Swift-Hohenberg equation for lasers

Pattern formation in large aspect ratio, single longitudinal mode, two-level lasers with flat end reflectors, operating near peak gain, is shown to be described by a complex Swift-Hohenberg equation for class A and C lasers and by a complex Swift-Hohenberg equation coupled to a mean flow for the case of a class B laser

Neuronal Activity in the Human Subthalamic Nucleus Encodes Decision Conflict during Action Selection

The subthalamic nucleus (STN), which receives excitatory inputs from the cortex and has direct connections with the inhibitory pathways\ud of the basal ganglia, is well positioned to efficiently mediate action selection. Here, we use microelectrode recordings captured during\ud deep brain stimulation surgery as participants engage in a decision task to examine the role of the human STN in action selection. We\ud demonstrate that spiking activity in the STN increases when participants engage in a decision and that the level of spiking activity\ud increases with the degree of decision conflict. These data implicate the STN as an important mediator of action selection during decision\ud processes.\u

Control of Integrable Hamiltonian Systems and Degenerate Bifurcations

We discuss control of low-dimensional systems which, when uncontrolled, are integrable in the Hamiltonian sense. The controller targets an exact solution of the system in a region where the uncontrolled dynamics has invariant tori. Both dissipative and conservative controllers are considered. We show that the shear flow structure of the undriven system causes a Takens-Bogdanov birfurcation to occur when control is applied. This implies extreme noise sensitivity. We then consider an example of these results using the driven nonlinear Schrodinger equation.Comment: 25 pages, 11 figures, resubmitted to Physical Review E March 2004 (originally submitted June 2003), added content and reference

External Fluctuations in a Pattern-Forming Instability

The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the bifurcation point controlled by the intensity of the multiplicative noise. This shift takes place in the ordering direction (i.e. produces patterns), but its magnitude decreases with that of the noise correlation length. Analytical arguments are presented to explain these facts.Comment: 11 pages, Revtex, 10 Postscript figures added with psfig style (included). To appear in Physical Review

On the connection between the Nekhoroshev theorem and Arnold Diffusion

The analytical techniques of the Nekhoroshev theorem are used to provide estimates on the coefficient of Arnold diffusion along a particular resonance in the Hamiltonian model of Froeschl\'{e} et al. (2000). A resonant normal form is constructed by a computer program and the size of its remainder $||R_{opt}||$ at the optimal order of normalization is calculated as a function of the small parameter $\epsilon$. We find that the diffusion coefficient scales as $D\propto||R_{opt}||^3$, while the size of the optimal remainder scales as $||R_{opt}|| \propto\exp(1/\epsilon^{0.21})$ in the range $10^{-4}\leq\epsilon \leq 10^{-2}$. A comparison is made with the numerical results of Lega et al. (2003) in the same model.Comment: Accepted in Celestial Mechanics and Dynamical Astronom

Disordered Regimes of the one-dimensional complex Ginzburg-Landau equation

I review recent work on the ``phase diagram'' of the one-dimensional complex Ginzburg-Landau equation for system sizes at which chaos is extensive. Particular attention is paid to a detailed description of the spatiotemporally disordered regimes encountered. The nature of the transition lines separating these phases is discussed, and preliminary results are presented which aim at evaluating the phase diagram in the infinite-size, infinite-time, thermodynamic limit.Comment: 14 pages, LaTeX, 9 figures available by anonymous ftp to amoco.saclay.cea.fr in directory pub/chate, or by requesting them to [email protected]

Thermal Pattern and Thermal Tracking: fingerprints of an environmental illicit

Abstract Being able to identify crime/guilty relationship is central to police investigation and new technologies enable authorities to do this faster and more accurately than ever before. In recent years, our research team has introduced the use of a range of aerial platforms and an innovative application of thermography to detect several illegal activities; for example illegal sanitary sewer and storm-drain connections, illicit discharges and other "anomalies" on the surface waters can be easily identified using their thermal infrared signatures. This paper introduces first results of a Thermal Pattern and Thermal Tracking approach, that can be used to identify different phenomena and several pollutants

Remarks on the Configuration Space Approach to Spin-Statistics

The angular momentum operators for a system of two spin-zero indistinguishable particles are constructed, using Isham's Canonical Group Quantization method. This mathematically rigorous method provides a hint at the correct definition of (total) angular momentum operators, for arbitrary spin, in a system of indistinguishable particles. The connection with other configuration space approaches to spin-statistics is discussed, as well as the relevance of the obtained results in view of a possible alternative proof of the spin-statistics theorem.Comment: 18 page

Characterizing emergency admissions of patients with sickle cell crisis in NHS brent: observational study

OBJECTIVES: To characterize emergency admissions for patients with sickle cell crisis in NHS Brent and to determine which patients and practices may benefit most from primary care intervention. DESIGN: Observational study SETTING: Emergency departments attended by residents of the London borough of Brent PARTICIPANTS: Patients with sickle cell disease registered with a general practitioner (GP) in the borough of Brent MAIN OUTCOME MEASURES: Analysis of admissions between January 2008 and July 2010 that included length of stay (average and <2 days versus ≥2 days) by age group and registered GP practice. RESULTS: Thirty six percent of sickle cell disease admission spells resulted in a length of stay of less than two days. Seventy four percent of total bed days are associated with patients with more than one admission during the period of analysis, i.e. multiple admissions. Two general practices in Brent were identified as having the highest number of patients admitted to the emergency department for sickle cell crisis and may benefit most from primary care intervention. DISCUSSION: Patients with short length of stay and multiple admissions may be potentially amenable to primary care intervention. The practices which have the highest numbers of sickle cell disease patients who frequently seek emergency care will be earmarked for an education intervention designed to help further engage general practitioners in the care and management of their sickle cell patients

The dispersion-managed Ginzburg-Landau equation and its application to femtosecond lasers

The complex Ginzburg-Landau equation has been used extensively to describe various non-equilibrium phenomena. In the context of lasers, it models the dynamics of a pulse by averaging over the effects that take place inside the cavity. Ti:sapphire femtosecond lasers, however, produce pulses that undergo significant changes in different parts of the cavity during each round-trip. The dynamics of such pulses is therefore not adequately described by an average model that does not take such changes into account. The purpose of this work is severalfold. First we introduce the dispersion-managed Ginzburg-Landau equation (DMGLE) as an average model that describes the long-term dynamics of systems characterized by rapid variations of dispersion, nonlinearity and gain in a general setting, and we study the properties of the equation. We then explain how in particular the DMGLE arises for Ti:sapphire femtosecond lasers and we characterize its solutions. In particular, we show that, for moderate values of the gain/loss parameters, the solutions of the DMGLE are well approximated by those of the dispersion-managed nonlinear Schrodinger equation (DMNLSE), and the main effect of gain and loss dynamics is simply to select one among the one-parameter family of solutions of the DMNLSE.Comment: 22 pages, 4 figures, to appear in Nonlinearit