Periodic and Localized Solutions of the Long Wave-Short Wave Resonance Interaction Equation

In this paper, we investigate the (2+1) dimensional long wave-short wave resonance interaction (LSRI) equation and show that it possess the Painlev\'e property. We then solve the LSRI equation using Painlev\'e truncation approach through which we are able to construct solution in terms of three arbitrary functions. Utilizing the arbitrary functions present in the solution, we have generated a wide class of elliptic function periodic wave solutions and exponentially localized solutions such as dromions, multidromions, instantons, multi-instantons and bounded solitary wave solutions.Comment: 13 pages, 6 figure

Global axisymmetric stability analysis for a composite system of two gravitationally coupled scale-free discs

In a composite system of gravitationally coupled stellar and gaseous discs, we perform linear stability analysis for axisymmetric coplanar perturbations using the two-fluid formalism. The background stellar and gaseous discs are taken to be scale-free with all physical variables varying as powers of cylindrical radius $r$ with compatible exponents. The unstable modes set in as neutral modes or stationary perturbation configurations with angular frequency $\omega=0$.Comment: 7 pages using AAS styl

A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions and its applications

A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions is derived by using the homogeneous balance method. With the aid of the transformation given here, exact solutions of the equations are obtained

Boosting Stop Searches with a 100 TeV Proton Collider

A proton-proton collider with center of mass energy around 100 TeV is the energy frontier machine that is likely to succeed the LHC. One of the primary physics goals will be the continued exploration of weak scale naturalness. Here we focus on the pair-production of stops that decay to a top and a neutralino. Most of the heavy stop parameter space results in highly boosted tops, populating kinematic regimes inaccessible at the LHC. New strategies for boosted top-tagging are needed and a simple, detector-independent tagger can be constructed by requiring a muon inside a jet. Assuming 20% systematic uncertainties, this future collider can discover (exclude) stops with masses up to 6.5 (8) TeV with 3000 fb^-1 of integrated luminosity. Studying how the exclusion limits scale with luminosity motivates going beyond this benchmark in order to saturate the discovery potential of the machine.Comment: v2: 16 pages, 17 figures, results updated using NLL+NLO cross sections, journal versio

New variable separation approach: application to nonlinear diffusion equations

The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the derivative-dependent functional separable solutions is obtained and some exact solutions to the resulting equations are described.Comment: 19 pages, 2 fig

Redundancy relations and robust failure detection

All failure detection methods are based on the use of redundancy, that is on (possible dynamic) relations among the measured variables. Consequently the robustness of the failure detection process depends to a great degree on the reliability of the redundancy relations given the inevitable presence of model uncertainties. The problem of determining redundancy relations which are optimally robust in a sense which includes the major issues of importance in practical failure detection is addressed. A significant amount of intuition concerning the geometry of robust failure detection is provided

Effect of manganese doping on the size effect of lead zirconate titanate thin films and the extrinsic nature of dead layers

We have investigated the size effect in lead zirconate titanate (PZT) thin films with a range of manganese (Mn) doping concentrations. We found that the size effect in the conventional Pt/PZT/Pt thin-film capacitors could be systematically reduced and almost completely eliminated by increasing Mn doping concentration. The interfacial layer at the electrode-film interface appears to disappear almost entirely for the PZT films with 2% Mn doping levels, confirmed by the fits using the conventional in-series capacitor model. Our work indicates that the size effect in ferroelectrics is extrinsic in nature, supporting the work by Saad et al. Other implications of our results have also been discussed. By comparing a variety of experimental studies in the literature we propose a scenario that the dead layer between PZT (or barium strontium titanate, BST) and metal electrodes such as Pt and Au might have a defective pyrochlore/fluorite structure (possibly with a small portion of ferroelectric perovskite phase).Comment: 21 pages, 6 figure

Differential Maintenance of DNA Sequences in Telomeric and Centromeric Heterochromatin

Repeated DNA in heterochromatin presents enormous difficulties for whole-genome sequencing; hence, sequence organization in a significant portion of the genomes of multicellular organisms is relatively unknown. Two sequenced BACs now allow us to compare telomeric retrotransposon arrays from Drosophila melanogaster telomeres with an array of telomeric retrotransposons that transposed into the centromeric region of the Y chromosome >13 MYA, providing a unique opportunity to compare the structural evolution of this retrotransposon in two contexts. We find that these retrotransposon arrays, both heterochromatic, are maintained quite differently, resulting in sequence organizations that apparently reflect different roles in the two chromosomal environments. The telomere array has grown only by transposition of new elements to the chromosome end; the centromeric array instead has grown by repeated amplifications of segments of the original telomere array. Many elements in the telomere have been variably 5′-truncated apparently by gradual erosion and irregular deletions of the chromosome end; however, a significant fraction (4 and possibly 5 or 6 of 15 elements examined) remain complete and capable of further retrotransposition. In contrast, each element in the centromere region has lost ≥40% of its sequence by internal, rather than terminal, deletions, and no element retains a significant part of the original coding region. Thus the centromeric array has been restructured to resemble the highly repetitive satellite sequences typical of centromeres in multicellular organisms, whereas, over a similar or longer time period, the telomere array has maintained its ability to provide retrotransposons competent to extend telomere ends.National Institutes of Health (U.S.) (grant GM50315

Note on the hydrodynamic description of thin nematic films: strong anchoring model

We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clarify how the elastic energy enters the evolution equation for the film thickness in order to provide a solid basis for further investigation: several conflicting models exist in the literature that predict qualitatively different behaviour. We consolidate the various approaches and show that the long-wave model derived through an asymptotic expansion of the full nemato-hydrodynamic equations with consistent boundary conditions agrees with the model one obtains by employing a thermodynamically motivated gradient dynamics formulation based on an underlying free energy functional. As a result, we find that in the case of strong anchoring the elastic distortion energy is always stabilising. To support the discussion in the main part of the paper, an appendix gives the full derivation of the evolution equation for the film thickness via asymptotic expansion