Calculation of mutual information for nonlinear communication channel at large signal-to-noise ratio

Using the path-integral technique we examine the mutual information for the communication channel modeled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications - the backbone of the internet. At large signal-to-noise ratio we present the mutual information through the path-integral, which is convenient for the perturbative expansion in nonlinearity. In the limit of small noise and small nonlinearity we derive analytically the first nonzero nonlinear correction to the mutual information for the channel.

UT Austin | Portugal Workshop on Nonlinear Mechanics and Applications in Life Sciences

This is a CoLab Workshop organized as an initiative of the UT Austin | Portugal Program to reinforce the Portuguese competences in Nonlinear Mechanics and in complex problems arising from applications to the mathematical modeling and simulations in the Life Sciences. The Workshop provides a place to exchange recent developments, discoveries and progresses in this challenging research field. The main goal is to bring together doctoral candidates, postdoctoral scientists and graduates interested in the field, giving them the opportunity to make scientific interactions and new connections with established experts in the interdisciplinary topics covered by the event. Another important goal of the Workshop is to promote collaboration between members of the different areas of the UT Austin | Portugal community.

Spectral Region Optimization for Raman-Based Optical Biopsy of Inflammatory Lesions

Objective: The biochemical alterations between inflammatory fibrous hyperplasia (IFH) and normal tissues of buccal mucosa were probed by using the FT-Raman spectroscopy technique. The aim was to find the minimal set of Raman bands that would furnish the best discrimination. Background: Raman-based optical biopsy is a widely recognized potential technique for noninvasive real-time diagnosis. However, few studies had been devoted to the discrimination of very common subtle or early pathologic states as inflammatory processes that are always present on, for example, cancer lesion borders. Methods: Seventy spectra of IFH from 14 patients were compared with 30 spectra of normal tissues from six patients. The statistical analysis was performed with principal components analysis and soft independent modeling class analogy cross-validated, leave-one-out methods. Results: Bands close to 574, 1,100, 1,250 to 1,350, and 1,500 cm(-1) (mainly amino acids and collagen bands) showed the main intragroup variations that are due to the acanthosis process in the IFH epithelium. The 1,200 (C-C aromatic/DNA), 1,350 (CH(2) bending/collagen 1), and 1,730 cm(-1) (collagen III) regions presented the main intergroup variations. This finding was interpreted as originating in an extracellular matrix-degeneration process occurring in the inflammatory tissues. The statistical analysis results indicated that the best discrimination capability (sensitivity of 95% and specificity of 100%) was found by using the 530-580 cm(-1) spectral region. Conclusions: The existence of this narrow spectral window enabling normal and inflammatory diagnosis also had useful implications for an in vivo dispersive Raman setup for clinical applications.

Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark beta algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples. Copyright (C) 2009 H. B. Coda and R. R. Paccola.

Trajectory Sensitivity Method and Master-Slave Synchronization to Estimate Parameters of Nonlinear Systems

A combination of trajectory sensitivity method and master-slave synchronization was proposed to parameter estimation of nonlinear systems. It was shown that master-slave coupling increases the robustness of the trajectory sensitivity algorithm with respect to the initial guess of parameters. Since synchronization is not a guarantee that the estimation process converges to the correct parameters, a conditional test that guarantees that the new combined methodology estimates the true values of parameters was proposed. This conditional test was successfully applied to Lorenz's and Chua's systems, and the proposed parameter estimation algorithm has shown to be very robust with respect to parameter initial guesses and measurement noise for these examples. Copyright (C) 2009 Elmer P. T. Cari et al.

Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Uncertainties in damping estimates can significantly affect the dynamic response of a given flexible structure. A common practice in linear structural dynamics is to consider a linear viscous damping model as the major energy dissipation mechanism. However, it is well known that different forms of energy dissipation can affect the structure's dynamic response. The major goal of this paper is to address the effects of the turbulent frictional damping force, also known as drag force on the dynamic behavior of a typical flexible structure composed of a slender cantilever beam carrying a lumped-mass on the tip. First, the system's analytical equation is obtained and solved by employing a perturbation technique. The solution process considers variations of the drag force coefficient and its effects on the system's response. Then, experimental results are presented to demonstrate the effects of the nonlinear quadratic damping due to the turbulent frictional force on the system's dynamic response. In particular, the effects of the quadratic damping on the frequency-response and amplitude-response curves are investigated. Numerically simulated as well as experimental results indicate that variations on the drag force coefficient significantly alter the dynamics of the structure under investigation. Copyright (c) 2008 D. G. Silva and P. S. Varoto.

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

Possibility for a full optical determination of photodynamic therapy outcome

The efficacy of photodynamic therapy (PDT) depends on a variety of parameters: concentration of the photosensitizer at the time of treatment, light wavelength, fluence, fluence rate, availability of oxygen within the illuminated volume, and light distribution in the tissue. Dosimetry in PDT requires the congregation of adequate amounts of light, drug, and tissue oxygen. The adequate dosimetry should be able to predict the extension of the tissue damage. Photosensitizer photobleaching rate depends on the availability of molecular oxygen in the tissue. Based on photosensitizers photobleaching models, high photobleaching has to be associated with high production of singlet oxygen and therefore with higher photodynamic action, resulting in a greater depth of necrosis. The purpose of this work is to show a possible correlation between depth of necrosis and the in vivo photosensitizer (in this case, Photogem (R)) photodegradation during PDT. Such correlation allows possibilities for the development of a real time evaluation of the photodynamic action during PDT application. Experiments were performed in a range of fluence (0-450 J/cm(2)) at a constant fluence rate of 250 mW/cm(2) and applying different illumination times (0-1800 s) to achieve the desired fluence. A quantity was defined (psi) as the product of fluorescence ratio (related to the photosensitizer degradation at the surface) and the observed depth of necrosis. The correlation between depth of necrosis and surface fluorescence signal is expressed in psi and could allow, in principle, a noninvasive monitoring of PDT effects during treatment. High degree of correlation is observed and a simple mathematical model to justify the results is presented.

