Gradient Eigen-decomposition Invariance Biogeography-based Optimization for Mobile Robot Path Planning

The path planning for mobile robots has attracted extensive attention, and evolutionary algorithms have been applied to this problem increas-ingly. In this paper, we propose a novel gradient eigen-decomposition invariance biogeography-based optimization (GEI-BBO) for mobile robot path planning, which has the merits of high rotation invariance and excel-lent search performance. In GEI-BBO, we design an eigen-decomposition mechanism for migration operation, which can reduce the dependence of biogeography-based optimization (BBO) on the coordinate system, improve the rotation invariance and share the information between eigen solutions more effectively. Meanwhile, to find the local opti-mal solution better, gradient descent is added, and the system search strategy can reduce the occurrence of local trapping phenomenon. In addition, combining the GEI-BBO with cubic spline interpola-tion will solve the problem of mobile robot path planning through a defined coding method and fitness function. A series of experiments are implemented on benchmark functions, whose results indicated that the optimization performance of GEI-BBO is superior to other algo-rithms. And the successful application of GEI-BBO for path planning in different environments confirms its effectiveness and practicability.

A sharper image: the quest of science and recursive production of objective realities

This article explores the metaphor of Science as provider of sharp images of ourenvironment, using the epistemological framework of Objective Cognitive Constructivism.These sharp images are conveyed by precise scientific hypotheses that, in turn, are encodedby mathematical equations. Furthermore, this article describes how such knowledge is pro-duced by a cyclic and recursive development, perfection and reinforcement process, leadingto the emergence of eigen-solutions characterized by the four essential properties of preci-sion, stability, separability and composability. Finally, this article discusses the role playedby ontology and metaphysics in the scientific production process, and in which sense theresulting knowledge can be considered objective.

ROTATIONAL-VIBRATIONAL EIGEN SOLUTIONS OF THE D-DIMENSIONAL SCHRÖDINGER EQUATION FOR THE IMPROVED WEI POTENTIAL

In this present study, we have employed the techniques of exact quantization rule and ansatz solution method to obtain closed form expressions for the rotational-vibrational eigensolutions of the D-dimensional Schrödinger equation for the improved Wei potential, for cases of h′ ≠ 0 and h′ = 0. By using our derived energy equation and choosing arbitrary values of n and ℓ, we have computed the bound state rotational-vibrational energies of CO, H2 and LiH for various quantum states. The mean absolute percentage deviation (MAPD) and the Lippincott criterion ware used as a goodness-of-fit indices to compare our result with the Rydberg-Klein-Rees (RKR) and improved Tietz potential data in the literature. MAPD of 0.2862%, 0.2896% and 0.0662% relative to the RKR data for CO ware obtained. For the improved Wei and Morse potential, our computed energy eigenvalues for CO, H2 and LiH are in excellent agreement with existing results in the literature

Eigen-Solutions to Schrodinger Equation with Trigonometric Inversely Quadratic Plus Coulombic Hyperbolic Potential

In this work, we applied parametric Nikiforov-Uvarov method to analytically obtained eigen solutions to Schrodinger wave equation with Trigonometric Inversely Quadratic plus Coulombic Hyperbolic Potential. We obtain energy-Eigen equation and total normalised wave function expressed in terms of Jacobi polynomial. The numerical solutions produce positive and negative bound state energies which signifies that the potential is suitable for describing both particle and anti-particle. The numerical bound state energies decreases with an increase in quantum state with fixed orbital angular quantum number 0, 1, 2 and 3. The numerical bound state energies decreases with an increase in the screening parameter and 0.5. The energy spectral diagrams show unique quantisation of the different energy levels. This potential reduces to Coulomb potential as a special case. The numerical solutions were carried out with algorithm implemented using MATLAB 8.0 software using the resulting energy-Eigen equation.

Quantification of Energy Transformation Processes Between Acoustic and Hydrodynamic Modes in Non-Compact Thermoacoustic Systems via a Helmholtz-Hodge Decomposition Approach

Solutions of the Linearized Euler Equations (LEE) are composed of acoustic, entropy and vortical perturbation types. The excitation of the latter can be provoked by a transformation of acoustic into rotational energy, which originates from the interaction between acoustics and a mean flow shear-layer. This is known as acoustically induced vortex shedding and represents the phenomenon of interest in this study. In the field of thermoacoustics, numerical eigenfrequency simulations with the LEE have moved into focus to determine the acoustic damping rates associated with vortex shedding to complete thermoacoustic stability analyses of gas turbine combustors. However, there is yet no fundamental investigation existent, which establishes the legitimation to consider these LEE damping rates for this purpose. This question arises due to the implicit presence of vortical disturbances caused by vortex shedding next to the acoustic ones in LEE eigensolutions. In conclusion, the corresponding damping rates are not expected to represent the pure acoustic damping rates, which are exclusively required for a thermoacoustic stability analysis. The main objective of this work comprises the clarification, whether damping rates obtained by straightforwardly performed LEE eigenfrequency simulations can be used for a thermoacoustic stability assessment, although their eigen-solutions are “polluted” by further disturbance types, i.e. the vortical one in this study. Therefore, a Helmholtz-Hodge decomposition approach is applied to LEE eigenmode shapes, which allows to explicitly access acoustic and vortical disturbance fields. These are used to extract the unambiguous, pure acoustic damping rates from LEE eigensolutions via evaluations of appropriate energy terms. The resulting damping rates are finally compared to the corresponding, original LEE damping rates and their experimental counterparts.

A Symplectic Analytical Singular Element for Steady-State Thermal Conduction With Singularities in Anisotropic Material

Modeling of steady-state thermal conduction for crack and v-notch in anisotropic material remains challenging. Conventional numerical methods could bring significant error and the analytical solution should be used to improve the accuracy. In this study, crack and v-notch in anisotropic material are studied. The analytical symplectic eigen solutions are obtained for the first time and used to construct a new symplectic analytical singular element (SASE). The shape functions of the SASE are defined by the obtained eigen solutions (including higher order terms), hence the temperature as well as heat flux fields around the crack/notch tip can be described accurately. The formulation of the stiffness matrix of the SASE is then derived based on a variational principle with two kinds of variables. The nodal variable is transformed into temperature such that the proposed SASE can be connected with conventional finite elements (FE) directly without transition element. Structures of complex geometries and complicated boundary conditions can be analyzed numerically. The generalized flux intensity factors (GFIFs) can be calculated directly without any postprocessing. A few numerical examples are worked out and it is proven that the proposed method is effective for the discussed problem, and the structure can be analyzed accurately and efficiently.