We consider a simple Maier-Saupe statistical model with the inclusion of disorder degrees of freedom to mimic the phase diagram of a mixture of rod-like and disc-like molecules. A quenched distribution of shapes leads to the existence of a stable biaxial nematic phase, in qualitative agreement with experimental findings for some ternary lyotropic liquid mixtures. An annealed distribution, however, which is more adequate to liquid mixtures, precludes the stability of this biaxial phase. We then use a two-temperature formalism, and assume a separation of relaxation times, to show that a partial degree of annealing is already sufficient to stabilize a biaxial nematic structure.Quenched and annealed degrees of freedom of statistical systems are known to produce phase diagrams with a number of distinct features [1]. The ferromagnetic site-diluted Ising model provides an example of a continuous transition, in the quenched case, which turns into a first-order boundary beyond a certain tricritical point, if we consider thermalized site dilution [2]. Disordered degrees of freedom in solid compounds, as random magnets and spin-glasses, are examples of quenched disorder, which lead to well-known problems related to averages of sets of disordered free energies. In liquid systems, however, relaxation times are shorter, and the simpler problems of annealed disorder are more relevant from the physical perspective. In this paper, we show that distinctions between quenched and annealed degrees 1

Insects in the order Hymenoptera (bees, wasps and ants) present an haplodiploid system of sexual determination in which fertilized eggs become females and unfertilized eggs males. Under single locus complementary sex-determination (sl-CSD) system, the sex of a specimen depends on the alleles at a single locus: when diploid, an individual will be a female if heterozygous and male if homozygous. Significant diploid male (DM) production may drive a population to an extinction scenario called "diploid male vortex". We aimed at studying the dynamics of populations of a sl-CSD organism under several combinations of two parameters: male flight abilities and number of sexual alleles. In these simulations, we evaluated the frequency of DM and a genetic diversity measure over 10,000 generations. The number of sexual alleles varied from 10 to 100 and, at each generation, a male offspring might fly to another random site within a varying radius R. Two main results emerge from our simulations: (i) the number of DM depends more on male flight radius than on the number of alleles; (ii) in large geographic regions, the effect of males flight radius on the allelic diversity turns out much less pronounced than in small regions. In other words, small regions where inbreeding normally appears recover genetic diversity due to large flight radii. These results may be particularly relevant when considering the population dynamics of species with increasingly limited dispersal ability (e.g., forest-dependent species of euglossine bees in fragmented landscapes).

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results.

In this manuscript, a very simple experiment was mounted to explore the fractal dimension of a popcorn grain before (popcorn grains) and after (popcorn itself) the popping process.

Sexually reproducing populations with a small number of individuals may go extinct by stochastic fluctuations in sex determination, causing all their members to become male or female in a generation. In this work we calculate the time to extinction of isolated populations with fixed number N of individuals that are updated according to the Moran birth and death process. At each time step, one individual is randomly selected and replaced by its offspring resulting from mating with another individual of the opposite sex; the offspring can be male or female with equal probability. A set of N time steps is called a generation, the average time it takes for the entire population to be replaced. The number k of females fluctuates in time, similarly to a random walk, and extinction, which is the only asymptotic possibility, occurs when k=0 or k=N. We show that it takes only one generation for an arbitrary initial distribution of males and females to approach the binomial distribution. This distribution, however, is unstable and the population eventually goes extinct in 2(N)/N generations. We also discuss the robustness of these results against bias in the determination of the sex of the offspring, a characteristic promoted by infection by the bacteria Wolbachia in some arthropod species or by temperature in reptiles.