Accurate Reaction-Diffusion Operator Splitting on Tetrahedral Meshes for Parallel Stochastic Molecular Simulations

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, meaning that the serial limit has already been reached in sub-cellular models. This calls for parallel simulations that can take advantage of the power of modern supercomputers; however exact methods are known to be inherently serial. We introduce an operator splitting implementation for irregular grids with a novel method to improve accuracy, and demonstrate potential for scalable parallel simulations in an initial MPI version. We foresee that this groundwork will enable larger scale, whole-cell stochastic simulations in the near future.Comment: 33 pages, 10 figure

Localized gap soliton trains of Bose-Einstein condensates in an optical lattice

We develop a systematic analytical approach to study the linear and nonlinear solitary excitations of quasi-one-dimensional Bose-Einstein condensates trapped in an optical lattice. For the linear case, the Bloch wave in the $nth$ energy band is a linear superposition of Mathieu's functions $ce_{n-1}$ and $se_n$; and the Bloch wave in the $nth$ band gap is a linear superposition of $ce_n$ and $se_n$. For the nonlinear case, only solitons inside the band gaps are likely to be generated and there are two types of solitons -- fundamental solitons (which is a localized and stable state) and sub-fundamental solitons (which is a lacalized but unstable state). In addition, we find that the pinning position and the amplitude of the fundamental soliton in the lattice can be controlled by adjusting both the lattice depth and spacing. Our numerical results on fundamental solitons are in quantitative agreement with those of the experimental observation [Phys. Rev. Lett. {\bf92}, 230401 (2004)]. Furthermore, we predict that a localized gap soliton train consisting of several fundamental solitons can be realized by increasing the length of the condensate in currently experimental conditions.Comment: 9 pages, 6 figures, accepted for publicaiton in PR

An approach for assessing software prototypes

A procedure for evaluating a software prototype is presented. The need to assess the prototype itself arises from the use of prototyping to demonstrate the feasibility of a design or development stategy. The assessment procedure can also be of use in deciding whether to evolve a prototype into a complete system. The procedure consists of identifying evaluations criteria, defining alterative design approaches, and ranking the alternatives according to the criteria

Thermal correlators of anyons in two dimensions

The anyon fields have trivial $\alpha$-commutator for $\alpha$ not integer. For integer $\alpha$ the commutators become temperature-dependent operator valued distributions. The $n$-point functions do not factorize as for quasifree states.Comment: 14 pages, LaTeX (misprints corrected, a reference added

Reconstructed Intentions in Collaborative Problem Solving Dialogues

We provide evidence that speech act recognition, is 1) difficult for humans to do and 2) likely to misidentify proposals involving reconstructed intentions. We examine the reliability of coding for speech acts in collaborative dialogues and we present an approach for recognizing reconstructed proposals using domain context and other more easily recognized features. 1 Introduction Speech act recognition plays a prominent role in dialogue understanding, in traditional approaches that infer a plan using plan construction operators [PA80], [LA90], [LC91, LC92], and in more recent techniques relying on statistical correlations or finite state machines [RM95, QDL + 97]. Both approaches recognize surface speech acts, using surface form and information provided by the discourse context and the discourse operators, or by a finite state approximation of the planning information. These approaches assume that it is (relatively) simple to recognize speech acts, and that speech acts are a requi..

The world-sheet description of A and B branes revisited

We give a manifest supersymmetric description of A and B branes on Kahler manifolds using a completely local N=2 superspace formulation of the world-sheet nonlinear sigma-model in the presence of a boundary. In particular, we show that an N=2 superspace description of type A boundaries is possible, at least when the background is Kahler. This leads to an elegant and concrete setting for studying coisotropic A branes. Here, apgesan important role is played by the boundary potential, whose precise physical meaning remains to be fully understood. Duality transformations relating A and B branes in the presence of isometries are studied as well.Comment: LaTeX, 32 page

An astronomical search for evidence of new physics: Limits on gravity-induced birefringence from the magnetic white dwarf RE J0317-853

The coupling of the electromagnetic field directly with gravitational gauge fields leads to new physical effects that can be tested using astronomical data. Here we consider a particular case for closer scrutiny, a specific nonminimal coupling of torsion to electromagnetism, which enters into a metric-affine geometry of space-time. We show that under the assumption of this nonminimal coupling, spacetime is birefringent in the presence of such a gravitational field. This leads to the depolarization of light emitted from extended astrophysical sources. We use polarimetric data of the magnetic white dwarf ${RE J0317-853}$ to set strong constraints on the essential coupling constant for this effect, giving k^2 \lsim (19 {m})^2 .Comment: Statements about Moffat's NGT modified. Accepted for publication in Phys.Rev.

(Never) Mind your p's and q's: Von Neumann versus Jordan on the Foundations of Quantum Theory

In two papers entitled "On a new foundation [Neue Begr\"undung] of quantum mechanics," Pascual Jordan (1927b,g) presented his version of what came to be known as the Dirac-Jordan statistical transformation theory. As an alternative that avoids the mathematical difficulties facing the approach of Jordan and Paul A. M. Dirac (1927), John von Neumann (1927a) developed the modern Hilbert space formalism of quantum mechanics. In this paper, we focus on Jordan and von Neumann. Central to the formalisms of both are expressions for conditional probabilities of finding some value for one quantity given the value of another. Beyond that Jordan and von Neumann had very different views about the appropriate formulation of problems in quantum mechanics. For Jordan, unable to let go of the analogy to classical mechanics, the solution of such problems required the identication of sets of canonically conjugate variables, i.e., p's and q's. For von Neumann, not constrained by the analogy to classical mechanics, it required only the identication of a maximal set of commuting operators with simultaneous eigenstates. He had no need for p's and q's. Jordan and von Neumann also stated the characteristic new rules for probabilities in quantum mechanics somewhat differently. Jordan (1927b) was the first to state those rules in full generality. Von Neumann (1927a) rephrased them and, in a subsequent paper (von Neumann, 1927b), sought to derive them from more basic considerations. In this paper we reconstruct the central arguments of these 1927 papers by Jordan and von Neumann and of a paper on Jordan's approach by Hilbert, von Neumann, and Nordheim (1928). We highlight those elements in these papers that bring out the gradual loosening of the ties between the new quantum formalism and classical mechanics.Comment: New version. The main difference with the old version is that the introduction has been rewritten. Sec. 1 (pp. 2-12) in the old version has been replaced by Secs. 1.1-1.4 (pp. 2-31) in the new version. The paper has been accepted for publication in European Physical Journal

On second-order differential equations with highly oscillatory forcing terms

We present a method to compute efficiently solutions of systems of ordinary differential equations that possess highly oscillatory forcing terms. This approach is based on asymptotic expansions in inverse powers of the oscillatory parameter,and features two fundamental advantages with respect to standard ODE solvers: rstly, the construction of the numerical solution is more efficient when the system is highly oscillatory, and secondly, the cost of the computation is essentially independent of the oscillatory parameter. Numerical examples are provided, motivated by problems in electronic engineering

Symmetric three-particle motion in Stokes flow: equilibrium for heavy spheres in contrast to "end-of-world" for point forces

A stationary stable solution of the Stokes equations for three identical heavy solid spheres falling in a vertical plane is found. It has no analog in the point-particle approximation. Three spheres aligned horizontally at equal distances evolve towards the equilibrium relative configuration while the point particles collapse onto a single point in a finite time.Comment: 4 pages, 7 figure