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An Improved Linear Tetrahedral Element for Plasticity

Description: A stabilized, nodally integrated linear tetrahedral is formulated and analyzed. It is well known that linear tetrahedral elements perform poorly in problems with plasticity, nearly incompressible materials, and acute bending. For a variety of reasons, linear tetrahedral elements are preferable to quadratic tetrahedral elements in most nonlinear problems. Whereas, mixed methods work well for linear hexahedral elements, they don't for linear tetrahedrals. On the other hand, automatic mesh generation is typically not feasible for building many 3D hexahedral meshes. A stabilized, nodally integrated linear tetrahedral is developed and shown to perform very well in problems with plasticity, nearly incompressible materials and acute bending. Furthermore, the formulation is analytically and numerically shown to be stable and optimally convergent. The element is demonstrated to perform well in several standard linear and nonlinear benchmarks.
Date: April 25, 2005
Creator: Puso, M
Partner: UNT Libraries Government Documents Department

Use of response surface metamodels for damage identification of a simple nonlinear system.

Description: The need for low order models capable of performing damage identification has become apparent in many structural dynamics applications where structural health monitoring and damage prognosis programs are implemented. These programs require that damage identification routines have low computational requirements and be reliable with some quantifiable degree of accuracy. Response surface metamodels (RSMs) are proposed to fill this need. Popular in the fields of chemical and industrial engineering, RSMs have only recently been applied in the field of structural dynamics and to date there have been no studies which fully demonstrate the potential of these methods. In this thesis, several RSMs are developed in order to demonstrate the potential of the methodology. They are shown to be robust to noise (experimental variability) and have success in solving the damage identification problem, both locating and quantifying damage with some degree of accuracy, for both linear and nonlinear systems. A very important characteristic of the RSMs developed in this thesis is that they require very little information about the system in order to generate relationships between damage indicators and measureable system responses for both linear and nonlinear structures. As such, the potential of these methods for damage identification has been demonstrated and it is recommended that these methods be developed further.
Date: January 1, 2003
Creator: Cundy, A. L. (Amanda L.); Hemez, F. M. (Fran├žois M.); Inman, D. J. & Park, G. H. (Gyu Hae)
Partner: UNT Libraries Government Documents Department

Ultrafast and nonlinear optical characterization of optical limiting processes in fullerenes

Description: The authors present recent results of broadband femotosecond (fs) transient absorption (TA) and broadband nanosecond (ns) optical limiting (OL) studies of C{sub 60} and derivatized C{sub 60}. Improvements in measurement techniques for fs TA spectra provide sensitivity to 10{sup {minus}5} in differential transmission, allowing detailed comparison of excited-state spectra with established energy level diagrams, as well as comparison of the ratio of triplet to singlet excited-state absorption cross sections from TA spectra with those obtained by modeling time transients at different wavelengths. For derivatized fullerenes, which provide enhanced solubility and a ground-state absorption extended into the infrared compared with C{sub 60} there is no spectral region where the triplet absorption cross section dominates the singlet as strongly as demonstrating broadband limiting in all 6, 6 mono-adducts and neat C{sub 60}. The authors report new approaches to processing sol-gel encapsulated fullerenes to improve the OL performance of solid-state materials to approach the response of solution limiters.
Date: October 1, 1997
Creator: Kohlman, R.; Klimov, V. & Shi, X.
Partner: UNT Libraries Government Documents Department

Self-Consistent Multiscale Theory of Internal Wave, Mean-Flow Interactions

Description: This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). The research reported here produced new effective ways to solve multiscale problems in nonlinear fluid dynamics, such as turbulent flow and global ocean circulation. This was accomplished by first developing new methods for averaging over random or rapidly varying phases in nonlinear systems at multiple scales. We then used these methods to derive new equations for analyzing the mean behavior of fluctuation processes coupled self consistently to nonlinear fluid dynamics. This project extends a technology base relevant to a variety of multiscale problems in fluid dynamics of interest to the Laboratory and applies this technology to those problems. The project's theoretical and mathematical developments also help advance our understanding of the scientific principles underlying the control of complex behavior in fluid dynamical systems with strong spatial and temporal internal variability.
Date: June 3, 1999
Creator: Holm, D.D.; Aceves, A.; Allen, J.S.; Alber, M.; Camassa, R.; Cendra, H. et al.
Partner: UNT Libraries Government Documents Department

