Discrete soliton collisions in a waveguide array with saturable nonlinearity

We study the symmetric collisions of two mobile breathers/solitons in a model for coupled wave guides with a saturable nonlinearity. The saturability allows the existence of breathers with high power. Three main regimes are observed: breather fusion, breather reflection and breather creation. The last regime seems to be exclusive of systems with a saturable nonlinearity, and has been previously observed in continuous models. In some cases a ``symmetry breaking'' can be observed, which we show to be an numerical artifact.Comment: 5 pages, 7 figure

Some New Addition Formulae for Weierstrass Elliptic Functions

We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit addition formulae for the 2- and 3-variable cases. These new results were inspired by new addition formulae found in the case of an equianharmonic curve, which we can now observe as a specialisation of the results here. The new formulae, and the techniques used to find them, also follow the recent work for the generalisation of Weierstrass' functions to curves of higher genus.Comment: 20 page

Steady State Solutions of a Mass-Conserving Bistable Equation with a Saturating Flux

We consider a mass-conserving bistable equation with a saturating flux on an interval. This is the quasilinear analogue of the Rubinstein-Steinberg equation, suitable for description of order parameter conserving solid-solid phase transitions in the case of large spatial gradients in the order parameter. We discuss stationary solutions and investigate the change in bifurcation diagrams as the mass constraint and the length of the interval are varied.Comment: 26 pages, 14 figure

Artificial boundary conditions for the linearized Benjamin-Bona-Mahony equation

International audienceWe consider various approximations of artificial boundary conditions for linearized Benjamin-Bona-Mahoney equation. Continuous (respectively discrete) artificial boundary conditions involve non local operators in time which in turn requires to compute time convolutions and invert the Laplace transform of an analytic function (respectively the Z-transform of an holomorphic function). In this paper, we derive explicit transparent boundary conditions both continuous and discrete for the linearized BBM equation. The equation is discretized with the Crank Nicolson time discretization scheme and we focus on the difference between the upwind and the centered discretization of the convection term. We use these boundary conditions to compute solutions with compact support in the computational domain and also in the case of an incoming plane wave which is an exact solution of the linearized BBM equation. We prove consistency, stability and convergence of the numerical scheme and provide many numerical experiments to show the efficiency of our tranparent boundary conditions

Out-of-equilibrium physics in driven dissipative coupled resonator arrays

Coupled resonator arrays have been shown to exhibit interesting many- body physics including Mott and Fractional Hall states of photons. One of the main differences between these photonic quantum simulators and their cold atoms coun- terparts is in the dissipative nature of their photonic excitations. The natural equi- librium state is where there are no photons left in the cavity. Pumping the system with external drives is therefore necessary to compensate for the losses and realise non-trivial states. The external driving here can easily be tuned to be incoherent, coherent or fully quantum, opening the road for exploration of many body regimes beyond the reach of other approaches. In this chapter, we review some of the physics arising in driven dissipative coupled resonator arrays including photon fermionisa- tion, crystallisation, as well as photonic quantum Hall physics out of equilibrium. We start by briefly describing possible experimental candidates to realise coupled resonator arrays along with the two theoretical models that capture their physics, the Jaynes-Cummings-Hubbard and Bose-Hubbard Hamiltonians. A brief review of the analytical and sophisticated numerical methods required to tackle these systems is included.Comment: Chapter that appeared in "Quantum Simulations with Photons and Polaritons: Merging Quantum Optics with Condensed Matter Physics" edited by D.G.Angelakis, Quantum Science and Technology Series, Springer 201

Genome Assembly Has a Major Impact on Gene Content: A Comparison of Annotation in Two Bos Taurus Assemblies

