The Experts below are selected from a list of 1554 Experts worldwide ranked by ideXlab platform

Bohua Sun - One of the best experts on this subject based on the ideXlab platform.

  • Explicit representation for the SO(3) rotation tensor of deformable bodies
    Applied Mathematics Letters, 2021
    Co-Authors: Bohua Sun
    Abstract:

    Abstract Computation of rotation tensor is essential in the analysis of deformable bodies. This paper proposes an explicit expression for rotation tensor R of deformation gradient F , and successfully establishes an intrinsic relation between the exponential mapping Q = exp A and the deformation F . As an application, Truesdell’s simple shear deformation is revisited. For easy use of our formulation, we provide a Maple Code for a general 2D problem.

  • Small Symmetrical Deformation of Thin Torus with Circular Cross-Section
    2020
    Co-Authors: Bohua Sun
    Abstract:

    By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, a complex-form ordinary differential equation (ODE) for the small symmetrical deformation of an elastic torus is successfully transformed into the well-known Heun's ODE, whose exact solution is obtained in terms of Heun's functions. To overcome the computational difficulties of the complex-form ODE in dealing with boundary conditions, a real-form ODE system is proposed. A general Code of numerical solution of the real-form ODE is written by using Maple. Some numerical studies are carried out and verified by finite element analysis. Our investigations show that the mechanics of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell. A general Maple Code is provided as essential part of this paper.

  • Influence of Physical Parameters on the Collapse of a Spherical Bubble
    2020
    Co-Authors: Bohua Sun
    Abstract:

    This paper examines the influence of physical parameters on the collapse dynamics of a spherical bubble filled with diatomic gas ($\kappa=7/5$). The present numerical investigation shows that each physical parameter affects the bubble collapse dynamics differently. After comparing the contribution of each physical parameter, it appears that, of all the parameters, the surrounding liquid environment affects the bubble collapse dynamics the most. Meanwhile, surface tension has the weakest influence and can be ignored in the bubble collapse dynamics. However, surface tension must be retained in the initial analysis since this, as well as the pressure difference jointly control initial bubble formation. As an essential part of this study, a general Maple Code is provided.

  • Hertz Elastic Dynamics of Two Colliding Elastic Spheres
    2020
    Co-Authors: Bohua Sun
    Abstract:

    This paper revisits a classic problem in physics - Hertz elastic dynamics of two colliding elastic spheres. This study obtains impact period in terms of hypergeometric function and successfully combines Deresiewicz's three segmental solutions into one single solution. Our numerical investigation confirms that Deresiewicz's inversion is a good approximation. As an essential part of this study, a general Maple Code is provided.

  • Solving Prandtl-Blasius Boundary Layer Equation Using Maple
    2020
    Co-Authors: Bohua Sun
    Abstract:

    A solution for the Prandtl-Blasius equation is essential to all kinds of boundary layer problems. This paper revisits this classic problem and presents a general Maple Code as its numerical solution. The solutions were obtained from the Maple Code, using the Runge-Kutta method. The study also considers convergence radius expanding and an approximate analytic solution is proposed by curve fitting. Similarly, the study resolves some boundary layer related problems and provide relevant Maple Codes for these.

Alexei F. Cheviakov - One of the best experts on this subject based on the ideXlab platform.

  • Symbolic Computation of Nonlocal Symmetries and Nonlocal Conservation Laws of Partial Differential Equations Using the GeM Package for Maple
    Similarity and Symmetry Methods, 2014
    Co-Authors: Alexei F. Cheviakov
    Abstract:

    The use of the symbolic software package GeM for Maple is illustrated with examples of computation of nonlocal symmetries and nonlocal conservation laws of nonlinear partial differential equations. In the considered examples, the nonlocal symmetries and conservation laws arise as local symmetries and conservation laws of potential systems. Full Maple Code with detailed comments is presented. Examples of automated symmetry and conservation law classification are included.

  • GeM software package for computation of symmetries and conservation laws of differential equations
    Computer Physics Communications, 2007
    Co-Authors: Alexei F. Cheviakov
    Abstract:

    We present a recently developed Maple-based \GeM" software package for automated symmetry and conservation law analysis of systems of partial and ordinary difierential equations (DE). The package contains a collection of powerful easyto-use routines for mathematicians and applied researchers. A standard program that employs \GeM" routines for symmetry, adjoint symmetry or conservation law analysis of any given DE system occupies several lines of Maple Code, and produces output in the canonical form. Classiflcation of symmetries and conservation laws with respect to constitutive functions and parameters present in the given DE system is implemented. The \GeM" package is being successfully used in ongoing research. Run examples include classical and new results.

Eamonn A. Gaffney - One of the best experts on this subject based on the ideXlab platform.

  • Fock space, symbolic algebra, and analytical solutions for small stochastic systems
    Physical Review E - Statistical Nonlinear and Soft Matter Physics, 2015
    Co-Authors: Fernando A.n. Santos, Hermes Gadêlha, Eamonn A. Gaffney
    Abstract:

    Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic Maple Code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.

E. A. Galperin - One of the best experts on this subject based on the ideXlab platform.

  • Maple Code of the cubic algorithm for multiobjective optimization with box constraints
    Numerical Algebra Control and Optimization, 2013
    Co-Authors: M. Delgado Pineda, E. A. Galperin, P. Jim # Nez Guerra
    Abstract:

    A generalization of the cubic algorithm is presented for global optimization of nonconvex nonsmooth multiobjective optimization programs $\min f_{s}(x),\ s=1,\dots,k,$ with box constraints $x\in X=[a_{1},b_{1}]\times \dots\times\lbrack a_{n},b_{n}]$.     This monotonic set contraction algorithm converges onto the entire exact Pareto set, if nonempty, and yields its approximation with given precision in a finite number of iterations. Simultaneously, approximations for the ideal point and for the function values over Pareto set are obtained. The method is implemented by Maple Code, and this Code does not create ill-conditioned situations.     Results of numerical experiments are presented, with graphs, to illustrate the use of the Code, and the solution set can be visualized in projections on coordinate planes. The Code is ready for engineering and economic applications.

