Singular Laplacian Growth

The general equations of motion for two dimensional Laplacian growth are derived using the conformal mapping method. In the singular case, all singularities of the conformal map are on the unit circle, and the map is a degenerate Schwarz-Christoffel map. The equations of motion describe the motions of these singularities. Despite the typical fractal-like outcomes of Laplacian growth processes, the equations of motion are shown to be not particularly sensitive to initial conditions. It is argued that the sensitivity of this system derives from a novel cause, the non-uniqueness of solutions to the differential system. By a mechanism of singularity creation, every solution can become more complex, even in the absence of noise, without violating the growth law. These processes are permitted, but are not required, meaning the equation of motion does not determine the motion, even in the small.Comment: 8 pages, Latex, 4 figures, Submitted to Phys. Rev.

Multidimensional Pattern Formation Has an Infinite Number of Constants of Motion

Extending our previous work on 2D growth for the Laplace equation we study here {\it multidimensional} growth for {\it arbitrary elliptic} equations, describing inhomogeneous and anisotropic pattern formations processes. We find that these nonlinear processes are governed by an infinite number of conservation laws. Moreover, in many cases {\it all dynamics of the interface can be reduced to the linear time--dependence of only one ``moment" $M_0$} which corresponds to the changing volume while {\it all higher moments, $M_l$, are constant in time. These moments have a purely geometrical nature}, and thus carry information about the moving shape. These conserved quantities (eqs.~(7) and (8) of this article) are interpreted as coefficients of the multipole expansion of the Newtonian potential created by the mass uniformly occupying the domain enclosing the moving interface. Thus the question of how to recover the moving shape using these conserved quantities is reduced to the classical inverse potential problem of reconstructing the shape of a body from its exterior gravitational potential. Our results also suggest the possibility of controlling a moving interface by appropriate varying the location and strength of sources and sinks.Comment: CYCLER Paper 93feb00

A theory for the impact of a wave breaking onto a permeable barrier with jet generation

We model a water wave impact onto a porous breakwater. The breakwater surface is modelled as a thin barrier composed of solid matter pierced by channels through which water can flow freely. The water in the wave is modelled as a finite-length volume of inviscid, incompressible fluid in quasi-one-dimensional flow during its impact and flow through a typical hole in the barrier. The fluid volume moves at normal incidence to the barrier. After the initial impact the wave water starts to slow down as it passes through holes in the barrier. Each hole is the source of a free jet along whose length the fluid velocity and width vary in such a way as to conserve volume and momentum at zero pressure. We find there are two types of flow, depending on the porosity, ß , of the barrier. If ß : 0 = ß < 0.5774 then the barrier is a strong impediment to the flow, in that the fluid velocity tends to zero as time tends to infinity. But if ß : 0.5774 = ß = 1 then the barrier only temporarily holds up the flow, and the decelerating wave water passes through in a finite time. We report results for the velocity and impact pressure due to the incident wave water, and for the evolving shape of the jet, with examples from both types of impact. We account for the impulse on the barrier and the conserved kinetic energy of the flow. Consideration of small ß gives insight into the sudden changes in flow and the high pressures that occur when a wave impacts a nearly impermeable seawall

A New Class of Nonsingular Exact Solutions for Laplacian Pattern Formation

We present a new class of exact solutions for the so-called {\it Laplacian Growth Equation} describing the zero-surface-tension limit of a variety of 2D pattern formation problems. Contrary to common belief, we prove that these solutions are free of finite-time singularities (cusps) for quite general initial conditions and may well describe real fingering instabilities. At long times the interface consists of N separated moving Saffman-Taylor fingers, with ``stagnation points'' in between, in agreement with numerous observations. This evolution resembles the N-soliton solution of classical integrable PDE's.Comment: LaTeX, uuencoded postscript file

Integrable Structure of Interface Dynamics

We establish the equivalence of a 2D contour dynamics to the dispersionless limit of the integrable Toda hierarchy constrained by a string equation. Remarkably, the same hierarchy underlies 2D quantum gravity.Comment: 5 pages, no figures, submitted to Phys. Rev. Lett, typos correcte

Bayesian genome assembly and assessment by Markov Chain Monte Carlo sampling

Most genome assemblers construct point estimates, choosing a genome sequence from among many alternative hypotheses that are supported by the data. We present a Markov Chain Monte Carlo approach to sequence assembly that instead generates distributions of assembly hypotheses with posterior probabilities, providing an explicit statistical framework for evaluating alternative hypotheses and assessing assembly uncertainty. We implement this approach in a prototype assembler and illustrate its application to the bacteriophage PhiX174.Comment: 17 pages, 5 figure

Three-dimensional steep wave impact on a vertical plate with an open rectangular section

The present study treats the three-dimensional hydrodynamic slamming problem on a vertical plate subjected to the impact of a steep wave moving towards the plate with a constant velocity. The problem is complicated significantly by assuming that there is a rectangular opening on the plate which allows a discharge of the liquid. The analysis is conducted analytically assuming linear potential theory. The examined configuration determines two boundary value problems with mixed conditions which fully are taken into account. The mathematical process assimilates the plate with a degenerate elliptical cylinder allowing the employment of elliptical harmonics that ensure the satisfaction of the free-surface boundary condition of the front face of the steep wave, away from the plate. This assumption leads to an additional boundary value problem with mixed conditions in the vertical direction. The associated problem involves triple trigonometrical series and it is solved through a transformation into integral equations. To tackle the boundary value problem in the vertical direction a perturbation technique is employed. Extensive numerical calculations are presented as regards the variation of the velocity potential on the plate at the instant of the impact which reveals the influence of the opening. The theory is extended to the computation of the total impulse exerted on the plate using pressure-impulse theory

Hybrid Parallelism for Volume Rendering on Large, Multi- and Many-core Systems

With the computing industry trending towards multi- and many-core processors, we study how a standard visualization algorithm, ray-casting volume rendering, can benefit from a hybrid parallelism approach. Hybrid parallelism provides the best of both worlds: using distributed-memory parallelism across a large numbers of nodes increases available FLOPs and memory, while exploiting shared-memory parallelism among the cores within each node ensures that each node performs its portion of the larger calculation as efficiently as possible. We demonstrate results from weak and strong scaling studies, at levels of concurrency ranging up to 216,000, and with datasets as large as 12.2 trillion cells. The greatest benefit from hybrid parallelism lies in the communication portion of the algorithm, the dominant cost at higher levels of concurrency. We show that reducing the number of participants with a hybrid approach significantly improves performance

H5hut: A high-performance I/O library for particle-based simulations

Particle-based simulations running on large high-performance computing systems over many time steps can generate an enormous amount of particle- and field-based data for post-processing and analysis. Achieving high-performance I/O for this data, effectively managing it on disk, and interfacing it with analysis and visualization tools can be challenging, especially for domain scientists who do not have I/O and data management expertise. We present the H5hut library, an implementation of several data models for particle-based simulations that encapsulates the complexity of HDF5 and is simple to use, yet does not compromise performance