A. E. Carlsson

Beyond Pair Potentials in Elemental Transition Metals and Semiconductors

Publisher Summary The chapter presents a review that describes the main approaches to transcending pair potential descriptions of transition metals and semiconductors. The chapter discusses the technologically important materials, because the desire to understand their materials properties has led to a large number of atomistic simulation studies, and, consequently, a great need for simplified energy functionals. At first glance, the bonding mechanisms in these two classes of materials seem to be quite distinct. One naively thinks of metallic atoms as closely packed hard balls with relatively weak attractive forces. In semiconductors, one generally focuses on strong bonds with charge accumulations between the atoms. The open structures of diamond structure semiconductors immediately suggest the presence of strong angular forces; if radial pair forces dominated, one would expect that the energy could be lowered by filling in the holes in the structure, thereby increasing the coordination number. In contrast, the closely packed structures of transition metals are at least consistent with a description based on radial forces. However, to obtain a more sophisticated picture of transition metals, including structural energy differences, the chapter mentions that angular forces are necessary, Furthermore, much of the understanding that has recently been gained of transition metal bonding is also applicable to semiconductors, and is being incorporated in the most recent semiconductor energy functionals.

Growth Velocities of Branched Actin Networks

The growth of an actin network against an obstacle that stimulates branching locally is studied using several variants of a kinetic rate model based on the orientation-dependent number density of filaments. The model emphasizes the effects of branching and capping on the density of free filament ends. The variants differ in their treatment of side versus end branching and dimensionality, and assume that new branches are generated by existing branches (autocatalytic behavior) or independently of existing branches (nucleation behavior). In autocatalytic models, the network growth velocity is rigorously independent of the opposing force exerted by the obstacle, and the network density is proportional to the force. The dependence of the growth velocity on the branching and capping rates is evaluated by a numerical solution of the rate equations. In side-branching models, the growth velocity drops gradually to zero with decreasing branching rate, while in end-branching models the drop is abrupt. As the capping rate goes to zero, it is found that the behavior of the velocity is sensitive to the thickness of the branching region. Experiments are proposed for using these results to shed light on the nature of the branching process.

An ab initio pair potential applied to metals

Abstract An exact procedure is derived for inverting the cohesive energy of an isostructural one-component system as a function of volume to find the radial pair potential that will reproduce the cohesive energy function. Pair potentials for K, Cu and Mo constructed in this way are compared with standard pair potentials from the literature, and used to calculate elastic properties.

Exchange mechanisms in diluted magnetic semiconductors

Abstract The hierarchy of Mn-Mn exchange mechanisms in Cd 1− x Mn x Te and related alloys is calculated perturbatively using a generalized Anderson Hamiltonian. Realistic parameters are obtained from experimental band structure information and local spin density ASW calculations. Super-exchange is found to dominate at nearest and next-neighbor distances, in agreement with the observed antiferromagnetic coupling. Calculated Cd 1− x Mn x Te exchange constants and predicted chemical trends are in good agreement with experiment and with ASW total energy calculations.

Dendritic actin filament nucleation causes traveling waves and patches.

The polymerization of actin via branching at a cell membrane containing nucleation-promoting factors is simulated using a stochastic-growth methodology. The polymerized-actin distribution displays three types of behavior: (a) traveling waves, (b) moving patches, and (c) random fluctuations. Increasing actin concentration causes a transition from patches to waves. The waves and patches move by a treadmilling mechanism not involving myosin II. The effects of downregulation of key proteins on actin wave behavior are evaluated.

Actin Dynamics: From Nanoscale to Microscale

The dynamic nature of actin in cells manifests itself constantly. Polymerization near the cell edge is balanced by depolymerization in the interior, externally induced actin polymerization is followed by depolymerization, and spontaneous oscillations of actin at the cell periphery are frequently seen. I discuss how mathematical modeling relates quantitative measures of actin dynamics to the rates of underlying molecular level processes. The dynamic properties addressed include the rate of actin assembly at the leading edge of a moving cell, the disassembly rates of intracellular actin networks, the polymerization time course in externally stimulated cells, and spontaneous spatiotemporal patterns formed by actin. Although several aspects of actin assembly have been clarified by increasingly sophisticated models, our understanding of rapid actin disassembly is limited, and the origins of nonmonotonic features in externally stimulated actin polymerization remain unclear. Theory has generated several concrete, testable hypotheses for the origins of spontaneous actin waves and cell-edge oscillations. The development and use of more biomimetic systems applicable to the geometry of a cell will be key to obtaining a quantitative understanding of actin dynamics in cells.

