Related papers: Driven linear modes: Analytical solutions for fini…
This paper considers linear rational expectations models in the frequency domain. The paper characterizes existence and uniqueness of solutions to particular as well as generic systems. The set of all solutions to a given system is shown to…
We establish a connection between finite fields and finite dynamical systems. We show how this connection can be used to shed light on some problems in finite dynamical systems and in particular, in linear systems.
We analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit. An analytic solution is found for traveling waves. The procedure is used to find oscillatory as well as solitary waves. A comparison…
We present a linear mode analysis of the relativistic MHD equations in the presence of finite electrical conductivity. Starting from the fully relativistic covariant formulation, we derive the dispersion relation in the limit of small…
We present an analytical description of the large-amplitude stationary oscillations of the finite discrete system of harmonically-coupled pendulums without any restrictions to their amplitudes (excluding a vicinity of $\pi$). Although this…
Linear response spectra of a driven intrinsic localized mode in a micromechanical array are measured as it approaches two fundamentally different kinds of bifurcation points. A linear phase mode associated with this autoresonant state…
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
Certain lattice wave systems in translationally invariant settings have one or more spectral bands that are strictly flat or independent of momentum in the tight binding approximation, arising from either internal symmetries or fine-tuned…
Using the density matrix formalism, we prove an existence theorem of the periodic steady-state for an arbitrary periodically-driven system. This state has the same period as the modulated external influence, and it is realized as an…
A finite element model and its equivalent electronic analogue circuit of hydraulic transmission lines have been developed. Basic equations are approximated to be a set of ordinary differential equations that can be represented in state…
We consider modeling for strong-strong beam-beam interactions beyond preceding linearized/perturbative methods such as soft gaussian approximation or FMM (HFMM) etc. In our approach discrete coherent modes, discovered before, and possible…
We solve for waves in an isothermal, stratified medium with a magnetic field that points along a direction perpendicular to that of gravity and varies exponentially in the direction of gravity. We find exact analytical solutions for two…
We study the analyticity of bounded solutions of systems of analytic state-dependent delay differential equations. We obtain the analyticity of solutions by transforming the system of state-dependent delay equations into an abstract…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the…
Dynamic homogenization aims at describing the macroscopic characteristics of wave propagation in microstructured systems. Using a simple method, we derive frequency-dependent homogenized parameters that reproduce the exact dispersion…
We study discrete linear divergence-form operators with random coefficients, also known as the random conductance model. We assume that the conductances are bounded, independent and stationary; the law of a conductance may depend on the…
We consider a discrete dynamical system with internal degrees of freedom (DOF). Due to the symmetry between the internal DOFs, certain internal modes cannot be excited by external forcing (in a case of linear interactions) and thus are…
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…