The existence of poloidal flow transforms the elliptic Grad4hafranovSchliitr (GSS) equation into an EGSS system (Extented GSS) of partial differential equation and an algebraic Bernoulli's equation. The EGSS System becomes alternatively elliptic and hyperbolic as the Mach numkr of the poloidal flow increases with.respect to the Alfven Epeed of the paloidal magnetic field. A computer p r o p m for solving EGSS equations in elliptic res;ons ushg Ihe iovene method and Fourier decomposition'has been prepared. The solutions in the first and second elliptic regions have been found for different plasma cross-sections, not necessarily u p down-symmiric. The solulions in different elliptic regions exibit the significart differences in the poloidal magnetic held configuration and the shifts between magnetic axis and density axis differ in sign and magnitude,
In this paper a generalization of the Riemann invariant method to the case of a nonhomogeneous system of equations has been formulated. We have discussed in detail the necessary and sufficient conditions for the existence of Riemann invariants. We perform the analysis using the apparatus of differential forms and Cartan theory of systems in involution. The problem has been reduced to examining Pfaff forms. We have considered the connections between the structure of the set of integral elements and the possibility of a construction of special classes of solutions depending on k arbitrary functions of one variable. These solutions can be interpreted physically as the interactions between k simple waves on a simple state. We have proven that, in the case of interaction of many simple waves described by Riemann invariants, a conservation law for the type and quantity of waves holds. It has been also shown that such a solution, resulting from the interaction of many simple waves propagating on the simple state, decay for a large time in an exact way into simple waves (of the same kind as those entering the interaction) on the state. The Cauchy problem for the nonlinear superposition of k-sample waves has been formulated. A couple of theorems useful for this problem have been given in the Sec. III. The functorial properties of the system of equations determining Riemann invariants have been described. The last part of the work contains an analysis of some examples of the solutions of nonhomogeneous magnetohydrodynamic equations from the point of view of the method described above.
Is atmospheric dispersion forecasting an important asset of the early-phase nuclear emergency response management? Is there a 'perfect atmospheric dispersion model'? Is there a way to make the results of dispersion models more reliable and trustworthy? While seeking to answer these questions the multi-model ensemble dispersion forecast system ENSEMBLE will be presented.
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