40,373 research outputs found
A compact finite element method for elastic bodies
A nonconforming finite method is described for treating linear equilibrium problems, and a convergence proof showing second order accuracy is given. The close relationship to a related compact finite difference scheme due to Phillips and Rose is examined. A condensation technique is shown to preserve the compactness property and suggests an approach to a certain type of homogenization
A finite difference treatment of Stokes-type flows: Preliminary report
The equations Laplacian operator omega = 0, (1.1a) and omega = Laplacian operator Chi, (1.1b) describe, in suitable units, 2-D Stokes flow of an incompressible fluid occupying a domain D in which omega is the vorticity and Chi is the stream function. The flow is uniquely determined by specifying the velocity on the boundary B of D, a condition which leads to specifying the stream function Chi and its normal derivative Chi sub n on B. A mathematically similar problem arises in describing the equilibrium of a flat plate in structural mechanics where a related 1-D problem by finite difference or finite element methods is to introduce effective methods for imposing the boundary conditions through which (1.1a) is coupled to (1.1b). These models thus provide a simple starting point for examining the general treatment of boundary conditions for more general time dependent Navier-Stokes incompressible flows. For the purpose of discussion it is assumed that D is a square domain. A standard finite difference method to solve (1.1) is to introduce a uniform grid and then use standard five point finite difference operators to express each equation in (1.1). At any point on the boundary B a value of Chi is specified by the boundary conditions but a value of omega at the same boundary mesh point will also be required to complete the computation. Methods are discussed which overcome the difficulty in solving these problems
Stress correlations in glasses
We rigorously establish that, in disordered three-dimensional (3D) isotropic
solids, the stress autocorrelation function presents anisotropic terms that
decay as at long-range, with the distance, as soon as either
pressure or shear stress fluctuations are normal. By normal, we mean that the
fluctuations of stress, as averaged over spherical domains, decay as the
inverse domain volume. Since this property is required for macroscopic stress
to be self-averaging, it is expected to hold generically in all glasses and we
thus conclude that the presence of stress correlation tails is the rule
in these systems. Our proof follows from the observation that, in an infinite
medium, when both material isotropy and mechanical balance hold, (i) the stress
autocorrelation matrix is completely fixed by just two radial functions: the
pressure autocorrelation and the trace of the autocorrelation of stress
deviators; furthermore, these two functions (ii) fix the decay of the
fluctuations of sphere-averaged pressure and deviatoric stresses for windows of
increasing volume. Our conclusion is reached because, due to the precise
analytic relation (i) fixed by isotropy and mechanical balance, the constraints
arising via (ii) from the normality of stress fluctuations demand the spatially
anisotropic stress correlation terms to decay as at long-range. For the
sake of generality, we also examine situations when stress fluctuations are not
normal
Numerical methods for incompressible viscous flows with engineering applications
A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems
A finite difference scheme for the equilibrium equations of elastic bodies
A compact difference scheme is described for treating the first-order system of partial differential equations which describe the equilibrium equations of an elastic body. An algebraic simplification enables the solution to be obtained by standard direct or iterative techniques
A compact finite difference scheme for div(Rho grad u) - q2u = 0
A representative class of elliptic equations is treated by a dissipative compact finite difference scheme and a general solution technique by relaxation methods is discussed in detail for the Laplace equation
One hundred angstrom niobium wire
Composite of fine niobium wires in copper is used to study the size and proximity effects of a superconductor in a normal matrix. The niobium rod was drawn to a 100 angstrom diameter wire on a copper tubing
Covariant nucleon wave function with S, D, and P-state components
Expressions for the nucleon wave functions in the covariant spectator theory
(CST) are derived. The nucleon is described as a system with a off-mass-shell
constituent quark, free to interact with an external probe, and two spectator
constituent quarks on their mass shell. Integrating over the internal momentum
of the on-mass-shell quark pair allows us to derive an effective nucleon wave
function that can be written only in terms of the quark and diquark
(quark-pair) variables. The derived nucleon wave function includes
contributions from S, P and D-waves.Comment: 13 pages and 1 figur
Thermal Storage Advanced Thruster System (TSATS) Experimental Program
The Thermal Storage Advanced Thruster System (TSATS) rocket test stand is completely assembled and operational. The first trial experimental runs of a low-energy TSATS prototype rocket was made using the test stand. The features of the rocket test stand and the calibration of the associated diagnostics are described and discussed. Design and construction of the TSATS prototype are discussed, and experimental objectives, procedures, and results are detailed
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