Discrete embedded solitons

We address the existence and properties of discrete embedded solitons (ESs), i.e., localized waves existing inside the phonon band in a nonlinear dynamical-lattice model. The model describes a one-dimensional array of optical waveguides with both the quadratic (second-harmonic generation) and cubic nonlinearities. A rich family of ESs was previously known in the continuum limit of the model. First, a simple motivating problem is considered, in which the cubic nonlinearity acts in a single waveguide. An explicit solution is constructed asymptotically in the large-wavenumber limit. The general problem is then shown to be equivalent to the existence of a homoclinic orbit in a four-dimensional reversible map. From properties of such maps, it is shown that (unlike ordinary gap solitons), discrete ESs have the same codimension as their continuum counterparts. A specific numerical method is developed to compute homoclinic solutions of the map, that are symmetric under a specific reversing transformation. Existence is then studied in the full parameter space of the problem. Numerical results agree with the asymptotic results in the appropriate limit and suggest that the discrete ESs may be semi-stable as in the continuous case.Comment: A revtex4 text file and 51 eps figure files. To appear in Nonlinearit

Dielectric spectroscopy of water at low frequencies: The existence of an isopermitive point

We have studied the real part of the dielectric constant of water from 100 Hz to 1 MHz. We have found that there is a frequency where the dielectric constant is independent of temperature, and called this the isopermitive point. Below this point the dielectric constant increases with temperature, above, it decreases. To understand this behavior, we consider water as a system of two species: ions and dipoles. The first give rise to the so called Maxwell-Wagner-Sillars effect, the second obey the Maxwell-Boltzmann statistics. At the isopermitive point the effect of both mechanisms in the dielectric response compensate each other.Comment: 4 pages, 4 figures, submitted to Chem. Phys. Let

Gap solitons in Bragg gratings with a harmonic superlattice

Solitons are studied in a model of a fiber Bragg grating (BG) whose local reflectivity is subjected to periodic modulation. The superlattice opens an infinite number of new bandgaps in the model's spectrum. Averaging and numerical continuation methods show that each gap gives rise to gap solitons (GSs), including asymmetric and double-humped ones, which are not present without the superlattice.Computation of stability eigenvalues and direct simulation reveal the existence of completely stable families of fundamental GSs filling the new gaps - also at negative frequencies, where the ordinary GSs are unstable. Moving stable GSs with positive and negative effective mass are found too.Comment: 7 pages, 3 figures, submitted to EP

Anomalous magnetotransport in (Y1−x_{1-x}Gdx_{x})Co2_{2} alloys: interplay of disorder and itinerant metamagnetism

New mechanism of magnetoresistivity in itinerant metamagnets with a structural disorder is introduced basing on analysis of experimental results on magnetoresistivity, susceptibility, and magnetization of structurally disordered alloys (Y$_{1-x}$Gd$_{x}$)Co$_{2}$. In this series, YCo$_{2}$ is an enhanced Pauli paramagnet, whereas GdCo$_{2}$ is a ferrimagnet (T$_{\rm c}$=400 K) with Gd sublattice coupled antiferromagnetically to the itinerant Co-3d electrons. The alloys are paramagnetic for $x < 0.12$. Large positive magnetoresistivity has been observed in the alloys with magnetic ground state at temperatures T$<$T$_{\rm c}$. We show that this unusual feature is linked to a combination of structural disorder and metamagnetic instability of itinerant Co-3d electrons. This new mechanism of the magnetoresistivity is common for a broad class of materials featuring a static magnetic disorder and itinerant metamagnetism.Comment: 7 pages 7 figure

A study of low-energy transfer orbits to the Moon: towards an operational optimization technique

In the Earth-Moon system, low-energy orbits are transfer trajectories from the earth to a circumlunar orbit that require less propellant consumption when compared to the traditional methods. In this work we use a Monte Carlo approach to study a great number of such transfer orbits over a wide range of initial conditions. We make statistical and operational considerations on the resulting data, leading to the description of a reliable way of finding "optimal" mission orbits with the tools of multi-objective optimization

On Optimal Two-Impulse Earth-Moon Transfers in a Four-Body Model

In this paper two-impulse Earth-Moon transfers are treated in the restricted four-body problem with the Sun, the Earth, and the Moon as primaries. The problem is formulated with mathematical means and solved through direct transcription and multiple shooting strategy. Thousands of solutions are found, which make it possible to frame known cases as special points of a more general picture. Families of solutions are defined and characterized, and their features are discussed. The methodology described in this paper is useful to perform trade-off analyses, where many solutions have to be produced and assessed

Overexpression of β2-microglobulin is associated with poor survival in patients with oral cavity squamous cell carcinoma and contributes to oral cancer cell migration and invasion

β2-Microglobulin (β2M), a component of MHC class I molecules, is believed to be associated with tumour status in various cancers. In this study, we examined the expression of β2M at different malignant stages of oral cavity squamous cell carcinoma (OCSCC). To determine the possible correlation between β2M expression and various clinical characteristics, 256 samples from patients with OCSCC were evaluated by immunohistochemical staining. Strong β2M expression was significantly correlated with a relatively advanced tumour stage (P<0.001), positive nodal status (P<0.001), and TNM stage (P<0.001). The cumulative 5-year survival rate was significantly correlated with a relatively advanced tumour stage (P<0.001), positive nodal status (P<0.001), TNM stage (P<0.001), and strong expression of β2M (P<0.001). Thus, elevated β2M expression is an indicator of poor survival (P<0.001). In addition, we extended our analysis of β2M expression to the FaDu and SCC25 oral cancer cell lines. β2-Microglobulin expression was positively correlated with cell migration and invasion in β2M-overexpressing transfectants in Transwell chambers. The suppression of β2M expression using small interfering RNA (siRNA) was sufficient to decrease cell migration and invasion in vitro. Taken together, our results suggest that β2M expression in the tissues is associated with survival and may be involved in tumour progression and metastasis in OCSCC