Non-periodic driving of coupled oscillators:a spherical swing

Nonlinearly coupled, damped oscillators at 1:1 frequency ratio, one oscillator being driven coherently for efficient excitation, are exemplified by a spherical swing with some phase-mismatch between drive and response. For certain damping range, excitation is found to succeed if it lags behind, but to produce a chaotic attractor if it leads the response. Although a period-doubhng sequence, for damping increasing, leads to the attractor, this is actually born as a hard (as regards amplitude) bifurcation at a zero growth-rate parametric line; as damping decreases, an unstable fixed point crosses an invariant plane to enter as saddle-focus a phase-space domain of physical solutions. A second hard bifurcation occurs at the zero mismatch line, the saddle-focus leaving that domain. Times on the attractor diverge when approaching either fine, leading to exactly one-dimensional and noninvertible limit maps, which are analytically determined.

Dynamic stabilization of L2 periodic orbits using attitude-orbit coupling effects

Numerical explorations show how the known periodic solutions of the Hill problem are modified in the case of the attitude-orbit coupling that may occur for large satellite structures. We focus on the case in which the elongation is the dominant satellite?s characteristic and find that a rotating structure may remain with its largest dimension in a plane parallel to the plane of the primaries. In this case, the effect produced by the non-negligible physical dimension is dynamically equivalent to the perturbation produced by an oblate central body on a masspoint satellite. Based on this, it is demonstrated that the attitude-orbital coupling of a long enough body may change the dynamical characteristics of a periodic orbit about the collinear Lagrangian points.

Temporal task allocation in periodic environments. An approach based on synchronization

In this paper, we study a robot swarm that has to perform task allocation in an environment that features periodic properties. In this environment, tasks appear in different areas following periodic temporal patterns. The swarm has to reallocate its workforce periodically, performing a temporal task allocation that must be synchronized with the environment to be effective. We tackle temporal task allocation using methods and concepts that we borrow from the signal processing literature. In particular, we propose a distributed temporal task allocation algorithm that synchronizes robots of the swarm with the environment and with each other. In this algorithm, robots use only local information and a simple visual communication protocol based on light blinking. Our results show that a robot swarm that uses the proposed temporal task allocation algorithm performs considerably more tasks than a swarm that uses a greedy algorithm.

Gromov hyperbolicity of periodic planar graphs

The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it. The main result in this paper is a very simple characterization of the hyperbolicity of a large class of periodic planar graphs.

Analysis of the railway track as a spatially periodic structure

This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structural analysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, i.e. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (DFT) in order to reduce a large system of q(2N + 1) linear stiffness equilibrium equations to a set of 2N + 1 uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q = 2, the vertical displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartín [1], i.e. the continuous beam railway track response. The comparison between the proposed method and other methods of analysis of railway tracks, such as Lorente de Nó and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N. In addition, identical results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Small but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article also presents a detailed sensitivity analysis of the vertical displacement of the sleepers. Although standard matrix methods of structural analysis can handle this railway model, one of the objectives of this article is to show the efficiency of DFT method with respect to standard matrix structural analysis. A comparative analysis between standard matrix structural analysis and the proposed method (DFT), in terms of computational time, input, output and also software programming, will be carried out. Finally, a URL link to a MatLab computer program list, based on the proposed method, is given

Vortex pinning vs superconducting wire network: origin of periodic oscillations induced by applied magnetic fields in superconducting films with arrays of nanomagnets

Hybrid magnetic arrays embedded in superconducting films are ideal systems to study the competition between different physical (such as the coherence length) and structural length scales such as are available in artificially produced structures. This interplay leads to oscillation in many magnetically dependent superconducting properties such as the critical currents, resistivity and magnetization. These effects are generally analyzed using two distinct models based on vortex pinning or wire network. In this work, we show that for magnetic dot arrays, as opposed to antidot (i.e. holes) arrays, vortex pinning is the main mechanism for field induced oscillations in resistance R(H), critical current Ic(H), magnetization M(H) and ac-susceptibility χ ac(H) in a broad temperature range. Due to the coherence length divergence at Tc, a crossover to wire network behaviour is experimentally found. While pinning occurs in a wide temperature range up to Tc, wire network behaviour is only present in a very narrow temperature window close to Tc. In this temperature interval, contributions from both mechanisms are operational but can be experimentally distinguished.

