Particle-based and Meshless Methods with Aboria

Aboria is a powerful and flexible C++ library for the implementation of particle-based numerical methods. The particles in such methods can represent actual particles (e.g. Molecular Dynamics) or abstract particles used to discretise a continuous function over a domain (e.g. Radial Basis Functions). Aboria provides a particle container, compatible with the Standard Template Library, spatial search data structures, and a Domain Specific Language to specify non-linear operators on the particle set. This paper gives an overview of Aboria's design, an example of use, and a performance benchmark

Reactions, Diffusion and Volume Exclusion in a Heterogeneous System of Interacting Particles

Complex biological and physical transport processes are often described through systems of interacting particles. Excluded-volume effects on these transport processes are well studied, however the interplay between volume exclusion and reactions between heterogenous particles is less well known. In this paper we develop a novel framework for modeling reaction-diffusion processes which directly incorporates volume exclusion. From an off-lattice microscopic individual based model we use the Fokker--Planck equation and the method of matched asymptotic expansions to derive a low-dimensional macroscopic system of nonlinear partial differential equations describing the evolution of the particles. A biologically motivated, hybrid model of chemotaxis with volume exclusion is explored, where reactions occur at rates dependent upon the chemotactic environment. Further, we show that for reactions due to contact interactions the appropriate reaction term in the macroscopic model is of lower order in the asymptotic expansion than the nonlinear diffusion term. However, we find that the next reaction term in the expansion is needed to ensure good agreement with simulations of the microscopic model. Our macroscopic model allows for more direct parameterization to experimental data than the models available to date.Comment: 13 pages, 4 figure

Diffusion of particles with short-range interactions

A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of matched asymptotic expansions. Numerical simulations are performed to compare the results of the model with those of the commonly used mean-field and Kirkwood-superposition approximations, as well as with Monte Carlo simulation of the stochastic particle system, for various interaction potentials. Our approach works best for very repulsive short-range potentials, while the mean-field approximation is suitable for long-range interactions. The Kirkwood superposition approximation provides an accurate description for both short- and long-range potentials, but is considerably more computationally intensive

Cross-diffusion systems with excluded volume effects and asymptotic gradient flows

In this paper we discuss the analysis of a cross-diffusion PDE system for a mixture of hard spheres, which was derived by Bruna and Chapman from a stochastic system of interacting Brownian particles using the method of matched asymptotic expansions. The resulting cross-diffusion system is valid in the limit of small volume fraction of particles. While the system has a gradient flow structure in the symmetric case of all particles having the same size and diffusivity, this is not valid in general. We discuss local stability and global existence for the symmetric case using the gradient flow structure and entropy variable techniques. For the general case, we introduce the concept of an asymptotic gradient flow structure and show how it can be used to study the behavior close to equilibrium. Finally we illustrate the behavior of the model with various numerical simulations

Umbral Methods and Harmonic Numbers

The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.Comment: 6 page

Personality Dimensions and Attributional Styles in Individuals with and without Gender Dysphoria

This research investigates personality dimensions and attributional styles among individuals with and without gender dysphoria in relationship to gender, educational level, and ethnicity. Participants were 60 men and women with and without gender dysphoria. A demographic sheet and two inventories were used. Results showed that patients with gender dysphoria had significantly higher neuroticism and lower agreeableness compared with individuals without gender dysphoria. No significance differences in extraversion, openness to experience, and conscientiousness (based on the “big five” personality model) were found between those with and without gender dysphoria. Also, individuals without gender dysphoria had higher positive attributional styles compared to patients with gender dysphoria. Finally, there were significant effects for gender and ethnicity on personality dimensions, but not for gender, ethnicity, or the ethnicity by gender interaction on the attributional styles