Search results for "integral"
showing 10 items of 902 documents
Single amino acids in the lumenal loop domain influence the stability of the major light-harvesting chlorophyll a/b complex.
2004
The major light-harvesting complex of photosystem II (LHCIIb) is one of the most abundant integral membrane proteins. It greatly enhances the efficiency of photosynthesis in green plants by binding a large number of accessory pigments that absorb light energy and conduct it toward the photosynthetic reaction centers. Most of these pigments are associated with the three transmembrane and one amphiphilic alpha helices of the protein. Less is known about the significance of the loop domains connecting the alpha helices for pigment binding. Therefore, we randomly exchanged single amino acids in the lumenal loop domain of the bacterially expressed apoprotein Lhcb1 and then reconstituted the muta…
A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional
2012
Abstract We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.
Kirkwood–Buff integrals of finite systems
2018
The Kirkwood–Buff (KB) theory provides an important connection between microscopic density fluctuations in liquids and macroscopic properties. Recently, Krüger et al. derived equations for KB integrals for finite subvolumes embedded in a reservoir. Using molecular simulation of finite systems, KB integrals can be computed either from density fluctuations inside such subvolumes, or from integrals of radial distribution functions (RDFs). Here, based on the second approach, we establish a framework to compute KB integrals for subvolumes with arbitrary convex shapes. This requires a geometric function w(x) which depends on the shape of the subvolume, and the relative position inside the subvolu…
Discussion on triangle singularities in the Λb→J/ψK−p reaction
2016
We have analyzed the singularities of a triangle loop integral in detail and derived a formula for an easy evaluation of the triangle singularity on the physical boundary. It is applied to the ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{\ensuremath{-}}p$ process via ${\mathrm{\ensuremath{\Lambda}}}^{*}$-charmonium-proton intermediate states. Although the evaluation of absolute rates is not possible, we identify the ${\ensuremath{\chi}}_{c1}$ and the $\ensuremath{\psi}(2S)$ as the relatively most relevant states among all possible charmonia up to the $\ensuremath{\psi}(2S)$. The $\mathrm{\ensuremath{\Lambda}}(1890){\ensuremath{\chi}}_{c1}p$ loop is ver…
The electron self-energy in QED at two loops revisited
2018
We reconsider the two-loop electron self-energy in quantum electrodynamics. We present a modern calculation, where all relevant two-loop integrals are expressed in terms of iterated integrals of modular forms. As boundary points of the iterated integrals we consider the four cases $p^2=0$, $p^2=m^2$, $p^2=9m^2$ and $p^2=\infty$. The iterated integrals have $q$-expansions, which can be used for the numerical evaluation. We show that a truncation of the $q$-series to order ${\mathcal O}(q^{30})$ gives numerically for the finite part of the self-energy a relative precision better than $10^{-20}$ for all real values $p^2/m^2$.
SPI/INTEGRAL observation of the Cygnus region
2003
We present the analysis of the first observations of the Cygnus region by the SPI spectrometer onboard the Integral Gamma Ray Observatory, encompassing ${\sim}$ 600 ks of data. Three sources namely Cyg X-1, Cyg X-3 and EXO 2030+375 were clearly detected. Our data illustrate the temporal variability of Cyg X-1 in the energy range from 20 keV to 300 keV. The spectral analysis shows a remarkable stability of the Cyg X-1 spectra when averaged over one day timescale. The other goal of these observations is SPI inflight calibration and performance verification. The latest objective has been achieved as demonstrated by the results presented in this paper.
Application of the Pontryagin maximum principle to the time-optimal control in a chain of three spins with unequal couplings
2014
We solve a time-optimal control problem in a linear chain of three coupled spins 1/2 with unequal couplings. We apply the Pontryagin maximum principle and show that the associated Hamiltonian system is the one of a three-dimensional rigid body. We express the optimal control fields in terms of the components of the classical angular momentum of the rigid body. The optimal trajectories and the minimum control time are given in terms of elliptic functions and elliptic integrals.
On Fučík type spectrum for problem with integral nonlocal boundary condition
2019
The Fučík equation x' '= -μ x+λ x- with two types of nonlocal boundary value conditions are considered. The Fučík type spectrum for both problems are constructed. The visualization of the spectrum for some values of parameter γ is provided.
Analytical Solutions for the Self- and Mutual Inductances of Concentric Coplanar Disk Coils
2013
In this paper, closed-form solutions are presented for the self- and mutual inductances of disk coils which lie concentrically in a plane. The solutions are given as generalized hypergeometric functions which are closely related to elliptic integrals. The method used is a Legendre polynomial expansion of the inductance integral, which renders all integrations straightforward. Excellent numerical agreement with previous studies is obtained. An asymptotic formula for the approach to the ring coil limit is also derived and numerically validated. The methods presented here can be applied to noncoaxial and noncoplanar cases.
The Three-Body Problem
1972
The quantum mechanical three-body problem has been studied with increasing interest in the last decade. The main progress was achieved by deriving integral equations which are not only theoretically correct, but also practically applicable. Such equations allow us in particular to investigate, besides three-body bound states, the scattering of an elementary particle from a bound two-particle system.