Non-linear unbalanced Bessel beams: Stationary conical waves supported by nonlinear losses

Nonlinear losses accompanying Kerr self-focusing substantially impacts the dynamic balance of diffraction and nonlinearity, permitting the existence of localized and stationary solutions of the 2D+1 nonlinear Schrodinger equation which are stable against radial collapse. These are featured by linear conical tails that continually refill the nonlinear, central spot. An experiment shows that the discovered solution behaves as strong attractor for the self-focusing dynamics in Kerr media.Comment: 4 pages, 2 figures; experimental verification adde

A CrC^{r} Closing Lemma for a Class of Symplectic Diffeomorphisms

We prove a $C^r$ closing lemma for a class of partially hyperbolic symplectic diffeomorphisms. We show that for a generic $C^r$ symplectic diffeomorphism, $r =1, 2, ...,$, with two dimensional center and close to a product map, the set of all periodic points is dense

Herman's Theory Revisited

We prove that a $C^{2+\alpha}$-smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class $D_\delta$, $0<\delta<\alpha\le1$, is $C^{1+\alpha-\delta}$-smoothly conjugate to a rigid rotation. We also derive the most precise version of Denjoy's inequality for such diffeomorphisms.Comment: 10 page

Measuring the mixing efficiency in a simple model of stirring:some analytical results and a quantitative study via Frequency Map Analysis

We prove the existence of invariant curves for a $T$--periodic Hamiltonian system which models a fluid stirring in a cylindrical tank, when $T$ is small and the assigned stirring protocol is piecewise constant. Furthermore, using the Numerical Analysis of the Fundamental Frequency of Laskar, we investigate numerically the break down of invariant curves as $T$ increases and we give a quantitative estimate of the efficiency of the mixing.Comment: 10 figure

Sparse Randomized Kaczmarz for Support Recovery of Jointly Sparse Corrupted Multiple Measurement Vectors

While single measurement vector (SMV) models have been widely studied in signal processing, there is a surging interest in addressing the multiple measurement vectors (MMV) problem. In the MMV setting, more than one measurement vector is available and the multiple signals to be recovered share some commonalities such as a common support. Applications in which MMV is a naturally occurring phenomenon include online streaming, medical imaging, and video recovery. This work presents a stochastic iterative algorithm for the support recovery of jointly sparse corrupted MMV. We present a variant of the Sparse Randomized Kaczmarz algorithm for corrupted MMV and compare our proposed method with an existing Kaczmarz type algorithm for MMV problems. We also showcase the usefulness of our approach in the online (streaming) setting and provide empirical evidence that suggests the robustness of the proposed method to the distribution of the corruption and the number of corruptions occurring.Comment: 13 pages, 6 figure

Multi-Bunch Solutions of Differential-Difference Equation for Traffic Flow

Newell-Whitham type car-following model with hyperbolic tangent optimal velocity function in a one-lane circuit has a finite set of the exact solutions for steady traveling wave, which expressed by elliptic theta function. Each solution of the set describes a density wave with definite number of car-bunches in the circuit. By the numerical simulation, we observe a transition process from a uniform flow to the one-bunch analytic solution, which seems to be an attractor of the system. In the process, the system shows a series of cascade transitions visiting the configurations closely similar to the higher multi-bunch solutions in the set.Comment: revtex, 7 pages, 5 figure

Excited states in bilayer graphene quantum dots

We report on ground- and excited state transport through an electrostatically defined few-hole quantum dot in bilayer graphene in both parallel and perpendicular applied magnetic fields. A remarkably clear level scheme for the two-particle spectra is found by analyzing finite bias spectroscopy data within a two-particle model including spin and valley degrees of freedom. We identify the two-hole ground-state to be a spin-triplet and valley-singlet state. This spin alignment can be seen as Hund's rule for a valley-degenerate system, which is fundamentally different to quantum dots in carbon nano tubes and GaAs-based quantum dots. The spin-singlet excited states are found to be valley-triplet states by tilting the magnetic field with respect to the sample plane. We quantify the exchange energy to be 0.35meV and measure a valley and spin g-factor of 36 and 2, respectively

Monitorización de la oxidación del aceite de semillas de sacha inchi (Plukenetia volubilis) suplementado con extractos de vainas de tara (Caesalpinia spinosa) mediante técnicas convencionales y MIR

