Efficient Preconditioning for the p-Version Finite Element Method in Two Dimensions

DTIC Science & Technology

1989-10-01

paper, we study fast parallel preconditioners for systems of equations arising from the p-version finite element method. The p-version finite element...computations and the solution of a relatively small global auxiliary problem. We study two different methods. In the first (Section 3), the global...20], will be studied in the next section. Problem (3.12) is obviously much more easily solved than the original problem ,nd the procedure is highly

Finite Element Analysis of Tube Hydroforming in Non-Symmetrical Dies

NASA Astrophysics Data System (ADS)

Nulkar, Abhishek V.; Gu, Randy; Murty, Pilaka

2011-08-01

Tube hydroforming has been studied intensively using commercial finite element programs. A great deal of the investigations dealt with models with symmetric cross-sections. It is known that additional constraints due to symmetry may be imposed on the model so that it is properly supported. For a non-symmetric model, these constraints become invalid and the model does not have sufficient support resulting in a singular finite element system. Majority of commercial codes have a limited capability in solving models with insufficient supports. Recently, new algorithms using penalty variable and air-like contact element (ALCE) have been developed to solve positive semi-definite finite element systems such as those in contact mechanics. In this study the ALCE algorithm is first validated by comparing its result against a commercial code using a symmetric model in which a circular tube is formed to polygonal dies with symmetric shapes. Then, the study investigates the accuracy and efficiency of using ALCE in analyzing hydroforming of tubes with various cross-sections in non-symmetrical dies in 2-D finite element settings.

Two-particle multichannel systems in a finite volume with arbitrary spin

DOE PAGES

Briceno, Raul A.

2014-04-08

The quantization condition for two-particle systems with arbitrary number of two-body open coupled channels, spin and masses in a finite cubic volume with either periodic or twisted boundary conditions is presented. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. The result is relativistic, holds for all momenta below the three- and four-particle thresholds, and is exact up to exponential volume corrections that are governed by L/r, where L is the spatial extent of the volume and r is the range of the interactions between the particles. With hadronic systems the rangemore » of the interaction is set by the inverse of the pion mass, m π, and as a result the formalism presented is suitable for m πL>>1. Implications of the formalism for the studies of multichannel baryon-baryon systems are discussed.« less

Finite micro-tab system for load control on a wind turbine

NASA Astrophysics Data System (ADS)

Bach, A. B.; Lennie, M.; Pechlivanoglou, G.; Nayeri, C. N.; Paschereit, C. O.

2014-06-01

Finite micro-tabs have been investigated experimentally to evaluate the potential for load control on wind turbines. Two dimensional full span, as well as multiple finite tabs of various aspect ratios have been studied on an AH93W174 airfoil at different chord wise positions. A force balance was used to measure the aerodynamic loads. Furthermore, the wake vortex system consisting of the Karman vortex street as well as the tab tip vortices was analyzed with a 12-hole probe and hot wire anemometry. Finally, conventional oil paint as well as a quantitative digital flow analysis technique called SMARTviz were used to visualize the flow around the finite tab configurations. Results have shown that the devices are an effective solution to alleviate the airfoils overall load. The influence of the tab height, tab position as well as the finite tab aspect ratio on the lift and lift to drag ratio have been evaluated. It could be shown, that the lift difference can either be varied by changing the tab height as well as by altering the aspect ratio of the finite tabs. The drag of a two-dimensional flap is directly associated with the vortex street, while in the case of the finite tab, the solidity ratio of the tabs has the strongest effect on the drag. Therefore, the application of a finite tab system showed to improve the lift to drag ratio.

Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions. Numerical Analysis in Continuous Time

NASA Astrophysics Data System (ADS)

Guevara Hidalgo, Esteban; Nemoto, Takahiro; Lecomte, Vivien

Rare trajectories of stochastic systems are important to understand because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provide a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to a selection rule that favors the rare trajectories of interest. However, such algorithms are plagued by finite simulation time- and finite population size- effects that can render their use delicate. Using the continuous-time cloning algorithm, we analyze the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of the rare trajectories. We use these scalings in order to propose a numerical approach which allows to extract the infinite-time and infinite-size limit of these estimators.

Responses to applied forces and the Jarzynski equality in classical oscillator systems coupled to finite baths: an exactly solvable nondissipative nonergodic model.

PubMed

Hasegawa, Hideo

2011-07-01

Responses of small open oscillator systems to applied external forces have been studied with the use of an exactly solvable classical Caldeira-Leggett model in which a harmonic oscillator (system) is coupled to finite N-body oscillators (bath) with an identical frequency (ω(n) = ω(o) for n = 1 to N). We have derived exact expressions for positions, momenta, and energy of the system in nonequilibrium states and for work performed by applied forces. A detailed study has been made on an analytical method for canonical averages of physical quantities over the initial equilibrium state, which is much superior to numerical averages commonly adopted in simulations of small systems. The calculated energy of the system which is strongly coupled to a finite bath is fluctuating but nondissipative. It has been shown that the Jarzynski equality is valid in nondissipative nonergodic open oscillator systems regardless of the rate of applied ramp force.

Quality Assessment and Control of Finite Element Solutions.

DTIC Science & Technology

1986-05-01

solutions. However, some special-purpose and pilot finite element systems have implemented adaptive algorithms 17 p." for practical performance studies ...simulator (SAFES code) developed at the University of Wyoming (Ref. 148); and the PROBE system developed by NOETIC Technologies Corporation in St. Louis (Ref...displacements. Recent studies have demonstrated that the accuracy and rate of convergence of stresses (and strains) r. depend on how (and where) they

Numerical Analysis of Solids at Failure

DTIC Science & Technology

2011-08-20

failure analyses include the formulation of invariant finite elements for thin Kirchhoff rods, and preliminary initial studies of growth in...analysis of the failure of other structural/mechanical systems, including the finite element modeling of thin Kirchhoff rods and the constitutive...algorithm based on the connectivity graph of the underlying finite element mesh. In this setting, the discontinuities are defined by fronts propagating

Discontinuous Observers Design for Finite-Time Consensus of Multiagent Systems With External Disturbances.

