4,422 research outputs found
The auxiliary region method: A hybrid method for coupling PDE- and Brownian-based dynamics for reaction-diffusion systems
Reaction-diffusion systems are used to represent many biological and physical
phenomena. They model the random motion of particles (diffusion) and
interactions between them (reactions). Such systems can be modelled at multiple
scales with varying degrees of accuracy and computational efficiency. When
representing genuinely multiscale phenomena, fine-scale models can be
prohibitively expensive, whereas coarser models, although cheaper, often lack
sufficient detail to accurately represent the phenomenon at hand. Spatial
hybrid methods couple two or more of these representations in order to improve
efficiency without compromising accuracy.
In this paper, we present a novel spatial hybrid method, which we call the
auxiliary region method (ARM), which couples PDE and Brownian-based
representations of reaction-diffusion systems. Numerical PDE solutions on one
side of an interface are coupled to Brownian-based dynamics on the other side
using compartment-based "auxiliary regions". We demonstrate that the hybrid
method is able to simulate reaction-diffusion dynamics for a number of
different test problems with high accuracy. Further, we undertake error
analysis on the ARM which demonstrates that it is robust to changes in the free
parameters in the model, where previous coupling algorithms are not. In
particular, we envisage that the method will be applicable for a wide range of
spatial multi-scales problems including, filopodial dynamics, intracellular
signalling, embryogenesis and travelling wave phenomena.Comment: 29 pages, 14 figures, 2 table
Spin-resolved optical conductivity of two-dimensional group-VIB transition-metal dichalcogenides
We present an ab-initio study of the spin-resolved optical conductivity of
two-dimensional (2D) group-VIB transition-metal dichalcogenides (TMDs). We
carry out fully-relativistic density-functional-theory calculations combined
with maximally localized Wannier functions to obtain band manifolds at
extremely high resolutions and focus on the photo-response of 2D TMDs to
circularly-polarized light in a wide frequency range. We present extensive
numerical results for monolayer TMDs involving molybdenum and tungsten combined
with sulphur and selenium. Our numerical approach allows us to locate with a
high degree of accuracy the positions of the points in the Brillouin zone that
are responsible for van Hove singularities in the optical response.
Surprisingly, some of the saddle points do not occur exactly along
high-symmetry directions in the Brillouin zone, although they happen to be in
their close proximity.Comment: 9 pages, 5 figure
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