Fractional motions

Brownian motion is the archetypal model for random transport processes in science and engineering. Brownian motion displays neither wild fluctuations (the “Noah effect”), nor long-range correlations (the “Joseph effect”). The quintessential model for processes displaying the Noah effect is Lévy motion, the quintessential model for processes displaying the Joseph effect is fractional Brownian motion, and the prototypical model for processes displaying both the Noah and Joseph effects is fractional Lévy motion. In this paper we review these four random-motion models–henceforth termed “fractional motions” –via a unified physical setting that is based on Langevin’s equation, the Einstein–Smoluchowski paradigm, and stochastic scaling limits. The unified setting explains the universal macroscopic emergence of fractional motions, and predicts–according to microscopic-level details–which of the four fractional motions will emerge on the macroscopic level. The statistical properties of fractional motions are classified and parametrized by two exponents—a “Noah exponent” governing their fluctuations, and a “Joseph exponent” governing their dispersions and correlations. This self-contained review provides a concise and cohesive introduction to fractional motions.     

Frequency dependence of the photonic noise spectrum in an absorbing or amplifying diffusive medium

A theory is presented for the frequency dependence of the power spectrum of photon current fluctuations originating from a disordered medium. Both the cases of an absorbing medium (“grey body”) and of an amplifying medium (“random laser”) are considered in a waveguide geometry. The semiclassical approach (based on a Boltzmann-Langevin equation) is shown to be in complete agreement with a fully quantum mechanical theory, provided that the effects of wave localization can be neglected. The width of the peak in the power spectrum around zero frequency is much smaller than the inverse coherence time, characteristic for black-body radiation. Simple expressions for the shape of this peak are obtained, in the absorbing case, for waveguide lengths large compared to the absorption length, and, in the amplifying case, close to the laser threshold. Received 8 August 2000     

Nonholonomic Mapping Principle for Classical and Quantum Mechanics in Spaces with Curvature and Torsion

I explain the geometric basis for the recently-discovered nonholonomic mapping principle which permits deriving laws of nature in spacetimes with curvature and torsion from those in flat spacetime, thus replacing and extending Einstein's equivalence principle. As an important consequence, it yields a new action principle for determining the equation of motion of a free spinless point particle in such spacetimes. Surprisingly, this equation contains a torsion force, although the action involves only the metric. This force makes trajectories autoparallel rather than geodesic, as a manifestation of inertia. A generalization of the mapping principle transforms path integrals from flat spacetimes to those with curvature and torsion, thus playing the role of a quantum equivalence principle. This generalization yields consistent results only for completely antisymmetric or for gradient torsion.     

All- optical phase encoded 4-to-1 phase multiplexer using four wave mixing in semiconductor optical amplifier

Optics has already showed its potency over its electronic complements in case of superfast computing and communication systems. Semiconductor optical amplifier, (SOA) with its several nonlinear properties, plays a very crucial role in the development of high-speed all-optical processor. Multiplexer and demultiplexer are the extremely important element of the processor which takes part in utilizing different actions like encoding, decoding, routing, and the different process of data conversion and generation, etc. In this paper, the authors have proposed a scheme of phase encoded all-optical phase multiplexer using four wave mixing (FWM) property of semiconductor optical amplifier. Thus, the improved tolerance against fiber-nonlinearity and higher receiver sensitivity of phase encoding method with the fast occurring processes like FWM in SOA offers higher speed in this proposed scheme of multiplexing.     

An ODE Model of the Motion of Pelagic Fish

A system of ordinary differential equations (ODEs) is derived from a discrete system of Vicsek, Czirók et al. [Phys. Rev. Lett. 75(6):1226–1229, 1995], describing the motion of a school of fish. Classes of linear and stationary solutions of the ODEs are found and their stability explored using equivariant bifurcation theory. The existence of periodic and toroidal solutions is also proven under deterministic perturbations and structurally stable heteroclinic connections are found. Applications of the model to the migration of the capelin, a pelagic fish that undertakes an extensive migration in the North Atlantic, are discussed and simulation of the ODEs presented.     