Regimes of wave type patterning driven by refractory actin feedback: transition from static polarization to dynamic wave behaviour.

Patterns of waves, patches, and peaks of actin are observed experimentally in many living cells. Models of this phenomenon have been based on the interplay between filamentous actin (F-actin) and its nucleation promoting factors (NPFs) that activate the Arp2/3 complex. Here we present an alternative biologically-motivated model for F-actin-NPF interaction based on properties of GTPases acting as NPFs. GTPases (such as Cdc42, Rac) are known to promote actin nucleation, and to have active membrane-bound and inactive cytosolic forms. The model is a natural extension of a previous mathematical mini-model of small GTPases that generates static cell polarization. Like other modellers, we assume that F-actin negative feedback shapes the observed patterns by suppressing the trailing edge of NPF-generated wave-fronts, hence localizing the activity spatially. We find that our NPF-actin model generates a rich set of behaviours, spanning a transition from static polarization to single pulses, reflecting waves, wave trains, and oscillations localized at the cell edge. The model is developed with simplicity in mind to investigate the interaction between nucleation promoting factor kinetics and negative feedback. It explains distinct types of pattern initiation mechanisms, and identifies parameter regimes corresponding to distinct behaviours. We show that weak actin feedback yields static patterning, moderate feedback yields dynamical behaviour such as travelling waves, and strong feedback can lead to wave trains or total suppression of patterning. We use a recently introduced nonlinear bifurcation analysis to explore the parameter space of this model and predict its behaviour with simulations validating those results.

Quantitative Analysis of Actin Patch Movement in Yeast

To investigate the mechanism of cortical actin patch movement in yeast, we implement a method for computer tracking the motion of the patches. Digital images from fluorescence microscope movies of living cells are fed into an image-processing program, which generates two-dimensional patch coordinates in the plane of focus for each movie frame via an algorithm based on detection of rapid intensity variations. The patch coordinates in neighboring frames are connected by a minimum-distance algorithm. The method is used to analyze control cells and cells treated with the actin-depolymerizing agent latrunculin. The motion of the patches in both cases, as analyzed by mean-square patch displacements, is found to be a random walk on average, with a much lower diffusion coefficient for the latrunculin-treated cells. The mean-squared patch travel distances for all of the latrunculin-treated cells are lower than those for all of the control cells. The patches move independently of one another. We develop a quantitative criterion for the presence of directed motion, and show that numerous patches in the control cells display directed motion to a very high degree of certainty. A small number of patches in the latrunculin-treated cells display directed motion.

First-principles calculations of the theoretical tensile strength of copper

Abstract Three ab initio calculations of the theoretical tensile strength of an ideal crystalline metal (f.c.c. Cu) are presented. The first two employ a full band-theoretic approach to compute the cohesive energy as a function of uniaxial lattice deformation. One of these is based on non-self-consistent KKR calculations using the muffin-tin approximation. The other uses the self-consistent augmented spherical wave (ASW) method. The third calculation is based on a new, non-empirical pair potential φ that can be expressed formally in terms of the cohesive energy E and can be evaluated if E is known as a function of the nearest-neighbour distance r 1. The theoretical tensile strengths obtained using these three approaches differ by about 40%, but all are consistent with available measurements.

Significance of non-central forces in atomistic studies of grain boundaries in bcc transition metals

Abstract The effects of non-central forces in atomistic studies of grain boundaries in molybdenum and tungsten, the transition metals with half-filled d-band, are investigated. For this purpose we have used two different types of potential which include different number of moments of the local density of electronic states when evaluating the total energy: the central-force Finnis-Sinclair potentials which include the scalar second moment and the potentials constructed by Carlsson which include the fourth and the matrix second moments. The energy terms associated with these two moments represent non-central interactions and assure that the bcc-fcc structural energy difference is reproduced with good accuracy. For the three boundaries studied, the non-central forces have been found to be very important in determining the lowest energy structures. In particular, the energy differences between multiple structures depend on specific orientations and geometries of the atomic clusters at and near the interface. ...