Non-Hamiltonian dynamics in optical microcavities resulting from wave-inspired corrections to geometric optics

We introduce and investigate billiard systems with an adjusted ray dynamics that accounts for modifications of the conventional reflection of rays due to universal wave effects. We show that even small modifications of the specular reflection law have dramatic consequences on the phase space of classical billiards. These include the creation of regions of non-Hamiltonian dynamics, the breakdown of symmetries, and changes in the stability and morphology of periodic orbits. Focusing on optical microcavities, we show that our adjusted dynamics provides the missing ray counterpart to previously observed wave phenomena and we describe how to observe its signatures in experiments. Our findings also apply to acoustic and ultrasound waves and are important in all situations where wavelengths are comparable to system sizes, an increasingly likely situation considering the systematic reduction of the size of electronic and photonic devices.Comment: 6 pages, 4 figures, final published versio

Modeling Barkhausen Noise in Magnetic Glasses with Dipole-Dipole Interactions

Long-ranged dipole-dipole interactions in magnetic glasses give rise to magnetic domains having labyrinthine patterns. Barkhausen Noise is then expected to result from the movement of domain boundaries which is supposed to be modeled by the motion of elastic membranes with random pinning. We propose an atomistic model of such magnetic glasses in which we measure the Barkhausen Noise which indeed results from the movement of domain boundaries. Nevertheless the statistics of the Barkhausen Noise is found in striking disagreement with the expectations in the literature. In fact we find exponential statistics without any power law, stressing the fact that Barkhausen Noise can belong to very different universality classes. In this glassy system the essence of the phenomenon is the ability of spin-carrying particles to move and minimize the energy without any spin flip. A theory is offered in excellent agreement with the measured data without any free parameter.Comment: 5 Pages, 5 Figures, Submitted to EP

Near-field diffraction of fs and sub-fs pulses: super-resolutions of NSOM in space and time

The near-field diffraction of fs and sub-fs light pulses by nm-size slit-type apertures and its implication for near-field scanning optical microscopy (NSOM) is analyzed. The amplitude distributions of the diffracted wave-packets having the central wavelengths in the visible spectral region are found by using the Neerhoff and Mur coupled integral equations, which are solved numerically for each Fourier's component of the wave-packet. In the case of fs pulses, the duration and transverse dimensions of the diffracted pulse remain practically the same as that of the input pulse. This demonstrates feasibility of the NSOM in which a fs pulse is used to provide the fs temporal resolution together with nm-scale spatial resolution. In the sub-fs domain, the Fourier spectrum of the transmitted pulse experiences a considerable narrowing that leads to the increase of the pulse duration in a few times. This imposes a limit on the simultaneous resolutions in time and space.Comment: 5 figure

Detailing the relation between renal T(2)* and renal tissue pO2 using an integrated approach of parametric magnetic resonance imaging and invasive physiological measurements

OBJECTIVES: This study was designed to detail the relation between renal T2* and renal tissue pO2 using an integrated approach that combines parametric magnetic resonance imaging (MRI) and quantitative physiological measurements (MR-PHYSIOL. MATERIALS AND METHODS: Experiments were performed in 21 male Wistar rats. In vivo modulation of renal hemodynamics and oxygenation was achieved by brief periods of aortic occlusion, hypoxia, and hyperoxia. Renal perfusion pressure (RPP), renal blood flow (RBF), local cortical and medullary tissue pO2, and blood flux were simultaneously recorded together with T2*, T2 mapping, and magnetic resonance-based kidney size measurements (MR-PHYSIOL). Magnetic resonance imaging was carried out on a 9.4-T small-animal magnetic resonance system. Relative changes in the invasive quantitative parameters were correlated with relative changes in the parameters derived from MRI using Spearman analysis and Pearson analysis. RESULTS: Changes in T2* qualitatively reflected tissue pO2 changes induced by the interventions. T2* versus pO2 Spearman rank correlations were significant for all interventions, yet quantitative translation of T2*/pO2 correlations obtained for one intervention to another intervention proved not appropriate. The closest T2*/pO2 correlation was found for hypoxia and recovery. The interlayer comparison revealed closest T2*/pO2 correlations for the outer medulla and showed that extrapolation of results obtained for one renal layer to other renal layers must be made with due caution. For T2* to RBF relation, significant Spearman correlations were deduced for all renal layers and for all interventions. T2*/RBF correlations for the cortex and outer medulla were even superior to those between T2* and tissue pO2. The closest T2*/RBF correlation occurred during hypoxia and recovery. Close correlations were observed between T2* and kidney size during hypoxia and recovery and for occlusion and recovery. In both cases, kidney size correlated well with renal vascular conductance, as did renal vascular conductance with T2*. Our findings indicate that changes in T2* qualitatively mirror changes in renal tissue pO2 but are also associated with confounding factors including vascular volume fraction and tubular volume fraction. CONCLUSIONS: Our results demonstrate that MR-PHYSIOL is instrumental to detail the link between renal tissue pO2 and T2* in vivo. Unravelling the link between regional renal T2* and tissue pO2, including the role of the T2* confounding parameters vascular and tubular volume fraction and oxy-hemoglobin dissociation curve, requires further research. These explorations are essential before the quantitative capabilities of parametric MRI can be translated from experimental research to improved clinical understanding of hemodynamics/oxygenation in kidney disorders

Multifractal nature of stock exchange prices

The multifractal structure of the temporal dependence of the Deutsche Aktienindex (DAX) is analyzed. The $q$-th order moments of the structure functions and the singular measures are calculated. The generalized Hurst exponent $H(q)$ and the $h(\gamma(q))$ curve indicate a hierarchy of power law exponents. This approach leads to characterizing the nonstationarity and intermittency pertinent to such financial signals, indicating differences with turbulence data. A list of results on turbulence and financial markets is presented for asserting the analogy.Comment: 6 pages, 3 figures; an invited talk at: Conference on Computational Physics 2001, Sept 5-8, Aachen, German

Nonlinear anomalous diffusion equation and fractal dimension: Exact generalized gaussian solution

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the $N$-dimensional nonlinear diffusion equation $\partial\rho /\partial{t}={\bf \nabla} \cdot (K{\bf \nabla} \rho^{\nu})-{\bf \nabla}\cdot(\mu{\bf F} \rho)-\alpha \rho ,$ where $K=D r^{-\theta}$, $\nu$, $\theta$, $\mu$ and $D$ are real parameters and $\alpha$ is a time-dependent source. This equation unifies the O'Shaugnessy-Procaccia anomalous diffusion equation on fractals ($\nu =1$) and the spherical anomalous diffusion for porous media ($\theta=0$). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.Comment: Latex, 6 pages. To appear in Phys. Rev.