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

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 Thermostat and Intraband Discrete Breathers

We investigate the dynamics of a macroscopic system which consists of an anharmonic subsystem embedded in an arbitrary harmonic lattice, including quenched disorder. Elimination of the harmonic degrees of freedom leads to a nonlinear Langevin equation for the anharmonic coordinates. For zero temperature, we prove that the support of the Fourier transform of the memory kernel and of the time averaged velocity-velocity correlations functions of the anharmonic system can not overlap. As a consequence, the asymptotic solutions can be constant, periodic,quasiperiodic or almost periodic, and possibly weakly chaotic. For a sinusoidal trajectory with frequency $\Omega$ we find that the energy $E_T$ transferred to the harmonic system up to time $T$ is proportional to $T^{\alpha}$. If $\Omega$ equals one of the phonon frequencies $\omega_\nu$, it is $\alpha=2$. We prove that there is a full measure set such that for $\Omega$ in this set it is $\alpha=0$, i.e. there is no energy dissipation. Under certain conditions there exists a zero measure set such that for $\Omega \in this set the dissipation rate is nonzero and may be subdissipative$(0 \leq \alpha < 1)$or superdissipative$(1 <\alpha \leq 2)$. Consequently, the harmonic bath does act as an anomalous thermostat. Intraband discrete breathers are such solutions which do not relax. We prove for arbitrary anharmonicity and small but finite coupling that intraband discrete breathers with frequency$\Omega$exist for all$\Omega$in a Cantor set$\mathcal{C}(k)$of finite Lebesgue measure. This is achieved by estimating the contribution of small denominators appearing in the memory kernel. For$\Omega\in\mathcal{C}(k)$the small denominators do not lead to divergencies such that this kernel is a smooth and bounded function in$t$.Comment: Physica D in prin

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

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

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

Tumoral CD105 is a novel independent prognostic marker for prognosis in clear-cell renal cell carcinoma

International audienceBackground: Angiogenesis is essential for tumour growth and metastasis. There are conflicting reports as to whether microvessel density (MVD) using the endothelial marker CD105 (cluster of differentiation molecule 105) in clear-cell renal cell carcinomas (ccRCC) is associated with prognosis. Recently, CD105 has been described as a RCC cancer stem cell marker.Methods: A total of 102 ccRCC were analysed. Representative tumour sections were stained for CD105. Vascularity (endothelial CD105) was quantified by MVD. The immunohistochemistry analysis detected positive (if present) or negative (if absent) CD105 tumoral staining. This retrospective population-based study was evaluated using Kaplan–Meier method, t-test and Cox proportional hazard model.Results: We found that the expression of endothelial CD105 (MVD) negatively correlated with nuclear grade (P<0.001), tumour stage (P<0.001) and Leibovitch score (P<0.001), whereas the expression of tumoral CD105 positively correlated with these three clinicopathological factors (P<0.001). In multivariate analysis, tumoral CD105 was found to be an independent predictor of poor overall survival (P=0.002).Conclusions: We have shown for the first time that tumoral CD105 is an independent predictive marker for death risk and unfavourable prognosis in patients with ccRCC after curative resection

Correlation between CD105 expression and postoperative recurrence and metastasis of hepatocellular carcinoma

BACKGROUND: Angiogenesis is one of the mechanisms most critical to the postoperative recurrence and metastasis of hepatocellular carcinoma (HCC). Thus, finding the molecular markers associated with angiogenesis may help identify patients at increased risk for recurrence and metastasis of HCC. This study was designed to investigate whether CD105 or CD34 could serve as a valid prognostic marker in patients with HCC by determining if there is a correlation between CD105 or CD34 expression and postoperative recurrence or metastasis. METHODS: Immunohistochemical staining for the CD105, CD34 and vascular endothelial growth factor (VEGF) antibodies was performed in 113 HCC tissue specimens containing paracarcinomatous tissue and in 14 normal liver tissue specimens. The quantitation of microvessels identified by anti-CD105 and anti-CD34 monoclonal antibodies and the semiquantitation of VEGF expression identified by anti-VEGF monoclonal antibody were analyzed in conjunction with the clinicopathological characteristics of the HCC and any available follow-up information about the patients from whom the specimens were obtained. RESULTS: CD105 was not expressed in the vascular endothelial cells of any normal liver tissue or paracarcinomatous liver tissue but was expressed in the vascular endothelial cells of all HCC tissue. In contrast, CD34 was expressed in the vascular endothelial cells of normal liver tissue, paracarcinomatous tissue, and HCC tissue in the following proportions of specimens: 86.7%, 93.8%, and 100%, respectively. The microvascular densities (MVDs) of HCC determined by using an anti-CD105 mAb (CD105-MVD) and an anti-CD34 mAb (CD34-MVD), were 71.7 ± 8.3 (SD) and 106.3 ± 10.4 (SD), respectively. There was a significant correlation between CD105-MVD and CD34-MVD (r = 0.248, P = 0.021). Although CD34-MVD was significantly correlated with VEGF expression (r = 0.243, P = 0.024), CD105-MVD was more closely correlated (r = 0.300, P= 0.005). The correlation between microscopic venous invasion and CD105-MVD, but not CD34-MVD, was also statistically significant (r = 0.254, P = 0.018). Univariate analysis showed that CD105-MVD was significantly correlated with the 2-year overall survival rate (P = 0.014); CD34-MVD was not (P = 0.601). Multivariate analysis confirmed that CD105-MVD was an independent prognostic factor and that CD34-MVD was not. CONCLUSION: The anti-CD105 mAb is an ideal instrument to quantify new microvessels in HCC as compared with anti-CD34 mAb. CD105-MVD as compared with CD34-MVD is relevant a significant and independent prognostic indicator for recurrence and metastasis in HCC patients