Self-trapping transition for nonlinear impurities embedded in a Cayley tree

The self-trapping transition due to a single and a dimer nonlinear impurity embedded in a Cayley tree is studied. In particular, the effect of a perfectly nonlinear Cayley tree is considered. A sharp self-trapping transition is observed in each case. It is also observed that the transition is much sharper compared to the case of one-dimensional lattices. For each system, the critical values of $\chi$ for the self-trapping transitions are found to obey a power-law behavior as a function of the connectivity $K$ of the Cayley tree.Comment: 6 pages, 7 fig

Do nonlinear waves in random media follow nonlinear diffusion equations?

Probably yes, since we find a striking similarity in the spatio-temporal evolution of nonlinear diffusion equations and wave packet spreading in generic nonlinear disordered lattices, including self-similarity and scaling.Comment: 6 pages, 4 figure

A note on quasinormal modes: A tale of two treatments

There is an apparent discrepancy in the literature with regard to the quasinormal mode frequencies of Schwarzschild-de Sitter black holes in the degenerate-horizon limit. On the one hand, a Poschl-Teller-inspired method predicts that the real part of the frequencies will depend strongly on the orbital angular momentum of the perturbation field whereas, on the other hand, the degenerate limit of a monodromy-based calculation suggests there should be no such dependence (at least, for the highly damped modes). In the current paper, we provide a possible resolution by critically re-assessing the limiting procedure used in the monodromy analysis.Comment: 11 pages, Revtex format; (v2) new addendum in response to reader comments, also references, footnote and acknowledgments adde

Silicon-on-insulator polarization controller with relaxed fabrication tolerances

Polarization control is essential in applications ranging from optical communications to interferometric sensors. The implementation of in- tegrated polarization controllers is challenging as they require polariza- tion rotating waveguides with stringent fabrication tolerances. Here, we present a fully integrated polarization controller scheme that signi cantly relaxes the requirements on the rotating waveguides, alleviating fabri- cation tolerances. We analytically establish a technology-independent, easily measurable tolerance condition for the rotating waveguides. Po- larization control in the presence of waveguide width errors of 25% is shown through full vectorial simulation.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Heat kernel regularization of the effective action for stochastic reaction-diffusion equations

The presence of fluctuations and non-linear interactions can lead to scale dependence in the parameters appearing in stochastic differential equations. Stochastic dynamics can be formulated in terms of functional integrals. In this paper we apply the heat kernel method to study the short distance renormalizability of a stochastic (polynomial) reaction-diffusion equation with real additive noise. We calculate the one-loop {\emph{effective action}} and its ultraviolet scale dependent divergences. We show that for white noise a polynomial reaction-diffusion equation is one-loop {\emph{finite}} in $d=0$ and $d=1$, and is one-loop renormalizable in $d=2$ and $d=3$ space dimensions. We obtain the one-loop renormalization group equations and find they run with scale only in $d=2$.Comment: 21 pages, uses ReV-TeX 3.

Nonlinear Lattice Waves in Random Potentials

Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in photonic crystals, and dynamics of ultra-cold atoms in optical arrays. Large intensity light can induce nonlinear response, ultracold atomic gases can be tuned into an interacting regime, which leads again to nonlinear wave equations on a mean field level. The interplay between disorder and nonlinearity, their localizing and delocalizing effects is currently an intriguing and challenging issue in the field. We will discuss recent advances in the dynamics of nonlinear lattice waves in random potentials. In the absence of nonlinear terms in the wave equations, Anderson localization is leading to a halt of wave packet spreading. Nonlinearity couples localized eigenstates and, potentially, enables spreading and destruction of Anderson localization due to nonintegrability, chaos and decoherence. The spreading process is characterized by universal subdiffusive laws due to nonlinear diffusion. We review extensive computational studies for one- and two-dimensional systems with tunable nonlinearity power. We also briefly discuss extensions to other cases where the linear wave equation features localization: Aubry-Andre localization with quasiperiodic potentials, Wannier-Stark localization with dc fields, and dynamical localization in momentum space with kicked rotors.Comment: 45 pages, 19 figure

Equation of state for Universe from similarity symmetries

In this paper we proposed to use the group of analysis of symmetries of the dynamical system to describe the evolution of the Universe. This methods is used in searching for the unknown equation of state. It is shown that group of symmetries enforce the form of the equation of state for noninteracting scaling multifluids. We showed that symmetries give rise the equation of state in the form $p=-\Lambda+w_{1}\rho(a)+w_{2}a^{\beta}+0$ and energy density $\rho=\Lambda+\rho_{01}a^{-3(1+w)}+\rho_{02}a^{\beta}+\rho_{03}a^{-3}$, which is commonly used in cosmology. The FRW model filled with scaling fluid (called homological) is confronted with the observations of distant type Ia supernovae. We found the class of model parameters admissible by the statistical analysis of SNIa data. We showed that the model with scaling fluid fits well to supernovae data. We found that $\Omega_{\text{m},0} \simeq 0.4$ and $n \simeq -1$ ($\beta = -3n$), which can correspond to (hyper) phantom fluid, and to a high density universe. However if we assume prior that $\Omega_{\text{m},0}=0.3$ then the favoured model is close to concordance $\Lambda$CDM model. Our results predict that in the considered model with scaling fluids distant type Ia supernovae should be brighter than in $\Lambda$CDM model, while intermediate distant SNIa should be fainter than in $\Lambda$CDM model. We also investigate whether the model with scaling fluid is actually preferred by data over $\Lambda$CDM model. As a result we find from the Akaike model selection criterion prefers the model with noninteracting scaling fluid.Comment: accepted for publication versio

