Dan Marchesin

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MICHAEL K. TIPPETTy, STEPHEN E. COHNz, RICARDO TODLINGx, AND DAN MARCHESIN{ Abstract. The Schatten p-norm condition of the discrete-time Lyapunov operator LA defined on matrices P 2 Rn n by LAP P APAT is studied for stable matrices A 2 Rn n . Bounds are obtained for the norm of LA and its inverse that depend on the spectrum, singular values and radius of(More)
This paper deals with the application of steam to enhance the recovery from petroleum reservoirs. We formulate a mathematical and numerical model that simulates coinjection of volatile oil with steam into a porous rock in a one-dimensional setting. We utilize the mathematical theory of conservation laws to validate the numerical simulations. This combined(More)
We present a numerical method, based on the Dafermos regularization, for computing a one-parameter family of Riemann solutions of a system of conservation laws. The family is obtained by varying either the left or right state of the Riemann problem. The Riemann solutions are required to have shock waves that satisfy the viscous profile criterion prescribed(More)
Recently, B. Roth and M. Woods [7] suggested a reexamination of MCG interpretation through currents transversal to the wave propagation direction. They also gave a formula J'(theta) for the dependence of the current intensity on the angle theta between straight fibers and the plane wave front. Here we study more general situations, including current(More)
The purpose of this paper is to classify the solutions of Riemann problems near a hyperbolic singularity in a nonlinear system of conservation laws. Hyperbolic singularities play the role in the theory of Riemann problems that rest points play in the theory of ordinary differential equations: Indeed, generically, only a finite number of structures can(More)
In immiscible three-phase flow, the lead oil bank can split nto two, a Buckley-Leverett shock wave followed by anew ty pe of shock wave. Such a non-classical “transitional” s hock wave is common in three-phase flow. Its sensitivity to diffusion implies that capillary pressure must be modeled correctly in order to calculate the flow. In particula r,(More)
New upper bounds for the solution of the discrete algebraic Lyapunov equation (DALE) P = APAT + Q are presented. The only restriction on their applicability is that A be stable; there are no restrictions on the singular values of A nor on the diagonalizability of A. The new bounds relate the size of P to the radius of stability of A. The upper bounds are(More)