PubMed

Liu, Xiaoyang; Ho, Daniel W C; Cao, Jinde; Xu, Wenying

This brief investigates the problem of finite-time robust consensus (FTRC) for second-order nonlinear multiagent systems with external disturbances. Based on the global finite-time stability theory of discontinuous homogeneous systems, a novel finite-time convergent discontinuous disturbed observer (DDO) is proposed for the leader-following multiagent systems. The states of the designed DDO are then used to design the control inputs to achieve the FTRC of nonlinear multiagent systems in the presence of bounded disturbances. The simulation results are provided to validate the effectiveness of these theoretical results.This brief investigates the problem of finite-time robust consensus (FTRC) for second-order nonlinear multiagent systems with external disturbances. Based on the global finite-time stability theory of discontinuous homogeneous systems, a novel finite-time convergent discontinuous disturbed observer (DDO) is proposed for the leader-following multiagent systems. The states of the designed DDO are then used to design the control inputs to achieve the FTRC of nonlinear multiagent systems in the presence of bounded disturbances. The simulation results are provided to validate the effectiveness of these theoretical results.

IFEMS, an Interactive Finite Element Modeling System Using a CAD/CAM System

NASA Technical Reports Server (NTRS)

Mckellip, S.; Schuman, T.; Lauer, S.

1980-01-01

A method of coupling a CAD/CAM system with a general purpose finite element mesh generator is described. The three computer programs which make up the interactive finite element graphics system are discussed.

Emergent kink statistics at finite temperature

DOE PAGES

Lopez-Ruiz, Miguel Angel; Yepez-Martinez, Tochtli; Szczepaniak, Adam; ...

2017-07-25

In this paper we use 1D quantum mechanical systems with Higgs-like interaction potential to study the emergence of topological objects at finite temperature. Two different model systems are studied, the standard double-well potential model and a newly introduced discrete kink model. Using Monte-Carlo simulations as well as analytic methods, we demonstrate how kinks become abundant at low temperatures. These results may shed useful insights on how topological phenomena may occur in QCD.

Higher-order adaptive finite-element methods for Kohn–Sham density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Motamarri, P.; Nowak, M.R.; Leiter, K.

2013-11-15

We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposedmore » solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using modest computational resources, and good scalability of the present implementation up to 192 processors.« less

Modelling and finite-time stability analysis of psoriasis pathogenesis

NASA Astrophysics Data System (ADS)

Oza, Harshal B.; Pandey, Rakesh; Roper, Daniel; Al-Nuaimi, Yusur; Spurgeon, Sarah K.; Goodfellow, Marc

2017-08-01

A new systems model of psoriasis is presented and analysed from the perspective of control theory. Cytokines are treated as actuators to the plant model that govern the cell population under the reasonable assumption that cytokine dynamics are faster than the cell population dynamics. The analysis of various equilibria is undertaken based on singular perturbation theory. Finite-time stability and stabilisation have been studied in various engineering applications where the principal paradigm uses non-Lipschitz functions of the states. A comprehensive study of the finite-time stability properties of the proposed psoriasis dynamics is carried out. It is demonstrated that the dynamics are finite-time convergent to certain equilibrium points rather than asymptotically or exponentially convergent. This feature of finite-time convergence motivates the development of a modified version of the Michaelis-Menten function, frequently used in biology. This framework is used to model cytokines as fast finite-time actuators.

Quasi-finite-time control for high-order nonlinear systems with mismatched disturbances via mapping filtered forwarding technique

NASA Astrophysics Data System (ADS)

Zhang, X.; Huang, X. L.; Lu, H. Q.

2017-02-01

In this study, a quasi-finite-time control method for designing stabilising control laws is developed for high-order strict-feedback nonlinear systems with mismatched disturbances. By using mapping filtered forwarding technique, a virtual control is designed to force the off-the-manifold coordinate to converge to zero in quasi-finite time at each step of the design; at the same time, the manifold is rendered insensitive to time-varying, bounded and unknown disturbances. In terms of standard forwarding methodology, the algorithm proposed here not only does not require the Lyapunov function for controller design, but also avoids to calculate the derivative of sign function. As far as the dynamic performance of closed-loop systems is concerned, we essentially obtain the finite-time performances, which is typically reflected in the following aspects: fast and accurate responses, high tracking precision, and robust disturbance rejection. Spring, mass, and damper system and flexible joints robot are tested to demonstrate the proposed controller performance.

Attitude output feedback control for rigid spacecraft with finite-time convergence.

PubMed

Hu, Qinglei; Niu, Guanglin

2017-09-01

The main problem addressed is the quaternion-based attitude stabilization control of rigid spacecraft without angular velocity measurements in the presence of external disturbances and reaction wheel friction as well. As a stepping stone, an angular velocity observer is proposed for the attitude control of a rigid body in the absence of angular velocity measurements. The observer design ensures finite-time convergence of angular velocity state estimation errors irrespective of the control torque or the initial attitude state of the spacecraft. Then, a novel finite-time control law is employed as the controller in which the estimate of the angular velocity is used directly. It is then shown that the observer and the controlled system form a cascaded structure, which allows the application of the finite-time stability theory of cascaded systems to prove the finite-time stability of the closed-loop system. A rigorous analysis of the proposed formulation is provided and numerical simulation studies are presented to help illustrate the effectiveness of the angular-velocity observer for rigid spacecraft attitude control. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Finite-time master-slave synchronization and parameter identification for uncertain Lurie systems.

PubMed

Wang, Tianbo; Zhao, Shouwei; Zhou, Wuneng; Yu, Weiqin

2014-07-01

This paper investigates the finite-time master-slave synchronization and parameter identification problem for uncertain Lurie systems based on the finite-time stability theory and the adaptive control method. The finite-time master-slave synchronization means that the state of a slave system follows with that of a master system in finite time, which is more reasonable than the asymptotical synchronization in applications. The uncertainties include the unknown parameters and noise disturbances. An adaptive controller and update laws which ensures the synchronization and parameter identification to be realized in finite time are constructed. Finally, two numerical examples are given to show the effectiveness of the proposed method. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Average dynamics of a finite set of coupled phase oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dima, Germán C., E-mail: gdima@df.uba.ar; Mindlin, Gabriel B.

2014-06-15

We study the solutions of a dynamical system describing the average activity of an infinitely large set of driven coupled excitable units. We compared their topological organization with that reconstructed from the numerical integration of finite sets. In this way, we present a strategy to establish the pertinence of approximating the dynamics of finite sets of coupled nonlinear units by the dynamics of its infinitely large surrogate.

Average dynamics of a finite set of coupled phase oscillators

PubMed Central

Dima, Germán C.; Mindlin, Gabriel B.

2014-01-01

We study the solutions of a dynamical system describing the average activity of an infinitely large set of driven coupled excitable units. We compared their topological organization with that reconstructed from the numerical integration of finite sets. In this way, we present a strategy to establish the pertinence of approximating the dynamics of finite sets of coupled nonlinear units by the dynamics of its infinitely large surrogate. PMID:24985426

Average dynamics of a finite set of coupled phase oscillators.

