Brownian motion of spiral waves driven by spatiotemporal structured noise

Spiral chemical waves subjected to a spatiotemporal random excitability are experimentally and numerically investigated in relation to the light-sensitive Belousov-Zhabotinsky reaction. Brownian motion is identified and characterized by an effective diffusion coefficient which shows a rather complex dependence on the time and length scales of the noise relative to those of the spiral. A kinematically based model is proposed whose results are in good qualitative agreement with experiments and numerics.

Noise-induced Brownian motion of spiral waves

We study the erratic displacement of spiral waves forced to move in a medium with random spatiotemporal excitability. Analytical work and numerical simulations are performed in relation to a kinematic scheme, assumed to describe the autowave dynamics for weakly excitable systems. Under such an approach, the Brownian character of this motion is proved and the corresponding dispersion coefficient is evaluated. This quantity shows a nontrivial dependence on the temporal and spatial correlation parameters of the external fluctuations. In particular, a resonantlike behavior is neatly evidenced in terms of the noise correlation time for the particular situation of spatially uniform fluctuations. Actually, this case turns out to be, to a large extent, exactly solvable, whereas a pair of dispersion mechanisms are discussed qualitatively and quantitatively to explain the results for the more general scenario of spatiotemporal disorder.

Non-Markovian Dynamics and the Quantum-To-Classical Transition for Quantum Brownian Motion

In this Thesis I discuss the dynamics of the quantum Brownian motion model in harmonic potential. This paradigmatic model has an exact solution, making it possible to consider also analytically the non-Markovian dynamics. The issues covered in this Thesis are themed around decoherence. First, I consider decoherence as the mediator of quantum-to-classical transition. I examine five different definitions for nonclassicality of quantum states, and show how each definition gives qualitatively different times for the onset of classicality. In particular I have found that all characterizations of nonclassicality, apart from one based on the interference term in the Wigner function, result in a finite, rather than asymptotic, time for the emergence of classicality. Second, I examine the diverse effects which coupling to a non-Markovian, structured reservoir, has on our system. By comparing different types of Ohmic reservoirs, I derive some general conclusions on the role of the reservoir spectrum in both the short-time and the thermalization dynamics. Finally, I apply these results to two schemes for decoherence control. Both of the methods are based on the non-Markovian properties of the dynamics.

Non-Markovian expansion in quantum Brownian motion

We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion. We present detailed results for the free and the quadratic cases, which can be compared to exact solutions to test the convergence of the method, and discuss potentials of a general nonlinear form. © 2013 Elsevier B.V. All rights reserved.

Anisotropic Brownian motion in ordered phases of DNA fragments

Using Fluorescence Recovery After Photobleaching, we investigate the Brownian motion of DNA rod-like fragments in two distinct anisotropic phases with a local nematic symmetry. The height of the measurement volume ensures the averaging of the anisotropy of the in-plane diffusive motion parallel or perpendicular to the local nematic director in aligned domains. Still, as shown in using a model specifically designed to handle such a situation and predicting a non-Gaussian shape for the bleached spot as fluorescence recovery proceeds, the two distinct diffusion coefficients of the DNA particles can be retrieved from data analysis. In the first system investigated (a ternary DNA-lipid lamellar complex), the magnitude and anisotropy of the diffusion coefficient of the DNA fragments confined by the lipid bilayers are obtained for the first time. In the second, binary DNA-solvent system, the magnitude of the diffusion coefficient is found to decrease markedly as DNA concentration is increased from isotropic to cholesteric phase. In addition, the diffusion coefficient anisotropy measured within cholesteric domains in the phase coexistence region increases with concentration, and eventually reaches a high value in the cholesteric phase.

