The motion of the shoreline in sedimentary ocean basin were investigated and solved using modified variational iteration method since it provides an efficient approximate solution problem under consideration, which appears to be accurate when consecutive error between iterative solutions is evaluated. A diffusion equation with specified beginning boundary conditions, a moving interface type ref...

We present for the first time an exact treatment of the production of radiation by a mirror which accelerates along a smooth, asymptotically static trajectory in twodimensional Minkowski space. The treatment confirms the general expectations of earlier work which was based on questionable approximations and unrealistic asymptotic behaviour. In the recent spate of investigations of quantum field...

Previous literature on the Traveling Salesman Problem (TSP) assumed that the sites to be visited are stationary. Motivated by practical applications, we introduce a time-dependent generalization of TSP which we call Moving-Target TSP, where a pursuer must intercept in minimum time a set of targets which move with constant velocities. We propose approximate and exact algorithms for several natur...

In this paper, a moving mesh technique and a non-standard finite difference method are combined, and a moving mesh non-standard finite difference (MMNSFD) method is developed to solve an initial boundary value problem involving a quartic nonlinearity that arises in heat transfer with thermal radiation. In this method, the moving spatial grid is obtained by a simple geometric adaptive algorithm ...

The wetting and contact angle hysteresis on chemically patterned surfaces in two dimensions are analyzed from a stationary phase-field model for immiscible two phase fluid. We first study the sharp interface limit of the model by the method of matched asymptotic expansions. We then justify the results rigorously by the Γ-convergence theory for the related variational problem and study the prope...

A method for reducing the spurious pressure oscillations observed when simulating moving boundary flow problems with sharp-interface immersed boundary methods (IBMs) is proposed. By first identifying the primary cause of these oscillations to be the violation of the geometric conservation law near the immersed boundary, we adopt a cut-cell based approach to strictly enforce geometric conservati...

Of concern is a moving boundary problem modelling the growth of multicellular spheroids or in vitro tumors. This model consists of two elliptic equations describing the concentration of a nutrient and the distribution of the internal pressure in the tumor’s body, respectively. The driving mechanism of the evolution is governed by Darcy’s law. Finally surface tension effects on the moving interf...

We consider a stochastic perturbation of a moving boundary problem proposed by Ludford and Stewart and studied by Caffarelli and Vazquez. We prove existence and uniqueness.

Recent studies have shown that experts in military tactical command treat decision making as a problemsolving process. Experts have large collections of schemas, enabling them to recognise a large number of situations as familiar. Another capacity of experts are their problem solving skills if an immediate match between the actual problem situation and available schemas in memory cannot be esta...