PubMed

Dima, Germán C; Mindlin, Gabriel B

2014-06-01

We study the solutions of a dynamical system describing the average activity of an infinitely large set of driven coupled excitable units. We compared their topological organization with that reconstructed from the numerical integration of finite sets. In this way, we present a strategy to establish the pertinence of approximating the dynamics of finite sets of coupled nonlinear units by the dynamics of its infinitely large surrogate.

Size-dependent chemical transformation, structural phase-change, and optical properties of nanowires

PubMed Central

Piccione, Brian; Agarwal, Rahul; Jung, Yeonwoong; Agarwal, Ritesh

2013-01-01

Nanowires offer a unique approach for the bottom up assembly of electronic and photonic devices with the potential of integrating photonics with existing technologies. The anisotropic geometry and mesoscopic length scales of nanowires also make them very interesting systems to study a variety of size-dependent phenomenon where finite size effects become important. We will discuss the intriguing size-dependent properties of nanowire systems with diameters in the 5 – 300 nm range, where finite size and interfacial phenomena become more important than quantum mechanical effects. The ability to synthesize and manipulate nanostructures by chemical methods allows tremendous versatility in creating new systems with well controlled geometries, dimensions and functionality, which can then be used for understanding novel processes in finite-sized systems and devices. PMID:23997656

Many-body localization in disorder-free systems: The importance of finite-size constraints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Papić, Z., E-mail: zpapic@perimeterinstitute.ca; Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5; Stoudenmire, E. Miles

2015-11-15

Recently it has been suggested that many-body localization (MBL) can occur in translation-invariant systems, and candidate 1D models have been proposed. We find that such models, in contrast to MBL systems with quenched disorder, typically exhibit much more severe finite-size effects due to the presence of two or more vastly different energy scales. In a finite system, this can artificially split the density of states (DOS) into bands separated by large gaps. We argue for such models to faithfully represent the thermodynamic limit behavior, the ratio of relevant coupling must exceed a certain system-size depedent cutoff, chosen such that variousmore » bands in the DOS overlap one another. Setting the parameters this way to minimize finite-size effects, we study several translation-invariant MBL candidate models using exact diagonalization. Based on diagnostics including entanglement and local observables, we observe thermal (ergodic), rather than MBL-like behavior. Our results suggest that MBL in translation-invariant systems with two or more very different energy scales is less robust than perturbative arguments suggest, possibly pointing to the importance of non-perturbative effects which induce delocalization in the thermodynamic limit.« less

A new multipartite plate system for anterior cervical spine surgery; finite element analysis.

PubMed

Şimşek, Hakan; Zorlu, Emre; Kaya, Serdar; Baydoğan, Murat; Atabey, Cem; Çolak, Ahmet

2017-12-19

There are numerous available plates, almost all of which are compact one-piece plates. During the placement of relatively long plates in the treatment of multi-level cervical pathologies, instrument related complications might appear. In order to overcome this potential problem, a novel 'articulated plate system' is designed. We aimed to delineate finite element analysis and mechanical evaluations. A new plate system consisting of multi partite structure for anterior cervical stabilization was designed. Segmental plates were designed for application onto the ventral surface of the vertebral body. Plates differed from 9 to13 mm in length. There are rods at one end and hooks at the other end. Terminal points consisted of either hooks or rods at one end but the other ends are blind. Finite element and mechanical tests of the construct were performed applying bending, axial loading, and distraction forces. Finite element and mechanical testing results yielded the cut off values for functional failure and breakage of the system. The articulated system proved to be mechanically safe and it lets extension of the system on either side as needed. Ease of application needs further verification via a cadaveric study.

Numerical analysis for finite-range multitype stochastic contact financial market dynamic systems

NASA Astrophysics Data System (ADS)

Yang, Ge; Wang, Jun; Fang, Wen

2015-04-01

In an attempt to reproduce and study the dynamics of financial markets, a random agent-based financial price model is developed and investigated by the finite-range multitype contact dynamic system, in which the interaction and dispersal of different types of investment attitudes in a stock market are imitated by viruses spreading. With different parameters of birth rates and finite-range, the normalized return series are simulated by Monte Carlo simulation method and numerical studied by power-law distribution analysis and autocorrelation analysis. To better understand the nonlinear dynamics of the return series, a q-order autocorrelation function and a multi-autocorrelation function are also defined in this work. The comparisons of statistical behaviors of return series from the agent-based model and the daily historical market returns of Shanghai Composite Index and Shenzhen Component Index indicate that the proposed model is a reasonable qualitative explanation for the price formation process of stock market systems.

A study of the diffusional behavior of a two-phase metal matrix composite exposed to a high temperature environment

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1974-01-01

The progress of diffusion-controlled filament-matrix interaction in a metal matrix composite where the filaments and matrix comprise a two-phase binary alloy system was studied by mathematically modeling compositional changes resulting from prolonged elevated temperature exposure. The analysis treats a finite, diffusion-controlled, two-phase moving-interface problem by means of a variable-grid finite-difference technique. The Ni-W system was selected as an example system. Modeling was carried out for the 1000 to 1200 C temperature range for unidirectional composites containing from 6 to 40 volume percent tungsten filaments in a Ni matrix. The results are displayed to show both the change in filament diameter and matrix composition as a function of exposure time. Compositional profiles produced between first and second nearest neighbor filaments were calculated by superposition of finite-difference solutions of the diffusion equations.

Application of mass spectrometer-inverse gas chromatography to study polymer-solvent diffusivity and solubility.

PubMed

Galdámez, J Román; Danner, Ronald P; Duda, J Larry

2007-07-20

The application of a mass spectrometer detector in capillary column inverse gas chromatography is shown to be a valuable tool in the measurement of diffusion and solubility in polymer-solvent systems. The component specific detector provides excellent results for binary polymer-solvent systems, but it is particularly valuable because it can be readily applied to multicomponent systems. Results for a number of infinitely dilute solvents in poly(vinyl acetate) (PVAc) are reported over a range of temperature from 60 to 150 degrees C. Results are also reported for finite concentrations of toluene and methanol in PVAc from 60 to 110 degrees C. Finally, the technique was applied to study the effect of finite concentrations of toluene on the diffusion coefficients of THF and cyclohexane in PVAc. The experimental data compare well with literature values for both infinite and finite concentrations, indicating that the experimental protocol described in this work is sound.

