Structure-dependent Coefficient Research Articles

Full-potential KKR within the removed-sphere method: A practical and accurate solution to the Poisson equation

An efficient and accurate generalization of the removed-sphere method (RSM) to solve the Poisson equation for total charge density in a solid with space-filling convex Voronoi polyhedra (VPs) and any symmetry is presented. The generalized RSM avoids the use of multipoles and VP shape functions for cellular integrals, which have associated ill-convergent large, double-internal $L$ sums in spherical-harmonic expansions, so that fast convergence in single-$L$ sums is reached. Our RSM adopts full Ewald formulation to work for all configurations or when symmetry breaking occurs, such as for atomic displacements or elastic constant calculations. The structure-dependent coefficients ${A}_{L}$ that define RSM can be calculated once for a fixed structure and speed up the whole self-consistent-field procedure. The accuracy and rapid convergence properties are confirmed using two analytic models, including the Coulomb potential and energy. We then implement the full-potential RSM using the Green's function Korringa-Kohn-Rostoker (KKR) method for real applications and compare the results with other first-principle methods and experimental data, showing that they are equally as accurate.

An Unusual Damped Stability Property and its Remedy for an Integration Method

An unusual stability property is found for a structure-dependent integration method since it exhibits a different nonlinearity interval of unconditional stability for zero and nonzero damping. Although it is unconditionally stable for the systems of stiffness softening and invariant as well as most systems of stiffness hardening, an unstable solution that is unexpected is obtained as it is applied to solve damped stiffness hardening systems. It is found herein that a nonlinearity interval of unconditional stability for a structure-dependent method may be drastically shrunk for nonzero damping when compared to zero damping. In fact, it will become conditionally stable for any damped stiffness hardening systems. This might significantly restrict its applications. An effective scheme is proposed to surmount this difficulty by introducing a stability factor into the structure-dependent coefficients of the integration method. This factor can effectively amplify the nonlinearity intervals of unconditional stability for structure-dependent methods. A large stability factor will result in a large nonlinearity interval of unconditional stability. However, it also introduces more period distortion. Consequently, a stability factor must be appropriately selected for accurate integration. After choosing a proper stability factor, a structure-dependent method can be widely and easily applied to solve general structural dynamic problems.

Relativistic, model-independent determination of electromagnetic finite-size effects beyond the pointlike approximation

We present a relativistic and model-independent method to derive structure-dependent electromagnetic finite-size effects. This is a systematic procedure, particularly well-suited for automation, which works at arbitrarily high orders in the large-volume expansion. Structure-dependent coefficients appear as zero-momentum derivatives of physical form factors which can be obtained through experimental measurements or auxiliary lattice calculations. As an application we derive the electromagnetic finite-size effects on the pseudoscalar meson mass and leptonic decay amplitude, through orders $\mathcal{O}(1/{L}^{3})$ and $\mathcal{O}(1/{L}^{2})$, respectively. The structure dependence appears at this order through the meson charge radius and the real radiative leptonic amplitude, which are known experimentally.

A time-dependent non-Newtonian extension of a 1D blood flow model

Blood pulsatility, aneurysms, stenoses and general low shear stress hemodynamics enhance non-Newtonian blood effects which generate local changes in the space-time evolution of the blood pressure, flow rate and cross-sectional area of elastic vessels. Even though these local changes are known to cause global unexpected hemodynamical behaviors, all one-dimensional (1D) blood flow models are built under Newtonian fluid hypothesis.In this work, we present a time-dependent non-Newtonian extension of a 1D blood flow model, able to describe local space-time variations of the viscous behavior of blood. The rheological model is based on a simplified Maxwell viscoelastic equation for the shear stress with structure dependent coefficients. We compare the numerical predictions of the 1D non-Newtonian model to experimental rheological data available in the literature. Specifically, we explore four well documented shear stress protocols and we show that the results predicted by the 1D non-Newtonian model in a single artery accurately compare, both qualitatively and quantitatively, to the steady and unsteady shear stresses measured experimentally. We then use the 1D non-Newtonian model to compute the flow in idealized healthy and pathological symmetric and asymmetric networks of increasing size. We show that aggregation occurs in such networks occurs, leading to non-Newtonian blood behaviors especially in the presence of pathologies.This non-Newtonian extension of a 1D blood flow model will be useful in the future to improve our understanding of the large-scale hemodynamics in micro- and macro-circulation networks.

