Search results for "Calculus"

Fractional-Order Theory of Thermoelasticity. II: Quasi-Static Behavior of Bars

2018

This work aims to shed light on the thermally-anomalous coupled behavior of slightly deformable bodies, in which the strain is additively decomposed in an elastic contribution and in a thermal part. The macroscopic heat flux turns out to depend upon the time history of the corresponding temperature gradient, and this is the result of a multiscale rheological model developed in Part I of the present study, thereby resembling a long-tail memory behavior governed by a Caputo's fractional operator. The macroscopic constitutive equation between the heat flux and the time history of the temperature gradient does involve a power law kernel, resulting in the anomaly mentioned previously. The interp…

Reduced dynamical equations for solid-state lasers and VCSELs

2007

It is the aim of this presentation to show that a reduction in the number of coupled equations is feasible for spatio-temporal laser models with generic values of the pump and other parameters. Reduced equations have been derived via the application of two separate, yet equivalent, methods: one based on the CM and the other on operational calculus. The long term dynamics of the reduced models for solid-state lasers and VCSELs have been compared with that of the full systems by using both mathematical methods. Extensive numerical simulations for the complex dynamics of these and other laser models become suddenly feasible within reasonable computational time.

Flux of a Vector Field

2012

In this chapter we concentrate on aspects of vector calculus. A common physical application of this theory is the fluid flow problem of calculating the amount of fluid passing through a permeable surface. The abstract generalization of this leads us to the flux of a vector field through a regular 2-surface in \(\mathbb{R}^3\). More precisely, let the vector field F in \(\mathbb{R}^3\) represent the velocity vector field of a fluid. We immerse a permeable surface S in that fluid, and we are interested in the amount of fluid flow across the surface S per unit time. This is the flux integral of the vector field F across the surface S

Evaluation of the temperature effect on the fractional linear viscoelastic model for an epoxy resin

2016

The paper deals with the evolution of the parameters of a fractional model for different values of temperature. An experimental campaign has been performed on epoxy resin at different levels of temperature. It is shown that epoxy resin is very sensitive to the temperature.

Asymptotical Convergence Evaluation for a Parabolic Problem Arising in Circuit Theory

1990

New Results in Generalized Minimum Variance Control of Computer Networks

2014

In this paper new results in adaptive (generalized) minimum variance control of packet switching computer networks are presented. New solutions, corresponding to the new inverses of the nonsquare polynomial matrices, can be used for design of robust control of multivariable systems with different number of inputs and outputs. Application of polynomial matrix inverses with arbitrary degrees of freedom creates the possibilities to optimal control of computer networks in terms of usage their maximal bandwidth. Simulation examples made in Matlab environment show big potential of presented approach. DOI: http://dx.doi.org/10.5755/j01.itc.43.3.6268

Jacobian-free approximate solvers for hyperbolic systems: Application to relativistic magnetohydrodynamics

2017

Abstract We present recent advances in PVM (Polynomial Viscosity Matrix) methods based on internal approximations to the absolute value function, and compare them with Chebyshev-based PVM solvers. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Another important feature of the proposed methods is that they are suitable to be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems for which the Jacobians involve complex expressions, e.g., the relativistic magnetohydrodynamics (RMHD) equations. On the other hand, the proposed Jacobian-free solvers hav…

A new representation of power spectral density and correlation function by means of fractional spectral moments

2009

In this paper, a new perspective for the representation of both the power spectral density and the correlation function by a unique class of function is introduced. We define the moments of order gamma (gamma being a complex number) of the one sided power spectral density and we call them Fractional Spectral Moments (FSM). These complex quantities remain finite also in the case in which the ordinary spectral moments diverge, and are able to represent the whole Power Spectral Density and the corresponding correlation function.

Full Sliding “Adhesive-Like” Contact of V-Belts

2002

Abstract Analysis of power transmission in a belt drive consisting of e. g. two pulleys might be treated as a boundary value problem. Tight side tension FT, slack side tension FS and the wrap angle α are the three natural boundary conditions. In the literature, theories are developed where seating and unseating as well as the power transmitting part of the contact are considered. The solutions presented so far don’t fulfil the boundary conditions properly, since a certain tension ratio FT/FS is associated with a certain contact angle and not an a priori specified one. It appears that a new type of full sliding solution must be introduced to handle the boundary condition problem. During part…

Monadic second-order logic over pictures and recognizability by tiling systems

1994

We show that a set of pictures (rectangular arrays of symbols) is recognized by a finite tiling system if and only if it is definable in existential monadic second-order logic. As a consequence, finite tiling systems constitute a notion of recognizability over two-dimensional inputs which at the same time generalizes finite-state recognizability over strings and matches a natural logic. The proof is based on the Ehrenfeucht-FraIsse technique for first-order logic and an implementation of “threshold counting” within tiling systems.