Search results for "integral"

Coulomb effects in three-body reactions with two charged particles

1978

We present the details of a novel approach to the treatment of Coulomb effects in atomic and nuclear reactions of the three-body type in which two of the particles are charged. Based on three-body integral equations the formalism allows the practical calculation of elastic, inelastic, rearrangement, and breakup processes with full inclusion of the Coulomb repulsion or attraction in a mathematically correct way. No restrictions need to be made concerning the form of the short-range interactions between the three pairs. A particular virtue of our method lies in the fact that it corroborates, and gives precise meaning to, the intuitively anticipated conception of how to describe such reactions.

Special Section on Fractional Operators in the Analysis of Mechanical Systems Under Stochastic Agencies

2017

Conductivity reconstructions using real data from a new planar electrical impedance tomography device

2013

Abstract In this paper, we present results of reconstructions using real data from a new planar electrical impedance tomography device developed at the Institut fur Physik, Johannes Gutenberg Universitat, Mainz, Germany. The prototype consists of a planar sensing head of circular geometry, and it was designed mainly for breast cancer detection. There are 12 large outer electrodes arranged on a ring of radius  cm where the external currents are injected, and a set of 54 point-like high-impedance inner electrodes where the induced voltages are measured. Two direct (i.e. non-iterative) reconstruction algorithms are considered: one is based on a discrete resistor model, and the other one is an …

Size effects of small-scale beams in bending addressed with a strain-difference based nonlocal elasticity theory

2019

Abstract A strain-difference based nonlocal elasticity model devised by the authors elsewhere (Polizzotto et al., Int. J. Solids Struct. 25 (2006) 308–333) is applied to small-scale homogeneous beam models in bending under static loads in the purpose to describe the inherent size effects. With this theory —belonging to the strain-integral nonlocal model family, but exempt from anomalies typical of the Eringen nonlocal theory— the relevant beam problem is reduced to a set of three mutually independent Fredholm integral equations of the second kind (each independent of the beam’s ordinary boundary conditions, only one depends on the given load), which can be routinely solved numerically. Appl…

Coherent potential approximation for diffusion and wave propagation in topologically disordered systems

2013

Using Gaussian integral transform techniques borrowed from functional-integral field theory and the replica trick we derive a version of the coherent-potential approximation (CPA) suited for describing ($i$) the diffusive (hopping) motion of classical particles in a random environment and ($ii$) the vibrational properties of materials with spatially fluctuating elastic coefficients in topologically disordered materials. The effective medium in the present version of the CPA is not a lattice but a homogeneous and isotropic medium, representing an amorphous material on a mesoscopic scale. The transition from a frequency-independent to a frequency-dependent diffusivity (conductivity) is shown …

Many-body quantum dynamics by adiabatic path-integral molecular dynamics: Disordered Frenkel Kontorova models

2005

The spectral density of quantum mechanical Frenkel Kontorova chains moving in disordered, external potentials is investigated by means of path-integral molecular dynamics. If the second moment of the embedding potential is well defined (roughness exponent ), there is one regime in which the chain is pinned (large masses of chain particles) and one in which it is unpinned (small ). If the embedding potential can be classified as a random walk on large length scales ( ), then the chain is always pinned irrespective of the value of . For , two phonon-like branches appear in the spectra.

Reduced scaling in electronic structure calculations using Cholesky decompositions

2003

The small numerical rank of the two-electron integral matrix for large molecular systems and large basis sets was demonstrated. Though, the current implementation still requires some improvements on the calculations done in the inner most loop of the decomposition do not exploit the parsity in the Cholesky vectors. With respect to the practical applicability of the presented method an efficient approach to geometrical derivatives was imperative. Such an approach was obtained including certain derivative product functions and decomposing an expanded integral matrix.

QUASIPARTICLE CALCULATIONS FOR THE THREE-NUCLEON SYSTEM

1972

Publisher Summary This chapter discusses the quasiparticle calculations for the three-nucleon system. There are three methods for solving the integral equations for the three-body problem with local two-body potentials; one method consists of the direct solution of the Faddeev equations, and the other two methods make different use of the quasiparticle idea that is based on the splitting of the occurring two-body potentials into a sum of separable terms and a rest potential. The chapter describes the term “form factors” and “coupling strengths.” A similar splitting is obtained for the T-matrices Tγ. With its help, it is possible to transform the Faddeev-type equations for the three-body tra…

Statistical Mechanics of the Sine-Gordon Equation

1986

We give two fundamental methods for evaluation of classical free energies of all the integrable models admitting soliton solutions; the sine-Gordon equation is one example. Periodic boundary conditions impose integral equations for allowed phonon and soliton momenta. From these, generalized Bethe-Ansatz and functional-integration methods using action-angle variables follow. Results for free energies coincide, and coincide with those that we find by transfer-integral methods. Extension to the quantum case, and quantum Bethe Ansatz, on the lines to be reported elsewhere for the sinh-Gordon equation, is indicated.

Measuring the black hole spin direction in 3D Cartesian numerical relativity simulations

2015

We show that the so-called flat-space rotational Killing vector method for measuring the Cartesian components of a black hole spin can be derived from the surface integral of Weinberg's pseudotensor over the apparent horizon surface when using Gaussian normal coordinates in the integration. Moreover, the integration of the pseudotensor in this gauge yields the Komar angular momentum integral in a foliation adapted to the axisymmetry of the spacetime. As a result, the method does not explicitly depend on the evolved lapse $\ensuremath{\alpha}$ and shift ${\ensuremath{\beta}}^{i}$ on the respective time slice, as they are fixed to Gaussian normal coordinates while leaving the coordinate label…