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Linear theory of boundary effects in open wind tunnels with finite jet lengths

Description: In the first part, the boundary conditions for an open wind tunnel (incompressible flow) are examined with special reference to the effects of the closed entrance and exit sections. Basic conditions are that the velocity must be continuous at the entrance lip and that the velocities in the upstream and downstream closed portions must be equal. In the second part, solutions are derived for four types of two-dimensional open tunnels, including one in which the pressures on the two free surfaces are not equal. Numerical results are given for every case. In general, if the lifting element is more than half the tunnel height from the inlet, the boundary effect at the lifting element is the same as for an infinitely long open tunnel. In the third part, a general method is given for calculating the boundary effect in an open circular wind tunnel of finite jet length. Numerical results are given for a lifting element concentrate at a point on the axis.
Date: December 20, 1948
Creator: Katzoff, S.; Gardner, Clifford S.; Diesendruck, Leo & Eisenstadt, Bertram J.
Partner: UNT Libraries Government Documents Department

Bound states and the Bekenstein bound

Description: We explore the validity of the generalized Bekenstein bound, S<= pi M a. We define the entropy S as the logarithm of the number of states which have energy eigenvalue below M and are localized to a flat space region of width alpha. If boundary conditions that localize field modes are imposed by fiat, then the bound encounters well-known difficulties with negative Casimir energy and large species number, as well as novel problems arising only in the generalized form. In realistic systems, however, finite-size effects contribute additional energy. We study two different models for estimating such contributions. Our analysis suggests that the bound is both valid and nontrivial if interactions are properly included, so that the entropy S counts the bound states of interacting fields.
Date: October 16, 2003
Creator: Bousso, Raphael
Partner: UNT Libraries Government Documents Department

Characterizing soil preferential flow using iodine--starch staining experiments and the active region model

Description: Thirteen iodine-starch staining experiments with different boundary conditions and measurement scales were conducted at two sites to study preferential flow processes in natural unsaturated soils. Digital imaging analyses were implemented to obtain the corresponding preferential flow patterns. The test results are used to evaluate a recently proposed active region model in terms of its usefulness and robustness for characterizing unsaturated flow processes at field scale. Test results provide useful insights into flow patterns in unsaturated soils. They show that flow pattern depends on the top boundary condition. As the total infiltrating-water depth increased form 20 mm to 80 mm for the 100 x 100 cm{sup 2} plots, the corresponding flow pattern changed from few preferential flow paths associated with a relatively small degree of stained coverage and a small infiltration depth, to a pattern characterized by a higher stained coverage and a larger infiltration depth, and to (finally) a relatively homogeneous flow pattern with few unstained area and a much larger infiltration depth. Test results also show that the preferential flow pattern became generally more heterogeneous and complex for a larger measurement scale (or size of infiltration plot). These observations support the general idea behind the active region model that preferential flow pattern in unsaturated soils are dynamic and depend on water flow conditions. Further analyses of the test results indicate that the active-region model is able to capture the major features of the observed flow pattern at the scale of interest, and the determined parameter values do not significantly depend on the test conditions (initial water content and total amount of infiltrating water) for a given test site. This supports the validity of the active region model that considers that parameter to be a property of the corresponding unsaturated soil. Results also show that some intrinsic relation seems to ...
Date: March 1, 2009
Creator: Sheng, Feng; Wang, Kang; Zhang, Renduo & Liu, Hui-Hai
Partner: UNT Libraries Government Documents Department

