We have so far proved a number of equivalent characteristic properties of transient and recurrent states. Theorem 2.1. A state x in a finite Markov chain is transient iff it satisfies the following equivalent conditions: 1. The probability ρxx of returning to x, is less than 1. 2. Starting at x the expected number of returns to x, Ex(Nx) is finite. 3. In the Markov chain graph there is a direct...

the rapid melting of a semi- infinite body due to the absorption of a cw laser beam radiation has been studied. the enthalpy technique for the solution of phase change problems has been used in an explicit finite difference form to calculate the transient temperature distribution in the semi-infinite body and the growth rate of the melt pool. the technique has been modified so that it is not ne...

Vector clock algorithms are basic wait-free building blocks that facilitate causal ordering of events. As wait-free algorithms, they are guaranteed to complete their operations within a finite number of steps. Stabilizing algorithms allow the system to recover after the occurrence of transient faults, such as soft errors and arbitrary violations of the assumptions according to which the system ...

Studies in performance evaluation of automated manufacturing systems, us. ing simulation or analytical models, have always emphasized steady-state or equilibrium performance in preference to transient performance. In this study, we present several situations in manufacturing systems where transient analysis is very important. Manufacturing systems and models in which such situations arise inclu...

In typical Lamb wave simulation practices, effects of plate edge reflections are often not considered in order to simplify the wave signal interpretations. Methods that are based on infinite plates such as the semi-analytical finite element method is effective in simulating Lamb waves as it excludes the effect of plate edges. However, the inclusion of plate edges in a finite plate could render ...

We consider the optimization of nonquadratic measures of the transient response. We present a computational implementation of dynamic programming recursions to solve finite-horizon problems. In the limit, the finite-horizon performance converges to the infinite-horizon performance. We provide conditions based on finite-horizon computations which only assure that a receding horizon implementatio...

The analysis of the velocity skin effect (VSE) in electromagnetic launchers (EMLs) requires a 3-D transient finite element method, unlike magnetic and proximity effects. However, VSE is dominant at high speeds, this creates convergence problems when moving or deformed mesh physics used FEM analysis. Commercial software cannot solve aspects such high-speed application with solver 3-D. Although 2...

Continuous time random walk (CTRW) subdiffusion along with the associated fractional Fokker-Planck equation (FFPE) is traditionally based on the premise of random clock with divergent mean period. This work considers an alternative CTRW and FFPE description which is featured by finite mean residence times (MRTs) in any spatial domain of finite size. Transient subdiffusive transport can occur on...

Consider a discrete time queue with i.i.d. arrivals (see the generalisation below) and a single server with a buuer length m. Let Tm be the rst time an overrow occurs. We obtain asymptotic rate of growth of moments and distributions of Tm as m !1. We also show that under general conditions, the overrow epochs converge to a compound Poisson process. Furthermore, we show that the results for the ...

We present novel overlapping finite elements used with the Bathe time integration method to solve transient wave propagation problems. The solution scheme shows two important properties that have been difficult to achieve in the numerical solution of general wave propagations: monotonic convergence of calculated solutions with decreasing time step size and a solution accuracy almost independent...