This work focuses on the characterization of the oxidation of the oil from sacha inchi seeds (Plukenetia volubilis) under accelerated conditions at 60 ºC for 15 days. Five samples were monitored: three supplemented with 200 ppm of non-hydrolyzed or partially hydrolyzed (for 4 and 9 hours) extracts from tara (Caesalpinia spinosa) pods, one without antioxidant and one with 200 ppm of BHT. Several conventional tech­niques (induction time, peroxide value, conjugated dienoic acid, p-anisidine value, total unsaturated fatty acids and α-linolenic acid contents) and the MIR spectroscopy coupled with chemometric tools were used and com­pared. The results revealed that whatever the antioxidant added, the oil from sacha inchi is fairly stable over time. The results also pointed out that extracts from tara pods, mainly those partially hydrolyzed, were more efficient than BHT against oil oxidation for up to 7 days. Finally, this paper shows that MIR spectroscopy pres­ents an interesting alternative technique for the monitoring of the oxidation of the oil from sacha inchi.Este trabajo se centra en la caracterización de la oxidación de aceites de sacha inchi (Plukenetia volubilis) en condiciones aceleradas a 60 ºC durante 15 días. Se monitorean cinco muestras: tres suplementadas con 200 ppm de extractos no hidrolizados o par­cialmente hidrolizados (durante 4 y 9 horas) de vainas de tara (Caesalpinia spinosa), una sin antioxidante y otra con 200 ppm de BHT. Se utilizan y comparan varias técnicas convencionales (tiempo de inducción, índice de peróxido, ácido dienoico conjugado, índice de p-anisidina, ácidos grasos insaturados totales y contenido de ácido α-linolénico) y la espectroscopía MIR junto con herramientas quimiométricas. Los resultados revelan que, cualquiera que sea el antioxidante agregado, el aceite de sacha inchi es bastante estable a lo largo del tiempo. Los resultados también seña­lan que los extractos de las vainas de tara, principalmente aquellos parcialmente hidrolizados, son más eficientes que el BHT contra la oxidación del aceite hasta los 7 días. Finalmente, el trabajo muestra que la espectroscopía MIR se presenta como una técnica alternativa interesante para el monitoreo de la oxidación del aceite de sacha inchi

White Lines and 3d-Occupancy for the 3d Transition-Metal Oxides

Electron energy-loss spectrometry was employed to measure the white lines at the L23 absorption edges of the 3d transition-metal oxides and lithium transition-metal oxides. The white-line ratio (L3/L2) was found to increase between d^0 and d^5 and decrease between d^5 and d^10, consistent with previous results for the transition metals and their oxides. The intensities of the white lines, normalized to the post-edge background, are linear for the 3d transition-metal oxides and lithium transition-metal oxides. An empirical correlation between normalized white-line intensity and 3d occupancy is established. It provides a method for measuring changes in the 3d-state occupancy. As an example, this empirical relationship is used to measure changes in the transition-metal valences of Li_{1-x}Ni_{0.8}Co_{0.2}O_2 in the range of 0 < x < 0.64. In these experiments the 3d occupancy of the nickel ion decreased upon lithium deintercalation, while the cobalt valence remained constant.Comment: 6 pages, 7 figure

Boundaries of Siegel Disks: Numerical Studies of their Dynamics and Regularity

Siegel disks are domains around fixed points of holomorphic maps in which the maps are locally linearizable (i.e., become a rotation under an appropriate change of coordinates which is analytic in a neighborhood of the origin). The dynamical behavior of the iterates of the map on the boundary of the Siegel disk exhibits strong scaling properties which have been intensively studied in the physical and mathematical literature. In the cases we study, the boundary of the Siegel disk is a Jordan curve containing a critical point of the map (we consider critical maps of different orders), and there exists a natural parametrization which transforms the dynamics on the boundary into a rotation. We compute numerically this parameterization and use methods of harmonic analysis to compute the global Holder regularity of the parametrization for different maps and rotation numbers. We obtain that the regularity of the boundaries and the scaling exponents are universal numbers in the sense of renormalization theory (i.e., they do not depend on the map when the map ranges in an open set), and only depend on the order of the critical point of the map in the boundary of the Siegel disk and the tail of the continued function expansion of the rotation number. We also discuss some possible relations between the regularity of the parametrization of the boundaries and the corresponding scaling exponents. (C) 2008 American Institute of Physics.NSFMathematic