Nonequilibrium Probabilistic Dynamics of the Logistic Map at the Edge of Chaos

We consider nonequilibrium probabilistic dynamics in logistic-like maps $x_{t+1}=1-a|x_t|^z$, $(z>1)$ at their chaos threshold: We first introduce many initial conditions within one among $W>>1$ intervals partitioning the phase space and focus on the unique value $q_{sen}<1$ for which the entropic form $S_q \equiv \frac{1-\sum_{i=1}^{W} p_i^q}{q-1}$ {\it linearly} increases with time. We then verify that $S_{q_{sen}}(t) - S_{q_{sen}}(\infty)$ vanishes like $t^{-1/[q_{rel}(W)-1]}$ [$q_{rel}(W)>1$]. We finally exhibit a new finite-size scaling, $q_{rel}(\infty) - q_{rel}(W) \propto W^{-|q_{sen}|}$. This establishes quantitatively, for the first time, a long pursued relation between sensitivity to the initial conditions and relaxation, concepts which play central roles in nonextensive statistical mechanics.Comment: Final version with new Title and small modifications. REVTeX, 8 pages and 4 eps figure

Surface tension implementation for Gensmac 2D

In the present work we describe a method which allows the incorporation of surface tension into the GENSMAC2D code. This is achieved on two scales. First on the scale of a cell, the surface tension effects are incorporated into the free surface boundary conditions through the computation of the capillary pressure. The required curvature is estimated by fitting a least square circle to the free surface using the tracking particles in the cell and in its close neighbors. On a sub-cell scale, short wavelength perturbations are filtered out using a local 4-point stencil which is mass conservative. An efficient implementation is obtained through a dual representation of the cell data, using both a matrix representation, for ease at identifying neighbouring cells, and also a tree data structure, which permits the representation of specific groups of cells with additional information pertaining to that group. The resulting code is shown to be robust, and to produce accurate results when compared with exact solutions of selected fluid dynamic problems involving surface tension

Stochastic Dynamic Programming Applied to Hydrothermal Power Systems Operation Planning Based on the Convex Hull Algorithm

This paper presents a new approach for the expected cost-to-go functions modeling used in the stochastic dynamic programming (SDP) algorithm. The SDP technique is applied to the long-term operation planning of electrical power systems. Using state space discretization, the Convex Hull algorithm is used for constructing a series of hyperplanes that composes a convex set. These planes represent a piecewise linear approximation for the expected cost-to-go functions. The mean operational costs for using the proposed methodology were compared with those from the deterministic dual dynamic problem in a case study, considering a single inflow scenario. This sensitivity analysis shows the convergence of both methods and is used to determine the minimum discretization level. Additionally, the applicability of the proposed methodology for two hydroplants in a cascade is demonstrated. With proper adaptations, this work can be extended to a complete hydrothermal system

Landscape dynamics and diversification of the megadiverse South American freshwater fish fauna

Landscape dynamics are widely thought to govern the tempo and mode of continental radiations, yet the effects of river network rearrangements on dispersal and lineage diversification remain poorly understood. We integrated an unprecedented occurrence dataset of 4,967 species with a newly compiled, time-calibrated phylogeny of South American freshwater fishes—the most species-rich continental vertebrate fauna on Earth—to track the evolutionary processes associated with hydrogeographic events over 100 Ma. Net lineage diversification was heterogeneous through time, across space, and among clades. Five abrupt shifts in net diversification rates occurred during the Paleogene and Miocene (between 30 and 7 Ma) in association with major landscape evolution events. Net diversification accelerated from the Miocene to the Recent (c. 20 to 0 Ma), with Western Amazonia having the highest rates of in situ diversification, which led to it being an important source of species dispersing to other regions. All regional biotic interchanges were associated with documented hydrogeographic events and the formation of biogeographic corridors, including the Early Miocene (c. 23 to 16 Ma) uplift of the Serra do Mar and Serra da Mantiqueira and the Late Miocene (c. 10 Ma) uplift of the Northern Andes and associated formation of the modern transcontinental Amazon River. The combination of high diversification rates and extensive biotic interchange associated with Western Amazonia yielded its extraordinary contemporary richness and phylogenetic endemism. Our results support the hypothesis that landscape dynamics, which shaped the history of drainage basin connections, strongly affected the assembly and diversification of basin-wide fish fauna

Synthesis, Biological Evaluation, and Molecular Modeling Studies of New Thiadiazole Derivatives as Potent P2X7 Receptor Inhibitors

Twenty new 2-(1H-pyrazol-1-yl)-1,3,4-thiadiazole analogs were synthetized to develop P2X7 receptor (P2X7R) inhibitors. P2X7R inhibition in vitro was evaluated in mouse peritoneal macrophages, HEK-293 cells transfected with hP2X7R (dye uptake assay), and THP-1 cells (IL-1β release assay). The 1-(5-phenyl-1,3,4-thiadiazol-2-yl)-1H-pyrazol-5-amine derivatives 9b, 9c, and 9f, and 2-(3,5-dimethyl-1H-pyrazol-1-yl)-5-(4-fluorophenyl)-1,3,4-thiadiazole (11c) showed inhibitory effects with IC50 values ranging from 16 to 122 nM for reduced P2X7R-mediated dye uptake and 20 to 300 nM for IL-1β release. In addition, the in vitro ADMET profile of the four most potent derivatives was determined to be in acceptable ranges concerning metabolic stability and cytotoxicity. Molecular docking and molecular dynamics simulation studies of the molecular complexes human P2X7R/9f and murine P2X7R/9f indicated the putative intermolecular interactions. Compound 9f showed affinity mainly for the Arg268, Lys377, and Asn266 residues. These results suggest that 2-(1H-pyrazol-1-yl)-1,3,4-thiadiazole analogs may be promising novel P2X7R inhibitors with therapeutic potential