Computational polarization imaging from a single speckle image

We experimentally demonstrate that imaging of the degree of polarization (DOP) can be achieved from a single intensity image acquired under coherent illumination. This computational technique is based on the analysis of the speckle characteristics in a statistically homogeneous neighborhood of the pixel. Over a variety of samples obtained experimentally, we show that a simple calibration step allows this method to quickly and simply provide correct estimated values of the DOP, with precision in agreement with theoretical predictions. It is shown that unlike linear polarimetric contrast imaging, this method remains valid on birefringent samples.     

Chromatophores and color revelation in the blue variant of the Siamese fighting fish (Betta splendens)

Our light and electron microscopy observations have revealed that the chromatic unit for the caudal fin in the blue variant of the Siamese fighting fish consists exclusively of dermal chromatophores comprised of compact and overlapping light-reflecting motile iridophores underlined by a layer of light absorbing melanophores. The 2 subtypes that make up about 70% of the skin tissue are located just below the basal layer of the considerably thin epidermis. The administration of K-rich saline or norepinephrine induced prompt, but gradual and reversible, changes in the color of the skin from blue to a brown-yellowish color. The induced color change is attributable either to the neurotransmitter releasing effects of the K-rich saline or to the direct effects of norepinephrine on the postsynaptic alpha adrenergic receptors. Both of these agents induced aggregation of the melanosomes within the melanophores and apparently shifted the wavelength of the light reflected by the iridophores towards the shorter (blue) end of the spectrum. Based on the distribution and architectural arrangement of the iridophores and melanophores as well as their physiological responses, we conclude that the generation of the blue coloration in this fish predominantly occurs through motile iridophores via a multilayered thin-film interference phenomenon of the non-ideal type. The presence of the underlying melanophores provides a black sheet of melanin that enhances the chroma and purity of the color.     

A spectral element method for solving the Pennes bioheat transfer equation by using triangular and quadrilateral elements

A spectral element method is developed for the numerical solution of the Pennes bioheat transfer equation which models the thermal behavior of the living tissue. For the one and two dimensional cases, the implementation of this method is completely explained. In the two dimensional case, both triangular and quadrilateral elements are investigated. Through test problems, the discretization error generated from this method is reported. In the triangular elements, the error is obtained when quadrature points coincide and do not coincide with nodal points. This method is employed to solve the equation in order to obtain the temperature of the skin layers, healthy tissue, and tissue that contains the tumor.     

Determination of a control function in three‐dimensional parabolic equations by Legendre pseudospectral method

A Legendre pseudospectral method is proposed for solving approximately an inverse problem of determining an unknown control parameter p(t) which is the coefficient of the solution u(x, y, z, t) in a diffusion equation in a three‐dimensional region. The diffusion equation is to be solved subject to suitably prescribed initial‐boundary conditions. The presence of the unknown coefficient p(t) requires an extra condition. This extra condition considered as the integral overspecification over the spacial domain. For discretizing the problem, after homogenization of the boundary conditions, we apply the Legendre pseudospectral method in a matrix based manner. As a results a system of nonlinear differential algebraic equations is generated. Then by using suitable transformation, the problem will be converted to a homogeneous time varying system of linear ordinary differential equations. Also a pseudospectral method for efficient solving of the resulted system of ordinary differential equations is proposed. The solution of this system gives the approximation to values of u and p. The matrix based structure of the present method makes it easy to implement. Numerical experiments are presented to demonstrate the accuracy and the efficiency of the proposed computational procedure. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 74‐93, 2012     

New implementation of radial basis functions for solving Burgers‐Fisher equation

In this article, we consider the problem of solving Burgers‐Fisher equation. The approximate solution is found using the radial basis functions collocation method. Also for solving of the resulted nonlinear system of equations, we proposed a predictor corrector method based on the fixed point iterations. The numerical tests show that this method is accurate and efficient for finding a closed form approximation of the solution of nonlinear partial differential equations. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 248–262, 2012     

Optimal sliding mode control of single degree-of-freedom hysteretic structural system

This paper addresses the controller design problem of a nonlinear single degree-of-freedom structural system excited by the earthquake. Bouc–Wen model, as an efficient hysteresis modeling method, is used to model the system nonlinearity. Sliding mode control (SMC), due to its robustness in dealing with uncertainty, is utilized as the main control strategy. An optimal sliding surface is presented which minimizes the displacement and control force in terms of a quadratic cost function. Two numerical examples are given to illustrate the effectiveness of the proposed strategy subject to three earthquakes of El-Centro, Rinaldi and Kobe. Simulation results show a significant and considerable reduction in structural response and indicate that the performance of suggested optimal SMC strategy is remarkable.     

Symmetry analysis and conservation laws of the geodesic equations for the Reissner-Nordström de Sitter black hole with a global monopole

This paper is devoted to the comprehensive analysis of the problem of symmetries and conservation laws for the geodesic equations of the Reissner-Nordström de Sitter (RNdS) black hole with a global monopole. For this purpose, the system of geodesic equations is determined and the corresponding classical Lie point symmetry operators are obtained. An optimal system of one dimensional subalgebras is constructed and a brief discussion about the algebraic structure of the Lie algebra of symmetries is presented. Also, the Noether symmetries of the geodesic Lagrangian is calculated. Finally, by applying two methods including Noether’s theorem and direct method the conservation laws associated to the system of geodesic equations are obtained.     

Minimum entropy control of chaos via online particle swarm optimization method

One of the recently developed approaches for control of chaos is the minimum entropy (ME) control technique. In this method an entropy function based on the Shannon definition, is defined for a chaotic system. The control action is designed such that the entropy as a cost function is minimized which results in more regular pattern of motion for the system trajectories. In this paper an online optimization technique using particle swarm optimization (PSO) method is developed to calculate the control action based on ME strategy. The method is examined on some standard chaotic maps with error feedback and delayed feedback forms. Considering the fact that the optimization is online, simulation results show very good effectiveness of the presented technique in controlling chaos.     

The general Jacobi matrix method for solving some nonlinear ordinary differential equations

In this paper, we obtain the approximate solutions for some nonlinear ordinary differential equations by using the general Jacobi matrix method. Explicit formulae which express the Jacobi expansion coefficients for the powers of derivatives and moments of any differentiable function in terms of the original expansion coefficients of the function itself are given in the matrix form. Three test problems are discussed to illustrate the efficiency of the proposed method.     

Transmission line model for extraction of transmission characteristics in photonic crystal waveguides with stubs: optical filter design

A simple and efficient transmission line model is proposed here to study how the transmission characteristics of photonic crystal waveguides are tailored by introduction of stubs patterned in the photonic crystal lattice. It is shown that band-pass and band-stop optical filters can be easily designed and optimized when stubs of appropriate length are brought in. Since the lengths of the designed stubs are not necessarily integer multiples of the photonic crystal lattice constant, a geometric shift in a portion of the photonic crystal structure is shown to be essential. The proposed model is verified by using a rigorous numerical method. An excellent agreement is observed between the numerical results and the transmission characteristics as extracted by the proposed model.