interesting physical phenomena both in cosmology and in the context of heavy-ion collisions. We discuss the spectrum and…

We consider nonlinear elliptic systems satisfying componentwise coercivity condition. The nonlinear terms have controlled growths with respect to the solution and its gradient, while the behaviour in the independent variable is governed by…

We investigate general properties of non-deterministic self-assembly with asymmetric interactions, using a computational model and DNA tile assembly experiments. By contrasting symmetric and asymmetric interactions we show that the latter…