On Theories for Reacting Immiscible Mixtures

Description: On some small scale each constituent of an immiscible mixture occupies a separate region of space. Given sufficient time and computing power, we could solve the continuum field equations and boundary conditions for this het erogenous system. This usually represents an enormously difficult task that is well beyond today's computational ca- pabilities. Mixture theories approximate this complex heterogeneous formulation with a set of field equations for an equivalent homoge- neous mat erial. In this work, we compare the theory for immiscible mixtures by Drumheller and Bedford with the theory of Passman, Nunziato, and Walsh. We describe the conditions under which these theories reduce to an equivalent formulation, and we also investigate the differences in their microinertial descriptions. Two variables play special roles in both theories. They are t he true material density and the volume fraction. Here we use a kinematical approach based on two new variables-t he true deformation gradient and the distention gradient. We show how the true deformation gra- dient is connected to the true material density and, in the absence of chemical reactions, the volume fraction is the inverse of the deter- minant of the distention gradient. However, when chemical reactions occur, the distention gradient and the volume fraction are not directly connected. We ako present a mixture model for a granuIar expIosive. This model is based upon the work of Baer and Nunziato, but our theory differs from their work in that we Present a three-dimension-al rnodd, `.. ` - - we cast the constitutive postulates in terms of the distention gradient rather than the volume fraction, and we incorporate elastic-plastic effects into the constitutive description of the solid granules.
Date: November 5, 1998
Creator: Drumheller, D.S.
Partner: UNT Libraries Government Documents Department

Local Electrostatic Moments and Periodic Boundary Conditition

Description: Electronic structure calculations frequently invoke periodic boundary conditions to solve for electrostatic potentials. For systems that are electronically charged, or contain dipole (or higher) moments, this artifice introduces spurious potentials due to the interactions between the system and multipole moments of its periodic images in aperiodic directions. I describe a method to properly handle the multipole moments of the electron density in electronic structure calculations using periodic boundary conditions. The density for which an electrostatic potential is to be evaluated is divided into two pieces. A local density is constructed that matches the desired moments of the full density, and its potential computed treating this density as isolated. With the density of this local moment countercharge removed from the full density, the remainder density lacks the troublesome moments and its electrostatic potential can be evaluated accurately using periodic boundary conditions.
Date: December 4, 1998
Creator: Schultz, P.A.
Partner: UNT Libraries Government Documents Department


Description: We have previously reported on the incorporation of a circular boundary condition into the program POISSON for two-dimensional problems (Incorporation of a Circular Boundary Condition into the Program POISSON, S. Caspi, M. Helm, and L.J. Laslett, LBID-887, SSC MAG Note-S, February 13, 1984). The least square method has now been generalized to accept any suitable set of orthogonal functions which can describe the vector potential function outside a circular boundary so located that no external sources are present. We have proceeded to incorporate the boundary condition into cartesian problems which involve no symmetry, and into axis-symmetry cylindrical problems that may have left-right symmetry, antisymmetry or no symmetry.
Date: July 1, 1984
Creator: Caspi, S.; Helm, M. & Laslett, L.J.
Partner: UNT Libraries Government Documents Department

Perturbation Method for Calculation of Narrow-Band Impedance and Trapped Modes

Description: An iterative method for calculation of the narrow-band impedance is described for a system with a small variation in boundary conditions, so that the variation can be considered as a perturbation.The results are compared with the degeneracy of the spectrum of an unperturbed system.The method also can be applied to transverse impedance calculations.
Date: August 1, 1987
Creator: Heifets, Sam
Partner: UNT Libraries Government Documents Department

An Explicit Time-Domain Hybrid Formulation Based on the Unified Boundary Condition

Description: An approach to stabilize the two-surface, time domain FEM/BI hybrid by means of a unified boundary condition is presented. The first-order symplectic finite element formulation [1] is used along with a version of the unified boundary condition of Jin [2] reformulated for Maxwell's first-order equations in time to provide both stability and accuracy over the first-order ABC. Several results are presented to validate the numerical solutions. In particular the dipole in a free-space box is analyzed and compared to the Dirchlet boundary condition of Ziolkowski and Madsen [3] and to a Neuman boundary condition approach.
Date: February 28, 2007
Creator: Madsen, N; Fasenfest, B J; White, D; Stowell, M; Jandhyala, V; Pingenot, J et al.
Partner: UNT Libraries Government Documents Department