A discrete model to study reaction-diffusion-mechanics systems.

PubMed

Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.

A Discrete Model to Study Reaction-Diffusion-Mechanics Systems

PubMed Central

Weise, Louis D.; Nash, Martyn P.; Panfilov, Alexander V.

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects. PMID:21804911

Finite Group Invariance and Solution of Jaynes-Cummings Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haydargil, Derya; Koc, Ramazan

2004-10-04

The finite group invariance of the E x {beta} and Jaynes-Cummings models are studied. A method is presented to obtain finite group invariance of the E x {beta} system.A suitable transformation of a Jaynes-Cummings Hamiltonian leads to equivalence of E x {beta} system. Then a general method is applied to obtain the solution of Jaynes-Cummings Hamiltonian with Kerr nonlinearity. Number operator for this structure and the generators of su(2) algebra are used to find the eigenvalues of the Jaynes-Cummings Hamiltonian for different states. By using the invariance of number operator the solution of modified Jaynes-Cummings Hamiltonian is also discussed.

An interactive graphics system to facilitate finite element structural analysis

NASA Technical Reports Server (NTRS)

Burk, R. C.; Held, F. H.

1973-01-01

The characteristics of an interactive graphics systems to facilitate the finite element method of structural analysis are described. The finite element model analysis consists of three phases: (1) preprocessing (model generation), (2) problem solution, and (3) postprocessing (interpretation of results). The advantages of interactive graphics to finite element structural analysis are defined.

Three dimensional finite element methods: Their role in the design of DC accelerator systems

NASA Astrophysics Data System (ADS)

Podaru, Nicolae C.; Gottdang, A.; Mous, D. J. W.

2013-04-01

High Voltage Engineering has designed, built and tested a 2 MV dual irradiation system that will be applied for radiation damage studies and ion beam material modification. The system consists of two independent accelerators which support simultaneous proton and electron irradiation (energy range 100 keV - 2 MeV) of target sizes of up to 300 × 300 mm2. Three dimensional finite element methods were used in the design of various parts of the system. The electrostatic solver was used to quantify essential parameters of the solid-state power supply generating the DC high voltage. The magnetostatic solver and ray tracing were used to optimize the electron/ion beam transport. Close agreement between design and measurements of the accelerator characteristics as well as beam performance indicate the usefulness of three dimensional finite element methods during accelerator system design.

Discreteness effects in a reacting system of particles with finite interaction radius.

PubMed

Berti, S; López, C; Vergni, D; Vulpiani, A

2007-09-01

An autocatalytic reacting system with particles interacting at a finite distance is studied. We investigate the effects of the discrete-particle character of the model on properties like reaction rate, quenching phenomenon, and front propagation, focusing on differences with respect to the continuous case. We introduce a renormalized reaction rate depending both on the interaction radius and the particle density, and we relate it to macroscopic observables (e.g., front speed and front thickness) of the system.

Global Existence Results for Viscoplasticity at Finite Strain

NASA Astrophysics Data System (ADS)

Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe

2018-01-01

We study a model for rate-dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor, and investigate the existence of global-in-time solutions to the related PDE system. We reveal its underlying structure as a generalized gradient system, where the driving energy functional is highly nonconvex and features the geometric nonlinearities related to finite-strain elasticity as well as the multiplicative decomposition of finite-strain plasticity. Moreover, the dissipation potential depends on the left-invariant plastic rate, and thus depends on the plastic state variable. The existence theory is developed for a class of abstract, nonsmooth, and nonconvex gradient systems, for which we introduce suitable notions of solutions, namely energy-dissipation-balance and energy-dissipation-inequality solutions. Hence, we resort to the toolbox of the direct method of the calculus of variations to check that the specific energy and dissipation functionals for our viscoplastic models comply with the conditions of the general theory.

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

PubMed

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

Study of propellant dynamics in a shuttle type launch vehicle

NASA Technical Reports Server (NTRS)

Jones, C. E.; Feng, G. C.

1972-01-01

A method and an associated digital computer program for evaluating the vibrational characteristics of large liquid-filled rigid wall tanks of general shape are presented. A solution procedure was developed in which slosh modes and frequencies are computed for systems mathematically modeled as assemblages of liquid finite elements. To retain sparsity in the assembled system mass and stiffness matrices, a compressible liquid element formulation was incorporated in the program. The approach taken in the liquid finite element formulation is compatible with triangular and quadrilateral structural finite elements so that the analysis of liquid motion can be coupled with flexible tank wall motion at some future time. The liquid element repertoire developed during the course of this study consists of a two-dimensional triangular element and a three-dimensional tetrahedral element.

Three-Dimensional Finite Element Ablative Thermal Response and Thermostructural Design of Thermal Protection Systems

NASA Technical Reports Server (NTRS)

Dec, John A.; Braun, Robert D.

2011-01-01

A finite element ablation and thermal response program is presented for simulation of three-dimensional transient thermostructural analysis. The three-dimensional governing differential equations and finite element formulation are summarized. A novel probabilistic design methodology for thermal protection systems is presented. The design methodology is an eight step process beginning with a parameter sensitivity study and is followed by a deterministic analysis whereby an optimum design can determined. The design process concludes with a Monte Carlo simulation where the probabilities of exceeding design specifications are estimated. The design methodology is demonstrated by applying the methodology to the carbon phenolic compression pads of the Crew Exploration Vehicle. The maximum allowed values of bondline temperature and tensile stress are used as the design specifications in this study.

Finite time control for MIMO nonlinear system based on higher-order sliding mode.

PubMed

Liu, Xiangjie; Han, Yaozhen

2014-11-01

Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Altabet, Y. Elia; Debenedetti, Pablo G., E-mail: pdebene@princeton.edu; Stillinger, Frank H.