  • Maple Code for the gamma algorithm for global optimization of uncertain functions in economy and finance
    Computers & Mathematics with Applications, 2010
    Co-Authors: M. Delgado Pineda, E. A. Galperin
    Abstract:

    Problems with uncertainties are ubiquitous in many areas of life and the economy. Due to a lack of information as regards the economy and in finance, problems with uncertainties (stock prices, marketing problems, inflation, unemployment) are usually formulated by giving bounds on maximum and minimum values of certain parameters, i.e. box constraints. In such situations, it is necessary to make a choice of better parameters that produce finite intervals of possible values for a given uncertain function at each point of the parameter space. The gamma algorithm presents a method for making that choice. A variant of the gamma algorithm based on the cubic algorithm is considered, for global optimization of uncertain functions with box constraints in R^n. The set-monotonic algorithm contains a block for problems with equality constraints, and operates within the unit cube [0,1]^n for all problems. On this basis, a Maple Code of modular structure is developed for full global optimization of uncertain functions in n variables. The Code does not create ill-conditioned situations. Graphics are included, and the solution set can be visualized in plane projections and sections. An example related to Minsky's Financial Instability Hypothesis is presented, with a graph, to illustrate the use of the Code.

  • Maple Code of gamma algorithm for global optimization of uncertain functions over compact robust sets
    Computers & Mathematics with Applications, 2008
    Co-Authors: M. Delgado Pineda, E. A. Galperin
    Abstract:

    Problems with uncertainties are ubiquitous in many areas of science and technology. Due to imprecision of measurements (Heisenberg's relation), such problems are normal in nuclear physics. Due to fluidity of media, ships at sea and planes in the air have to deal with instability of the currents they move in. Yields in agriculture depend on the whims of weather. Due to the lack of information in economy and finance, problems with uncertainties (stock prices, marketing problems, inflation, unemployment) are commonplace. In such situations, it is necessary to make a choice of better parameters that produce finite intervals of possible values of a given uncertain function at each point of the parameter space. The gamma algorithm [E.A. Galperin, Global optimization in problems with uncertainties, Journal of Nonlinear Analysis 47 (2001) 941-952; E.A. Galperin, Global optimization in problems with uncertainties. The gamma algorithm. Computer and Mathematics with Applications 44 (2002) 853-862] presents a method to make that choice. A new variant of the gamma algorithm based on the beta algorithm is presented for global optimization of uncertain functions over compact robust sets in R^n. The set-monotonic algorithm contains a block for problems with equality constraints, and operates within the unit cube [0,1]^n for all problems. On this basis, a Maple Code of modular structure is developed for full global optimization of functions of n variables. The Code does not create ill-conditioned situations. Graphics are included, and the solution set can be visualized in plane projections and sections. The Code is ready for engineering applications. The results of numerical experiments are presented, with graphs, to illustrate the use of the Code.

  • Global optimization over general compact sets by the beta algorithm: A Maple Code
    Computers & Mathematics with Applications, 2006
    Co-Authors: M. Delgado Pineda, E. A. Galperin
    Abstract:

    AbstractA variant of the beta algorithm based on the cubic algorithm [1,2] is presented for global optimization of Hölder continuous functions over general compact sets. The set-monotonic algorithm contains a block for problems with equality constraints, and operates within the unit cube [0,1]n universal for all problems. On this basis, a Maple Code of modular structure is developed for full global optimization of functions of n variables. The Code does not create ill-conditioned situations. Graphics are included, and the solution set can be visualized in plane projections and sections. The Code is ready for engineering applications. Results of numerical experiments are presented, with graphs, to illustrate the use of the Code

  • Global optimization in Rn with box constraints and applications: A Maple Code
    Mathematical and Computer Modelling, 2003
    Co-Authors: M. Delgado Pineda, E. A. Galperin
    Abstract:

    A variant of the cubic algorithm [1] is presented for global optimization of continuous functions with box constraints. On this basis, a Maple Code is developed for full global optimization of functions of n variables with application to the finding of all roots of a polynomial, to the eigenvalue problems, and to the solution of nonlinear systems of equations, including underdetermined and overdetermined systems. The Code does not create ill-conditioned situations. Graphics are included, and the solution set can be visualized in projections on coordinate planes. The Code is ready for engineering applications. Results of numerical experiments are presented, with graphs, to illustrate the use of the Code.

M Van Daele - One of the best experts on this subject based on the ideXlab platform.

  • solution of the schrodinger equation by a high order perturbation method based on a linear reference potential
    Computer Physics Communications, 2006
    Co-Authors: Veerle Ledoux, M Rizea, Liviu Gr Ixaru, G Vanden Berghe, M Van Daele
    Abstract:

    The paper is devoted to the enhancement of the accuracy of the line-based perturbation method via the introduction of the perturbation corrections. We effectively construct the first and the second order corrections. We also perform the error analysis to predict that the introduction of successive corrections substantially enhances the order of the method from four, for the zeroth order version, to six and ten when the first and the second-order corrections are included. In order to remove the effect of the accuracy loss due to near-cancellation of like-terms when evaluating the perturbation corrections we construct alternative asymptotic formulae using a Maple Code. We also propose a procedure for choosing the step size in terms of the preset accuracy and give a number of numerical illustrations.