Developing a multi-metric habitat index for wadeable streams in Illinois (T-25-P-001), annual segment report to the Illinois Department of Natural Resources.

USFWS through IDNR State Wildlife Grant Grant/Contract No: T-25-P-001INHS Technical Report Prepared for USFWS through IDNR State Wildlife Gran

Contributions of Repulsive and Attractive Interactions to Nematic Order

Both repulsive and attractive molecular interactions can be used to explain the onset of nematic order. The object of this paper is to combine these two nematogenic molecular interactions in a unified theory. This attempt is not unprecedented; what is perhaps new is the focus on the understanding of nematics in the high density limit. There, the orientational probability distribution is shown to exhibit a unique feature: it has compact support on configuration space. As attractive interactions are turned on, the behavior changes, and at a critical attractive interaction strength, thermotropic behavior of the Maier-Saupe type is attained.Comment: 14 pages, 4 figure

Developing a multi-metric habitat index for wadeable streams in Illinois (T-25-P-001). Annual Segment Report to the Illinois Department of Natural Resources.

Illinois Department of Natural Resources Grant/Contract No: (T-25-P-001)This project was initiated to describe key aquatic habitat characteristics and their association to anthropogenic disturbance by developing a field based, rapid assessment method for qualitatively monitoring instream conditions using a multi-metric habitat index. We have developed and applied a method for rating disturbance in wadeable streams throughout Illinois and collected information on physical habitat at 299 sites to date. Index development is in the preliminary stages with field work to continue during the summer of 2008. This report summarizes work performed for the period ending April 30, 2008 (Appendix A contains Eastern Illinois University subcontract annual report).INHS Technical Report Prepared for Illinois Department of Natural Resource

Bistable curvature potential at hyperbolic points of nematic shells

none2siNematic shells are colloidal particles coated with nematic liquid crystal molecules which may freely glide and rotate on the colloid's surface while keeping their long axis on the local tangent plane. We describe the nematic order on a shell by a unit director field on an orientable surface. Equilibrium fields can then be found by minimising the elastic energy, which in general is a function of the surface gradient of the director field. We learn how to extract systematically out of this energy a fossil component, related only to the surface and its curvatures, which expresses a curvature potential for the molecular torque. At hyperbolic points on the colloid's surface, and only there, the alignment preferred by the curvature potential may fail to be a direction of principal curvature. There the fossil energy becomes bistable.openSonnet, André M; Virga, Epifanio GSonnet, André M; Virga, EPIFANIO GUIDO GIOVANN

Density functional theory for dense nematics with steric interactions

The celebrated work of Onsager on hard particle systems, based on the truncated second order virial expansion, is valid at relatively low volume fractions for large aspect ratio particles. While it predicts the isotropic-nematic phase transition, it fails to provide a realistic equation of state in that the pressure remains finite for arbitrarily high densities. In this work, we derive a mean field density functional form of the Helmholtz free energy for nematics with hard core repulsion. In addition to predicting the isotropic-nematic transition, the model provides a more realistic equation of state. The energy landscape is much richer, and the orientational probability distribution function in the nematic phase possesses a unique feature: it vanishes on a nonzero measure set in orientational space

Nivat's conjecture holds for sums of two periodic configurations

Nivat's conjecture is a long-standing open combinatorial problem. It concerns two-dimensional configurations, that is, maps $\mathbb Z^2 \rightarrow \mathcal A$ where $\mathcal A$ is a finite set of symbols. Such configurations are often understood as colorings of a two-dimensional square grid. Let $P_c(m,n)$ denote the number of distinct $m \times n$ block patterns occurring in a configuration $c$. Configurations satisfying $P_c(m,n) \leq mn$ for some $m,n \in \mathbb N$ are said to have low rectangular complexity. Nivat conjectured that such configurations are necessarily periodic. Recently, Kari and the author showed that low complexity configurations can be decomposed into a sum of periodic configurations. In this paper we show that if there are at most two components, Nivat's conjecture holds. As a corollary we obtain an alternative proof of a result of Cyr and Kra: If there exist $m,n \in \mathbb N$ such that $P_c(m,n) \leq mn/2$, then $c$ is periodic. The technique used in this paper combines the algebraic approach of Kari and the author with balanced sets of Cyr and Kra.Comment: Accepted for SOFSEM 2018. This version includes an appendix with proofs. 12 pages + references + appendi

Database management and analysis of fisheries in Illinois: Final report, 1 March 1999-28 February 2002

Issued May 2002; F-69-RReport issued on: May 200

A confined rod: mean field theory for hard rod-like particles

In this paper, we model the configurations of a system of hard rods by viewing each rod in a cell formed by its neighbors. By minimizing the free energy in the model and performing molecular dynamics, where, in both cases, the shape of the cell is a free parameter, we obtain the equilibrium orientational order parameter, free energy and pressure of the system. Our model enables the calculation of anisotropic stresses exerted on the walls of the cell due to shape change of the rod in photoisomerization. These results are a key step towards understanding molecular shape change effects in photomechanical systems under illumination.Comment: 15 pages, 8 figure