Perturbations in maturation of secretory proteins and their association with endoplasmic reticulum chaperones in a cell culture model for epithelial ischemia.

The effects of ischemia on the maturation of secretory proteins are not well understood. Among several events that occur during ischemia-reperfusion are a rapid and extensive decrease in ATP levels and an alteration of cellular oxidative state. Since the normal folding and assembly of secretory proteins are mediated by endoplasmic reticulum (ER) molecular chaperones, the function of which depends on ATP and maintenance of an appropriate redox environment, ischemia might be expected to perturb folding of secretory proteins. In this study, whole animal and cultured cell models for the epithelial ischemic state were used to examine this possibility. After acute kidney ischemia, marked increases in the mRNA levels of the ER chaperones glucose-regulated protein (grp)78/immunoglobulin-binding protein (BiP), grp94, and ER protein (ERp)72 were noted. Likewise, when cellular ATP was depleted to less than 10% of control with antimycin A, mRNA levels of BiP, ERp72, and grp94 were increased in kidney and thyroid epithelial cell culture models. Since the signal for the up-regulation of these stress proteins is believed to be the accumulation of misfolded/misassembled secretory proteins in the ER, their induction after ischemia in vivo and antimycin treatment of cultured cells suggests that maturation of secretory proteins in the ER lumen might indeed be perturbed. To analyze the effects of antimycin A on the maturation of secretory proteins, we studied the fate of thyroglobulin (Tg), a large oligomeric secretory glycoprotein, the folding and assembly of which seems to require a variety of ER chaperones. Treatment of cultured thyroid epithelial cells with antimycin A greatly inhibited ( > 90%) the secretion of Tg. Sucrose density gradient analysis revealed that in antimycin A-treated cells Tg associates into large macromolecular complexes which, by immunofluorescence, appeared to localize to the ER. Furthermore, coimmunoprecipitation studies after antimycin A treatment demonstrated that Tg stably associates with BiP, grp94, and ERp72. Together, our results suggest that a key cellular lesion in ischemia is the misfolding of secretory proteins as they transit the ER, and this leads not only to increased expression of ER chaperones but also to their stable association with and the subsequent retention of at least some misfolded secretory proteins.

Periodic variation in side-chain polarities of T-cell antigenic peptides correlates with their structure and activity.

We present an analysis that synthesizes information on the sequence, structure, and motifs of antigenic peptides, which previously appeared to be in conflict. Fourier analysis of T-cell antigenic peptides indicates a periodic variation in amino acid polarities of 3-3.6 residues per period, suggesting an amphipathic alpha-helical structure. However, the diffraction patterns of major histocompatibility complex (MHC) molecules indicate that their ligands are in an extended non-alpha-helical conformation. We present two mutually consistent structural explanations for the source of the alpha-helical periodicity, based on an observation that the side chains of MHC-bound peptides generally partition with hydrophobic (hydrophilic) side chains pointing into (out of) the cleft. First, an analysis of haplotype-dependent peptide motifs indicates that the locations of their defining residues tend to force a period 3-4 variation in hydrophobicity along the peptide sequence, in a manner consistent with the spacing of pockets in the MHC. Second, recent crystallographic determination of the structure of a peptide bound to a class II MHC molecule reveals an extended but regularly twisted peptide with a rotation angle of about 130 degrees. We show that similar structures with rotation angles of 100-130 degrees are energetically acceptable and also span the length of the MHC cleft. These results provide a sound physical chemical and structural basis for the existence of a haplotype-independent antigenic motif which can be particularly important in limiting the search time for antigenic peptides.

Tilted excitation implies odd periodic resonances

This work was supported by the Brazilian agencies FAPESP and CNPq. MSB also acknowledges the Engineering and Physical Sciences Research Council grant Ref. EP/I032606/1. GID thanks Felipe A. C. Pereira for fruitful discussions.

