Soliton Interactions in Perturbed Nonlinear Schroedinger Equations

We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schroedinger equation under the influence of a small correction to the nonlinear potential. We assume that the solitons are all moving with the same velocity at the initial instant; this maximizes the effect each soliton has on the others as a consequence of the perturbation. Over the long time scales that we consider, the amplitudes of the solitons remain fixed, while their center of mass coordinates obey Newton's equations with a force law for which we present an integral formula. For the interaction of two solitons with a quintic perturbation term we present more details since symmetries -- one related to the form of the perturbation and one related to the small number of particles involved -- allow the problem to be reduced to a one-dimensional one with a single parameter, an effective mass. The main results include calculations of the binding energy and oscillation frequency of nearby solitons in the stable case when the perturbation is an attractive correction to the potential and of the asymptotic "ejection" velocity in the unstable case. Numerical experiments illustrate the accuracy of the perturbative calculations and indicate their range of validity.Comment: 28 pages, 7 figures, Submitted to Phys Rev E Revised: 21 pages, 6 figures, To appear in Phys Rev E (many displayed equations moved inline to shorten manuscript

One-parameter Darboux-transformed quantum actions in Thermodynamics

We use nonrelativistic supersymmetry, mainly Darboux transformations of the general (one-parameter) type, for the quantum oscillator thermodynamic actions. Interesting Darboux generalizations of the fundamental Planck and pure vacuum cases are discussed in some detail with relevant plots. It is shown that the one-parameter Darboux-transformed Thermodynamics refers to superpositions of boson and fermion excitations of positive and negative absolute temperature, respectively. Recent results of Arnaud, Chusseau, and Philippe physics/0105048 regarding a single mode oscillator Carnot cycle are extended in the same Darboux perspective. We also conjecture a Darboux generalization of the fluctuation-dissipation theoremComment: 14 pages, 13 figures, correction of the formula in the text after Eq. 7, accepted at Physica Script

Development and Application of a Functional Human Esophageal Mucosa Explant Platform to Eosinophilic Esophagitis.

There is an increasing prevalence of esophageal diseases but intact human tissue platforms to study esophageal function, disease mechanisms, and the interactions between cell types in situ are lacking. To address this, we utilized full thickness human donor esophagi to create and validate the ex vivo function of mucosa and smooth muscle (n = 25). Explanted tissue was tested for contractile responses to carbachol and histamine. We then treated ex vivo human esophageal mucosa with a cytokine cocktail to closely mimic the Th2 and inflammatory milieu of eosinophilic esophagitis (EoE) and assessed alterations in smooth muscle and extracellular matrix function and stiffening. We found that full thickness human esophagus as well as the individual layers of circular and longitudinal muscularis propria developed tension in response to carbachol ex vivo and that mucosa demonstrated squamous cell differentiation. Treatment of mucosa with Th2 and fibrotic cytokines recapitulated the majority of the clinical Eosinophilic Esophagitis Diagnostic Profile (EDP) on fluidic transcriptional microarray. Transforming growth factor-beta-1 (TGFβ1) increased gene expression of fibronectin, smooth muscle actin, and phospholamban (p < 0.001). The EoE cocktail also increased stiffness and decreased mucosal compliance, akin to the functional alterations in EoE (p = 0.001). This work establishes a new, transcriptionally intact and physiologically functional human platform to model esophageal tissue responses in EoE

Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential

We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schr\"{o}dinger operator and the relevant coupled-mode equations to describe this bifurcation. The coupled-mode equations are derived by the rigorous analysis based on the Fourier--Bloch decomposition and the Implicit Function Theorem in the space of bounded continuous functions vanishing at infinity. Persistence of reversible localized solutions, called gap solitons, beyond the coupled-mode equations is proved under a non-degeneracy assumption on the kernel of the linearization operator. Various branches of reversible localized solutions are classified numerically in the framework of the coupled-mode equations and convergence of the approximation error is verified. Error estimates on the time-dependent solutions of the Gross--Pitaevskii equation and the coupled-mode equations are obtained for a finite-time interval.Comment: 32 pages, 16 figure

The Environments of Low and High Luminosity Radio Galaxies at Moderate Redshifts

In the local Universe, high-power radio galaxies live in lower density environments than low-luminosity radio galaxies. If this trend continues to higher redshifts, powerful radio galaxies would serve as efficient probes of moderate redshift groups and poor clusters. Photometric studies of radio galaxies at 0.3 < z < 0.5 suggest that the radio luminosity-environment correlation disappears at moderate redshifts, though this could be the result of foreground/background contamination affecting the photometric measures of environment. We have obtained multi-object spectroscopy of in the fields of 14 lower luminosity (L_1.4GHz 1.2x10^25 W/Hz) radio galaxies at z ~ 0.3 to spectroscopically investigate the link between the environment and the radio luminosity of radio galaxies at moderate redshifts. Our results support the photometric analyses; there does not appear to be a correlation between the luminosity of a radio galaxy and its environment at moderate redshifts. Hence, radio galaxies are not efficient signposts for group environments at moderate redshifts.Comment: 7 pages, 9 figures, Accepted for publication in A