Four Lessons in Versatility or How Query Languages Adapt to the Web

Exposing not only human-centered information, but machine-processable data on the Web is one of the commonalities of recent Web trends. It has enabled a new kind of applications and businesses where the data is used in ways not foreseen by the data providers. Yet this exposition has fractured the Web into islands of data, each in different Web formats: Some providers choose XML, others RDF, again others JSON or OWL, for their data, even in similar domains. This fracturing stifles innovation as application builders have to cope not only with one Web stack (e.g., XML technology) but with several ones, each of considerable complexity. With Xcerpt we have developed a rule- and pattern based query language that aims to give shield application builders from much of this complexity: In a single query language XML and RDF data can be accessed, processed, combined, and re-published. Though the need for combined access to XML and RDF data has been recognized in previous work (including the W3C’s GRDDL), our approach differs in four main aspects: (1) We provide a single language (rather than two separate or embedded languages), thus minimizing the conceptual overhead of dealing with disparate data formats. (2) Both the declarative (logic-based) and the operational semantics are unified in that they apply for querying XML and RDF in the same way. (3) We show that the resulting query language can be implemented reusing traditional database technology, if desirable. Nevertheless, we also give a unified evaluation approach based on interval labelings of graphs that is at least as fast as existing approaches for tree-shaped XML data, yet provides linear time and space querying also for many RDF graphs. We believe that Web query languages are the right tool for declarative data access in Web applications and that Xcerpt is a significant step towards a more convenient, yet highly efficient data access in a “Web of Data”

ParadisEO-MOEO: A Software Framework for Evolutionary Multi-Objective Optimization

This chapter presents ParadisEO-MOEO, a white-box object-oriented software framework dedicated to the flexible design of metaheuristics for multi-objective optimization. This paradigm-free software proposes a unified view for major evolutionary multi-objective metaheuristics. It embeds some features and techniques for multi-objective resolution and aims to provide a set of classes allowing to ease and speed up the development of computationally efficient programs. It is based on a clear conceptual distinction between the solution methods and the problems they are intended to solve. This separation confers a maximum design and code reuse. This general-purpose framework provides a broad range of fitness assignment strategies, the most common diversity preservation mechanisms, some elitistrelated features as well as statistical tools. Furthermore, a number of state-of-the-art search methods, including NSGA-II, SPEA2 and IBEA, have been implemented in a user-friendly way, based on the fine-grained ParadisEO-MOEO components

Commissioning of a synchrotron-based proton beam therapy system for use with a Monte Carlo treatment planning system

This work tackles the commissioning and validation of a novel combination of a synchrotron-based proton beam therapy system (Hitachi, Ltd.) for use with a Monte Carlo treatment planning system (TPS). Four crucial aspects in this configuration have been investigated: (1) Monte Carlo-based correction performed by the TPS to the measured integrated depth-dose curves (IDD), (2) circular spot modelling with a single Gaussian function to characterize the synchrotron physical spot, which is elliptical, (3) the modelling of the range shifter that enables using only one set of measurements in open beams, and (4) the Monte Carlo dose calculation model in small fields. Integrated depth-dose curves were measured with a PTW Bragg peak chamber and corrected, with a Monte Carlo model, to account for energy absorbed outside the detector. The elliptical spot was measured by IBA Lynx scintillator, EBT3 films and PTW microDiamond. The accuracy of the TPS (RayStation, RaySearch Laboratories) at spot modelling with a circular Gaussian function was assessed. The beam model was validated using spread-out Bragg peak (SOBP) fields. We took single-point doses at several depths through the central axis using a PTW Farmer chamber, for fields between 2 × 2cm and 30 × 30cm. We checked the range-shifter modelling from open-beam data. We tested clinical cases with film and an ioni- zation chamber array (IBA Matrix). Sigma differences for spots fitted using 2D images and 1D profiles to elliptical and circular Gaussian models were below 0.22 mm. Differences between SOBP measurements at single points and TPS calculations for all fields between 5 × 5 and 30 × 30cm were below 2.3%. Smaller fields had larger differences: up to 3.8% in the 2 × 2cm field. Mean differences at several depths along the central axis were generally below 1%. Differences in range- shifter doses were below 2.4%. Gamma test (3%, 3 mm) results for clinical cases were generally above 95% for Matrix and film. Approaches for modelling synchrotron proton beams have been validated. Dose values for open and range- shifter fields demonstrate accurate Monte Carlo correction for IDDs. Elliptical spots can be successfully modelled using a circular Gaussian, which is accurate for patient calculations and can be used for small fields. A double-Gaussian spot can improve small-field calculations. The range-shifter modelling approach, which reduces clinical commissioning time, is adequat