Chromospheric activity and rotation of FGK stars in the solar vicinity. An estimation of the radial velocity jitter

Context. Chromospheric activity produces both photometric and spectroscopic variations that can be mistaken as planets. Large spots crossing the stellar disc can produce planet-like periodic variations in the light curve of a star. These spots clearly affect the spectral line profiles, and their perturbations alter the line centroids creating a radial velocity jitter that might “contaminate” the variations induced by a planet. Precise chromospheric activity measurements are needed to estimate the activity-induced noise that should be expected for a given star. Aims. We obtain precise chromospheric activity measurements and projected rotational velocities for nearby (d ≤ 25 pc) cool (spectral types F to K) stars, to estimate their expected activity-related jitter. As a complementary objective, we attempt to obtain relationships between fluxes in different activity indicator lines, that permit a transformation of traditional activity indicators, i.e., Ca II H & K lines, to others that hold noteworthy advantages. Methods. We used high resolution (~50 000) echelle optical spectra. Standard data reduction was performed using the IRAF ECHELLE package. To determine the chromospheric emission of the stars in the sample, we used the spectral subtraction technique. We measured the equivalent widths of the chromospheric emission lines in the subtracted spectrum and transformed them into fluxes by applying empirical equivalent width and flux relationships. Rotational velocities were determined using the cross-correlation technique. To infer activity-related radial velocity (RV) jitter, we used empirical relationships between this jitter and the R’_HK index. Results. We measured chromospheric activity, as given by different indicators throughout the optical spectra, and projected rotational velocities for 371 nearby cool stars. We have built empirical relationships among the most important chromospheric emission lines. Finally, we used the measured chromospheric activity to estimate the expected RV jitter for the active stars in the sample.

Cosmological perturbations in coherent oscillating scalar field models

The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these theories assuming general power law potentials V(ϕ) = λ|ϕ|^n /n. At leading order in the wavenumber expansion, a simple expression for the effective sound speed of perturbations is obtained c_eff^ 2  = ω = (n − 2)/(n + 2) with ω the effective equation of state. We also obtain the first order correction in k^ 2/ω_eff^ 2 , when the wavenumber k of the perturbations is much smaller than the background oscillation frequency, ω_eff. For the standard massive case we have also analysed general anharmonic contributions to the effective sound speed. These results are reached through a perturbed version of the generalized virial theorem and also studying the exact system both in the super-Hubble limit, deriving the natural ansatz for δϕ; and for sub-Hubble modes, exploiting Floquet’s theorem.

Profiling in sport using momentum and perturbations

Examining a team’s performance from a physical point of view their momentum might indicate unexpected turning points in defeat or success. Physicists describe this value as to require some effort to be started, but also that it is relatively easy to keep it going once a sufficient level is reached (Reed and Hughes, 2006). Unlike football, rugby, handball and many more sports, a regular volleyball match is not limited by time but by points that need to be gathered. Every minute more than one point is won by either one team or the other. That means a series of successive points enlarges the gap between the teams making it more and more difficult to catch up with the leading one. This concept of gathering momentum, or the reverse in a performance, can give the coaches, athletes and sports scientists further insights into winning and losing performances. Momentum investigations also contain dependencies between performances or questions if future performances are reliant upon past streaks. Squash and volleyball share the characteristic of being played up to a certain amount of points. Squash was examined according to the momentum of players by Hughes et al. (2006). The initial aim was to expand normative profiles of elite squash players using momentum graphs of winners and errors to explore ‘turning points’ in a performance. Dynamic systems theory has enabled the definition of perturbations in sports exhibiting rhythms (Hughes et al., 2000; McGarry et al., 2002; Murray et al., 2008), and how players and teams cause these disruptions of rhythm can inform on the way they play, these techniques also contribute to profiling methods. Together with the analysis of one’s own performance it is essential to have an understanding of your oppositions’ tactical strengths and weaknesses. By modelling the oppositions’ performance it is possible to predict certain outcomes and patterns, and therefore intervene or change tactics before the critical incident occurs. The modelling of competitive sport is an informative analytic technique as it directs the attention of the modeller to the critical aspects of data that delineate successful performance (McGarry & Franks, 1996). Using tactical performance profiles to pull out and visualise these critical aspects of performance, players can build justified and sophisticated tactical plans. The area is discussed and reviewed, critically appraising the research completed in this element of Performance Analysis.

Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l ∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel–Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system’s data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504–1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system’s coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.

A note on the periodic orbits of a self excited rigid body

The aim of the present paper is to study the periodic orbits of a perturbed self excited rigid body with a fixed point. For studying these periodic orbits we shall use averaging theory of first order.