Ornstein-Zernike equation and Percus-Yevick theory for molecular crystals

We derive the Ornstein-Zernike equation for molecular crystals of axially symmetric particles and apply the Percus-Yevick approximation to this system. The one-particle orientational distribution function has a nontrivial dependence on the orientation and is needed as an input. Despite some differences, the Ornstein-Zernike equation for molecular crystals has a similar structure as for liquids. We solve both equations for hard ellipsoids on a sc lattice. Compared to molecular liquids, the tensorial orientational correlators exhibit less structure. However, depending on the lengths a and b of the rotation axis and the perpendicular axes of the ellipsoids, different behavior is found. For oblate and prolate ellipsoids with b >= 0.35 (units of the lattice constant), damped oscillations in distinct directions of direct space occur for some correlators. They manifest themselves in some correlators in reciprocal space as a maximum at the Brillouin zone edge, accompanied by maxima at the zone center for other correlators. The oscillations indicate alternating orientational fluctuations, while the maxima at the zone center originate from nematic-like orientational fluctuations. For a <= 2.5 and b <= 0.35, the oscillations are weaker. For a >= 3.0 and b <= 0.35, no oscillations occur any longer. For many of the correlators in reciprocal space, an increase of a at fixed b leads to a divergence at the zone center q = 0, consistent with nematic-like long range fluctuations, and for some oblate and prolate systems with b ~< 1.0 a simultaneous tendency to divergence of few other correlators at the zone edge is observed. Comparison with correlators from MC simulations shows satisfactory agreement. We also obtain a phase boundary for order-disorder transitions.Comment: 20 pages, 13 figures, submitted to Phys. Rev.

Phase behavior of the Confined Lebwohl-Lasher Model

The phase behavior of confined nematogens is studied using the Lebwohl-Lasher model. For three dimensional systems the model is known to exhibit a discontinuous nematic-isotropic phase transition, whereas the corresponding two dimensional systems apparently show a continuous Berezinskii-Kosterlitz-Thouless like transition. In this paper we study the phase transitions of the Lebwohl-Lasher model when confined between planar slits of different widths in order to establish the behavior of intermediate situations between the pure planar model and the three-dimensional system, and compare with previous estimates for the critical thickness, i.e. the slit width at which the transition switches from continuous to discontinuous.Comment: Submitted to Physical Review

Ecological niche conservatism spurs diversification in response to climate change

Lengthy debate has surrounded the theoretical and empirical science of whether climatic niche evolution is related to increased or decreased rates of biological diversification. Since species can persist for thousands to millions of years, these questions cross broad scales of time and space. Thus, short-term experiments may not provide comprehensive understanding of the system, leading to the emergence of contrasting opinions: niche evolution may increase diversity by allowing species to explore and colonize new geographic areas across which they could speciate – or – niche conservatism might augment biodiversity by supporting isolation of populations that may then undergo allopatric speciation. Here, we use a simulation approach to test how biological diversification responds to different rates and modes of niche evolution. We find that niche conservatism promotes biological diversification, whereas labile niches—whether adapting to conditions available or changing randomly—generally led to slower diversification rates. These novel results provide a framework for understanding how Earth–life interactions produced such a diverse biota

Signum Function Method for Generation of Correlated Dichotomic Chains

We analyze the signum-generation method for creating random dichotomic sequences with prescribed correlation properties. The method is based on a binary mapping of the convolution of continuous random numbers with some function originated from the Fourier transform of a binary correlator. The goal of our study is to reveal conditions under which one can construct binary sequences with a given pair correlator. Our results can be used in the construction of superlattices and waveguides with selective transport properties.Comment: 14 pages, 7 figure

Method for Generating Long-Range Correlations for Large Systems

We propose a new method to generate a sequence of random numbers with long-range power-law correlations that overcomes known difficulties associated with large systems. The new method presents an improvement on the commonly-used methods. We apply the algorithm to generate enhanced diffusion, isotropic and anisotropic self-affine surfaces, and isotropic and anisotropic correlated percolation.Comment: 4 pages, REVTEX, figures available upon request from [email protected]

High‐Frequency Sensor Data Reveal Across‐Scale Nitrate Dynamics in Response to Hydrology and Biogeochemistry in Intensively Managed Agricultural Basins

