A nonpolynomial Schroedinger equation for resonantly absorbing gratings

We derive a nonlinear Schroedinger equation with a radical term, in the form of the square root of (1-|V|^2), as an asymptotic model of the optical medium built as a periodic set of thin layers of two-level atoms, resonantly interacting with the electromagnetic field and inducing the Bragg reflection. A family of bright solitons is found, which splits into stable and unstable parts, exactly obeying the Vakhitov-Kolokolov criterion. The soliton with the largest amplitude, which is |V| = 1, is found in an explicit analytical form. It is a "quasi-peakon", with a discontinuity of the third derivative at the center. Families of exact cnoidal waves, built as periodic chains of quasi-peakons, are found too. The ultimate solution belonging to the family of dark solitons, with the background level |V| = 1, is a dark compacton, also obtained in an explicit analytical form. Those bright solitons which are unstable destroy themselves (if perturbed) attaining the critical amplitude, |V| = 1. The dynamics of the wave field around this critical point is studied analytically, revealing a switch of the system into an unstable phase. Collisions between bright solitons are investigated too. The collisions between fast solitons are quasi-elastic, while slowly moving ones merge into breathers, which may persist or perish (in the latter case, also by attaining |V| = 1).Comment: Physical Review A, in pres

New way to achieve chaotic synchronization in spatially extended systems

We study the spatio-temporal behavior of simple coupled map lattices with periodic boundary conditions. The local dynamics is governed by two maps, namely, the sine circle map and the logistic map respectively. It is found that even though the spatial behavior is irregular for the regularly coupled (nearest neighbor coupling) system, the spatially synchronized (chaotic synchronization) as well as periodic solution may be obtained by the introduction of three long range couplings at the cost of three nearest neighbor couplings.Comment: 5 pages (revtex), 7 figures (eps, included

Mapping the Evolution of Optically-Generated Rotational Wavepackets in a Room Temperature Ensemble of D2_2

A coherent superposition of rotational states in D$_2$ has been excited by nonresonant ultrafast (12 femtosecond) intense (2 $\times$ 10$^{14}$ Wcm$^{-2}$) 800 nm laser pulses leading to impulsive dynamic alignment. Field-free evolution of this rotational wavepacket has been mapped to high temporal resolution by a time-delayed pulse, initiating rapid double ionization, which is highly sensitive to the angle of orientation of the molecular axis with respect to the polarization direction, $\theta$. The detailed fractional revivals of the neutral D$_2$ wavepacket as a function of $\theta$ and evolution time have been observed and modelled theoretically.Comment: 4 pages, 3 figures. Accepted for publication in Phys. Rev. A. Full reference to follow.

Cognitive architectures as Lakatosian research programmes: two case studies

Cognitive architectures - task-general theories of the structure and function of the complete cognitive system - are sometimes argued to be more akin to frameworks or belief systems than scientific theories. The argument stems from the apparent non-falsifiability of existing cognitive architectures. Newell was aware of this criticism and argued that architectures should be viewed not as theories subject to Popperian falsification, but rather as Lakatosian research programs based on cumulative growth. Newell's argument is undermined because he failed to demonstrate that the development of Soar, his own candidate architecture, adhered to Lakatosian principles. This paper presents detailed case studies of the development of two cognitive architectures, Soar and ACT-R, from a Lakatosian perspective. It is demonstrated that both are broadly Lakatosian, but that in both cases there have been theoretical progressions that, according to Lakatosian criteria, are pseudo-scientific. Thus, Newell's defense of Soar as a scientific rather than pseudo-scientific theory is not supported in practice. The ACT series of architectures has fewer pseudo-scientific progressions than Soar, but it too is vulnerable to accusations of pseudo-science. From this analysis, it is argued that successive versions of theories of the human cognitive architecture must explicitly address five questions to maintain scientific credibility

Effects of solar wind magnetosphere coupling recorded at different geomagnetic latitudes: Separation of directly-driven and storage/release systems

The effect on geomagnetic activity of solar wind speed, compared with that of the strength of the interplanetary magnetic field, differs with geomagnetic latitude. In this study we construct a new index based on monthly standard deviations in the H-component of the geomagnetic field for all geomagnetic latitudes. We demonstrate that for this index the response at auroral regions correlates best with interplanetary coupling functions which include the solar wind speed while mid- and low-latitude regions respond to variations in the interplanetary magnetic field strength. These results are used to isolate the responsible geomagnetic current systems

"Doubled" generalized Landau-Lifshiz hierarchies and special quasigraded Lie algebras

Using special quasigraded Lie algebras we obtain new hierarchies of integrable nonlinear vector equations admitting zero-curvature representations. Among them the most interesting is extension of the generalized Landau-Lifshitz hierarchy which we call "doubled" generalized Landau-Lifshiz hierarchy. This hierarchy can be also interpreted as an anisotropic vector generalization of "modified" Sine-Gordon hierarchy or as a very special vector generalization of so(3) anisotropic chiral field hierarchy.Comment: 16 pages, no figures, submitted to Journal of Physics

Patterns from preheating

The formation of regular patterns is a well-known phenomenon in condensed matter physics. Systems that exhibit pattern formation are typically driven and dissipative with pattern formation occurring in the weakly non-linear regime and sometimes even in more strongly non-linear regions of parameter space. In the early universe, parametric resonance can drive explosive particle production called preheating. The fields that are populated then decay quantum mechanically if their particles are unstable. Thus, during preheating, a driven-dissipative system exists. In this paper, we show that a self-coupled inflaton oscillating in its potential at the end of inflation can exhibit pattern formation.Comment: 4 pages, RevTex, 6 figure

Intra-individual movement variability during skill transitions: A useful marker?

Applied research suggests athletes and coaches need to be challenged in knowing when and how much a movement should be consciously attended to. This is exacerbated when the skill is in transition between two more stable states, such as when an already well learnt skill is being refined. Using existing theory and research, this paper highlights the potential application of movement variability as a tool to inform a coach’s decision-making process when implementing a systematic approach to technical refinement. Of particular interest is the structure of co-variability between mechanical degrees-of-freedom (e.g., joints) within the movement system’s entirety when undergoing a skill transition. Exemplar data from golf are presented, demonstrating the link between movement variability and mental effort as an important feature of automaticity, and thus intervention design throughout the different stages of refinement. Movement variability was shown to reduce when mental effort directed towards an individual aspect of the skill was high (target variable). The opposite pattern was apparent for variables unrelated to the technical refinement. Therefore, two related indicators, movement variability and mental effort, are offered as a basis through which the evaluation of automaticity during technical refinements may be made

Shear induced grain boundary motion for lamellar phases in the weakly nonlinear regime

We study the effect of an externally imposed oscillatory shear on the motion of a grain boundary that separates differently oriented domains of the lamellar phase of a diblock copolymer. A direct numerical solution of the Swift-Hohenberg equation in shear flow is used for the case of a transverse/parallel grain boundary in the limits of weak nonlinearity and low shear frequency. We focus on the region of parameters in which both transverse and parallel lamellae are linearly stable. Shearing leads to excess free energy in the transverse region relative to the parallel region, which is in turn dissipated by net motion of the boundary toward the transverse region. The observed boundary motion is a combination of rigid advection by the flow and order parameter diffusion. The latter includes break up and reconnection of lamellae, as well as a weak Eckhaus instability in the boundary region for sufficiently large strain amplitude that leads to slow wavenumber readjustment. The net average velocity is seen to increase with frequency and strain amplitude, and can be obtained by a multiple scale expansion of the governing equations