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8125 results in Fluid dynamics and solid mechanics

Page 151 of 407

  • A TRANSFORMATION METHOD FOR SOLVING THE HAMILTON–JACOBI–BELLMAN EQUATION FOR A CONSTRAINED DYNAMIC STOCHASTIC OPTIMAL ALLOCATION PROBLEM

  • Part of
  • S. KILIANOVÁ, D. ŠEVČOVIČ
  • Journal:
    The ANZIAM Journal / Volume 55 / Issue 1 / July 2013
    Published online by Cambridge University Press:
    10 October 2013, pp. 14-38
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  • We propose and analyse a method based on the Riccati transformation for solving the evolutionary Hamilton–Jacobi–Bellman equation arising from the dynamic stochastic optimal allocation problem. We show how the fully nonlinear Hamilton–Jacobi–Bellman equation can be transformed into a quasilinear parabolic equation whose diffusion function is obtained as the value function of a certain parametric convex optimization problem. Although the diffusion function need not be sufficiently smooth, we are able to prove existence and uniqueness and derive useful bounds of classical Hölder smooth solutions. Furthermore, we construct a fully implicit iterative numerical scheme based on finite volume approximation of the governing equation. A numerical solution is compared to a semi-explicit travelling wave solution by means of the convergence ratio of the method. We compute optimal strategies for a portfolio investment problem motivated by the German DAX 30 index as an example of the application of the method.

  • ON LAGUERRE–SOBOLEV TYPE ORTHOGONAL POLYNOMIALS: ZEROS AND ELECTROSTATIC INTERPRETATION

  • Part of
  • LUIS ALEJANDRO MOLANO MOLANO
  • Journal:
    The ANZIAM Journal / Volume 55 / Issue 1 / July 2013
    Published online by Cambridge University Press:
    08 October 2013, pp. 39-54
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  • We study the sequence of monic polynomials orthogonal with respect to inner product

    $$\begin{eqnarray*}\langle p, q\rangle = \int \nolimits \nolimits_{0}^{\infty } p(x)q(x){e}^{- x} {x}^{\alpha } \hspace{0.167em} dx+ Mp(\zeta )q(\zeta )+ N{p}^{\prime } (\zeta ){q}^{\prime } (\zeta ),\end{eqnarray*}$$
    where $\alpha \gt - 1$, $M\geq 0$, $N\geq 0$, $\zeta \lt 0$, and $p$ and $q$ are polynomials with real coefficients. We deduce some interlacing properties of their zeros and, by using standard methods, we find a second-order linear differential equation satisfied by the polynomials and discuss an electrostatic model of their zeros.

Double-Diffusive Convection
  • Timour Radko
  • Published online:
    05 October 2013
    Print publication:
    19 September 2013
  • Double-diffusive convection is a mixing process driven by the interaction of two fluid components which diffuse at different rates. Leading expert Timour Radko presents the first systematic overview of the classical theory of double-diffusive convection in a coherent narrative, bringing together the disparate literature in this developing field. The book begins by exploring idealized dynamical models and illustrating key principles by examples of oceanic phenomena. Building on the theory, it then explains the dynamics of structures resulting from double-diffusive instabilities, such as the little-understood phenomenon of thermohaline staircases. The book also surveys non-oceanographic applications, such as industrial, astrophysical and geological manifestations, and discusses the climatic and biological consequences of double-diffusive convection. Providing a balanced blend of fundamental theory and real-world examples, this is an indispensable resource for academic researchers, professionals and graduate students in physical oceanography, fluid dynamics, applied mathematics, astrophysics, geophysics and climatology.

Cavitation and Bubble Dynamics
  • Christopher Earls Brennen
  • Published online:
    05 October 2013
    Print publication:
    14 October 2013
  • Cavitation and Bubble Dynamics deals with the fundamental physical processes of bubble dynamics and the phenomenon of cavitation. It is ideal for graduate students and research engineers and scientists, and a basic knowledge of fluid flow and heat transfer is assumed. The analytical methods presented are developed from basic principles. The book begins with a chapter on nucleation and describes both the theory and observations in flowing and non-flowing systems. Three chapters provide a systematic treatment of the dynamics and growth, collapse, or oscillation of individual bubbles in otherwise quiescent fluids. The following chapters summarise the motion of bubbles in liquids, describe some of the phenomena that occur in homogeneous bubbly flows, with emphasis on cloud cavitation, and summarise some of the experimental observations of cavitating flows. The last chapter provides a review of free streamline methods used to treat separated cavity flows with large attached cavities.

Page 151 of 407