The Kinetic Basis of Self-Organized Pattern Formation

In his seminal paper on morphogenesis (1952), Alan Turing demonstrated that different spatio-temporal patterns can arise due to instability of the homogeneous state in reaction-diffusion systems, but at least two species are necessary to produce even the simplest stationary patterns. This paper is aimed to propose a novel model of the analog (continuous state) kinetic automaton and to show that stationary and dynamic patterns can arise in one-component networks of kinetic automata. Possible applicability of kinetic networks to modeling of real-world phenomena is also discussed.Comment: 8 pages, submitted to the 14th International Conference on the Synthesis and Simulation of Living Systems (Alife 14) on 23.03.2014, accepted 09.05.201

Bypass transition and spot nucleation in boundary layers

The spatio-temporal aspects of the transition to turbulence are considered in the case of a boundary layer flow developing above a flat plate exposed to free-stream turbulence. Combining results on the receptivity to free-stream turbulence with the nonlinear concept of a transition threshold, a physically motivated model suggests a spatial distribution of spot nucleation events. To describe the evolution of turbulent spots a probabilistic cellular automaton is introduced, with all parameters directly fitted from numerical simulations of the boundary layer. The nucleation rates are then combined with the cellular automaton model, yielding excellent quantitative agreement with the statistical characteristics for different free-stream turbulence levels. We thus show how the recent theoretical progress on transitional wall-bounded flows can be extended to the much wider class of spatially developing boundary-layer flows

A Particular Bit of Universality: Scaling Limits of Some Dependent Percolation Models

We study families of dependent site percolation models on the triangular lattice ${\mathbb T}$ and hexagonal lattice ${\mathbb H}$ that arise by applying certain cellular automata to independent percolation configurations. We analyze the scaling limit of such models and show that the distance between macroscopic portions of cluster boundaries of any two percolation models within one of our families goes to zero almost surely in the scaling limit. It follows that each of these cellular automaton generated dependent percolation models has the same scaling limit (in the sense of Aizenman-Burchard [3]) as independent site percolation on ${\mathbb T}$.Comment: 25 pages, 7 figure

Lattice Boltzmann in micro- and nano- flow simulations

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.One of the fundamental difficulties in micro- and nano-flow simulations is that the validity’s of the continuum assumption and the hydro-dynamic equations start to become questionable in this flow regime. The lower-level kinetic/molecular alternatives are often either prohibitively expensive for practical purposes or poorly justified from a fundamental perspective. The lattice Boltzmann (LB) method, which originated from a simplistic Boolean kinetic model, is recently shown to converge asymptotically to the continuum Boltzmann-BGK equation and therefore offers a theoretically sound and computationally effective approach for micro- and nano-flow simulations. In addition, its kinetic nature allows certain microscopic physics to be modeled at the macroscopic level, leading to a highly efficient model for multiphase flows with phase transitions. With the inherent computational advantages of a lattice model, e.g., the algorithm simplicity and parallelizability, the ease of handling complex geometry and so on, the LB method has found many applications in various areas of Computational Fluid Dynamics (CFD) and matured to the extend of commercial applications. In this talk, I shall give an introduction to the LB method with the emphasis given to the theoretical justifications for its applications in micro- and nano-flow simulations. Some recent examples will also be reported

Overview of crowd simulation in computer graphics

High-powered technology use computer graphics in education, entertainment, games, simulation, and virtual heritage applications has led it to become an important area of research. In simulation, according to Tecchia et al. (2002), it is important to create an interactive, complex, and realistic virtual world so that the user can have an immersive experience during navigation through the world. As the size and complexity of the environments in the virtual world increased, it becomes more necessary to populate them with peoples, and this is the reason why rendering the crowd in real-time is very crucial. Generally, crowd simulation consists of three important areas. They are realism of behavioral (Thompson and Marchant 1995), high-quality visualization (Dobbyn et al. 2005) and convergence of both areas. Realism of behavioral is mainly used for simple 2D visualizations because most of the attentions are concentrated on simulating the behaviors of the group. High quality visualization is regularly used for movie productions and computer games. It gives intention on producing more convincing visual rather than realism of behaviors. The convergences of both areas are mainly used for application like training systems. In order to make the training system more effective, the element of valid replication of the behaviors and high-quality visualization is added

A way to synchronize models with seismic faults for earthquake forecasting: Insights from a simple stochastic model

Numerical models are starting to be used for determining the future behaviour of seismic faults and fault networks. Their final goal would be to forecast future large earthquakes. In order to use them for this task, it is necessary to synchronize each model with the current status of the actual fault or fault network it simulates (just as, for example, meteorologists synchronize their models with the atmosphere by incorporating current atmospheric data in them). However, lithospheric dynamics is largely unobservable: important parameters cannot (or can rarely) be measured in Nature. Earthquakes, though, provide indirect but measurable clues of the stress and strain status in the lithosphere, which should be helpful for the synchronization of the models. The rupture area is one of the measurable parameters of earthquakes. Here we explore how it can be used to at least synchronize fault models between themselves and forecast synthetic earthquakes. Our purpose here is to forecast synthetic earthquakes in a simple but stochastic (random) fault model. By imposing the rupture area of the synthetic earthquakes of this model on other models, the latter become partially synchronized with the first one. We use these partially synchronized models to successfully forecast most of the largest earthquakes generated by the first model. This forecasting strategy outperforms others that only take into account the earthquake series. Our results suggest that probably a good way to synchronize more detailed models with real faults is to force them to reproduce the sequence of previous earthquake ruptures on the faults. This hypothesis could be tested in the future with more detailed models and actual seismic data.Comment: Revised version. Recommended for publication in Tectonophysic