Directed Random Walk on the Lattices of Genus Two

The object of the present investigation is an ensemble of self-avoiding and directed graphs belonging to eight-branching Cayley tree (Bethe lattice) generated by the Fucsian group of a Riemann surface of genus two and embedded in the Pincar\'e unit disk. We consider two-parametric lattices and calculate the multifractal scaling exponents for the moments of the graph lengths distribution as functions of these parameters. We show the results of numerical and statistical computations, where the latter are based on a random walk model.Comment: 17 pages, 8 figure

Supersymmetry of FRW barotropic cosmologies

Barotropic FRW cosmologies are presented from the standpoint of nonrelativistic supersymmetry. First, we reduce the barotropic FRW system of differential equations to simple harmonic oscillator differential equations. Employing the factorization procedure, the solutions of the latter equations are divided into the two classes of bosonic (nonsingular) and fermionic (singular) cosmological solutions. We next introduce a coupling parameter denoted by K between the two classes of solutions and obtain barotropic cosmologies with dissipative features acting on the scale factors and spatial curvature of the universe. The K-extended FRW equations in comoving time are presented in explicit form in the low coupling regime. The standard barotropic FRW cosmologies correspond to the dissipationless limit K =0Comment: 6 page

Genetic distance predicts trait differentiation at the subpopulation but not the individual level in eelgrass, Zostera marina.

Ecological studies often assume that genetically similar individuals will be more similar in phenotypic traits, such that genetic diversity can serve as a proxy for trait diversity. Here, we explicitly test the relationship between genetic relatedness and trait distance using 40 eelgrass (Zostera marina) genotypes from five sites within Bodega Harbor, CA. We measured traits related to nutrient uptake, morphology, biomass and growth, photosynthesis, and chemical deterrents for all genotypes. We used these trait measurements to calculate a multivariate pairwise trait distance for all possible genotype combinations. We then estimated pairwise relatedness from 11 microsatellite markers. We found significant trait variation among genotypes for nearly every measured trait; however, there was no evidence of a significant correlation between pairwise genetic relatedness and multivariate trait distance among individuals. However, at the subpopulation level (sites within a harbor), genetic (FST) and trait differentiation were positively correlated. Our work suggests that pairwise relatedness estimated from neutral marker loci is a poor proxy for trait differentiation between individual genotypes. It remains to be seen whether genomewide measures of genetic differentiation or easily measured "master" traits (like body size) might provide good predictions of overall trait differentiation

Ac hopping conduction at extreme disorder takes place on the percolating cluster

Simulations of the random barrier model show that ac currents at extreme disorder are carried almost entirely by the percolating cluster slightly above threshold; thus contradicting traditional theories contributions from isolated low-activation-energy clusters are negligible. The effective medium approximation in conjunction with the Alexander-Orbach conjecture leads to an excellent analytical fit to the universal ac conductivity with no nontrivial fitting parameters

Anomalous biased diffusion in a randomly layered medium

We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The long-time behavior of the particle position is studied in the frame of a continuous-time random walk on a semi-infinite one-dimensional lattice. We formulate the conditions for anomalous diffusion, derive the diffusion laws and analyze their dependence on the particle mass and the distribution of the random force.Comment: 19 pages, 1 figur

The effects of disturbance threat on leaf-cutting ant colonies: a laboratory study

The flexibility of organisms to respond plastically to their environment is fundamental to their fitness and evolutionary success. Social insects provide some of the most impressive examples of plasticity, with individuals exhibiting behavioural and sometimes morphological adaptations for their specific roles in the colony, such as large soldiers for nest defence. However, with the exception of the honey bee model organism, there has been little investigation of the nature and effects of environmental stimuli thought to instigate alternative phenotypes in social insects. Here we investigate the effect of repeated threat disturbance over a prolonged (17 month) period on both behavioural and morphological phenotypes, using phenotypically plastic leaf-cutting ants (Atta colombica) as a model system. We found a rapid impact of threat disturbance on the behavioural phenotype of individuals within threat-disturbed colonies becoming more aggressive, threat-responsive and phototactic within as little as two weeks. We found no effect of threat disturbance on morphological phenotypes, potentially because constraints such as resource limitation outweighed the benefit for colonies of producing larger individuals. The results suggest that plasticity in behavioural phenotypes can enable insect societies to respond to threats even when constraints prevent alteration of morphological phenotypes

