Solitary waves under curved topography and beta approximation

In this paper, the mechanisms of excitation and propagation of nonlinear Rossby waves are investigated by the approach of topographic balance under the beta approximation for the first time. Using time-space elongation transformation and perturbation expansion method, a Korteweg–de Vries model equation for topographic Rossby wave amplitude is derived. The influences of topography parameters on Rossby solitary waves are discussed through qualitative and quantitative analysis.

Strategic Asset Allocation for Life Insurers with Stochastic Liability

The problem of strategic asset allocation and product mix choice of a life insurancecompany is considered where account is taken of the stochastic risk associated with both assets and liabilities. Using the methods of stochastic dynamic programming we derive equations for optimal weights of both risky and riskless assets under continuous time. The resulting equations can be solved exactly for some parameter values and utility functions. When this is not possible a general perturbation expansion method is set up for which explicit solutions are derived for the first terms but the method can be generalized to any order in the expansion parameter.

Similarity Solution and Heat Transfer Characteristics for a Class of Nonlinear Convection-Diffusion Equation with Initial Value Conditions

A class of nonlinear convection-diffusion equation is studied in this paper. The partial differential equation is converted into nonlinear ordinary differential equation by introducing a similarity transformation. The asymptotic analytical solutions are obtained by using double-parameter transformation perturbation expansion method (DPTPEM). The influences of convection functional coefficientk(z)and power law indexnon the heat transport characteristics are discussed and shown graphically. The comparison with the numerical results is presented and it is found to be in excellent agreement. The method and technique used in this paper have the significance in studying other engineering problems.

ANALYTICAL MODELING OF THE EFFECTS OF ELECTROSTATIC ACTUATION AND CASIMIR FORCE ON THE PULL-IN INSTABILITY AND STATIC BEHAVIOR OF TORSIONAL NANO/MICRO ACTUATORS

This paper studies the effect of Casimir force on the pull-in instability of electrostatically actuated torsional nano/micro actuators. Dependence of the actuator's pull-in angle and pull-in voltage on several design parameters are investigated and it is found that Casimir force can considerably reduce the stability limits of the torsional actuators. Nonlinear equilibrium equation is solved numerically and analytically using straight forward perturbation expansion method. It is observed that a fourth-order perturbation approximation can precisely model the behavior of a torsional actuator. The results of this paper can be used for safe and stable design of torsional nano/micro actuators.