Modeling reaction-diffusion of molecules on surface and in volume spaces with the E-Cell System

The-Cell System is an advanced open-source simulation platform to model and analyze biochemical reaction networks. The present algorithm modules of the system assume that the reacting molecules are all homogeneously distributed in the reaction compartments, which is not the case in some cellular processes. The MinCDE system in Escherichia coli, for example, relies on intricately controlled reaction, diffusion and localization of Min proteins on the membrane and in the cytoplasm compartments to inhibit cell division at the poles of the rod-shaped cell. To model such processes, we have extended the E-Cell System to support reaction-diffusion and dynamic localization of molecules in volume and surface compartments. We evaluated our method by modeling the in vivo dynamics of MinD and MinE and comparing their simulated localization patterns to the observations in experiments and previous computational work. In both cases, our simulation results are in good agreement

Statistical properties of fracture in a random spring model

Using large scale numerical simulations we analyze the statistical properties of fracture in the two dimensional random spring model and compare it with its scalar counterpart: the random fuse model. We first consider the process of crack localization measuring the evolution of damage as the external load is raised. We find that, as in the fuse model, damage is initially uniform and localizes at peak load. Scaling laws for the damage density, fracture strength and avalanche distributions follow with slight variations the behavior observed in the random fuse model. We thus conclude that scalar models provide a faithful representation of the fracture properties of disordered systems.Comment: 12 pages, 17 figures, 1 gif figur

Microscopic Simulation of Reaction-Diffusion Processes and Applications to Population Biology and Product Marketing

We simulate reaction-diffusion processes with discrete fields. We use a novel algorithm to simulate different autocatalytic processes with trace densities. Anderson localization with a diffusive potential is studied. A reaction-diffusion process with dynamic localization is discussed in a marketing context.Comment: To appear in Annual Reviews of Computational physic

Rupture by damage accumulation in rocks

The deformation of rocks is associated with microcracks nucleation and propagation, i.e. damage. The accumulation of damage and its spatial localization lead to the creation of a macroscale discontinuity, so-called "fault" in geological terms, and to the failure of the material, i.e. a dramatic decrease of the mechanical properties as strength and modulus. The damage process can be studied both statically by direct observation of thin sections and dynamically by recording acoustic waves emitted by crack propagation (acoustic emission). Here we first review such observations concerning geological objects over scales ranging from the laboratory sample scale (dm) to seismically active faults (km), including cliffs and rock masses (Dm, hm). These observations reveal complex patterns in both space (fractal properties of damage structures as roughness and gouge), time (clustering, particular trends when the failure approaches) and energy domains (power-law distributions of energy release bursts). We use a numerical model based on progressive damage within an elastic interaction framework which allows us to simulate these observations. This study shows that the failure in rocks can be the result of damage accumulation

On Quantum Jumps, Events and Spontaneous Localization Models

We propose a definite meaning to the concepts of "experiment", "measurement" and "event" in the event-enhanced formalism of quantum theory. A minimal piecewise deterministic process is given that can be used for a computer simulation of real time series of experiments on single quantum objects. As an example a generalized cloud chamber is described, including multiparticle case. Relation to the GRW spontaneous localization model is discussed. The second revised version of the paper contains references to papers by other authors that are are aiming in the same direction: to enhance quantum theory in such a way that it will provide stochastic description of events triggered by individual quantum systems.Comment: 20 page

Scan matching by cross-correlation and differential evolution

Scan matching is an important task, solved in the context of many high-level problems including pose estimation, indoor localization, simultaneous localization and mapping and others. Methods that are accurate and adaptive and at the same time computationally efficient are required to enable location-based services in autonomous mobile devices. Such devices usually have a wide range of high-resolution sensors but only a limited processing power and constrained energy supply. This work introduces a novel high-level scan matching strategy that uses a combination of two advanced algorithms recently used in this field: cross-correlation and differential evolution. The cross-correlation between two laser range scans is used as an efficient measure of scan alignment and the differential evolution algorithm is used to search for the parameters of a transformation that aligns the scans. The proposed method was experimentally validated and showed good ability to match laser range scans taken shortly after each other and an excellent ability to match laser range scans taken with longer time intervals between them.Web of Science88art. no. 85

Robust Hydraulic Fracture Monitoring (HFM) of Multiple Time Overlapping Events Using a Generalized Discrete Radon Transform

In this work we propose a novel algorithm for multiple-event localization for Hydraulic Fracture Monitoring (HFM) through the exploitation of the sparsity of the observed seismic signal when represented in a basis consisting of space time propagators. We provide explicit construction of these propagators using a forward model for wave propagation which depends non-linearly on the problem parameters - the unknown source location and mechanism of fracture, time and extent of event, and the locations of the receivers. Under fairly general assumptions and an appropriate discretization of these parameters we first build an over-complete dictionary of generalized Radon propagators and assume that the data is well represented as a linear superposition of these propagators. Exploiting this structure we propose sparsity penalized algorithms and workflow for super-resolution extraction of time overlapping multiple seismic events from single well data