Spin-orbit interactions in inversion-asymmetric two-dimensional hole systems: A variational analysis

We present an in-depth study of the spin-orbit (SO) interactions occurring in inversion-asymmetric two-dimensional hole gases at semiconductor heterointerfaces. We focus on common semiconductors such as GaAs, InAs, InSb, Ge, and Si. We develop a semi-analytical variational method to quantify SO interactions, accounting for both structure inversion asymmetry (SIA) and bulk inversion asymmetry (BIA). Under certain circumstances, using the Schrieffer-Wolff (SW) transformation, the dispersion of the ground state heavy hole subbands can be written as $E(k) = A k^2 - B k^4 \pm C k^3$ where $A$, $B$, and $C$ are material- and structure-dependent coefficients. We provide a simple method of calculating the parameters $A$, $B$, and $C$, yet demonstrate that the simple SW approximation leading to a SIA (Rashba) spin splitting $\propto k^3$ frequently breaks down. We determine the parameter regimes at which this happens for the materials above and discuss a convenient semi-analytical method to obtain the correct spin splitting, effective masses, Fermi level, and subband occupancy, together with their dependence on the charge density, dopant type, and dopant concentration for both inversion and accumulation layers. Our results are in good agreement with fully numerical calculations as well as with experimental findings. They suggest that a naive application of the simple cubic Rashba model is of limited use in common heterostructures, as well as quantum dots. Finally, we find that for the single heterojunctions studied here the magnitudes of BIA terms are always much smaller than those of SIA terms.

Generalized Polarizabilities and the Chiral Structure of the Nucleon

We are studying the electron scattering process e p to e' p' gamma in order to obtain information on the genuine virtual Compton scattering (VCS) process gamma^* N to gamma N. In addition to the two kinematical variables of real Compton scattering, e.g. the scattering angle theta and the energy omega' of the outgoing photon, the invariant amplitude for VCS depends on a third kinematical variable, which we choose as the absolute value of the three-momentum transfer to the nucleon. The structure-dependent coefficients in the VCS amplitude therefore acquire a momentum dependence and are termed ``generalized polarizabilities'' of the nucleon in analogy to real Compton scattering. Utilizing the heavy baryon formalism of chiral perturbation theory we present predictions for the momentum dependence of the ``generalized polarizabilities'' and discuss the VCS response functions to be measured in the scheduled electron scattering experiments.

POLARIZATION OF RECTANGULAR ARRAYS OF SPHERES IN A POTENTIAL FLOW

Abstract General theorems are derived, relating the impulse, polarization (internal dipole moment) and average velocity field for a dispersion of spheres in a potential flow. A constitutive equation is developed and a structure-dependent coefficient, λ, defined. A first approximation to λ, valid for low concentrations of spheres, is obtained and evaluated for rectangular arrays, using image methods.

Long time tail in the diffusion of a spherical polymer

We study the velocity autocorrelation function for the diffusion of a spherical macromolecule in solution. The diffusion is described by a generalized Langevin equation with memory character derived previously from fluctuation theory applied to the Debye-Bueche-Brinkman equation which describes the polymer-fluid interaction. The long time behaviour of the velocity autocorrelation function is obtained by establishing a low frequency expansion for the drag coefficient ζ(ω). To derive this expansion we prove a number of analyticity properties of ζ(ω). The longest lived contribution to the velocity autocorrelation function goes as t -3 2 as first discovered by Alder and Wainwright. We also obtain the first correction term of order t -5 2 which depends explicitly on the polymer structure. By use of a generalization of the Lorentz reciprocity theorem we show that the coefficient of this t -5 2 term is given in terms of the polymer mass and the two structure dependent coefficients that enter the static Faxén theorem for the total force on the polymer.