Related papers: Resonant forcing of nonlinear systems of different…
The friction force is derived using fractional calculus by considering the non-uniform flow of time in dissipative processes. The approach incorporates inhomogeneous velocity without unphysical approximations, resulting in a Lagrangian…
Within the traditional frame of reduced MHD, a new rigorous perturbation expansion provides the equation ruling the nonlinear growth and saturation of the tearing mode for any current gradient. The small parameter is the magnetic island…
We consider small oscillations of micro-particles and gaseous bubbles in viscous fluid around equilibrium states under the action of a sinusoidal external force. Exact solutions to the governing integro-differential equations containing…
The dynamics of self-oscillatory extended systems, resonantly forced at a frequency close to that of the natural oscillations (1:1 resonance), is shown to be universally described by a complex Ginzburg-Landau equation containing an…
We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an…
Extensive studies have investigated the transition mechanism of boundary layers initiated by a single primary instability. In a real-world scenario, however, multiple primary instabilities of different physical nature would coexist and…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
This paper is concerned with modeling the polarization process in ferroelectric media. We develop a thermodynamically consistent model, based on phenomenological descriptions of free energy as well as switching and saturation conditions in…
In this paper, we study the Lagrangian functions for a class of second-order differential systems arising from physics. For such systems, we present necessary and sufficient conditions for the existence of Lagrangian functions. Based on the…
Forced oscillation (FO) is a significant concern threating the power system stability. Its mechanisms are mostly studied via linear models. However, FO amplitude is increasing, e.g., Nordic and Western American FOs, which can stimulate…
We study locking of the modulation frequency of a relative periodic orbit in a general $S^1$-equivariant system of ordinary differential equations under an external forcing of modulated wave type. Our main result describes the shape of the…
In this paper, we propose an efficient numerical treatment for solving contact problems with friction between deformable bodies. The discretized normal and tangential constraints at the candidate contact interface are expressed by using…
There exists in nature many examples of systems presenting self-limiting behaviour: population dynamics, structure engineering, Townsend's electron breakdown, nuclear decay in radioactive equilibrium, histeresis process, meteorological…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
We describe in detail how to eliminate nonphysical degrees of freedom in the Lagrangian and Hamiltonian formulations of a constrained system. Two important and distinct steps in our method are the fixing of ambiguities in the dynamics and…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
In this paper, non-variational systems of differential equations containing small terms are considered, and a consistent approach for deriving approximate conservation laws through the introduction of approximate Lagrange multipliers is…
A necessary and sufficient condition ("nonresonance") is established for every solution of an autonomous linear difference equation, or more generally for every sequence $(x^\top A^n y)$ with $x,y\in \mathbb{R}^d$ and $A\in…
Mesons as bound states of quark and anti-quark in the framework of a relativistic potential model are studied. Interaction of constituents in bound state is described by the Lorentz-scalar QCD inspired funnel-type potential with the…
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…