Interim analysis of clinical trials: Simulation studies of fractional Brownian motion

Interim clinical trial monitoring procedures were motivated by ethical and economic considerations. Classical Brownian motion (Bm) techniques for statistical monitoring of clinical trials were widely used. Conditional power argument and α-spending function based boundary crossing probabilities are popular statistical hypothesis testing procedures under the assumption of Brownian motion. However, it is not rare that the assumptions of Brownian motion are only partially met for trial data. Therefore, I used a more generalized form of stochastic process, called fractional Brownian motion (fBm), to model the test statistics. Fractional Brownian motion does not hold Markov property and future observations depend not only on the present observations but also on the past ones. In this dissertation, we simulated a wide range of fBm data, e.g., H = 0.5 (that is, classical Bm) vs. 0.5< H <1, with treatment effects vs. without treatment effects. Then the performance of conditional power and boundary-crossing based interim analyses were compared by assuming that the data follow Bm or fBm. Our simulation study suggested that the conditional power or boundaries under fBm assumptions are generally higher than those under Bm assumptions when H > 0.5 and also matches better with the empirical results. ^

The timber-tree improved, or, The best practical methods of improving different lands with proper timber : and those fruit-trees whose woods make the most profitable returns to their owners, according to the newest inventions, by the plough, harrow, and other methods most approved of : in two parts /

Goldsmiths'-Kress no. 08045.

The wisdom of God manifested in the works of the creation : in two parts. Viz. The heavenly bodies, elements, meteors, fossils, vegetables, animals (beasts, birds, fishes, and insects), more particularly in the body of the earth, its figure, motion, and consistency, and in the admirable structure of the bodies of man and other animals, as also in their generation, &c. : with answers to some objections /

First published: 1691.

All-optical passive quasi-regeneration in transoceanic 40 Gbit/s return-to-zero transmission systems with strong dispersion management

A method of all-optical passive quasi-regeneration in transoceanic 40 Gbit/s return-to-zero transmission systems with strong dispersion management was described. The use of in-line nonlinear optical loop mirrors (NOLM) by the method was demonstrated. The quasi-regeneration of signals performed by NOLMs was found to improve the systems's performance.

Improving envelopment in Data Envelopment Analysis under variable returns to scale

In a Data Envelopment Analysis model, some of the weights used to compute the efficiency of a unit can have zero or negligible value despite of the importance of the corresponding input or output. This paper offers an approach to preventing inputs and outputs from being ignored in the DEA assessment under the multiple input and output VRS environment, building on an approach introduced in Allen and Thanassoulis (2004) for single input multiple output CRS cases. The proposed method is based on the idea of introducing unobserved DMUs created by adjusting input and output levels of certain observed relatively efficient DMUs, in a manner which reflects a combination of technical information and the decision maker's value judgements. In contrast to many alternative techniques used to constrain weights and/or improve envelopment in DEA, this approach allows one to impose local information on production trade-offs, which are in line with the general VRS technology. The suggested procedure is illustrated using real data. © 2011 Elsevier B.V. All rights reserved.

PIV measurements combined with the motion tracking technique to analyze flow around a moving porous structure

To gain a better understanding of the fluid–structure interaction and especially when dealing with a flow around an arbitrarily moving body, it is essential to develop measurement tools enabling the instantaneous detection of moving deformable interface during the flow measurements. A particularly useful application is the determination of unsteady turbulent flow velocity field around a moving porous fishing net structure which is of great interest for selectivity and also for the numerical code validation which needs a realistic database. To do this, a representative piece of fishing net structure is used to investigate both the Turbulent Boundary Layer (TBL) developing over the horizontal porous moving fishing net structure and the turbulent flow passing through the moving porous structure. For such an investigation, Time Resolved PIV measurements are carried out and combined with a motion tracking technique allowing the measurement of the instantaneous motion of the deformable fishing net during PIV measurements. Once the two-dimensional motion of the porous structure is accessed, PIV velocity measurements are analyzed in connection with the detected motion. Finally, the TBL is characterized and the effect of the structure motion on the volumetric flow rate passing though the moving porous structure is clearly demonstrated.