Unified treatment of collective instabilities and nonlinear beam dynamics

Description: Nonlinear dynamics deals with parametric resonances and diffusion, which are usually beam-intensity independent and rely on a particle Hamiltonian. Collective instabilities deal with beam coherent motion, where the Vlasov equa-tion is frequently used in conjunction with a beam-intensity dependent Hamiltonian. We address the questions: Are the two descriptions the same? Are collective instabilities the results of encountering parametric resonances whose driv-ing force is intensity dependent? The space-charge domi-nated beam governed by the Kapchinskij-Vladimirskij (K-V) envelope equation [1] is used as an example.
Date: April 19, 1999
Creator: Lee, K.Y. Ng and S.Y.
Partner: UNT Libraries Government Documents Department

Nonlinear Dynamics of Parametrically Excited Gyroscopic Systems

Description: The primary objective of this project is to determine how some of the powerful geometric methods of dynamical systems can be applied to study nonlinear gyroscopic systems. We proposed to develop techniques to predict local and global behavior and instability mechanisms and to analyze the interactions between noise, stability, and nonlinearities inherent in gyroscopic systems. In order to obtain these results we use the method of normal forms, global bifurcation techniques, and various other dynamical systems tools.
Date: June 1, 2001
Creator: Namachchivaya, N. S.
Partner: UNT Libraries Government Documents Department

Simulational studies of the Farley-Buneman in the equatorial electrojet

Description: The Farley-Buneman instability in the equatorial electrojet current system in the E-region of the ionosphere has been identified as the cause of the observed Type I electron density irregularities. The goal of this work was to study the instability in the equatorial region.
Date: July 1, 1995
Creator: Otani, N.; Seyler, C. & Kelley, M.
Partner: UNT Libraries Government Documents Department

Annual progress report

Description: The nonlinear analysis of plasma instabilities in the threshold regime is discussed. The emphasis remains on carrying out calculations in realistic geometry and making comparison with experiment. Attention has shifted entirely to fully ionized plasma. An analysis was made of the collisional drift-wave instability. Considerable progress was made in explaining the explosive nature of the mirror-flute instability and in understanding the flute instability in the presence of both density and temperature gradients. The application of the threshold method to parametric instabilities in nonuniform plasma is discussed. Details of the results and comparison with experiment are given. (auth)
Date: September 18, 1973
Creator: Simon, A.
Partner: UNT Libraries Government Documents Department

Variational particle scheme for the porous medium equation and for the system of isentropic Euler equations

Description: We introduce variational particle schemes for the porous medium equation and the system of isentropic Euler equations in one space dimension. The methods are motivated by the interpretation of each of these partial differential equations as a 'steepest descent' on a suitable abstract manifold. We show that our methods capture very well the nonlinear features of the flows.
Date: December 10, 2008
Creator: Westdickenberg, Michael & Wilkening, Jon
Partner: UNT Libraries Government Documents Department


Description: The existence of multipole components in the dipole and quadrupole magnets is one of the factors limiting the beam stability in the RHIC operations. So, a realistic non-linear model is crucial for understanding the beam behavior and to achieve the ultimate performance in RHIC. A procedure is developed to build a non-linear model using the available multipole component data obtained from measurements of RHIC magnets. We first discuss the measurements performed at different stages of manufacturing of the magnets in relation to their current state in RHIC. We then describe the procedure to implement these measurement data into tracking models, including the implementation of the multipole feed down effect due to the beam orbit offset from the magnet center. Finally, the field quality analysis in the RHIC interaction regions (IR) is presented.
Date: June 25, 2007
Creator: BEEBE-WANG,J. & JAIN, A.
Partner: UNT Libraries Government Documents Department

Overlapping Schwarz for Nonlinear Problems. An Element Agglomeration Nonlinear Additive Schwarz Preconditioned Newton Method for Unstructured Finite Element Problems

Description: This paper extends previous results on nonlinear Schwarz preconditioning ([4]) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The non-local finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in [8]. Then, the algebraic construction from [9] of the corresponding non-linear finite element subproblems is applied to generate the subspace based nonlinear preconditioner. The overall nonlinearly preconditioned problem is solved by an inexact Newton method. Numerical illustration is also provided.
Date: February 10, 2005
Creator: Cai, X C; Marcinkowski, L & Vassilevski, P S
Partner: UNT Libraries Government Documents Department

