Search results for "calculu"

Fractional-Order Thermal Energy Transport for Small-Scale Engineering Devices

2014

Fractional-order thermodynamics has proved to be an efficient tool to describe several small-scale and/or high-frequency thermodynamic processes, as shown in many engineering and physics applications. The main idea beyond fractional-order physics and engineering relies on replacing the integer-order operators of classical differential calculus with their real-order counterparts. In this study, the authors aim to extend a recently proposed physical picture of fractional-order thermodynamics to a generic 3D rigid heat conductor where the thermal energy transfer is due to two phenomena: a short-range heat flux ruled by stationary and nonstationary transport equations, and a long-range thermal …

Non-Markovian Wave Function Simulations of Quantum Brownian Motion

2005

The non-Markovian wave function method (NMWF) using the stochastic unravelling of the master equation in the doubled Hilbert space is implemented for quantum Brownian motion. A comparison between the simulation and the analytical results shows that the method can be conveniently used to study the non-Markovian dynamics of the system.

Phase space coordinates and the Hamiltonian constraint of Regge calculus.

1994

We suggest that the phase space of Regge calculus is spanned by the areas and the deficit angles corresponding to the two-simplexes on the spacelike hypersurface of simplicial spacetime. Our proposal is based on a slight modification of the Ashtekar formulation of canonical gravity. In terms of these phase space coordinates we write an equation which we suggest to be a simplicial version of the Hamiltonian constraint of canonical gravity.

Construction of the ground state in nonrelativistic QED by continuous flows

2006

AbstractFor a nonrelativistic hydrogen atom minimally coupled to the quantized radiation field we construct the ground state projection Pgs by a continuous approximation scheme as an alternative to the iteration scheme recently used by Fröhlich, Pizzo, and the first author [V. Bach, J. Fröhlich, A. Pizzo, Infrared-finite algorithms in QED: The groundstate of an atom interacting with the quantized radiation field, Comm. Math. Phys. (2006), doi: 10.1007/s00220-005-1478-3]. That is, we construct Pgs=limt→∞Pt as the limit of a continuously differentiable family (Pt)t⩾0 of ground state projections of infrared regularized Hamiltonians Ht. Using the ODE solved by this family of projections, we sho…

The Langevin Equation

2009

Wu et al. Reply:

2019

Non-linear viscoelastic behavior of polymer melts interpreted by fractional viscoelastic model

2016

Very recently, researchers dealing with constitutive law pertinent viscoelastic materials put forward the successful idea to introduce viscoelastic laws embedded with fractional calculus, relating the stress function to a real order derivative of the strain function. The latter consideration leads to represent both, relaxation and creep functions, through a power law function. In literature there are many papers in which the best fitting of the peculiar viscoelastic functions using a fractional model is performed. However there are not present studies about best fitting of relaxation function and/or creep function of materials that exhibit a non-linear viscoelastic behavior, as polymer melt…

Self-referenced phase reconstruction proposal of Ghz bandwidth non-periodical optical pulses by in-fiber semi-differintegration

2011

Abstract We propose two new techniques able to retrieve the phase profile of a given temporal optical pulse based on the use of in-fiber semi-differintegral operators, where by semi-differintegration we mean either a 0.5th-order differentiation or integration. In both cases, the signal's temporal phase can be obtained by simple dividing two temporal intensity profiles, namely the intensities of the input and output pulses of a spectrally shifted semi-differintegral operator. In both cases, we obtained simple analytical expressions for the phase profile. The techniques are self-referenced and well-suited for real-time applications. We numerically prove the viability of these proposals.

Stabilization of 1D solitons by fractional derivatives in systems with quintic nonlinearity

2022

AbstractWe study theoretically the properties of a soliton solution of the fractional Schrödinger equation with quintic nonlinearity. Under “fractional” we understand the Schrödinger equation, where ordinary Laplacian (second spatial derivative in 1D) is substituted by its fractional counterpart with Lévy index $$\alpha$$ α . We speculate that the latter substitution corresponds to phenomenological account for disorder in a system. Using analytical (variational and perturbative) and numerical arguments, we have shown that while in the case of Schrödinger equation with the ordinary Laplacian (corresponding to Lévy index $$\alpha =2$$ α = 2 ), the soliton is unstable, even infinitesimal diffe…

Elastic waves propagation in 1D fractional non-local continuum

2008

Aim of this paper is the study of waves propagation in a fractional, non-local 1D elastic continuum. The non-local effects are modeled introducing long-range central body interactions applied to the centroids of the infinitesimal volume elements of the continuum. These non-local interactions are proportional to a proper attenuation function and to the relative displacements between non-adjacent elements. It is shown that, assuming a power-law attenuation function, the governing equation of the elastic waves in the unbounded domain, is ruled by a Marchaud-type fractional differential equation. Wave propagation in bounded domain instead involves only the integral part of the Marchaud fraction…