DYNA3D Non-reflecting Boundary Conditions - Test Problems

Description: Two verification problems were developed to test non-reflecting boundary segments in DYNA3D (Whirley and Engelmann, 1993). The problems simulate 1-D wave propagation in a semi-infinite rod using a finite length rod and non-reflecting boundary conditions. One problem examines pure pressure wave propagation, and the other problem explores pure shear wave propagation. In both problems the non-reflecting boundary segments yield results that differ only slightly (less than 6%) during a short duration from their corresponding theoretical solutions. The errors appear to be due to the inability to generate a true step-function compressive wave in the pressure wave propagation problem and due to segment integration inaccuracies in the shear wave propagation problem. These problems serve as verification problems and as regression test problems for DYNA3D.
Date: September 28, 2006
Creator: Zywicz, E
Partner: UNT Libraries Government Documents Department

Active vibration damping in the presence of uncertainties.

Description: Several control design techniques including PlD, LQG, and PPF are investigated For adive vibration damping of a cantilever beam with uncertain boundary conditions. Step disturbances were used to evaluate the performance of the designed controllers.
Date: January 1, 2002
Creator: Farrar, C. R. (Charles R.); Eisenhour, T. A. (Travis A.); Hatchett, S. (Sam) & Salazar, I. (Isaac)
Partner: UNT Libraries Government Documents Department

Multidimensional spacial eigenmode analysis.

Description: Several recent papers have examined higher mode eigenvalues and eigenfunctions fo r multiplying systems. The general application focus of these papers is related to determining the dominance ratio, which is of great interest to people analyzing loosely coupled fissile systems . For large systems, we derived some simple approximations to the dominance ratio, and we continue this analysis in this paper. In the previous papers, we were able to utilize semianalytical techriiques because we mainly examined one-dimensional Cartesian systems. In this paper we analyze the effectiveness of using reflective boundary conditions for multi-dimensional system s and expand past work by examining two- and three-dimensional eigenfunctions.
Date: January 1, 2003
Creator: Parsons, Donald Kent & Kornreich, D. E. (Drew E.)
Partner: UNT Libraries Government Documents Department


Description: The construction and operation of a trigger system designed to fire a 30-kV 5000 A spark gap with a minimum delay following the arrival of a small signal pulse is described. In this particular experiment a 150-MeV/c muon is detected with scintillators on three 6199 phototubes, and the output pulse of the attached tunnel-diode triple-coincidence circuit is amplified and used to trigger the gap. Approximately 32 nanoseconds are needed from passage of the muon to the coincidence output, and approximately 25 nanoseconds are required from the coincidence output to the time of complete breakdown of the gap. These delays represent the shortest times that we could achieve with the particular boundary conditions under which the circuit had to operate. Sufficient detail is given to show how additional savings of nanoseconds could be made under different operating conditions.
Date: August 6, 1963
Creator: Schrank, Glen E.; Henry, George R.; Kerns, Quentin A. & Swanson, Robert A.
Partner: UNT Libraries Government Documents Department

Atom-to-continuum methods for gaining a fundamental understanding of fracture.

Description: This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. Under this aegis we developed new theory and a number of novel techniques to describe the fracture process at the atomic scale. These developments ranged from a material-frame connection between molecular dynamics and continuum mechanics to an atomic level J integral. Each of the developments build upon each other and culminated in a cohesive zone model derived from atomic information and verified at the continuum scale. This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. The effort is predicated on the idea that processes and information at the atomic level are missing in engineering scale simulations of fracture, and, moreover, are necessary for these simulations to be predictive. In this project we developed considerable new theory and a number of novel techniques in order to describe the fracture process at the atomic scale. Chapter 2 gives a detailed account of the material-frame connection between molecular dynamics and continuum mechanics we constructed in order to best use atomic information from solid systems. With this framework, in Chapter 3, we were able to make a direct and elegant extension of the classical J down to simulations on the scale of nanometers with a discrete atomic lattice. The technique was applied to cracks and dislocations with equal success and displayed high fidelity with expectations from continuum theory. Then, as a prelude to extension of the atomic J to finite temperatures, we explored the quasi-harmonic models as efficient and accurate surrogates of atomic lattices undergoing thermo-elastic processes (Chapter 4). With this in hand, in Chapter 5 we provide evidence that, by using the appropriate energy potential, the ...
Date: August 1, 2011
Creator: McDowell, David Lynn (Georgia Institute of Technology, Atlanta, GA); Reedy, Earl David, Jr.; Templeton, Jeremy Alan; Jones, Reese E.; Moody, Neville Reid; Zimmerman, Jonathan A. et al.
Partner: UNT Libraries Government Documents Department

