A survey of spinning test particle orbits in Kerr spacetime

We investigate the dynamics of the Papapetrou equations in Kerr spacetime. These equations provide a model for the motion of a relativistic spinning test particle orbiting a rotating (Kerr) black hole. We perform a thorough parameter space search for signs of chaotic dynamics by calculating the Lyapunov exponents for a large variety of initial conditions. We find that the Papapetrou equations admit many chaotic solutions, with the strongest chaos occurring in the case of eccentric orbits with pericenters close to the limit of stability against plunge into a maximally spinning Kerr black hole. Despite the presence of these chaotic solutions, we show that physically realistic solutions to the Papapetrou equations are not chaotic; in all cases, the chaotic solutions either do not correspond to realistic astrophysical systems, or involve a breakdown of the test-particle approximation leading to the Papapetrou equations (or both). As a result, the gravitational radiation from bodies spiraling into much more massive black holes (as detectable, for example, by LISA, the Laser Interferometer Space Antenna) should not exhibit any signs of chaos.Comment: Submitted to Phys. Rev. D. Follow-up to gr-qc/0210042. Figures are low-resolution in order to satisfy archive size constraints; a high-resolution version is available at http://www.michaelhartl.com/papers

Error threshold in the evolution of diploid organisms

The effects of error propagation in the reproduction of diploid organisms are studied within the populational genetics framework of the quasispecies model. The dependence of the error threshold on the dominance parameter is fully investigated. In particular, it is shown that dominance can protect the wild-type alleles from the error catastrophe. The analysis is restricted to a diploid analogue of the single-peaked landscape.Comment: 9 pages, 4 Postscript figures. Submitted to J. Phy. A: Mat. and Ge

The roles of \u3ci\u3ecis\u3c/i\u3e- and \u3ci\u3etrans\u3c/i\u3e-regulation in the evolution of regulatory incompatibilities and sexually dimorphic gene expression

Evolutionary changes in gene expression underlie many aspects of phenotypic diversity within and among species. Understanding the genetic basis for evolved changes in gene expression is therefore an important component of a comprehensive understanding of the genetic basis of phenotypic evolution. Using interspecific introgression hybrids, we examined the genetic basis for divergence in genome-wide patterns of gene expression between Drosophila simulans and Drosophila mauritiana. We find that cis-regulatory and trans-regulatory divergences differ significantly in patterns of genetic architecture and evolution. The effects of cis-regulatory divergence are approximately additive in heterozygotes, quantitatively different between males and females, and well predicted by expression differences between the two parental species. In contrast, the effects of trans-regulatory divergence are associated with largely dominant introgressed alleles, have similar effects in the two sexes, and generate expression levels in hybrids outside the range of expression in both parental species. Although the effects of introgressed trans-regulatory alleles are similar in males and females, expression levels of the genes they regulate are sexually dimorphic between the parental D. simulans and D. mauritiana strains, suggesting that purespecies genotypes carry unlinked modifier alleles that increase sexual dimorphism in expression. Our results suggest that independent effects of cis-regulatory substitutions in males and females may favor their role in the evolution of sexually dimorphic phenotypes, and that trans-regulatory divergence is an important source of regulatory incompatibilities

SORLA-mediated trafficking of TrkB enhances the response of neurons to BDNF

Stimulation of neurons with brain-derived neurotrophic factor (BDNF) results in robust induction of SORLA, an intracellular sorting receptor of the VPS10P domain receptor gene family. However, the relevance of SORLA for BDNF-induced neuronal responses has not previously been investigated. We now demonstrate that SORLA is a sorting factor for the tropomyosin-related kinase receptor B (TrkB) that facilitates trafficking of this BDNF receptor between synaptic plasma membranes, post-synaptic densities, and cell soma, a step critical for neuronal signal transduction. Loss of SORLA expression results in impaired neuritic transport of TrkB and in blunted response to BDNF in primary neurons; and it aggravates neuromotoric deficits caused by low BDNF activity in a mouse model of Huntington's disease. Thus, our studies revealed a key role for SORLA in mediating BDNF trophic signaling by regulating the intracellular location of TrkB

Temporal and dimensional effects in evolutionary graph theory

The spread in time of a mutation through a population is studied analytically and computationally in fully-connected networks and on spatial lattices. The time, t_*, for a favourable mutation to dominate scales with population size N as N^{(D+1)/D} in D-dimensional hypercubic lattices and as N ln N in fully-connected graphs. It is shown that the surface of the interface between mutants and non-mutants is crucial in predicting the dynamics of the system. Network topology has a significant effect on the equilibrium fitness of a simple population model incorporating multiple mutations and sexual reproduction. Includes supplementary information.Comment: 6 pages, 4 figures Replaced after final round of peer revie

Replica symmetry breaking in an adiabatic spin-glass model of adaptive evolution

We study evolutionary canalization using a spin-glass model with replica theory, where spins and their interactions are dynamic variables whose configurations correspond to phenotypes and genotypes, respectively. The spins are updated under temperature T_S, and the genotypes evolve under temperature T_J, according to the evolutionary fitness. It is found that adaptation occurs at T_S < T_S^{RS}, and a replica symmetric phase emerges at T_S^{RSB} < T_S < T_S^{RS}. The replica symmetric phase implies canalization, and replica symmetry breaking at lower temperatures indicates loss of robustness.Comment: 5pages, 2 figure

General-Relativistic Curvature of Pulsar Vortex Structure

The motion of a neutron superfluid condensate in a pulsar is studied. Several theorems of general-relativistic hydrodynamics are proved for a superfluid. The average density distribution of vortex lines in pulsars and their general-relativistic curvature are derived.Comment: 18 pages, 1 figure

A Population Genetic Approach to the Quasispecies Model

A population genetics formulation of Eigen's molecular quasispecies model is proposed and several simple replication landscapes are investigated analytically. Our results show a remarcable similarity to those obtained with the original kinetics formulation of the quasispecies model. However, due to the simplicity of our approach, the space of the parameters that define the model can be explored. In particular, for the simgle-sharp-peak landscape our analysis yelds some interesting predictions such as the existence of a maximum peak height and a mini- mum molecule length for the onset of the error threshold transition.Comment: 16 pages, 4 Postscript figures. Submited to Phy. Rev.

Stability of circular orbits of spinning particles in Schwarzschild-like space-times

Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being constant and normal to the plane of orbits. For the de Sitter background the orbits are always stable with particle velocity and momentum being co-linear along them. The world-line deviation equations for particles of the same spin-to-mass ratios are solved and the resulting deviation vectors are used to study the stability of orbits. It is shown that the orbits are stable against radial perturbations. The general criterion for stability against normal perturbations is obtained. Explicit calculations are performed in the case of the Schwarzschild space-time leading to the conclusion that the orbits are stable.Comment: eps figures, submitted to General Relativity and Gravitatio