PARTIAL STABILITY FOR A CLASS OF NONLINEAR SYSTEMS

This paper studies a nonlinear, discrete-time matrix system arising in the stability analysis of Kalman filters. These systems present an internal coupling between the state components that gives rise to complex dynamic behavior. The problem of partial stability, which requires that a specific component of the state of the system converge exponentially, is studied and solved. The convergent state component is strongly linked with the behavior of Kalman filters, since it can be used to provide bounds for the error covariance matrix under uncertainties in the noise measurements. We exploit the special features of the system-mainly the connections with linear systems-to obtain an algebraic test for partial stability. Finally, motivated by applications in which polynomial divergence of the estimates is acceptable, we study and solve a partial semistability problem.

Nonlinear diffraction of light beams propagating in photorefractive media with embedded reflecting wire

The theory of nonlinear diffraction of intensive light beams propagating through photorefractive media is developed. Diffraction occurs on a reflecting wire embedded in the nonlinear medium at a relatively small angle with respect to the direction of the beam propagation. It is shown that this process is analogous to the generation of waves by a flow of a superfluid past an obstacle. The ""equation of state"" of such a superfluid is determined by the nonlinear properties of the medium. On the basis of this hydrodynamic analogy, the notion of the ""Mach number"" is introduced where the transverse component of the wave vector plays the role of the fluid velocity. It is found that the Mach cone separates two regions of the diffraction pattern: inside the Mach cone oblique dark solitons are generated and outside the Mach cone the region of ""optical ship waves"" (the wave pattern formed by a two-dimensional packet of linear waves) is situated. Analytical theory of the ""optical ship waves"" is developed and two-dimensional dark soliton solutions of the generalized two-dimensional nonlinear Schrodinger equation describing the light beam propagation are found. Stability of dark solitons with respect to their decay into vortices is studied and it is shown that they are stable for large enough values of the Mach number.

Carrier transfer in the optical recombination of quantum dots

We report a study of dynamic effects detected in the time-resolved emission from quantum dot ensembles. Experimental procedures were developed to search for common behaviors found in quantum dot systems independently of their composition: three quantum dot samples were experimentally characterized. Systems with contrasting interdot coupling are compared and their sensitivity to the excitation energy is analyzed. Our experimental results are compared and contrasted with other results available in literature. The optical recombination time dependence on system parameters is derived and compared to the experimental findings. We discuss the effects of occupation of the ground state in both valence and conduction bands of semiconductor quantum dots in the dynamics of the system relaxation as well as the nonlinear effects.

Thermo-optical characteristics and concentration quenching effects in Nd(3+)doped yttrium calcium borate glasses

In this work we present a comprehensive study of the spectroscopic and thermo-optical properties of a set of samples with composition xNd(2)O(3)-(5-x)Y(2)O(3-)40CaO-55B(2)O(3) (0 <= x <= 1.0 mol%). Their fluorescence quantum efficiency (eta) values were determined using the thermal lens technique and the dependence on the ionic concentration was analyzed in terms of energy transfer processes, based on the Forster-Dexter model of multipolar ion-ion interactions. A maximum eta = 0.54 was found to be substantially higher than for yttrium aluminoborate crystals and glasses with comparable Nd(3+) content. As for the thermo-optical properties of yttrium calcium borate, they are comparable to other well-known laser glasses. The obtained energy transfer microparameters and the weak dependence of. on the Nd(3+) concentration with a high optimum Nd(3+) concentration put this system as a strong candidate for photonics applications. (C) 2011 American Institute of Physics. [doi:10.1063/1.3567091]

Nonlinear refraction and absorption through phase transition in a Nd:SBN laser crystal

Time-resolved Z-scan measurements were performed in a Nd(3+)-doped Sr(0.61)Ba(0.39)Nb(2)O(6) laser crystal through ferroelectric phase transition. Both the differences in electronic polarizability (Delta alpha(p)) and cross section (Delta sigma) of the neodymium ions have been found to be strongly modified in the surroundings of the transition temperature. This observed unusual behavior is concluded to be caused by the remarkable influence that the structural changes associated to the ferro-to-paraelectric phase transition has on the 4f -> 5d transition probabilities. The maximum polarizability change value Delta alpha(p)=1.2x10(-25) cm(3) obtained at room temperature is the largest ever measured for a Nd(3+)-doped transparent material.

Direct Solid-Phase Optical Measurements in Flow Systems: A Review

Measurements based on absorption, reflectance, or luminescence of molecular species or complex ions can be carried out directly on a solid support simultaneously to the retention of the analyte. The use of this strategy in flow-based systems is advantageous in view of the reproducible handling of solutions in retention and elution steps of the analyte. This approach can be exploited to increase sensitivity, minimize reagent consumption as well as waste generation, improve selectivity or for simultaneous determination based on selective retention or differences in sorption rates of the analytes. This review focuses on the main characteristics of direct solid-phase measurements in flow systems, including the discussion of advantages and limitations and practical guidelines to the successful implementation of this approach. Selected applications in diverse fields, such as pharmaceutical, food, and environmental analysis are discussed.

SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.