Noisy Nonlinear Systems

Description: During the one-year period 2004-2005 our work continued to focus on nonlinear noisy systems, with special attention to spatially extended systems. There is a history of many decades of research in the sciences and engineering on the behavior of noninear noisy systems, but only in the past ten years or so has a theoretical understanding of spatially extended systems begun to emerge. This has been the outcome of a symbiosis of numerical simulations not possible until recently, laboratory experiments, and new analytic methods.
Date: November 20, 2005
Creator: Lindenberg, Dr. Katja
Partner: UNT Libraries Government Documents Department

Mesh independent convergence of the modified inexact Newton method for a second order nonlinear problem

Description: In this paper, we consider an inexact Newton method applied to a second order nonlinear problem with higher order nonlinearities. We provide conditions under which the method has a mesh-independent rate of convergence. To do this, we are required to first, set up the problem on a scale of Hilbert spaces and second, to devise a special iterative technique which converges in a higher than first order Sobolev norm. We show that the linear (Jacobian) system solved in Newton's method can be replaced with one iterative step provided that the initial nonlinear iterate is accurate enough. The closeness criteria can be taken independent of the mesh size. Finally, the results of numerical experiments are given to support the theory.
Date: September 20, 2004
Creator: Kim, T; Pasciak, J E & Vassilevski, P S
Partner: UNT Libraries Government Documents Department

Nonlinear Bayesian Algorithms for Gas Plume Detection and Estimation from Hyper-spectral Thermal Image Data

Description: This paper presents a nonlinear Bayesian regression algorithm for the purpose of detecting and estimating gas plume content from hyper-spectral data. Remote sensing data, by its very nature, is collected under less controlled conditions than laboratory data. As a result, the physics-based model that is used to describe the relationship between the observed remotesensing spectra, and the terrestrial (or atmospheric) parameters that we desire to estimate, is typically littered with many unknown "nuisance" parameters (parameters that we are not interested in estimating, but also appear in the model). Bayesian methods are well-suited for this context as they automatically incorporate the uncertainties associated with all nuisance parameters into the error estimates of the parameters of interest. The nonlinear Bayesian regression methodology is illustrated on realistic simulated data from a three-layer model for longwave infrared (LWIR) measurements from a passive instrument. This shows that this approach should permit more accurate estimation as well as a more reasonable description of estimate uncertainty.
Date: June 13, 2007
Creator: Heasler, Patrick G.; Posse, Christian; Hylden, Jeff L. & Anderson, Kevin K.
Partner: UNT Libraries Government Documents Department

Modeling femtosecond pulse propagation in optical fibers.

Description: Femtosecond pulse propagation in optical fibers requires consideration of higher-order nonlinear effects when implementing the non-linear Schroedinger equation. We show excellent agreement of our model with experimental results both for the temporal and phase features of the pulses. Ultrafast pulse propagation in optical fibers presents a number of challenges given the effect of nonlinearities which become important on such a short time scale. The modeling of femtosecond pulse propagation becomes, consequently, a harder task which has to account for all these effects. In this work, we have included higher order corrections in the non-linear Schroedinger equation and compared the numerical simulation results with experimental data. Our work, besides taking into account the temporal evolution of the pulse, keeps into account also the phase behavior of the electric field, which we compare with experimental results obtained with Frequency Resolved Optical Gating [l]. We also account for self-frequency shift of the pulse and obtain excellent agreement with the experimental results on the Raman shift.
Date: January 1, 2001
Creator: Chung, Y. J. (Yeo-Jin); Schaefer, T. B. (Tobias B.); Gabitov, I. R. (Ildar R.); Omenetto, F. G. (Fiorenzo G.) & Taylor, Antoinette J.,
Partner: UNT Libraries Government Documents Department

Solving a Class of Nonlinear Eigenvalue Problems by Newton's Method

Description: We examine the possibility of using the standard Newton's method for solving a class of nonlinear eigenvalue problems arising from electronic structure calculation. We show that the Jacobian matrix associated with this nonlinear system has a special structure that can be exploited to reduce the computational complexity of the Newton's method. Preliminary numerical experiments indicate that the Newton's method can be more efficient for small problems in which a few smallest eigenpairs are needed.
Date: July 2, 2009
Creator: Gao, Weiguo; Yang, Chao & Meza, Juan C.
Partner: UNT Libraries Government Documents Department

CartaBlanca-rapid prototyping development environment for non-linear systems on unstructured grids.

