Search results for "calculu"

A non-local model of thermal energy transport: The fractional temperature equation

2013

Abstract Non-local models of thermal energy transport have been used in recent physics and engineering applications to describe several “small-scale” and/or high frequency thermodynamic processes as shown in several engineering and physics applications. The aim of this study is to extend a recently proposed fractional-order thermodynamics ( [5] ), where the thermal energy transfer is due to two phenomena: A short-range heat flux ruled by a local transport equation; a long-range thermal energy transfer that represents a ballistic effects among thermal energy propagators. Long-range thermal energy transfer accounts for small-scale effects that are assumed proportional to the product of the in…

Closure to “New Stage-Discharge Equation for the SMBF Flume” by Francesco Giuseppe Carollo, Costanza Di Stefano, Vito Ferro, and Vincenzo Pampalone

2017

The moment equation closure method revisited through the use of complex fractional moments

2015

In this paper the solution of the Fokker Planck (FPK) equation in terms of (complex) fractional moments is presented. It is shown that by using concepts coming from fractional calculus, complex Mellin transform and related ones the probability density function response of nonlinear systems may be written in discretized form in terms of complex fractional moment not requiring a closure scheme.

On the derivation of the Fokker-Plank equation by using of Fractional calculus

2009

In this paper, fractional calculus has been used to find the spectral counterpart of the Fokker- Planck equations for non-linear systems driven by Lévy white noise processes. In particular it is shown that one can obtain the equation ruling the characteristic function of the response to a non-linear system, without using the Itô formula. Indeed, it is possible to reproduce the well-known results, already known in literature, by means of the characteristic function representation in terms of complex moments, recently proposed by the first two authors. The case of a-stable Lévy driven stochastic differential equation is also treated introducing an associated process constructed from the stabl…

Multiplicative cases from additive cases: Extension of Kolmogorov–Feller equation to parametric Poisson white noise processes

2007

Abstract In this paper the response of nonlinear systems driven by parametric Poissonian white noise is examined. As is well known, the response sample function or the response statistics of a system driven by external white noise processes is completely defined. Starting from the system driven by external white noise processes, when an invertible nonlinear transformation is applied, the transformed system in the new state variable is driven by a parametric type excitation. So this latter artificial system may be used as a tool to find out the proper solution to solve systems driven by parametric white noises. In fact, solving this new system, being the nonlinear transformation invertible, …

CTR: A calculus of timed refinement

1995

This paper presents CTR — a process algebraic framework for loose specification of time quantity sensitive operational behaviour of reactive systems. CTR terms are provided both with operational and specification semantics (via the notion of specification refinement). Besides the intuitive justification of appropriateness of the refinement notion, a preservation theorem is proved for a timed variant of Hennessy-Milner logic. A comparison of CTR with the related formalism of Timed Modal Specifications, and with the timed process calculi TCCS due to Wang is given. Some pragmatics of the application of CTR is sketched on a critical resource access example.

The fractal model of non-local elasticity with long-range interactions

2010

The mechanically-based model of non-local elasticity with long-range interactions is framed, in this study, in a fractal mechanics context. Non-local interactions are modelled introducing long-range central body forces between non-adjacent volume elements of the elastic continuum. Such long-range interactions are modelled as proportional to the product of interacting volumes, to the relative displacements of the centroids and to a distance-decaying function that is monotonically-decreasing with the distance. The choice of the decaying function is a key aspect of the model and it has been proved that any continuous function, strictly positive, is thermodynamically consistent and it leads to …

Fractional calculus for the solution of non-linear stochastic oscillators with viscous dampers devices

2009

Fluid viscoelastic dampers are of great interest in different fields of engineering. Examples of their applications can be found in seismic mitigation design of structures or in vibration absorption in airplane suspension. Such devices introduce a non-linear dissipative term in the equation of motion and therefore, the solution of even a single degree of freedom system excited by a white noise process, becomes prohibitive. The solution is usually obtained by approximated methods, like the stochastic linearization technique. In this paper it is shown that, by means of fractional operators, it is possible to find the solution of oscillators provided with fluid viscoelastic devices, approachin…

Non-Local Thermoelasticity: The Fractional Heat conduction

2011

THE MECHANICAL MODEL OF FRACTIONAL VISCOELASTICITY

2010

Viscoelastic materials have been more and more used nowadays for their low-cost productions as well as for their dissipative capabilities that may be coupled with others, more performing materials, to form complex-type engineering elements. The main feature of viscoelastic behavior is the relaxation of the stress state and the creep of the strain field that may be experienced, respectively, in hard or soft test devices. Such phenomenological consideration has been extensively analyzed yet at the beginning of the twentieth century and simple rheological models representing linear, constitutive, stress-velocity relations of the studied material have been proposed. Moreover the rheological rel…