Search results for "Mathematical analysis"

A kinematic method to obtain conformal factors

2000

Radial conformal motions are considered in conformally flat space-times and their properties are used to obtain conformal factors. The geodesic case leads directly to the conformal factor of Robertson-Walker universes. General cases admitting homogeneous expansion or orthogonal hypersurfaces of constant curvature are analyzed separately. When the two conditions above are considered together a subfamily of the Stephani perfect fluid solutions, with acceleration Fermi-Walker propagated along the flow of the fluid, follows. The corresponding conformal factors are calculated and contrasted with those associated with Robertson-Walker space-times.

The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter

2018

We compute systematically for the planar double box Feynman integral relevant to top pair production with a closed top loop the Laurent expansion in the dimensional regularisation parameter $\varepsilon$. This is done by transforming the system of differential equations for this integral and all its sub-topologies to a form linear in $\varepsilon$, where the $\varepsilon^0$-part is strictly lower triangular. This system is easily solved order by order in the dimensional regularisation parameter $\varepsilon$. This is an example of an elliptic multi-scale integral involving several elliptic sub-topologies. Our methods are applicable to similar problems.

Analytic form of the full two-loop five-gluon all-plus helicity amplitude

2019

We compute the full-color two-loop five-gluon amplitude for the all-plus helicity configuration. In order to achieve this, we calculate the required master integrals for all permutations of the external legs, in the physical scattering region. We verify the expected divergence structure of the amplitude, and extract the finite hard function. We further validate our result by checking the factorization properties in the collinear limit. Our result is fully analytic and valid in the physical scattering region. We express it in a compact form containing logarithms, dilogarithms and rational functions.

Analytic result for a two-loop five-particle amplitude

2019

We compute the symbol of the full-color two-loop five-particle amplitude in $\mathcal{N}=4$ super Yang-Mills, including all non-planar subleading-color terms. The amplitude is written in terms of permutations of Parke-Taylor tree-level amplitudes and pure functions to all orders in the dimensional regularization parameter, in agreement with previous conjectures. The answer has the correct collinear limits and infrared factorization properties, allowing us to define a finite remainder function. We study the multi-Regge limit of the non-planar terms, analyze its subleading power corrections, and present analytically the leading logarithmic terms.

Threshold expansion of Feynman diagrams within a configuration space technique

2000

The near threshold expansion of generalized sunset-type (water melon) diagrams with arbitrary masses is constructed by using a configuration space technique. We present analytical expressions for the expansion of the spectral density near threshold and compare it with the exact expression obtained earlier using the method of the Hankel transform. We formulate a generalized threshold expansion with partial resummation of the small mass corrections for the strongly asymmetric case where one particle in the intermediate state is much lighter than the others.

Nonlocally-induced (quasirelativistic) bound states: Harmonic confinement and the finite well

2015

Nonlocal Hamiltonian-type operators, like e.g. fractional and quasirelativistic, seem to be instrumental for a conceptual broadening of current quantum paradigms. However physically relevant properties of related quantum systems have not yet received due (and scientifically undisputable) coverage in the literature. In the present paper we address Schr\"{o}dinger-type eigenvalue problems for $H=T+V$, where a kinetic term $T=T_m$ is a quasirelativistic energy operator $T_m = \sqrt{-\hbar ^2c^2 \Delta + m^2c^4} - mc^2$ of mass $m\in (0,\infty)$ particle. A potential $V$ we assume to refer to the harmonic confinement or finite well of an arbitrary depth. We analyze spectral solutions of the per…

Matrix solutions of diffusion equation

2002

Structural damage detection using auto correlation functions of vibration response under sinusoidal excitation

2015

Structural damage detection using time domain vibration responses has attracted more and more researchers in recent years because of its simplicity in calculation and no requirement of a finite element model. This paper proposes a new approach to locate the damage using the auto correlation function of vibration response signals under sinusoidal excitation from different measurement points of the structure, based on which a vector named Auto Correlation Function at Maximum Point Value Vector (AMV) is formulated. A sensitivity analysis of the normalized AMV with respect to the local stiffness shows that under several specific frequency excitations, the normalized AMV has a sharp change aroun…

Effective coefficients of thermoconductivity on some symmetric periodically perforated plane structures

1996

In this article we discuss an auxiliary problem which arises in the homogenization theory for the Laplacian on the plane with periodic array of square holes and homogeneous Neumann boundary conditions on those. Independently, this problem describes the process of thermoconductivity. We find the explicit formulas for effective coefficients of thermoconductivity (homogenized modula). We make also the asymptotic analysis of these formulas in the cases of big and small holes.

Ideal Elastic-Plastic Oscillators Subjected to Stochastic Input

1999

Abstract The paper deals with the evaluation of the probabilistic response of an ideal elastic-plastic single degree of freedom oscillator subjected to a normal white noise. The analysis has been conducted on the hypothesis that accumulated plastic displacements are a compound homogeneous Poisson process independent of the external excitation. In this case plastic displacements can be treated as an additional external noise, to be identified, acting on a linear system. In the paper a time domain approach to obtain the two variable non stationary correlation function is proposed. Hence the evolutionary power spectral density function is also obtained. A numerical example is presented in orde…