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

Mother Operators and their Descendants

A mechanism deriving new well-posed evolutionary equations from given ones is inspected. It turns out that there is one particular spatial operator from which many of the standard evolutionary problems of mathematical physics can be generated by this abstract mechanism using suitable projections. The complexity of the dynamics of the phenomena considered can be described in terms of suitable material laws. The idea is illustrated with a number of concrete examples.Comment: This is a revised version of the earlier posted pre-print. The corrections concern predominantly Corollary 1.7 and Theorem 1.9 and their consequence

Efficient potential of mean force calculation from multiscale simulations: solute insertion in a lipid membrane

The determination of potentials of mean force for solute insertion in a membrane by means of all-atom molecular dynamics simulations is often hampered by sampling issues. A multiscale approach to conformational sampling was recently proposed by Bereau and Kremer (2016). It aims at accelerating the sampling of the atomistic conformational space by means of a systematic backmapping of coarse-grained snapshots. In this work, we first analyze the efficiency of this method by comparing its predictions for propanol insertion into a 1,2-Dimyristoyl-sn-glycero-3-phosphocholine membrane (DMPC) against reference atomistic simulations. The method is found to provide accurate results with a gain of one order of magnitude in computational time. We then investigate the role of the coarse-grained representation in affecting the reliability of the method in the case of a 1,2-Dioleoyl-sn-glycero-3-phosphocholine membrane (DOPC). We find that the accuracy of the results is tightly connected to the presence a good configurational overlap between the coarse-grained and atomistic models---a general requirement when developing multiscale simulation methods.Comment: 6 pages, 5 figure

A damage model based on failure threshold weakening

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with long range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding. We introduce a failure threshold weakening parameter into the cellular-automaton slider-block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event. We show that a critical point is reached beyond which the probability of a system-wide event scales with this weakening parameter. We provide a mapping to the percolation transition, and show that the values of the scaling exponents approach the values for mean-field percolation (spinodal nucleation) as lattice size $L$ is increased for fixed $R$. We also examine the effect of the weakening parameter on the frequency-magnitude scaling relationship and the ergodic behavior of the model