In particle systems with cohesive interactions, the pressure-density relationship of the mechanically stable inherent structures sampled along a liquid isotherm (i.e., the equation of state of an energy landscape) will display a minimum at the Sastry density ρ{sub S}. The tensile limit at ρ{sub S} is due to cavitation that occurs upon energy minimization, and previous characterizations of this behavior suggested that ρ{sub S} is a spinodal-like limit that separates all homogeneous and fractured inherent structures. Here, we revisit the phenomenology of Sastry behavior and find that it is subject to considerable finite-size effects, and the development of the inherentmore » structure equation of state with system size is consistent with the finite-size rounding of an athermal phase transition. What appears to be a continuous spinodal-like point at finite system sizes becomes discontinuous in the thermodynamic limit, indicating behavior akin to a phase transition. We also study cavitation in glassy packings subjected to athermal expansion. Many individual expansion trajectories averaged together produce a smooth equation of state, which we find also exhibits features of finite-size rounding, and the examples studied in this work give rise to a larger limiting tension than for the corresponding landscape equation of state.« less

Finite-time stability and synchronization of memristor-based fractional-order fuzzy cellular neural networks

NASA Astrophysics Data System (ADS)

Zheng, Mingwen; Li, Lixiang; Peng, Haipeng; Xiao, Jinghua; Yang, Yixian; Zhang, Yanping; Zhao, Hui

2018-06-01

This paper mainly studies the finite-time stability and synchronization problems of memristor-based fractional-order fuzzy cellular neural network (MFFCNN). Firstly, we discuss the existence and uniqueness of the Filippov solution of the MFFCNN according to the Banach fixed point theorem and give a sufficient condition for the existence and uniqueness of the solution. Secondly, a sufficient condition to ensure the finite-time stability of the MFFCNN is obtained based on the definition of finite-time stability of the MFFCNN and Gronwall-Bellman inequality. Thirdly, by designing a simple linear feedback controller, the finite-time synchronization criterion for drive-response MFFCNN systems is derived according to the definition of finite-time synchronization. These sufficient conditions are easy to verify. Finally, two examples are given to show the effectiveness of the proposed results.

A Version of the Graphics-Oriented Interactive Finite Element Time-Sharing System (GIFTS) for an IBM with CP/CMS.

DTIC Science & Technology

1982-03-01

POSTGRADUATE SCHOOL fMonterey, California THESIS A VERSION OF THE GRAPHICS-ORIENTED INTERACTIVE FINITE ELEMENT TIME-SHARING SYSTEM ( GIFTS ) FOR AN IBM...Master’s & Engineer’s active Finite Element Time-sharing System Thesis - March 1982 ( GIFTS ) for an IBM with CP/CMS 6. penromm.oOn. REPoRT MUlmiR 1. AUTHOIee...ss0in D dinuf 5W M memisi) ’A version of the Graphics-oriented, Interactive, Finite element, Time-sharing System ( GIFTS ) has been developed for, and

The English Verb System.

ERIC Educational Resources Information Center

Gorayska, Barbara

1978-01-01

Techniques of teaching the English finite verb to speakers of other languages must account for meaning that is signalled by the structure alone and meaning derived from the context. Accordingly, this study attempts to distinguish the semantic components of the finite verb structure. The structure is viewed as being always composed of the following…

The Mixed Finite Element Multigrid Method for Stokes Equations

PubMed Central

Muzhinji, K.; Shateyi, S.; Motsa, S. S.

2015-01-01

The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q 2-Q 1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361

A Finite-Rate Gas-Surface Interaction Model Informed by Fundamental Computational Chemistry Simulations

DTIC Science & Technology

2013-03-31

found to not thermally accommodate to the surface, rather they leave in excited vibrational levels. The new finite-rate model and thermal accommodation...vehicle’s thermal protection system (TPS). Many TPS materials act as a catalyst for the heterogeneous recombination of dissociated species back into...it is a significant component in both reusable (LI900, LI2200, FRSI) and ablative (SIRCA) thermal protection systems [24]. In addition, studies have

Gaussian impurity moving through a Bose-Einstein superfluid

NASA Astrophysics Data System (ADS)

Pinsker, Florian

2017-09-01

In this paper a finite Gaussian impurity moving through an equilibrium Bose-Einstein condensate at T = 0 is studied. The problem can be described by a Gross-Pitaevskii equation, which is solved perturbatively. The analysis is done for systems of 2 and 3 spatial dimensions. The Bogoliubov equation solutions for the condensate perturbed by a finite impurity are calculated in the co-moving frame. From these solutions the total energy of the perturbed system is determined as a function of the width and the amplitude of the moving Gaussian impurity and its velocity. In addition we derive the drag force the finite sized impurity approximately experiences as it moves through the superfluid, which proves the existence of a superfluid phase for finite extensions of the impurities below the speed of sound. Finally we find that the force increases with velocity until an inflection point from which it decreases again in 2 and 3d.

The MV model of the color glass condensate for a finite number of sources including Coulomb interactions

DOE PAGES

McLerran, Larry; Skokov, Vladimir V.

2016-09-19

We modify the McLerran–Venugopalan model to include only a finite number of sources of color charge. In the effective action for such a system of a finite number of sources, there is a point-like interaction and a Coulombic interaction. The point interaction generates the standard fluctuation term in the McLerran–Venugopalan model. The Coulomb interaction generates the charge screening originating from well known evolution in x. Such a model may be useful for computing angular harmonics of flow measured in high energy hadron collisions for small systems. In this study we provide a basic formulation of the problem on a lattice.

Two-Level Hierarchical FEM Method for Modeling Passive Microwave Devices

NASA Astrophysics Data System (ADS)

Polstyanko, Sergey V.; Lee, Jin-Fa

1998-03-01

In recent years multigrid methods have been proven to be very efficient for solving large systems of linear equations resulting from the discretization of positive definite differential equations by either the finite difference method or theh-version of the finite element method. In this paper an iterative method of the multiple level type is proposed for solving systems of algebraic equations which arise from thep-version of the finite element analysis applied to indefinite problems. A two-levelV-cycle algorithm has been implemented and studied with a Gauss-Seidel iterative scheme used as a smoother. The convergence of the method has been investigated, and numerical results for a number of numerical examples are presented.

Analysis of the transient behavior of rubbing components

NASA Technical Reports Server (NTRS)

Quezdou, M. B.; Mullen, R. L.

1986-01-01

Finite element equations are developed for studying deformations and temperatures resulting from frictional heating in sliding system. The formulation is done for linear steady state motion in two dimensions. The equations include the effect of the velocity on the moving components. This gives spurious oscillations in their solutions by Galerkin finite element methods. A method called streamline upwind scheme is used to try to deal with this deficiency. The finite element program is then used to investigate the friction of heating in gas path seal.

A parallel finite element simulator for ion transport through three-dimensional ion channel systems.

