Analytic Solution for the Ground State Energy of the Extensive Many-Body Problem

A closed form expression for the ground state energy density of the general extensive many-body problem is given in terms of the Lanczos tri-diagonal form of the Hamiltonian. Given the general expressions of the diagonal and off-diagonal elements of the Hamiltonian Lanczos matrix, $\alpha_n(N)$ and $\beta_n(N)$, asymptotic forms $\alpha(z)$ and $\beta(z)$ can be defined in terms of a new parameter $z\equiv n/N$ ($n$ is the Lanczos iteration and $N$ is the size of the system). By application of theorems on the zeros of orthogonal polynomials we find the ground-state energy density in the bulk limit to be given in general by ${\cal E}_0 = {\rm inf}\,\left[\alpha(z) - 2\,\beta(z)\right]$.Comment: 10 pages REVTex3.0, 3 PS figure

Prediction of heat transfer from laminar boundary layers, with emphasis on large free- stream velocity gradients and highly cooled walls

Prediction of heat transfer and shear stress from laminar boundary laye

A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desirable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to first order in the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.Comment: 18 Pages, 4 Figures. This updated version has a slightly more detailed introduction. In the current form, the paper will appear in SIAM Journal on Numerical Analysi

Heat transfer characteristics of an emergent strand

A mathematical model was developed to describe the heat transfer characteristics of a hot strand emerging into a surrounding coolant. A stable strand of constant efflux velocity is analyzed, with a constant (average) heat transfer coefficient on the sides and leading surface of the strand. After developing a suitable governing equation to provide an adequate description of the physical system, the dimensionless governing equation is solved with Laplace transform methods. The solution yields the temperature within the strand as a function of axial distance and time. Generalized results for a wide range of parameters are presented, and the relationship of the results and experimental observations is discussed

Evaluation of pressure and thermal data from a wind tunnel test of a large-scale, powered, STOL fighter model

A STOL fighter model employing the vectored-engine-over wing concept was tested at low speeds in the NASA/Ames 40 by 80-foot wind tunnel. The model, approximately 0.75 scale of an operational fighter, was powered by two General Electric J-97 turbojet engines. Limited pressure and thermal instrumentation were provided to measure power effects (chordwise and spanwise blowing) and control-surface-deflection effects. An indepth study of the pressure and temperature data revealed many flow field features - the foremost being wing and canard leading-edge vortices. These vortices delineated regions of attached and separated flow, and their movements were often keys to an understanding of flow field changes caused by power and control-surface variations. Chordwise blowing increased wing lift and caused a modest aft shift in the center of pressure. The induced effects of chordwise blowing extended forward to the canard and significantly increased the canard lift when the surface was stalled. Spanwise blowing effectively enhanced the wing leading-edge vortex, thereby increasing lift and causing a forward shift in the center of pressure

Preeminence of Lesser Splanchnic Blood Flow in Selected Patients With Generalized Portal Hypertension

Although restricted transhepatic portal flow is necessary for development of generalized portal hypertension (GPH), increased splanchnic arterial inflow also contributes to GPH and its clinical sequelae. In this context, we describe 7 male and 6 female patients (mean age 48 years) in whom the lesser splanchnic (gastrosplenic) system played a key role in the signs and symptoms of GPH. These 13 patients (9 with hepatic cirrhosis, 3 with primary myeloproliferative disorder, and 1 with extrahepatic portal block) shared common features of massive splenomegaly, huge splenofundic gastric varices, often with a prominent natural shunt to the left renal vein. Total or near total splenectomy alone or combined where appropriate with coronary vein ligation was effective in controlling varix hemorrhage (10 patients), ascites (3), or complications of an enlarged spleen-anorexia and abdominal pain (3), hemolytic anemia (1) and profound thrombocytopenia with severe epistaxis (1). Intraoperative jejunal portal venography was crucial in operative management in order to establish definitively the presence or absence of coronary venous collaterals, and when present, to verify their operative ligation