Fast Poisson, Fast Helmholtz and fast linear elastostatic solvers on rectangular parallelepipeds

Description: FFT-based fast Poisson and fast Helmholtz solvers on rectangular parallelepipeds for periodic boundary conditions in one-, two and three space dimensions can also be used to solve Dirichlet and Neumann boundary value problems. For non-zero boundary conditions, this is the special, grid-aligned case of jump corrections used in the Explicit Jump Immersed Interface method. Fast elastostatic solvers for periodic boundary conditions in two and three dimensions can also be based on the FFT. From the periodic solvers we derive fast solvers for the new 'normal' boundary conditions and essential boundary conditions on rectangular parallelepipeds. The periodic case allows a simple proof of existence and uniqueness of the solutions to the discretization of normal boundary conditions. Numerical examples demonstrate the efficiency of the fast elastostatic solvers for non-periodic boundary conditions. More importantly, the fast solvers on rectangular parallelepipeds can be used together with the Immersed Interface Method to solve problems on non-rectangular domains with general boundary conditions. Details of this are reported in the preprint The Explicit Jump Immersed Interface Method for 2D Linear Elastostatics by the author.
Date: June 1, 1999
Creator: Wiegmann, A.
Partner: UNT Libraries Government Documents Department


Description: A discussion of properties of operator solutions, of relations between operator solutions, and of the class of all operator solutions is given. Solutions of inhomogeneous boundary-value problems by Green operators are discussed. The connections between operator solutions of scalar and vector problems are studied. (C.J.G.)
Date: December 1, 1959
Creator: Wyler, O.
Partner: UNT Libraries Government Documents Department

Mechanics of layered anisotropic poroelastic media with applications to effective stress for fluid permeability

Description: The mechanics of vertically layered porous media has some similarities to and some differences from the more typical layered analysis for purely elastic media. Assuming welded solid contact at the solid-solid interfaces implies the usual continuity conditions, which are continuity of the vertical (layering direction) stress components and the horizontal strain components. These conditions are valid for both elastic and poroelastic media. Differences arise through the conditions for the pore pressure and the increment of fluid content in the context of fluid-saturated porous media. The two distinct conditions most often considered between any pair of contiguous layers are: (1) an undrained fluid condition at the interface, meaning that the increment of fluid content is zero (i.e., {delta}{zeta} = 0), or (2) fluid pressure continuity at the interface, implying that the change in fluid pressure is zero across the interface (i.e., {delta}p{sub f} = 0). Depending on the types of measurements being made on the system and the pertinent boundary conditions for these measurements, either (or neither) of these two conditions might be directly pertinent. But these conditions are sufficient nevertheless to be used as thought experiments to determine the expected values of all the poroelastic coefficients. For quasi-static mechanical changes over long time periods, we expect drained conditions to hold, so the pressure must then be continuous. For high frequency wave propagation, the pore-fluid typically acts as if it were undrained (or very nearly so), with vanishing of the fluid increment at the boundaries being appropriate. Poroelastic analysis of both these end-member cases is discussed, and the general equations for a variety of applications to heterogeneous porous media are developed. In particular, effective stress for the fluid permeability of such poroelastic systems is considered; fluid permeabilities characteristic of granular media or tubular pore shapes are treated in some detail, as ...
Date: June 1, 2010
Creator: Berryman, J. G.
Partner: UNT Libraries Government Documents Department

Determination of unsaturated flow paths in a randomly distributed fracture network