Magneto-optical evidence of the percolation nature of the metal-insulator transition in the 2D electron system

We compare the results of the transport and time-resolved magneto-luminescence measurements in disordered 2D electron systems in GaAs-AlGaAs heterostructures in the extreme quantum limit, in particular, in the vicinity of the metal-insulator transition (MIT). At filling factors $\nu <1$, the optical signal has two components: the single-rate exponentially decaying part attributed to a uniform liquid and a power-law long-living tail specific to a microscopically inhomogeneous state of electrons. We interprete this result as a separation of the 2D electron system into a liquid and localized phases, especially because the MIT occurs strikingly close to those filling factors where the liquid occupies ${1\over 2}$ of the sample area (the percollation threshold condition in two-component media).Comment: 5 pages RevTex + 4 fig., to appear in PRB, Rapid Com

Nonlinear physics of the ionosphere and LOIS/LOFAR

The ionosphere is the only large-scale plasma laboratory without walls that we have direct access to. From results obtained in systematic, repeatable experiments in this natural laboratory, where we can vary the stimulus and observe its response in a controlled, repeatable manner, we can draw conclusions on similar physical processes occurring naturally in the Earth's plasma environment as well as in parts of the plasma universe that are not easily accessible to direct probing. Of particular interest is electromagnetic turbulence excited in the ionosphere by beams of particles (photons, electrons) and its manifestation in terms of secondary radiation (electrostatic and electromagnetic waves), structure formation (solitons, cavitons, alfveons, striations), and the associated exchange of energy, linear momentum, and angular momentum. We present a new diagnostic technique, based on vector radio allowing the utilization of EM angular momentum (vorticity), to study plasma turbulence remotely.Comment: Six pages, two figures. To appear in Plasma Physics and Controlled Fusio

Scale-dependent variation in coral community similarity across sites, islands, and island groups

Community similarity is the proportion of species richness in a region that is shared on average among communities within that region. The slope of local richness (α diversity) regressed on regional richness (γ diversity) can serve as an index of community similarity across regions with different regional richness. We examined community similarity in corals at three spatial scales (among transects at a site, sites on an island, and islands within an island group) across a 10 000-km longitudinal diversity gradient in the west-central Pacific Ocean. When α diversity was regressed on γ diversity, the slopes, and thus community similarity, increased with scale (0.085, 0.261, and 0.407, respectively) because a greater proportion of γ diversity was subsumed within α diversity as scale increased. Using standard randomization methods, we also examined how community similarity differed between observed and randomized assemblages and how this difference was affected by spatial separation of species within habitat types and specialization of species to three habitat types (reef flats, crests, and slopes). If spatial separation within habitat types and/or habitat specialization (i.e., underdispersion) occurs, fewer species are shared among assemblages than the random expectation. When the locations of individual coral colonies were randomized within and among habitat types, community similarity was 46–47% higher than that for observed assemblages at all three scales. We predicted that spatial separation of coral species within habitat types should increase with scale due to dispersal/extinction dynamics in this insular system, but that specialization of species to different habitat types should not change because habitat differences do not change with scale. However, neither habitat specialization nor spatial separation within habitat types differed among scales. At the two larger scales, each accounted for 22–24% of the difference in community similarity between observed and randomized assemblages. At the smallest scale (transect–site), neither spatial separation within habitat types nor habitat specialization had significant effects on community similarity, probably due to the small size of transect samples. The results suggest that coral species can disperse among islands in an island group as easily as they can among sites on an island over time scales that are relevant to their establishment and persistence on reefs