Stochastic evolution of four species in cyclic competition

We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios, from single species domination to coexistence between non-interacting species. Using exact results and numerical simulations we discuss the temporal evolution of the system for different values of $N$, for different values of the reaction rates, as well as for different initial conditions. As expected, the stochastic evolution is found to closely follow the mean-field result for large $N$, with notable deviations appearing in proximity of extinction events. Different ways of characterizing and predicting extinction events are discussed.Comment: 19 pages, 6 figures, submitted to J. Stat. Mec

Development of an embedded Fabry Perot Fiber Optic Strain Rosette Sensor (FP-FOSRS)

We investigate the feasibility of utilizing a Fabry-Perot Fiber Optic Strain Rosette Sensor (FP-FOSRS) for the evaluation of the internal strain state of a material system. We briefly describe the manufacturing process for this sensor and point out some potential problem areas. Results of an embedded FP-FOSRS in an epoxy matrix with external resistance strain gauges applied for comparative purposes are presented. We show that the internal and external strain measurements are in close agreement. This work lays the foundation for embedding this sensor in actual composite laminas

Darboux Transformations, Infinitesimal Symmetries and Conservation Laws for Nonlocal Two-Dimensional Toda Lattice

The technique of Darboux transformation is applied to nonlocal partner of two-dimensional periodic A_{n-1} Toda lattice. This system is shown to admit a representation as the compatibility conditions of direct and dual overdetermined linear systems with quantized spectral parameter. The generalization of the Darboux transformation technique on linear equations of such a kind is given. The connections between the solutions of overdetermined linear systems and their expansions in series at singular points neighborhood are presented. The solutions of the nonlocal Toda lattice and infinite hierarchies of the infinitesimal symmetries and conservation laws are obtained.Comment: 12 pages, infinitesimal symmetries and conservation laws are adde

The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning

Pseudoclassical description of the massive Dirac particles in odd dimensions

A pseudoclassical model is proposed to describe massive Dirac (spin one-half) particles in arbitrary odd dimensions. The quantization of the model reproduces the minimal quantum theory of spinning particles in such dimensions. A dimensional duality between the model proposed and the pseudoclassical description of Weyl particles in even dimensions is discussed.Comment: 12 pages, LaTeX (RevTeX

How Gaussian competition leads to lumpy or uniform species distributions

A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving competition are more or less uniformly distributed over the resource spectrum, or their distribution is 'lumped' (or 'clumped'), consisting of clusters of species with similar resource use that are separated by gaps in resource space. Which of these outcomes will occur crucially depends on the competition kernel, which reflects the shape of the resource utilization pattern of the competing species. Most models considered in the literature assume a Gaussian competition kernel. This is unfortunate, since predictions based on such a Gaussian assumption are not robust. In fact, Gaussian kernels are a border case scenario, and slight deviations from this function can lead to either uniform or lumped species distributions. Here we illustrate the non-robustness of the Gaussian assumption by simulating different implementations of the standard competition model with constant carrying capacity. In this scenario, lumped species distributions can come about by secondary ecological or evolutionary mechanisms or by details of the numerical implementation of the model. We analyze the origin of this sensitivity and discuss it in the context of recent applications of the model.Comment: 11 pages, 3 figures, revised versio

Renormalization of the Inverse Square Potential

The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional regularization. In the renormalized version of the theory, there is a strong-coupling regime where quantum-mechanical breaking of scale symmetry takes place through dimensional transmutation, with the creation of a single bound state and of an energy-dependent s-wave scattering matrix element.Comment: 5 page

Sharks of the order Carcharhiniformes from the British Coniacian, Santonian and Campanian (Upper Cretaceous).

Bulk sampling of phosphate-rich horizons within the British Coniacian to Campanian (Upper Cretaceous) yielded very large samples of shark and ray teeth. All of these samples yielded teeth of diverse members of the Carcharhiniformes, which commonly dominate the fauna. The following species are recorded and described: Pseudoscyliorhinus reussi (Herman, 1977) comb. nov., Crassescyliorhinus germanicus (Herman, 1982) gen. nov., Scyliorhinus elongatus (Davis, 1887), Scyliorhinus brumarivulensis sp. nov., ? Palaeoscyllium sp., Prohaploblepharus riegrafi (Müller, 1989) gen. nov., ? Cretascyliorhinus sp., Scyliorhinidae inc. sedis 1, Scyliorhinidae inc. sedis 2, Pteroscyllium hermani sp. nov., Protoscyliorhinus sp., Leptocharias cretaceus sp. nov., Palaeogaleus havreensis Herman, 1977, Paratriakis subserratus sp. nov., Paratriakis tenuis sp. nov., Paratriakis sp. indet. and ? Loxodon sp. Taxa belonging to the families ?Proscylliidae, Leptochariidae, and Carcharhinidae are described from the Cretaceous for the first time. The evolutionary and palaeoecological implications of these newly recognised faunas are discussed