Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories

Dynamical equations are formulated and a numerical study is provided for self-oscillatory model systems based on the triple linkage hinge mechanism of Thurston -- Weeks -- Hunt -- MacKay. We consider systems with holonomic mechanical constraint of three rotators as well as systems, where three rotators interact by potential forces. We present and discuss some quantitative characteristics of the chaotic regimes (Lyapunov exponents, power spectrum). Chaotic dynamics of the models we consider are associated with hyperbolic attractors, at least, at relatively small supercriticality of the self-oscillating modes; that follows from numerical analysis of the distribution for angles of intersection of stable and unstable manifolds of phase trajectories on the attractors. In systems based on rotators with interacting potential the hyperbolicity is violated starting from a certain level of excitation.Comment: 30 pages, 18 figure

Some properties of nonlinear oscillations in a diode in the space charge–limited current regime

Both the initial and late non-linear stages of the oscillation process in a beam vacuum diode in the space-charge-limited current regime are numerically investigated. Two different numerical methods are applied: Birdsall's code (B-code) and Ender-Kuznetsov code (EK-code). The capabilities of both codes are compared. The high accuracy of the EK-code gives an opportunity to build dispersion branches of instability. The domain of the parameter values, when simultaneously several stable dynamical states (limit cycles) exist, is found. A sharp decrease in the amplitude of oscillations is revealed already under a comparatively small (about 2.5%) spread in velocities of the electron beam

Asynchronous locking in metamaterials of fluids of light and sound

Phonons, the quanta of vibrations, are very important for the equilibrium and dynamical properties of matter. GHz coherent phonons can also interact with and act as interconnects in a wide range of quantum systems. Harnessing and tailoring their coupling to opto-electronic excitations thus becomes highly relevant for engineered materials for quantum technologies. With this perspective we introduce polaromechanical metamaterials, two-dimensional arrays of μm-size zero-dimensional traps confining light-matter polariton fluids and GHz phonons. A strong exciton-mediated polariton-phonon interaction determines the inter-site polariton coupling with remarkable consequences for the dynamics. When locally perturbed by optical excitation, polaritons respond by locking the energy detuning between neighbor sites at integer multiples of the phonon energy, evidencing synchronization involving the polariton and phonon fields. These results open the path for the coherent control of quantum light fluids with hypersound in a scalable platform.Fil: Chafatinos, Dimitri Lisandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología - Nodo Bariloche | Comisión Nacional de Energía Atómica. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología - Nodo Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro | Universidad Nacional de Cuyo. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro; ArgentinaFil: Kuznetsov, A.S.. Leibniz-Institut im Forschungsverbund Berlin; AlemaniaFil: Reynoso, Andres Alejandro. Universidad de Sevilla; España. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro | Universidad Nacional de Cuyo. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología; ArgentinaFil: Usaj, Gonzalo. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro | Universidad Nacional de Cuyo. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología; ArgentinaFil: Sesin, Pablo Ezequiel. Comisión Nacional de Energía Atómica. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro | Universidad Nacional de Cuyo. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro; ArgentinaFil: Papuccio Fernández, Ignacio Agustín. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro | Universidad Nacional de Cuyo. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología; ArgentinaFil: Bruchhausen, Axel Emerico. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro | Universidad Nacional de Cuyo. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología; ArgentinaFil: Biermann, K.. Leibniz-Institut im Forschungsverbund Berlin; AlemaniaFil: Santos, P.V.. Leibniz-Institut im Forschungsverbund Berlin; AlemaniaFil: Fainstein, Alejandro. Comisión Nacional de Energía Atómica. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro | Universidad Nacional de Cuyo. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro; Argentin

Theory and computation of covariant Lyapunov vectors

Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate these directions. Though the concept of these vectors has been known for a long time, they became practically computable only recently due to algorithms suggested by Ginelli et al. [Phys. Rev. Lett. 99, 2007, 130601] and by Wolfe and Samelson [Tellus 59A, 2007, 355]. In view of the great interest in covariant Lyapunov vectors and their wide range of potential applications, in this article we summarize the available information related to Lyapunov vectors and provide a detailed explanation of both the theoretical basics and numerical algorithms. We introduce the notion of adjoint covariant Lyapunov vectors. The angles between these vectors and the original covariant vectors are norm-independent and can be considered as characteristic numbers. Moreover, we present and study in detail an improved approach for computing covariant Lyapunov vectors. Also we describe, how one can test for hyperbolicity of chaotic dynamics without explicitly computing covariant vectors.Comment: 21 pages, 5 figure