PubMed

Tu, Bin; Chen, Minxin; Xie, Yan; Zhang, Linbo; Eisenberg, Bob; Lu, Benzhuo

2013-09-15

A parallel finite element simulator, ichannel, is developed for ion transport through three-dimensional ion channel systems that consist of protein and membrane. The coordinates of heavy atoms of the protein are taken from the Protein Data Bank and the membrane is represented as a slab. The simulator contains two components: a parallel adaptive finite element solver for a set of Poisson-Nernst-Planck (PNP) equations that describe the electrodiffusion process of ion transport, and a mesh generation tool chain for ion channel systems, which is an essential component for the finite element computations. The finite element method has advantages in modeling irregular geometries and complex boundary conditions. We have built a tool chain to get the surface and volume mesh for ion channel systems, which consists of a set of mesh generation tools. The adaptive finite element solver in our simulator is implemented using the parallel adaptive finite element package Parallel Hierarchical Grid (PHG) developed by one of the authors, which provides the capability of doing large scale parallel computations with high parallel efficiency and the flexibility of choosing high order elements to achieve high order accuracy. The simulator is applied to a real transmembrane protein, the gramicidin A (gA) channel protein, to calculate the electrostatic potential, ion concentrations and I - V curve, with which both primitive and transformed PNP equations are studied and their numerical performances are compared. To further validate the method, we also apply the simulator to two other ion channel systems, the voltage dependent anion channel (VDAC) and α-Hemolysin (α-HL). The simulation results agree well with Brownian dynamics (BD) simulation results and experimental results. Moreover, because ionic finite size effects can be included in PNP model now, we also perform simulations using a size-modified PNP (SMPNP) model on VDAC and α-HL. It is shown that the size effects in SMPNP can effectively lead to reduced current in the channel, and the results are closer to BD simulation results. Copyright © 2013 Wiley Periodicals, Inc.

Purely hydrodynamic ordering of rotating disks at a finite Reynolds number.

PubMed

Goto, Yusuke; Tanaka, Hajime

2015-01-28

Self-organization of moving objects in hydrodynamic environments has recently attracted considerable attention in connection to natural phenomena and living systems. However, the underlying physical mechanism is much less clear due to the intrinsically nonequilibrium nature, compared with self-organization of thermal systems. Hydrodynamic interactions are believed to play a crucial role in such phenomena. To elucidate the fundamental physical nature of many-body hydrodynamic interactions at a finite Reynolds number, here we study a system of co-rotating hard disks in a two-dimensional viscous fluid at zero temperature. Despite the absence of thermal noise, this system exhibits rich phase behaviours, including a fluid state with diffusive dynamics, a cluster state, a hexatic state, a glassy state, a plastic crystal state and phase demixing. We reveal that these behaviours are induced by the off-axis and many-body nature of nonlinear hydrodynamic interactions and the finite time required for propagating the interactions by momentum diffusion.

Momentum distribution functions in ensembles: the inequivalence of microcannonical and canonical ensembles in a finite ultracold system.

PubMed

Wang, Pei; Xianlong, Gao; Li, Haibin

2013-08-01

It is demonstrated in many thermodynamic textbooks that the equivalence of the different ensembles is achieved in the thermodynamic limit. In this present work we discuss the inequivalence of microcanonical and canonical ensembles in a finite ultracold system at low energies. We calculate the microcanonical momentum distribution function (MDF) in a system of identical fermions (bosons). We find that the microcanonical MDF deviates from the canonical one, which is the Fermi-Dirac (Bose-Einstein) function, in a finite system at low energies where the single-particle density of states and its inverse are finite.

Pairing mechanism in Bi-O superconductors: A finite-size chain calculation

NASA Astrophysics Data System (ADS)

Aligia, A. A.; Nuez Regueiro, M. D.; Gagliano, E. R.

1989-09-01

We have studied the pairing mechanism in BiO3 systems by calculating the binding energy of a pair of holes in finite Bi-O chains, for parameters that simulate three-dimensional behavior. In agreement with previous results using perturbation theory in the hopping t, for covalent Bi-O binding and parameters for which the parent compound has a disproportionate ground state, pairing induced by the presence of biexcitons is obtained for sufficiently large interatomic Coulomb repulsion. The analysis of appropriate correlation functions shows a rapid metallization of the system as t and the number of holes increase. This fact shrinks the region of parameters for which the finite-size calculations can be trusted without further study. The same model for other parameters yields pairing in two other regimes: bipolaronic and magnetic excitonic.

Generating finite cyclic and dihedral groups using sequential insertion systems with interactions

NASA Astrophysics Data System (ADS)

Fong, Wan Heng; Sarmin, Nor Haniza; Turaev, Sherzod; Yosman, Ahmad Firdaus

2017-04-01

The operation of insertion has been studied extensively throughout the years for its impact in many areas of theoretical computer science such as DNA computing. First introduced as a generalization of the concatenation operation, many variants of insertion have been introduced, each with their own computational properties. In this paper, we introduce a new variant that enables the generation of some special types of groups called sequential insertion systems with interactions. We show that these new systems are able to generate all finite cyclic and dihedral groups.

A Note on Powers in Finite Fields

ERIC Educational Resources Information Center

Aabrandt, Andreas; Hansen, Vagn Lundsgaard

2016-01-01

The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In…

Numerical analysis for finite-range multitype stochastic contact financial market dynamic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Ge; Wang, Jun; Fang, Wen, E-mail: fangwen@bjtu.edu.cn

In an attempt to reproduce and study the dynamics of financial markets, a random agent-based financial price model is developed and investigated by the finite-range multitype contact dynamic system, in which the interaction and dispersal of different types of investment attitudes in a stock market are imitated by viruses spreading. With different parameters of birth rates and finite-range, the normalized return series are simulated by Monte Carlo simulation method and numerical studied by power-law distribution analysis and autocorrelation analysis. To better understand the nonlinear dynamics of the return series, a q-order autocorrelation function and a multi-autocorrelation function are also definedmore » in this work. The comparisons of statistical behaviors of return series from the agent-based model and the daily historical market returns of Shanghai Composite Index and Shenzhen Component Index indicate that the proposed model is a reasonable qualitative explanation for the price formation process of stock market systems.« less

Finite-temperature mechanical instability in disordered lattices.

PubMed

Zhang, Leyou; Mao, Xiaoming

2016-02-01

Mechanical instability takes different forms in various ordered and disordered systems and little is known about how thermal fluctuations affect different classes of mechanical instabilities. We develop an analytic theory involving renormalization of rigidity and coherent potential approximation that can be used to understand finite-temperature mechanical stabilities in various disordered systems. We use this theory to study two disordered lattices: a randomly diluted triangular lattice and a randomly braced square lattice. These two lattices belong to two different universality classes as they approach mechanical instability at T=0. We show that thermal fluctuations stabilize both lattices. In particular, the triangular lattice displays a critical regime in which the shear modulus scales as G∼T(1/2), whereas the square lattice shows G∼T(2/3). We discuss generic scaling laws for finite-T mechanical instabilities and relate them to experimental systems.