Description: We present a numerical investigation of steady flow paths in a two-dimensional, unsaturated discrete-fracture network. The fracture network is constructed using field measurement data including fracture density, trace lengths, and orientations from a particular site. The fracture network with a size of 100m x 150m contains more than 20,000 fractures. The steady state unsaturated flow in the fracture network is investigated for different boundary conditions. Simulation results indicate that the flow paths are generally vertical, and horizontal fractures mainly provide pathways between neighboring vertical paths. The simulation results support that the average spacing between flow paths in a layered system tends to increase or flow becomes more focused with depth as long as flow is gravity driven (Liu et al. 2002).
Date: February 17, 2003
Creator: Zhang, Keni; Wu, Yu-Shu; Bodvarsson, G.S. & Liu, Hui-Hai
Partner: UNT Libraries Government Documents Department

Fractured Petroleum Reservoirs

Description: In this report the results of experiments of water injection in fractured porous media comprising a number of water-wet matrix blocks are reported for the first time. The blocks experience an advancing fracture-water level (FWL). Immersion-type experiments are performed for comparison; the dominant recovery mechanism changed from co-current to counter-current imbibition when the boundary conditions changed from advancing FWL to immersion-type. Single block experiments of co-current and counter-current imbibition was performed and co-current imbibition leads to more efficient recovery was found.
Date: January 18, 2000
Creator: Firoozabadi, Dr. Abbas
Partner: UNT Libraries Government Documents Department

A specialized boundary element algorithm developed to calculate the state of stress in the Anza Gap, San Jacinto Fault Zone, Southern, CA

Description: The widely-used algorithm of Crouch and Starfield is unstable when used to solve our mixed boundary equation problem of interest. Altering the boundary conditions and correspondingly rearranging the system of equations to utilize double-sided boundary elements overcomes this drawback. The new algorithm described here is more physically realistic as in that it allows for rotation of the fault segments in the strain field resulting from satisfying the fault static shear strength condition. Preliminary test results indicate that a fault trifurcation gap model may describe the non-strike slip components to some of the seismicity.
Date: June 1, 1995
Creator: Aster, R.; Flores, R. & Fehler, M.
Partner: UNT Libraries Government Documents Department

Plane wave method for elastic wave scattering by a heterogeneous fracture

Description: A plane-wave method for computing the three-dimensional scattering of propagating elastic waves by a planar fracture with heterogeneous fracture compliance distribution is presented. This method is based upon the spatial Fourier transform of the seismic displacement-discontinuity (SDD) boundary conditions (also called linear slip interface conditions), and therefore, called the wave-number-domain SDD method (wd-SDD method). The resulting boundary conditions explicitly show the coupling between plane waves with an incident wave number component (specular component) and scattered waves which do not follow Snell's law (nonspecular components) if the fracture is viewed as a planar boundary. For a spatially periodic fracture compliance distribution, these boundary conditions can be cast into a linear system of equations that can be solved for the amplitudes of individual wave modes and wave numbers. We demonstrate the developed technique for a simulated fracture with a stochastic (correlated) surface compliance distribution. Low- and high-frequency solutions of the method are also compared to the predictions by low-order Born series in the weak and strong scattering limit.
Date: February 21, 2003
Creator: Nakagawa, Seiji; Nihei, Kurt T. & Myer, Larry R.
Partner: UNT Libraries Government Documents Department

Blackness Theory and Coefficients for Slab Geometry

Description: ''Blackaess theory'' is described as a class of procedures for matching a high order transport approximation in one region to a low order approximation in a second region. The matching conditions are presented as a generalization of the Marshak boundary conditions. The blackness coefficients necessary in setting up the conditions are defined and tables are given for slab geomrtry. A method which allows all regions to be treated by means of the blackness coefficients is developed and applied to two region cells. Numerical results are compared with other approximations in situations typical of those encountered in resonance capture and thermal utilization calculations. (auth)
Date: May 1, 1959
Creator: Maynard, C. W.
Partner: UNT Libraries Government Documents Department