Observational Tests of the Mass-Temperature Relation for Galaxy Clusters

We examine the relationship between the mass and x-ray gas temperature of galaxy clusters using data drawn from the literature. Simple theoretical arguments suggest that the mass of a cluster is related to the x-ray temperature as $M \propto T_x^{3/2}$. Virial theorem mass estimates based on cluster galaxy velocity dispersions seem to be accurately described by this scaling with a normalization consistent with that predicted by the simulations of Evrard, Metzler, & Navarro (1996). X-ray mass estimates which employ spatially resolved temperature profiles also follow a $T_x^{3/2}$ scaling although with a normalization about 40% lower than that of the fit to the virial masses. However, the isothermal $\beta$-model and x-ray surface brightness deprojection masses follow a steeper $\propto T_x^{1.8-2.0}$ scaling. The steepness of the isothermal estimates is due to their implicitly assumed dark matter density profile of $\rho(r) \propto r^{-2}$ at large radii while observations and simulations suggest that clusters follow steeper profiles (e.g., $\rho(r) \propto r^{-2.4}$).Comment: 25 pages, 10 figures, accepted by Ap

Stochastics theory of log-periodic patterns

We introduce an analytical model based on birth-death clustering processes to help understanding the empirical log-periodic corrections to power-law scaling and the finite-time singularity as reported in several domains including rupture, earthquakes, world population and financial systems. In our stochastics theory log-periodicities are a consequence of transient clusters induced by an entropy-like term that may reflect the amount of cooperative information carried by the state of a large system of different species. The clustering completion rates for the system are assumed to be given by a simple linear death process. The singularity at t_{o} is derived in terms of birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge

Two-soliton collisions in a near-integrable lattice system

We examine collisions between identical solitons in a weakly perturbed Ablowitz-Ladik (AL) model, augmented by either onsite cubic nonlinearity (which corresponds to the Salerno model, and may be realized as an array of strongly overlapping nonlinear optical waveguides), or a quintic perturbation, or both. Complex dependences of the outcomes of the collisions on the initial phase difference between the solitons and location of the collision point are observed. Large changes of amplitudes and velocities of the colliding solitons are generated by weak perturbations, showing that the elasticity of soliton collisions in the AL model is fragile (for instance, the Salerno's perturbation with the relative strength of 0.08 can give rise to a change of the solitons' amplitudes by a factor exceeding 2). Exact and approximate conservation laws in the perturbed system are examined, with a conclusion that the small perturbations very weakly affect the norm and energy conservation, but completely destroy the conservation of the lattice momentum, which is explained by the absence of the translational symmetry in generic nonintegrable lattice models. Data collected for a very large number of collisions correlate with this conclusion. Asymmetry of the collisions (which is explained by the dependence on the location of the central point of the collision relative to the lattice, and on the phase difference between the solitons) is investigated too, showing that the nonintegrability-induced effects grow almost linearly with the perturbation strength. Different perturbations (cubic and quintic ones) produce virtually identical collision-induced effects, which makes it possible to compensate them, thus finding a special perturbed system with almost elastic soliton collisions.Comment: Phys. Rev. E, in pres

Chocolate, Air Pollution and Children's Neuroprotection: What Cognition Tools should be at Hand to Evaluate Interventions?

Indexación: Web of ScienceMillions of children across the world are exposed to multiple sources of indoor and outdoor air pollutants, including high concentrations of fine particulate matter (PM2.5) and ozone (O-3). The established link between exposure to PM2.5, brain structural, volumetric and metabolic changes, severe cognitive deficits (1.5-2 SD from average IQ) in APOE 4 heterozygous females with >75 - <94% BMI percentiles, and the presence of Alzheimer's disease (AD) hallmarks in urban children and young adults necessitates exploration of ways to protect these individuals from the deleterious neural effects of pollution exposure. Emerging research suggests that cocoa interventions may be a viable option for neuroprotection, with evidence suggesting that early cocoa interventions could limit the risk of cognitive and developmental concerns including: endothelial dysfunction, cerebral hypoperfusion, neuroinflammation, and metabolic detrimental brain effects. Currently, however, it is not clear how early we should implement consumption of cocoa to optimize its neuroprotective effects. Moreover, we have yet to identify suitable instruments for evaluating cognitive responses to these interventions in clinically healthy children, teens, and young adults. An approach to guide the selection of cognitive tools should take into account neuropsychological markers of cognitive declines in patients with Alzheimer's neuropathology, the distinct patterns of memory impairment between early and late onset AD, and the key literature associating white matter integrity and poor memory binding performance in cases of asymptomatic familial AD. We highlight potential systemic and neural benefits of cocoa consumption. We also highlight Working Memory Capacity (WMC) and attention control tasks as opened avenues for exploration in the air pollution scenario. Exposures to air pollutants during brain development have serious brain consequences in the short and long term and reliable cognition tools should be at hand to evaluate interventions.http://journal.frontiersin.org/article/10.3389/fphar.2016.00232/ful

Stationary Localized States Due to a Nonlinear Dimeric Impurity Embedded in a Perfect 1-D Chain

The formation of Stationary Localized states due to a nonlinear dimeric impurity embedded in a perfect 1-d chain is studied here using the appropriate Discrete Nonlinear Schr$\ddot{o}$dinger Equation. Furthermore, the nonlinearity has the form, $\chi |C|^\sigma$ where $C$ is the complex amplitude. A proper ansatz for the Localized state is introduced in the appropriate Hamiltonian of the system to obtain the reduced effective Hamiltonian. The Hamiltonian contains a parameter, $\beta = \phi_1/\phi_0$ which is the ratio of stationary amplitudes at impurity sites. Relevant equations for Localized states are obtained from the fixed point of the reduced dynamical system. $|\beta|$ = 1 is always a permissible solution. We also find solutions for which $|\beta| \ne 1$. Complete phase diagram in the $(\chi, \sigma)$ plane comprising of both cases is discussed. Several critical lines separating various regions are found. Maximum number of Localized states is found to be six. Furthermore, the phase diagram continuously extrapolates from one region to the other. The importance of our results in relation to solitonic solutions in a fully nonlinear system is discussed.Comment: Seven figures are available on reques