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Application of hierarchical matrices for solving multiscale problems
Alexander Litvinenko
eLife
A multiphase theory for spreading microbial swarms and films
Siddarth Srinivasan
Bacterial swarming and biofilm formation are collective multicellular phenomena through which diverse microbial species colonize and spread over water-permeable tissue. During both modes of surface translocation, fluid uptake and transport play a key role in shaping the overall morphology and spreading dynamics. Here we develop a generalized two-phase thin-film model that couples bacterial growth, extracellular matrix swelling, fluid flow, and nutrient transport to describe the expansion of both highly motile bacterial swarms, and sessile bacterial biofilms. We show that swarm expansion corresponds to steady-state solutions in a nutrient-rich, capillarity dominated regime. In contrast, biofilm colony growth is described by transient solutions associated with a nutrient-limited, extracellular polymer stress driven limit. We apply our unified framework to explain a range of recent experimental observations of steady and unsteady expansion of microbial swarms and biofilms. Our results ...
Communications in Nonlinear Science and Numerical Simulation
Dynamics of three coupled limit cycle oscillators with application to artificial intelligence
2009 •
Richard Rand
Method of Green's potentials for elliptic PDEs in domains with random boundaries
2018 •
Viktor Reshniak
Problems with topological uncertainties appear in many fields ranging from nano-device engineering to the design of bridges. In many of such problems, a part of the domains boundaries is subjected to random perturbations making inefficient conventional schemes that rely on discretization of the whole domain. In this paper, we study elliptic PDEs in domains with boundaries comprised of both deterministic and random parts, and apply the method of modified potentials with Green’s kernels defined on the deterministic part of the domain. This approach allows to reduce the dimension of the original differential problem by reformulating it as a boundary integral equation posed on the random part of the boundary only. The multilevel Monte Carlo method is then applied to this modified integral equation. We provide the qualitative analysis of the proposed technique and support it with numerical results.
Symmetry
Influence of Spatial Dispersal among Species in a Prey–Predator Model with Miniature Predator Groups
Turki Aljrees
Dispersal among species is an important factor that can govern the prey–predator model’s dynamics and cause a variety of spatial structures on a geographical scale. These structures form when passive diffusion interacts with the reaction part of the reaction–diffusion system in such a way that even if the reaction lacks symmetry-breaking capabilities, diffusion can destabilize the symmetry and allow the system to have them. In this article, we look at how dispersal affects the prey–predator model with a Hassell–Varley-type functional response when predators do not form tight groups. By considering linear stability, the temporal stability of the model and the conditions for Hopf bifurcation at feasible equilibrium are derived. We explored spatial stability in the presence of diffusion and developed the criterion for diffusion-driven instability. Using amplitude equations, we then investigated the selection of Turing patterns around the Turing bifurcation threshold. The examination of...
Engineering Analysis with Boundary Elements
Meshless fracture analysis of 3D planar cracks with generalized thermo-mechanical stress intensity factors
2019 •
Farid Vakili-tahami
Dynamics of neural systems with time delays
2017 •
Bootan Rahman
Complex networks are ubiquitous in nature. Numerous neurological diseases, such as Alzheimer's, Parkinson's, epilepsy are caused by the abnormal collective behaviour of neurons in the brain. In particular, there is a strong evidence that Parkinson's disease is caused by the synchronisation of neurons, and understanding how and why such synchronisation occurs will bring scientists closer to the design and implementation of appropriate control to support desynchronisation required for the normal functioning of the brain. In order to study the emergence of (de)synchronisation, it is necessary first to understand how the dynamical behaviour of the system under consideration depends on the changes in systems parameters. This can be done using a powerful mathematical method, called bifurcation analysis, which allows one to identify and classify different dynamical regimes, such as, for example, stable/unstable steady states, Hopf and fold bifurcations, and find periodic soluti...
IMA Journal of Numerical Analysis
Two-level Schwarz method for unilateral variational inequalities
1999 •
Pasi Tarvainen
Applied Mathematics and Computation
On well-balanced implicit-explicit Lagrange-projection schemes for two-layer shallow water equations
Manuel J. Castro Díaz
Fuel and Energy Abstracts
Stability and non-normality of the k- ε equations
1997 •
Per Lötstedt
The analytical and numerical solutions of the equations of the k-ε turbulence model are analyzed. Under certain conditions on the boundary values and the interior values of k and ε the analytical and numerical solutions are bounded. If the steady state solution is obtained numerically by a Runge-Kutta time-stepping method, then severe constraints on the time-step and the non-normality of the jacobian matrix make the convergence very slow. The simplifications and conclusions are supported by data from a numerical solution of flow over a flat plate.
