Wave envelopes with second-order spatiotemporal dispersion : I. Bright Kerr solitons and cnoidal waves

We propose a simple scalar model for describing pulse phenomena beyond the conventional slowly-varying envelope approximation. The generic governing equation has a cubic nonlinearity and we focus here mainly on contexts involving anomalous group-velocity dispersion. Pulse propagation turns out to be a problem firmly rooted in frames-of-reference considerations. The transformation properties of the new model and its space-time structure are explored in detail. Two distinct representations of exact analytical solitons and their associated conservation laws (in both integral and algebraic forms) are presented, and a range of new predictions is made. We also report cnoidal waves of the governing nonlinear equation. Crucially, conventional pulse theory is shown to emerge as a limit of the more general formulation. Extensive simulations examine the role of the new solitons as robust attractors

A Fast and Accurate Cost Model for FPGA Design Space Exploration in HPC Applications

Heterogeneous High-Performance Computing (HPC) platforms present a significant programming challenge, especially because the key users of HPC resources are scientists, not parallel programmers. We contend that compiler technology has to evolve to automatically create the best program variant by transforming a given original program. We have developed a novel methodology based on type transformations for generating correct-by-construction design variants, and an associated light-weight cost model for evaluating these variants for implementation on FPGAs. In this paper we present a key enabler of our approach, the cost model. We discuss how we are able to quickly derive accurate estimates of performance and resource-utilization from the design’s representation in our intermediate language. We show results confirming the accuracy of our cost model by testing it on three different scientific kernels. We conclude with a case-study that compares a solution generated by our framework with one from a conventional high-level synthesis tool, showing better performance and power-efficiency using our cost model based approach

Spanning trees for the geometry and dynamics of compact polymers

Using a mapping of compact polymers on the Manhattan lattice to spanning trees, we calculate exactly the average number of bends at infinite temperature. We then find, in a high temperature approximation, the energy of the system as a function of bending rigidity and polymer elasticity. We identify the universal mechanism for the relaxation of compact polymers and then endow the model with physically motivated dynamics in the convenient framework of the trees. We find aging and domain coarsening after quenches in temperature. We explain the slow dynamics in terms of the geometrical interconnections between the energy and the dynamics.Comment: 10 pages, 8 figure

Wave envelopes with second-order spatiotemporal dispersion: II. Modulational instabilities and dark Kerr solitons

A simple scalar model for describing spatiotemporal dispersion of pulses, beyond the classic “slowly-varying envelopes + Galilean boost” approach, is studied. The governing equation has a cubic nonlinearity and we focus here mainly on contexts with normal group-velocity dispersion. A complete analysis of continuous waves is reported, including their dispersion relations and modulational instability characteristics. We also present a detailed derivation of exact analytical dark solitons, obtained by combining direct-integration methods with geometrical transformations. Classic results from conventional pulse theory are recovered as-ymptotically from the spatiotemporal formulation. Numerical simulations test new theoretical predictions for modulational instability, and examine the robustness of spatiotemporal dark solitons against perturbations to their local pulse shape

Bayesian Cosmic Web Reconstruction: BARCODE for Clusters

We describe the Bayesian BARCODE formalism that has been designed towards the reconstruction of the Cosmic Web in a given volume on the basis of the sampled galaxy cluster distribution. Based on the realization that the massive compact clusters are responsible for the major share of the large scale tidal force field shaping the anisotropic and in particular filamentary features in the Cosmic Web. Given the nonlinearity of the constraints imposed by the cluster configurations, we resort to a state-of-the-art constrained reconstruction technique to find a proper statistically sampled realization of the original initial density and velocity field in the same cosmic region. Ultimately, the subsequent gravitational evolution of these initial conditions towards the implied Cosmic Web configuration can be followed on the basis of a proper analytical model or an N-body computer simulation. The BARCODE formalism includes an implicit treatment for redshift space distortions. This enables a direct reconstruction on the basis of observational data, without the need for a correction of redshift space artifacts. In this contribution we provide a general overview of the the Cosmic Web connection with clusters and a description of the Bayesian BARCODE formalism. We conclude with a presentation of its successful workings with respect to test runs based on a simulated large scale matter distribution, in physical space as well as in redshift space.Comment: 18 pages, 8 figures, Proceedings of IAU Symposium 308 "The Zeldovich Universe: Genesis and Growth of the Cosmic Web", 23-28 June 2014, Tallinn, Estoni

Bistable Helmholtz bright solitons in saturable materials

We present, to the best of our knowledge, the first exact analytical solitons of a nonlinear Helmholtz equation with a saturable refractive-index model. These new two-dimensional spatial solitons have a bistable characteristic in some parameter regimes, and they capture oblique (arbitrary-angle) beam propagation in both the forward and backward directions. New conservation laws are reported, and the classic paraxial solution is recovered in an appropriate multiple limit. Analysis and simulations examine the stability of both solution branches, and stationary Helmholtz solitons are found to emerge from a range of perturbed input beams