Gene and SNP annotation are among the first and most important steps in analyzing a genome. As the number of sequenced genomes continues to grow, a key question is: how does the quality of the assembled sequence affect the annotations? We compared the gene and SNP annotations for two different Bos taurus genome assemblies built from the same data but with significant improvements in the later assembly. The same annotation software was used for annotating both sequences. While some annotation differences are expected even between high-quality assemblies such as these, we found that a staggering 40% of the genes (>9,500) varied significantly between assemblies, due in part to the availability of new gene evidence but primarily to genome mis-assembly events and local sequence variations. For instance, although the later assembly is generally superior, 660 protein coding genes in the earlier assembly are entirely missing from the later genome's annotation, and approximately 3,600 (15%) of the genes have complex structural differences between the two assemblies. In addition, 12–20% of the predicted proteins in both assemblies have relatively large sequence differences when compared to their RefSeq models, and 6–15% of bovine dbSNP records are unrecoverable in the two assemblies. Our findings highlight the consequences of genome assembly quality on gene and SNP annotation and argue for continued improvements in any draft genome sequence. We also found that tracking a gene between different assemblies of the same genome is surprisingly difficult, due to the numerous changes, both small and large, that occur in some genes. As a side benefit, our analyses helped us identify many specific loci for improvement in the Bos taurus genome assembly

A Semantic Problem Solving Environment for Integrative Parasite Research: Identification of Intervention Targets for Trypanosoma cruzi

Effective research in parasite biology requires analyzing experimental lab data in the context of constantly expanding public data resources. Integrating lab data with public resources is particularly difficult for biologists who may not possess significant computational skills to acquire and process heterogeneous data stored at different locations. Therefore, we develop a semantic problem solving environment (SPSE) that allows parasitologists to query their lab data integrated with public resources using ontologies. An ontology specifies a common vocabulary and formal relationships among the terms that describe an organism, and experimental data and processes in this case. SPSE supports capturing and querying provenance information, which is metadata on the experimental processes and data recorded for reproducibility, and includes a visual query-processing tool to formulate complex queries without learning the query language syntax. We demonstrate the significance of SPSE in identifying gene knockout targets for T. cruzi. The overall goal of SPSE is to help researchers discover new or existing knowledge that is implicitly present in the data but not always easily detected. Results demonstrate improved usefulness of SPSE over existing lab systems and approaches, and support for complex query design that is otherwise difficult to achieve without the knowledge of query language syntax

The Putative Liquid-Liquid Transition is a Liquid-Solid Transition in Atomistic Models of Water

We use numerical simulation to examine the possibility of a reversible liquid-liquid transition in supercooled water and related systems. In particular, for two atomistic models of water, we have computed free energies as functions of multiple order parameters, where one is density and another distinguishes crystal from liquid. For a range of temperatures and pressures, separate free energy basins for liquid and crystal are found, conditions of phase coexistence between these phases are demonstrated, and time scales for equilibration are determined. We find that at no range of temperatures and pressures is there more than a single liquid basin, even at conditions where amorphous behavior is unstable with respect to the crystal. We find a similar result for a related model of silicon. This result excludes the possibility of the proposed liquid-liquid critical point for the models we have studied. Further, we argue that behaviors others have attributed to a liquid-liquid transition in water and related systems are in fact reflections of transitions between liquid and crystal

The Chemical Information Ontology: Provenance and Disambiguation for Chemical Data on the Biological Semantic Web

Cheminformatics is the application of informatics techniques to solve chemical problems in silico. There are many areas in biology where cheminformatics plays an important role in computational research, including metabolism, proteomics, and systems biology. One critical aspect in the application of cheminformatics in these fields is the accurate exchange of data, which is increasingly accomplished through the use of ontologies. Ontologies are formal representations of objects and their properties using a logic-based ontology language. Many such ontologies are currently being developed to represent objects across all the domains of science. Ontologies enable the definition, classification, and support for querying objects in a particular domain, enabling intelligent computer applications to be built which support the work of scientists both within the domain of interest and across interrelated neighbouring domains. Modern chemical research relies on computational techniques to filter and organise data to maximise research productivity. The objects which are manipulated in these algorithms and procedures, as well as the algorithms and procedures themselves, enjoy a kind of virtual life within computers. We will call these information entities. Here, we describe our work in developing an ontology of chemical information entities, with a primary focus on data-driven research and the integration of calculated properties (descriptors) of chemical entities within a semantic web context. Our ontology distinguishes algorithmic, or procedural information from declarative, or factual information, and renders of particular importance the annotation of provenance to calculated data. The Chemical Information Ontology is being developed as an open collaborative project. More details, together with a downloadable OWL file, are available at http://code.google.com/p/semanticchemistry/ (license: CC-BY-SA)