6,156 research outputs found
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
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
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
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
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