Description: This talk describes a component-based nonlinear physical system simulation prototyping package written entirely in Java using objectoriented design, The package provides scientists and engineers a 'developer-friendly' software environment for large-scale computational algorithm and physical model development, on the Jacobian-Free Newton-Krylov solution method surrounding a finite-volume treatment of conservation equations. This enables a clean component-like implementation. We first provide motivation for the development of the software and then discuss software structure. Discussion .includes a description of the use of Java's built-in thread facility that enables parallel, shared-memory computations on a wide variety of unstructured grids with triangular, quadrilateral, tetrahedral and hexahedral elements. We also discuss the use of Java's inheritance mechanism in the construction of a hierarchy of physics systems objects and linear and nonlinear solver objects that simplify development and foster software re-use. Following this, we show results from example calculations and then discuss plans including the extension of the software to distributed memory computer systems.
Date: January 1, 2002
Creator: VanderHeyden, W. B. (William Brian); Livescu, D. (Daniel) & Padial-Collins, N. T. (Nely T.)
Partner: UNT Libraries Government Documents Department

Nonlinear generation of very high order UV modes in microstructured fibers pumped with femtosecond oscillator.

Description: We report generation of high-order spatial modes in the UV range through nonlinear frequency conversion of the femtosecond 800 nm radiation in microstructured fibers. The process is distinct from Supercontinuum generation and is sensitive to fiber tip morphology. One of the manifestations of the unusual nonlinear properties of the microstructured (PCF) fibers is the robust supercontinuum generation from a few centimeters of the fiber with femtosecond oscillator pumping around 800 nm. Even though the fiber can be multimode at wavelengths down to the fundamental, supercontinuum is usually observed exiting the fiber in the fundamental mode. Recent experiments, however, evidenced the existence of other nonlinear effects in PCFs indicating critical role of phase matching between various spatial modes of the fiber. When the PCF is pumped by the 1550 nm femtosecond pulses, distinct visible bands are generated at the output belonging to distinct spatial modes of the fiber. Here we report that similar nonlinear mechanism exists when PCF is pumped by Ti:Sapphire femtosecond oscillator near 800 nm central wavelength. In this case, however, higher-order modes are generated in the UV range with observed wavelengths up to 310 nm, Fig. 1. Moreover, the effect is observed only when the input tip of the fiber has a non-flat surface, that is freshly cleaved fiber is prepared by melting the tip as described. The experiment consists of a femtosecond oscillator delivering 150-fs pulses with average power of up to 1.3 W to the fiber tip. After the attenuator, Faraday isolator and polarization control optics, the light is focused on the tip of the PCF with an aspheric lens. The fiber was a high-air-filling fraction single strand fused silica suspended by a honeycomb web of silica pellicles running along the length of the fiber, which was a few tens of centimeters in our experiments. The ...
Date: January 1, 2002
Creator: Efimov, A. V. (Anatoly V.); Omenetto, F. G. (Fiorenzo G.); Taylor, Antoinette J.,; Knight, J. C. (Jonathan C.); Wadsworth, W. J. (William J.) & Russel, P. S. J. (Philip St. J.)
Partner: UNT Libraries Government Documents Department

Simulations and model of the nonlinear Richtmyer-Meshkov instability (U)

Description: The nonlinear evolution of the Richtmyer-Meshkov (RM) instability is investigated using numerical simulations with the FLASH code in two-dimensions (20). The purpose of the simulations is to develop a nonlinear model of the RM instability that is accurate to the regime of inertial confinement fusion (ICF) and ejecta formation, namely, at large Atwood number A and initial amplitude kh{sub o} (k {triple_bond} wavenumber) of the perturbation. The FLASH code is first validated by obtaining excellent agreement with RM experiments well into the nonlinear regime. The results are then compared with a variety of nonlinear models that are based on potential flow. We find that the models agree with simulations for moderate values of A and kh{sub o} but not for the values characteristic of ICF and ejecta formation. As a result, a new nonlinear model is developed that captures the simulation results consistent with potential flow and for a broader range of A and kh{sub o}.
Date: January 1, 2009
Creator: Dimonte, Guy
Partner: UNT Libraries Government Documents Department