Search results for "Characteristic equation"
showing 6 items of 16 documents
Stochastic response of linear and non-linear systems to α-stable Lévy white noises
2005
Abstract The stochastic response of linear and non-linear systems to external α -stable Levy white noises is investigated. In the literature, a differential equation in the characteristic function (CF) of the response has been recently derived for scalar systems only, within the theory of the so-called fractional Einstein–Smoluchowsky equations (FESEs). Herein, it is shown that the same equation may be built by rules of stochastic differential calculus, previously applied by one of the authors to systems driven by arbitrary delta-correlated processes. In this context, a straightforward formulation for multi-degree-of-freedom (MDOF) systems is also developed. Approximate CF solutions to the …
Interaction free and decoherence free states
2015
An interaction free evolving state of a closed bipartite system composed of two interacting subsystems is a generally mixed state evolving as if the interaction were a c-number. In this paper we find the characteristic equation of states possessing similar properties for a bipartite systems governed by a linear dynamical equation whose generator is sum of a free term and an interaction term. In particular in the case of a small system coupled to its environment, we deduce the characteristic equation of decoherence free states namely mixed states evolving as if the interaction term were effectively inactive. Several examples illustrate the applicability of our theory in different physical co…
Theoretical and experimental behaviour of the muscle viscosity coefficient during maximal concentric actions
1994
The aim of this study was to calculate the theoretical variation of the nonlinear damping factor (B) as a function of the muscle shortening velocity, and then to compare the theoretical values with the experimental data obtained on both the elbow flexor and the ankle extensor muscles. The theoretical variation of the B factor was determined from a muscle model consisting of a contractile component in parallel with a viscous damper both in series with an elastic component, and by using, the characteristic equation of the force velocity curve. In this muscle model, the viscous element modelled the inability of the muscle to generate as big a contracting force (while shortening) as possible un…
On the moving load problem in beam structures equipped with tuned mass dampers
2017
This paper proposes an original and efficient approach to the moving load problem on Euler–Bernoulli beams, with Kelvin–Voigt viscoelastic translational supports and rotational joints, and in addition, equipped with Kelvin–Voigt viscoelastic tuned mass dampers (TMDs). While supports are taken as representative of external devices such as grounded dampers or in-span supports with flexibility and damping, the rotational joints may model rotational dampers or connections with flexibility and damping arising from imperfections or damage. The theory of generalised functions is used to treat the discontinuities of the response variables, which involves deriving exact complex eigenvalues and eigen…
Hydrodynamics and Stochastic Differential Equation with Sobolev Coefficients
2013
In this chapter, we will explain how the Brenier’s relaxed variational principle for Euler equation makes involved the ordinary differential equations with Sobolev coefficients and how the investigation on stochastic differential equations (SDE) with Sobolev coefficients is useful to establish variational principles for Navier–Stokes equations. We will survey recent results on this topic.
Cylindrical surface waveguide modes using a surface impedance dyadic method
1987
The fields and characteristic parameters of nonradiating modes of a dielectric-coated wire with an intervening airgap are derived using a surface impedance dyadic method. This method shows several advantages and provides a straightforward method for working out the characteristic equation, cutoff conditions, far-from-cutoff conditions and field coefficients. Important results about the hybrid nature of these modes are shown, and some of them are common to any cylindrical surface waveguide.