Simple Analog Complementary Metal Oxide Semiconductor Circuit for Generating Motion Signal

We proposed in this study a novel analog complementary metal oxide semiconductor (CMOS) circuit for generating a motion signal when an object moves, which is a simple structure. The proposed unit circuit was constructed using a previously proposed edge detection circuit and a novel proposed circuit for generating a motion signal which accepts an edge signal. The part for generating the motion signal was constructed using six metal oxide semiconductor (MOS) transistors and one capacitor. Results obtained by the simulation program with integrated circuit emphasis (SPICE) and the measured results of a test circuit constructed with discrete MOS transistors and the test circuit fabricated with a 1.2 μm CMOS process showed that the proposed unit circuit can output pulsed current (motion signal) when an object moves on the circuit. It was clarified from the SPICE results that the two-dimensional network constructed with proposed unit circuits can output motion signals. The size of the novel unit circuit is expected to be about 110 × 110μm² obtained by the 1.2 μm CMOS process. It is possible to arrange 90 × 90 unit circuits on a chip which has an area of 1 × 1cm². The aperture ratio is expected to be about 21%, which is twice as large as that of the previously proposed circuit. An integrated circuit for image processing in real time can thus be realized by applying the two-dimensional network constructed with the proposed circuits.     

A nonextensive approach to the dynamics of financial observables

We present results about financial market observables, specifically returns and traded volumes. They are obtained within the current nonextensive statistical mechanical framework based on the entropy . More precisely, we present stochastic dynamical mechanisms which mimic probability density functions empirically observed. These mechanisms provide possible interpretations for the emergence of the entropic indices q in the time evolution of the corresponding observables. In addition to this, through multi-fractal analysis of return time series, we verify that the dual relation q_stat+q_sens=2 is numerically satisfied, q_stat and q_sens being associated to the probability density function and to the sensitivity to initial conditions respectively. This type of simple relation, whose understanding remains ellusive, has been empirically verified in various other systems.     

Comparison of accuracy of intravoxel incoherent motion and apparent diffusion coefficient techniques for predicting malignancy of head and neck tumors using half-Fourier single-shot turbo spin-echo diffusion-weighted imaging

Purpose

To evaluate the use of the intravoxel incoherent motion (IVIM) technique in half-Fourier single-shot turbo spin-echo (HASTE) diffusion-weighted imaging (DWI), and to compare its accuracy to that of apparent diffusion coefficient (ADC) to predict malignancy in head and neck tumors.

Patients and methods

HASTE DW images of 33 patients with head and neck tumors (10 benign and 23 malignant) were evaluated. Using the IVIM technique, parameters (D, true diffusion coefficient; f, perfusion fraction; D*, pseudodiffusion coefficient) were calculated for each tumor. ADC values were measured over a range of b values from 0 to 1000 s/mm². IVIM parameters and ADC values in benign and malignant tumors were compared using Student's t test, receiver operating characteristics (ROC) analysis, and multivariate logistic regression modeling.

Results

Mean ADC and D values of malignant tumors were significantly lower than those of benign tumors (P < 0.05). Mean D* values of malignant tumors were significantly higher than those of benign tumors (P < 0.05). There was no significant difference in mean f values between malignant and benign tumors (P > 0.05). The technique of combining D and D* was the best for predicting malignancy; accuracy for this model was higher than that for ADC.

Conclusions

The IVIM technique may be applied in HASTE DWI as a diagnostic tool to predict malignancy in head and neck masses. The use of D and D* in combination increases the diagnostic accuracy in comparison with ADC.     

Spherical particle Brownian motion in viscous medium as non-Markovian random process

The Brownian motion of a spherical particle in an infinite medium is described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. The features of Brownian motion in short time intervals and in small displacements are considered.