A finite element study of the EIDI system. [Electro-Impulse De-Icing System

NASA Technical Reports Server (NTRS)

Khatkhate, A. A.; Scavuzzo, R. J.; Chu, M. L.

1988-01-01

This paper presents a method for modeling the structural dynamics of an Electro-Impulse De-Icing System, using finite element analyses procedures. A guideline for building a representative finite element model is discussed. Modeling was done initially using four noded cubic elements, four noded isoparametric plate elements and eight noded isoparametric shell elements. Due to the size of the problem and due to the underestimation of shear stress results when compared to previous analytical work an approximate model was created to predict possible areas of shedding of ice. There appears to be good agreement with the test data provided by The Boeing Commercial Airplane Company. Thus these initial results of this method were found to be encouraging. Additional analytical work and comparison with experiment is needed in order to completely evaluate this approach.

Bounding the first exit from the basin: Independence times and finite-time basin stability

NASA Astrophysics Data System (ADS)

Schultz, Paul; Hellmann, Frank; Webster, Kevin N.; Kurths, Jürgen

2018-04-01

We study the stability of deterministic systems, given sequences of large, jump-like perturbations. Our main result is the derivation of a lower bound for the probability of the system to remain in the basin, given that perturbations are rare enough. This bound is efficient to evaluate numerically. To quantify rare enough, we define the notion of the independence time of such a system. This is the time after which a perturbed state has probably returned close to the attractor, meaning that subsequent perturbations can be considered separately. The effect of jump-like perturbations that occur at least the independence time apart is thus well described by a fixed probability to exit the basin at each jump, allowing us to obtain the bound. To determine the independence time, we introduce the concept of finite-time basin stability, which corresponds to the probability that a perturbed trajectory returns to an attractor within a given time. The independence time can then be determined as the time scale at which the finite-time basin stability reaches its asymptotic value. Besides that, finite-time basin stability is a novel probabilistic stability measure on its own, with potential broad applications in complex systems.

Fuzzy Finite-Time Command Filtered Control of Nonlinear Systems With Input Saturation.

PubMed

Yu, Jinpeng; Zhao, Lin; Yu, Haisheng; Lin, Chong; Dong, Wenjie

2017-08-22

This paper considers the fuzzy finite-time tracking control problem for a class of nonlinear systems with input saturation. A novel fuzzy finite-time command filtered backstepping approach is proposed by introducing the fuzzy finite-time command filter, designing the new virtual control signals and the modified error compensation signals. The proposed approach not only holds the advantages of the conventional command-filtered backstepping control, but also guarantees the finite-time convergence. A practical example is included to show the effectiveness of the proposed method.

Criticality in finite dynamical networks

NASA Astrophysics Data System (ADS)

Rohlf, Thimo; Gulbahce, Natali; Teuscher, Christof

2007-03-01

It has been shown analytically and experimentally that both random boolean and random threshold networks show a transition from ordered to chaotic dynamics at a critical average connectivity Kc in the thermodynamical limit [1]. By looking at the statistical distributions of damage spreading (damage sizes), we go beyond this extensively studied mean-field approximation. We study the scaling properties of damage size distributions as a function of system size N and initial perturbation size d(t=0). We present numerical evidence that another characteristic point, Kd exists for finite system sizes, where the expectation value of damage spreading in the network is independent of the system size N. Further, the probability to obtain critical networks is investigated for a given system size and average connectivity k. Our results suggest that, for finite size dynamical networks, phase space structure is very complex and may not exhibit a sharp order-disorder transition. Finally, we discuss the implications of our findings for evolutionary processes and learning applied to networks which solve specific computational tasks. [1] Derrida, B. and Pomeau, Y. (1986), Europhys. Lett., 1, 45-49

Coupled Finite Volume and Finite Element Method Analysis of a Complex Large-Span Roof Structure

NASA Astrophysics Data System (ADS)

Szafran, J.; Juszczyk, K.; Kamiński, M.

2017-12-01

The main goal of this paper is to present coupled Computational Fluid Dynamics and structural analysis for the precise determination of wind impact on internal forces and deformations of structural elements of a longspan roof structure. The Finite Volume Method (FVM) serves for a solution of the fluid flow problem to model the air flow around the structure, whose results are applied in turn as the boundary tractions in the Finite Element Method problem structural solution for the linear elastostatics with small deformations. The first part is carried out with the use of ANSYS 15.0 computer system, whereas the FEM system Robot supports stress analysis in particular roof members. A comparison of the wind pressure distribution throughout the roof surface shows some differences with respect to that available in the engineering designing codes like Eurocode, which deserves separate further numerical studies. Coupling of these two separate numerical techniques appears to be promising in view of future computational models of stochastic nature in large scale structural systems due to the stochastic perturbation method.

Primal-mixed formulations for reaction-diffusion systems on deforming domains

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo

2015-10-01

We propose a finite element formulation for a coupled elasticity-reaction-diffusion system written in a fully Lagrangian form and governing the spatio-temporal interaction of species inside an elastic, or hyper-elastic body. A primal weak formulation is the baseline model for the reaction-diffusion system written in the deformed domain, and a finite element method with piecewise linear approximations is employed for its spatial discretization. On the other hand, the strain is introduced as mixed variable in the equations of elastodynamics, which in turn acts as coupling field needed to update the diffusion tensor of the modified reaction-diffusion system written in a deformed domain. The discrete mechanical problem yields a mixed finite element scheme based on row-wise Raviart-Thomas elements for stresses, Brezzi-Douglas-Marini elements for displacements, and piecewise constant pressure approximations. The application of the present framework in the study of several coupled biological systems on deforming geometries in two and three spatial dimensions is discussed, and some illustrative examples are provided and extensively analyzed.

A cavitation transition in the energy landscape of simple cohesive liquids and glasses

NASA Astrophysics Data System (ADS)

Altabet, Y. Elia; Stillinger, Frank H.; Debenedetti, Pablo G.