An edited version of this paper was published by AGU. Copyright 2018 American Geophysical Union.Excess nitrate in rivers draining intensively managed agricultural watersheds has caused coastal hypoxic zones, harmful algal blooms, and degraded drinking water. Hydrology and biogeochemical transformations influence nitrate concentrations by changing nitrate supply, removal, and transport. For the Midwest Unites States, where much of the land is used for corn and soybean production, a better understanding of the response of nitrate to hydrology and biogeochemistry is vital in the face of high nitrate concentrations coupled with projected increases of precipitation frequency and magnitude. In this study, we capitalized on the availability of spatially and temporally extensive sensor data in the region to evaluate how nitrate concentration (NO3−) interacts with discharge (Q) and water temperature (T) within eight watersheds in Iowa, United States, by evaluating land use characteristics and multiscale temporal behavior from 5‐year, high‐frequency, time series records. We show that power spectral density of Q, NO3−, and T, all exhibit power law behavior with slopes greater than 2, implying temporal self‐similarity for a range of scales. NO3− was strongly cross correlated with Q for all sites and correlation increased significantly with drainage area across sites. Peak NO3− increased significantly with crop coverage across watersheds. Temporal offsets in peak NO3− and peak Q, seen at all study sites, reduced the impact of extreme events. This study illustrates a relatively new approach to evaluating environmental sensor data and revealed characteristics of watersheds in which extreme discharge events have the greatest consequences

Ecological niche and phylogeography elucidate complex biogeographic patterns in Loxosceles rufescens (Araneae, Sicariidae) in the Mediterranean Basin

Background: Understanding the evolutionary history of morphologically cryptic species complexes is difficult, and made even more challenging when geographic distributions have been modified by human-mediated dispersal. This situation is common in the Mediterranean Basin where, aside from the environmental heterogeneity of the region, protracted human presence has obscured the biogeographic processes that shaped current diversity. Loxosceles rufescens (Araneae, Sicariidae) is an ideal example: native to the Mediterranean, the species has dispersed worldwide via cohabitation with humans. A previous study revealed considerable molecular diversity, suggesting cryptic species, but relationships among lineages did not correspond to geographic location. Results: Delimitation analyses on cytochrome c oxidase subunit I identified 11 different evolutionary lineages, presenting two contrasting phylogeographic patterns: (1) lineages with well-structured populations in Morocco and Iberia, and (2) lineages lacking geographic structure across the Mediterranean Basin. Dating analyses placed main diversification events in the Pleistocene, and multiple Pleistocene refugia, identified using ecological niche modeling (ENM), are compatible with allopatric differentiation of lineages. Human-mediated transportation appears to have complicated the current biogeography of this medically important and synanthropic spider. Conclusions: We integrated ecological niche models with phylogeographic analyses to elucidate the evolutionary history of L. rufescens in the Mediterranean Basin, with emphasis on the origins of mtDNA diversity. We found support for the hypothesis that northern Africa was the center of origin for L. rufescens, and that current genetic diversity originated in allopatry, likely promoted by successive glaciations during the Pleistocene. We corroborated the scenario of multiple refugia within the Mediterranean, principally in northern Africa, combining results from eight atmosphereocean general circulation models (AOGCMs) with two different refugium-delimitation methodologies. ENM results were useful for providing general views of putative refugia, with fine-scale details depending on the level of stringency applied for agreement among models

Poisson-Bracket Approach to the Dynamics of Nematic Liquid Crystals. The Role of Spin Angular Momentum

Nematic liquid crystals are well modeled as a fluid of rigid rods. Starting from this model, we use a Poisson-bracket formalism to derive the equations governing the dynamics of nematic liquid crystals. We treat the spin angular momentum density arising from the rotation of constituent molecules about their centers of mass as an independent field and derive equations for it, the mass density, the momentum density, and the nematic director. Our equations reduce to the original Leslie-Ericksen equations, including the inertial director term that is neglected in the hydrodynamic limit, only when the moment of inertia for angular momentum parallel to the director vanishes and when a dissipative coefficient favoring locking of the angular frequencies of director rotation and spin angular momentum diverges. Our equations reduce to the equations of nematohydrodynamics in the hydrodynamic limit but with dissipative coefficients that depend on the coefficient that must diverge to produce the Leslie-Ericksen equations.Comment: 10 pages, to be published in Phys. Rev. E 72(5

Liquid crystal defects and confinement in Yang-Mills theory

We show that in the Landau gauge of the SU(2) Yang-Mills theory the residual global symmetry supports existence of the topological vortices which resemble disclination defects in the nematic liquid crystals and the Alice (half-quantum) vortices in the superfluid heluim 3 in the A-phase. The theory also possesses half-integer and integer charged monopoles which are analogous to the point-like defects in the nematic crystal and in the liquid helium. We argue that the deconfinement phase transition in the Yang-Mills theory in the Landau gauge is associated with the proliferation of these vortices and/or monopoles. The disorder caused by these defects is suggested to be responsible for the confinement of quarks in the low-temperature phase.Comment: 9 pages, 5 figures, RevTeX styl