Integration of Langevin equations with multiplicative noise and the viability of field theories for absorbing phase transitions

Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic part, the latter being performed by sampling exactly the solution of the associated Fokker-Planck equation. We demonstrate the computational power of this method by applying it to the most absorbing phase transitions for which Langevin equations have been proposed. This provides precise estimates of the associated scaling exponents, clarifying the classification of these nonequilibrium problems, and confirms or refutes some existing theories.     

Unidirectional optical Bloch oscillations in asymmetric waveguide arrays

We present an analytical proof of the existence of unidirectional optical Bloch oscillations in a waveguide array system. It is shown that the presence of nonreciprocity in the system allows for a complete normal-mode dephasing in one of the propagation directions, resulting in a unidirectional breakdown in Bloch oscillations. A model system consisting of an array of transversely magnetized asymmetric Si/SiO2 waveguides with a magneto-optic cover layer is presented. Large index contrasts between film and cover are critical for practical realizations.     

Stochastic quantization and path integral formulation of Fokker-Planck equation

The operator formalism (Fokker-Planck dynamics) associated to a general n-dimensional, non-linear drift, non-constant diffusion Fokker-Planck equation, is derived by a stochastic quantization from the corresponding path integral formulation in phase space.     

Bio-Organometallic Derivatives of Antibacterial Drugs

Overuse and misuse of antibacterial drugs has resulted in bacteria resistance and in an increase in mortality rates due to bacterial infections. Therefore, there is an imperative necessity of new antibacterial drugs. Bio-organometallic derivatives of antibacterial agents offer an opportunity to discover new active antibacterial drugs. These compounds are well-characterized products and, in several examples, their antibacterial activities have been studied. Both inhibition of the antibacterial activity and strong increase in the antibiotic activity of the parent drug have been found. The synthesis of the main classes of bio-organometallic derivatives of these drugs, as well as examples of the use of structure–activity relation (SAR) studies to increase the activity and to understand the mode of action of bio-organometallic antimicrobial peptides (BOAMPs) and platensimicyn bio-organometallic mimics is presented in this article.     

Partial control of delay-coordinate maps

Nonlinear Dynamics - Delay-coordinate maps have been widely used recently to study nonlinear dynamical systems, where there is only access to the time series of one of their variables. Here, we...     

Limit cycles and detailed balance in Fokker-Planck equations

A class of non-linear Fokker Planck equations with exactly known steady state solution is investigated and its relation with the models considered earlier in the literature is discussed. A characterisation of the absence of detailed balance and possible existence of limit cycles is given. The implications of detailed balance on the existence and the character of limit cycle behaviour are studied. It is shown that detailed balance does not determine the existence or non-existence of limit cycles but rather their character.     

Uniform saturation in linear inequality systems

Redundant constraints in linear inequality systems can be characterized as those inequalities that can be removed from an arbitrary linear optimization problem posed on its solution set without modifying its value and its optimal set. A constraint is saturated in a given linear optimization problem when it is binding at the optimal set. Saturation is a property related with the preservation of the value and the optimal set under the elimination of the given constraint, phenomena which can be seen as weaker forms of excess information in linear optimization problems. We say that an inequality of a given linear inequality system is uniformly saturated when it is saturated for any solvable linear optimization problem posed on its solution set. This paper characterizes the uniform saturated inequalities and other related classes of inequalities. This work was supported by the MCYT of Spain and FEDER of UE, Grant BFM2002-04114-C02-01.