Liouvillian first integrals for the planar Lotka-Volterra system

We complete the classication of all Lotka-Volterra systemsx=x(ax+by+c),y=y(Ax+By+C), having a Liouvillian first integral. In our classification we take into account the first integrals coming from the existence of exponential factors.     

Pavelka-style completeness in expansions of Łukasiewicz logic

An algebraic setting for the validity of Pavelka style completeness for some natural expansions of Łukasiewicz logic by new connectives and rational constants is given. This algebraic approach is based on the fact that the standard MV-algebra on the real segment [0, 1] is an injective MV-algebra. In particular the logics associated with MV-algebras with product and with divisible MV-algebras are considered. The author express his gratitude to Roberto Cignoli, for his advice during the preparation of this paper.     

Théorème de De Rham pour les variétés stratifées

Sans résumé     

Softening induced instability of a stretched cohesive granular layer

We report on a cellular pattern which spontaneously forms at the surface of a thin layer of a cohesive granular material submitted to in-plane stretching. We present a simple model in which the mechanism responsible of the instability is the "strain softening" exhibited by humid granular materials above a typical strain. Our analysis indicates that such a type of instability should be observed in any system presenting a negative stress sensitivity to strain perturbations.     

A simple osmotic stress test to predict boar sperm cryosurvival

This work was carried out to test whether viability of pig spermatozoa subjected to an osmotic test is correlated to sperm cryosurvival. Spermatozoa were cooled from 22 degrees C to -5 degrees C, aliquots were exposed to a series of hyperosmotic solutions (300-2100 mOsm/kg) for 15 min, immediately spermatozoa were re-warmed to 37 degrees C and isosmolarity was restored. Spermatozoa were cooled from 22 degrees C to -5 degrees C and one aliquot was exposed to the osmotic test while diluted spermatozoa were frozen-thawed. Plasma membrane-intact spermatozoa decreased as osmolarity increased (P < 0.0001), a further decreased (P < 0.0001) was observed when isotonicity was restored. Proportions of plasma membrane-intact and acrosome-intact cells from the osmotic test were no different from those after freeze-thawing: 36% vs. 35%, 80% vs. 80%, respectively. A significant correlation was found between the proportion of acrosome-intact cells after freeze-thawing and that from the osmotic test (r = 0.81, P <0.01). This test provides a useful and economical mean to predict in vitro boar sperm cryosurvival.     

Biotic patterns in LIGO recordings point to the creativity of gravitational interactions

The waves recorded by the Laser Interferometer Gravitational‐Wave Observatory (LIGO) presumably represent gravitational waves. Time series analyses revealed chaotic characteristics (nonperiodic oscillations, causal generation) and features of creativity that characterize Bios: increasing diversity (as contrasted to convergence to an attractor); novelty (lesser recurrence than randomized copies); and temporal complexity (a succession of different time‐limited patterns). Bios is also observed in quantum, cosmological, biological, and economic processes. Bios can be generated mathematically by bipolar feedback. Finding features of creativity in gravitational waves indicates that gravitational interactions causally generate complex patterns. As the gravitational wave background dates from the trillionth‐of‐a‐second after the Big Bang, these results indicate that causal and creative processes were important in the early universe, in contrast to the presumed predominance of random oscillations. © 2009 Wiley Periodicals, Inc. Complexity, 2010     

Classical spin dynamics of anisotropic Heisenberg dimmers

In the present work we study the deterministic spin dynamics of two interacting anisotropic magnetic particles in the presence of an external magnetic field using the Landau-Lifshitz equation. The interaction between particles is through the exchange energy. We study both conservative and dissipative cases. In the first one, we characterize the dynamical behavior of the system by monitoring the Lyapunov exponents and bifurcation diagrams. In particular, we explore the dependence of the largest Lyapunov exponent respect to the magnitude of applied magnetic field and exchange constant. We find that the system presents multiple transitions between regular and chaotic behaviors. We show that the dynamical phases display a very complicated topology of intricately intermingled chaotic and regular regions. In the dissipative case, we calculate the final saturation states as a function of the magnitude of the applied magnetic field, exchange constant as well as the anisotropy constants.