H. George E. Hentschel

A Framework for Three-Dimensional Simulation of Morphogenesis

We present COMPUCELL3D, a software framework for three-dimensional simulation of morphogenesis in different organisms. COMPUCELL3D employs biologically relevant models for cell clustering, growth, and interaction with chemical fields. COMPUCELL3D uses design patterns for speed, efficient memory management, extensibility, and flexibility to allow an almost unlimited variety of simulations. We have verified COMPUCELL3D by building a model of growth and skeletal pattern formation in the avian (chicken) limb bud. Binaries and source code are available, along with documentation and input files for sample simulations, at http:// compucell.sourceforge.net.

From Genes to Organisms Via the Cell: A Problem-Solving Environment for Multicellular Development

To gain performance, developers often build scientific applications in procedural languages, such as C or Fortran, which unfortunately reduces flexibility. To address this imbalance, the authors present CompuCell3D, a multitiered, flexible, and scalable problem-solving environment for morphogenesis simulations thats written in C++ using object-oriented design patterns.

Power-law singularities in gravity-capillary waves

Abstract Strongly driven waves break and lead to local singularities. Parametrically forced standing waves (Faraday waves) may break leading to a local power-law divergence on the free surface. We experimentally explore this state for its local structure, time dynamics and threshold for creation. A local analytical model for the surface height compares favorably with image sequences taken of individual events.

Quasistatic fractures in brittle media and iterated conformal maps

We study the geometrical characteristic of quasistatic fractures in brittle media, using iterated conformal maps to determine the evolution of the fracture pattern. This method allows an efficient and accurate solution of the Lamé equations without resorting to lattice models. Typical fracture patterns exhibit increased ramification due to the increase of the stress at the tips. We find the roughness exponent of the experimentally relevant backbone of the fracture pattern, it crosses over from about 0.5 for small scales to about 0.75 for large scales. We propose that this crossover reflects the increased ramification of the fracture pattern.

Microalloying and the mechanical properties of amorphous solids

The mechanical properties of amorphous solids like metallic glasses can be dramatically changed by adding small concentrations (as low as 0.1%) of foreign elements. The glass-forming-ability, the ductility, the yield stress and the elastic moduli can all be greatly effected. This paper presents theoretical considerations with the aim of explaining the magnitude of these changes in light of the small concentrations involved. The theory is built around the experimental evidence that the microalloying elements organise around them a neighbourhood that differs from both the crystalline and the glassy phases of the material in the absence of the additional elements. These regions act as isotropic defects that in unstressed systems modify the shear moduli. When strained, these defects interact with the incipient plastic responses which are quadrupolar in nature. It will be shown that this interaction interferes with the creation of system-spanning shear bands and increases the yield strain. We offer experimentally testable estimates of the lengths of nano-shear bands in the presence of the additional elements.

Atomistic simulations of magnetic amorphous solids: Magnetostriction, Barkhausen noise and novel singularities

We present results of atomistic simulations of a new model of a magnetic amorphous solid subjected to mechanical strains and magnetic fields. Contrary to standard magnetic random systems which are studied on a lattice with random interaction, in the present approach all the randomness comes from the glassy nature of the material. The model employed offers new perspectives on important effects like plasticity and magnetostriction. It is shown that the plastic response in such systems exhibit singularities characterized by new exponents; the spatial structure of these plastic events requires a new coarse grained elasto-magnetic theory which is provided here.

Transition in the fractal properties from diffusion-limited aggregation to Laplacian growth via their generalization

We study the fractal and multifractal properties (i.e., the generalized dimensions of the harmonic measure) of a two-parameter family of growth patterns that result from a growth model that interpolates between diffusion-limited aggregation (DLA) and Laplacian growth patterns in two dimensions. The two parameters are beta that determines the size of particles accreted to the interface, and C that measures the degree of coverage of the interface by each layer accreted to the growth pattern at every growth step. DLA and Laplacian growth are obtained at beta=0, C=0 and beta=2, C=1, respectively. The main purpose of this paper is to show that there exists a line in the beta-C phase diagram that separates fractal (D<2) from nonfractal (D=2) growth patterns. Moreover, Laplacian growth is argued to lie in the nonfractal part of the phase diagram. Some of our arguments are not rigorous, but together with the numerics they indicate this result rather strongly. We first consider the family of models obtained for beta=0, C>0, and derive for them a scaling relation D=2D(3). We then propose that this family has growth patterns for which D=2 for some C>C(cr), where C(cr) may be zero. Next we consider the whole beta-C phase diagram and define a line that separates two-dimensional growth patterns from fractal patterns with D<2. We explain that Laplacian growth lies in the region belonging to two-dimensional growth patterns, motivating the main conjecture of this paper, i.e., that Laplacian growth patterns are two dimensional. The meaning of this result is that the branches of Laplacian growth patterns have finite (and growing) area on scales much larger than any ultraviolet cutoff length.

Barkhausen noise in metallic glasses with strong local anisotropy: model and theory

We discuss a model metallic glass in which Barkhausen noise can be studied in exquisite detail, free of thermal effects and of the rate of ramping of the magnetic field. In this model the mechanism of the jumps in magnetic moment that cause the Barkhausen noise can be fully understood as consecutive instabilities where an eigenvalue of the Hessian matrix hits zero, leading to a magnetization jump Δm which is simultaneous with a stress and energy changes Δ σ and ΔU respectively. Due to a large effect of local anisotropy, in this model Barkhausen noise is not due to movements of magnetic domain boundaries across pinning sites. There are no fractal domains, no self-organized criticality and no exact scaling behavior. We present a careful numerical analysis of the statistical properties of the phenomenon, and show that with every care taken this analysis is tricky, and easily misleading. Without a guiding theory it is almost impossible to get the right answer for the statistics of Barkhausen noise. We therefore present an analytic theory that culminates in a probability distribution function that is in excellent agreement with the simulations.

Plasticity-induced magnetization in amorphous magnetic solids

Amorphous magnetic solids, like metallic glasses, exhibit a novel effect: the growth of magnetic order as a function of mechanical strain under athermal conditions in the presence of a magnetic field. The magnetic moment increases in steps whenever there is a plastic event. Thus, plasticity induces the magnetic ordering, acting as the effective noise driving the system towards equilibrium. We present results of atomistic simulations of this effect in a model of a magnetic amorphous solid subjected to pure shear and a magnetic field. To elucidate the dependence on external strain and magnetic field we offer a mean-field theory that provides an adequate qualitative understanding of the observed phenomenon.

Modeling Barkhausen Noise in magnetic glasses with dipole-dipole interactions

Long-ranged dipole-dipole interactions in magnetic glasses give rise to magnetic domains having labyrinthine patterns. Barkhausen Noise is then expected to result from the movement of domain boundaries which is supposed to be modeled by the motion of elastic membranes with random pinning. We propose an atomistic model of such magnetic glasses in which we measure the Barkhausen Noise which indeed results from the movement of domain boundaries. Nevertheless the statistics of the Barkhausen Noise is found in striking disagreement with the expectations in the literature. In fact we find exponential statistics without any power law, stressing the fact that Barkhausen Noise can belong to very different universality classes. In this glassy system the essence of the phenomenon is the ability of spin-carrying particles to move and minimize the energy without any spin flip. A theory is offered in excellent agreement with the measured data without any free parameter.