A Bayesian analysis of pentaquark signals from CLAS data

We examine the results of two measurements by the CLAS collaboration, one of which claimed evidence for a $\Theta^{+}$ pentaquark, whilst the other found no such evidence. The unique feature of these two experiments was that they were performed with the same experimental setup. Using a Bayesian analysis we find that the results of the two experiments are in fact compatible with each other, but that the first measurement did not contain sufficient information to determine unambiguously the existence of a $\Theta^{+}$. Further, we suggest a means by which the existence of a new candidate particle can be tested in a rigorous manner.Comment: 5 pages, 3 figure

First measurement of direct f0(980)f_0(980) photoproduction on the proton

We report on the results of the first measurement of exclusive $f_0(980)$ meson photoproduction on protons for $E_\gamma=3.0 - 3.8$ GeV and $-t = 0.4-1.0$ GeV$^2$. Data were collected with the CLAS detector at the Thomas Jefferson National Accelerator Facility. The resonance was detected via its decay in the $\pi^+ \pi^-$ channel by performing a partial wave analysis of the reaction $\gamma p \to p \pi^+ \pi^-$. Clear evidence of the $f_0(980)$ meson was found in the interference between $P$ and $S$ waves at $M_{\pi^+ \pi^-}\sim 1$ GeV. The $S$-wave differential cross section integrated in the mass range of the $f_0(980)$ was found to be a factor of 50 smaller than the cross section for the $\rho$ meson. This is the first time the $f_0(980)$ meson has been measured in a photoproduction experiment

Beam Spin Asymmetries in DVCS with CLAS at 4 .8 GeV

We report measurements of the beam spin asymmetry in Deeply Virtual Compton Scattering (DVCS) at an electron beam energy of 4.8 GeV using the CLAS detector at the Thomas Jefferson National Accelerator Facility. The DVCS beam spin asymmetry has been measured in a wide range of kinematics, 1(GeV/c)$^2$ $<Q^2<2.8$(GeV/c)$^2$, $0.12<x_B<0.48$, and 0.1 (GeV/c)$^2$ $<-t<0.8$(GeV/c)$^2$, using the reaction \pEpX. The number of H$(e,e^{\prime}\gamma p)$ and H$(e,e^{\prime}\pi^0 p)$ events are separated in each $(Q^2,x_B,t)$ bin by a fit to the line shape of the H$(e,e^{\prime}p)X$ $M_x^2$ distribution. The validity of the method was studied in detail using experimental and simulated data. It was shown, that with the achieved missing mass squared resolution and the available statistics, the separation of DVCS-BH and $\pi^0$ events can reliably be done with less than 5% uncertainty. The $Q^2$- and $t$-dependences of the $\sin\phi$ moments of the asymmetry are extracted and compared with theoretical calculations

K⋆(892)0K^{\star}(892)^{0} Production in Relativistic Heavy Ion Collisions at sNN=130\sqrt{s_{_{NN}}}=130 GeV

We report the first observation of $K^{\star}(892)^{0}\to\pi K$ in relativistic heavy ion collisions. The transverse momentum spectrum of $(K^{\star0}+\bar{K}^{\star0})/2$ from central Au+Au collisions at $\sqrt{s_{_{NN}}}=130$ GeV is presented. The ratios of the $K^{\star0}$ yield derived from these data to the yields of negative hadrons, charged kaons, and $\phi$ mesons have been measured in central and minimum bias collisions and compared with model predictions and comparable $e^{+}e^{-}$, $pp$, and $\bar{p}p$ results. The data indicate no dramatic reduction of $K^{\star0}$ production in relativistic heavy ion collisions despite expected losses due to rescattering effects.Comment: 6 pages, 3 figures, To be published in PRC