Birger Bergersen

Equilibrium configurations of particles on a sphere : the case of logarithmic interactions

We consider a system of N particles which are confined to the surface of a sphere and which interact via a potential that depends logarithmically on their separation. The ground-state properties of this system are investigated for N=2 to 65. Unlike the case of Coulomb interactions this system has ground-state configurations with zero dipole moment for all N. The thermal properties of a selected set of systems in the range N=2 to 500 are determined by Monte Carlo simulation. The results are compared with analytical calculations in the small- and large-N limits.

Motion of positrons in metals

In this review we discuss the different aspects of positron annihilation in metals that involve the dynamics of positron motion before annihilation. The emphasis is on the theory, but also some experimental evidence is quoted. The topics covered are: slowing down and thermalization, effective mass, temperature dependence of positron vacancy trapping, positron channeling, and escape of low energy positrons from metal surfaces.

Quantum diffusion of light interstitials in metals

Abstract A quantum theory of diffusion of self-trapped light interstitials in metals is presented. The theory encompasses both coherent and incoherent tunneling, but the approximation used neglects the dependence of the interstitial transfer matrix element on the vibrational state of the crystal. The coherent tunneling contribution is estimated by fitting the incoherent diffusion rate to experimental data for hydrogen and muon diffusion. It is predicted that coherent diffusion should be dominant below ∼ 80 K for H in Nb and below ∼ 190 K for μ + in Cu. Experimental verifications of these predictions would require high purity strain free samples and low concentrations of the diffusing species.

Positron trapping at dislocations in metals

Abstract The trapping rate of positrons at dislocations in metals, and its temperature dependence, are calculated. Two different trapping processes, with the excess energy absorbed in either electron-hole pair formation or by phonon creation, are considered and the former is found to be the most important. An extension of the theory to include depletion of the positron density around the dislocations in a diffusion approximation is included. The trapping is found to be transition limited if the temperature is low or the trap potential shallow. At room temperature diffusion is important for deep traps.

First passage times of driven DNA hairpin unzipping

We model the dynamics of voltage-driven transport of DNA hairpins through transmembrane channels. A two-dimensional stochastic model of the DNA translocation process is fit to the measurements of Mathé, who pulled self-hybridized DNA hairpins through lipid-embedded alpha-hemolysin channels. As the channel was too narrow to accommodate hybridized DNA, dehybridization of the hairpin became the rate-limiting step of the transport process. We show that the mean first passage time versus voltage curve for the escape of the DNA from the transmembrane channel can be divided into two regions: (1) a low-voltage region where the DNA slides out of the pore in reverse and without undergoing significant dehybridization, and (2) a region where the DNA dehybridizes under the influence of the applied voltage and translocates across the membrane.

Survival and Extinction in Cyclic and Neutral Three-Species Systems

Abstract:We study the ABC model ( A + B↦2B, B + C↦2C, C + A↦2A), and its counterpart: the three-component neutral drift model ( A + B↦2A or 2B, B + C↦2B or 2C, C + A↦2C or 2A.) In the former case, the mean-field approximation exhibits cyclic behaviour with an amplitude determined by the initial condition. When stochastic phenomena are taken into account the amplitude of oscillations will drift and eventually one and then two of the three species will become extinct. The second model remains stationary for all initial conditions in the mean-field approximation, and drifts when stochastic phenomena are considered. We analyzed the distribution of first extinction times of both models by simulations of the master equation, and from the point of view of the Fokker-Planck equation. Survival probability vs. time plots suggest an exponential decay. For the neutral model the extinction rate is inversely proportional to the system size, while the cyclic model exhibits anomalous behaviour for small system sizes. In the large system size limit the extinction times for both models will be the same. This result is compatible with the smallest eigenvalue obtained from the numerical solution of the Fokker-Planck equation. We also studied the behaviour of the probability distribution. The exponential decay is found to be robust against certain changes, such as the three reactions having different rates.

Random bonds and random fields in two-dimensional orientational glasses

Two-dimensional orientational glasses are studied using Monte Carlo simulation. The glasses are modelled using rigid rotors, with fixed positional distribution, chosen using either a random parking algorithm, or by randomly diluting a triangular lattice. The glass-like behaviour has its origin in the coupling, inherent in all anisotropic intermolecular pair potentials, between the rotational degrees of freedom and the quenched random positions. The authors show how this coupling can be broken down into random bond terms that lead to spin glass-like behaviour and random field terms that favour single-particle freezing. The authors study in detail the quadrupolar interaction and illustrate this behaviour by an ad hoc variation of the relative strength of the two types of term. For small random field a rich ground-state structure is observed, with the existence of many nonsymmetry related equivalent orientational states. At finite temperature they observe two temperature regimes for the spin glass order parameter. There is a field dependent regime giving some spin glass-like order out to high temperatures, while at low temperatures a cross-over to a field independent regime is observed, which the authors interpret as cooperative freezing to a low-temperature disordered phase. Comparison is made between their results and experiment, as well as with theoretical models for spin and orientational glasses. Finally they investigate the time dependence of the cooperative freezing, and find behaviour consistent with dynamical freezing, and loss of ergodicity on a finite observation time.

Impurity band states in SI(P)

Abstract A comparison is made between calculated impurity band densities of state in Si(P) for donor concentrations below that of the semiconductor-to-metal transition and experimental results obtained from photoluminescence spectra after subtracting an electron-hole droplet line. The theoretical results were obtained within the large interaction limit of the Hubbard model, assuming the impurities to be randomly distributed. The density of states was computed from cumulants appropriate to the low and high impurity density limit.

Self-organized ruptures in an elastic medium: a possible model for earthquakes

The authors propose a new discretization scheme for the elastic stress field. Local ruptures give rise to a stress redistribution which can be represented by double couples. The model is applied to earthquake simulation. Computational efficiency is achieved by the use of lattice Green functions. The model allows inclusion of phenomenological features such as annealing and static fatigue.

Crossover behaviour of 3-species systems with mutations or migrations

We study the ABC model in the cyclic competition (A+B → 2B, B+C → 2C, C+A → 2A) and the neutral drift (A+B → 2B or 2A, B+C → 2C or 2B, C+A → 2A or 2C) versions, with mutations and migrations introduced into the model. When stochastic phenomena are taken into account, there are three distinct regimes in the model. (i) In the “fixation” regime, the first extinction time scales with the system size N and has an exponential distribution, with an exponent that depends on the mutation/migration probability per particle μ. (ii) In the “diversity” regime, the order parameter remains nonzero for very long times, and becomes zero only rarely, almost never for large system sizes. (iii) In the critical regime, the first passage time for crossing the boundary (one of the populations becoming zero) has a power law distribution with exponent −1. The critical mutation/migration probability scales with system size as N−1. The transition corresponds to a crossover from diffusive behaviour to Gaussian fluctuations about a stable solution. The analytical results are checked against computer simulations of the model.