2016-12-01

In particle systems with cohesive interactions, the pressure-density relationship of the mechanically stable inherent structures sampled along a liquid isotherm (i.e., the equation of state of an energy landscape) will display a minimum at the Sastry density ρS. The tensile limit at ρS is due to cavitation that occurs upon energy minimization, and previous characterizations of this behavior suggested that ρS is a spinodal-like limit that separates all homogeneous and fractured inherent structures. Here, we revisit the phenomenology of Sastry behavior and find that it is subject to considerable finite-size effects, and the development of the inherent structure equation of state with system size is consistent with the finite-size rounding of an athermal phase transition. What appears to be a continuous spinodal-like point at finite system sizes becomes discontinuous in the thermodynamic limit, indicating behavior akin to a phase transition. We also study cavitation in glassy packings subjected to athermal expansion. Many individual expansion trajectories averaged together produce a smooth equation of state, which we find also exhibits features of finite-size rounding, and the examples studied in this work give rise to a larger limiting tension than for the corresponding landscape equation of state.

System Identification of Damped Truss-Like Space Structures. Ph.D. Thesis - Cleveland State Univ., Mar. 1994

NASA Technical Reports Server (NTRS)

Armand, Sasan

1995-01-01

A spacecraft payload flown on a launch vehicle experiences dynamic loads. The dynamic loads are caused by various phenomena ranging from the start-up of the launch vehicle engine to wind gusts. A spacecraft payload should be designed to meet launch vehicle dynamic loads. One of the major steps taken towards determining the dynamic loads is to correlate the finite element model of the spacecraft with the test results of a modal survey test. A test-verified finite element model of the spacecraft should possess the same spatial properties (stiffness, mass, and damping) and modal properties (frequencies and mode shapes) as the test hardware representing the spacecraft. The test-verified and correlated finite element model of the spacecraft is then coupled with the finite element model of the launch vehicle for analysis of loads and stress. Modal survey testing, verification of a finite element model, and modification of the finite element model to match the modal survey test results can easily be accomplished if the spacecraft structure is simple. However, this is rarely the case. A simple structure here is defined as a structure where the influence of nonlinearity between force and displacement (uncertainty in a test, for example, with errors in input and output), and the influence of damping (structural, coulomb, and viscous) are not pronounced. The objective of this study is to develop system identification and correlation methods with the focus on the structural systems that possess nonproportional damping. Two approaches to correct the nonproportional damping matrix of a truss structure were studied, and have been implemented on truss-like structures such as the National Aeronautics and Space Administration's space station truss. The results of this study showed nearly 100 percent improvement of the correlated eigensystem over the analytical eigensystem. The first method showed excellent results with up to three modes used in the system identification process. The second method could handle more modes, but required more computer usage time, and the results were less accurate than those of the first method.

Quantum dynamics at finite temperature: Time-dependent quantum Monte Carlo study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christov, Ivan P., E-mail: ivan.christov@phys.uni-sofia.bg

2016-08-15

In this work we investigate the ground state and the dissipative quantum dynamics of interacting charged particles in an external potential at finite temperature. The recently devised time-dependent quantum Monte Carlo (TDQMC) method allows a self-consistent treatment of the system of particles together with bath oscillators first for imaginary-time propagation of Schrödinger type of equations where both the system and the bath converge to their finite temperature ground state, and next for real time calculation where the dissipative dynamics is demonstrated. In that context the application of TDQMC appears as promising alternative to the path-integral related techniques where the realmore » time propagation can be a challenge.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vourdas, A.

The finite set of subsystems of a finite quantum system with variables in Z(n), is studied as a Heyting algebra. The physical meaning of the logical connectives is discussed. It is shown that disjunction of subsystems is more general concept than superposition. Consequently, the quantum probabilities related to commuting projectors in the subsystems, are incompatible with associativity of the join in the Heyting algebra, unless if the variables belong to the same chain. This leads to contextuality, which in the present formalism has as contexts, the chains in the Heyting algebra. Logical Bell inequalities, which contain “Heyting factors,” are discussed.more » The formalism is also applied to the infinite set of all finite quantum systems, which is appropriately enlarged in order to become a complete Heyting algebra.« less

Bioinspired Concepts: Unified Theory for Complex Biological and Engineering Systems

DTIC Science & Technology

2006-01-01

i.e., data flows of finite size arrive at the system randomly. For such a system , we propose a modified dual scheduling algorithm that stabilizes ...demon. We compute the efficiency of the controller over finite and infinite time intervals, and since the controller is optimal, this yields hard limits...and highly optimized tolerance. PNAS, 102, 2005. 51. G. N. Nair and R. J. Evans. Stabilizability of stochastic linear systems with finite feedback

A multitasking finite state architecture for computer control of an electric powertrain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burba, J.C.

1984-01-01

Finite state techniques provide a common design language between the control engineer and the computer engineer for event driven computer control systems. They simplify communication and provide a highly maintainable control system understandable by both. This paper describes the development of a control system for an electric vehicle powertrain utilizing finite state concepts. The basics of finite state automata are provided as a framework to discuss a unique multitasking software architecture developed for this application. The architecture employs conventional time-sliced techniques with task scheduling controlled by a finite state machine representation of the control strategy of the powertrain. The complexitiesmore » of excitation variable sampling in this environment are also considered.« less

Hybrid finite element and Brownian dynamics method for diffusion-controlled reactions.

PubMed

Bauler, Patricia; Huber, Gary A; McCammon, J Andrew

2012-04-28

Diffusion is often the rate determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetric diffusion systems.

Finite-Dimensional Representations for Controlled Diffusions with Delay

DOE Office of Scientific and Technical Information (OSTI.GOV)

Federico, Salvatore, E-mail: salvatore.federico@unimi.it; Tankov, Peter, E-mail: tankov@math.univ-paris-diderot.fr

2015-02-15

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay.

A note on powers in finite fields

NASA Astrophysics Data System (ADS)

Aabrandt, Andreas; Lundsgaard Hansen, Vagn

2016-08-01

The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In this connection, it is of interest to know criteria for the existence of squares and other powers in arbitrary finite fields. Making good use of polynomial division in polynomial rings over finite fields, we have examined a classical criterion of Euler for squares in odd prime fields, giving it a formulation that is apt for generalization to arbitrary finite fields and powers. Our proof uses algebra rather than classical number theory, which makes it convenient when presenting basic methods of applied algebra in the classroom.

Examples of finite element mesh generation using SDRC IDEAS

NASA Technical Reports Server (NTRS)

Zapp, John; Volakis, John L.

1990-01-01

IDEAS (Integrated Design Engineering Analysis Software) offers a comprehensive package for mechanical design engineers. Due to its multifaceted capabilities, however, it can be manipulated to serve the needs of electrical engineers, also. IDEAS can be used to perform the following tasks: system modeling, system assembly, kinematics, finite element pre/post processing, finite element solution, system dynamics, drafting, test data analysis, and project relational database.

Finite-Time Adaptive Control for a Class of Nonlinear Systems With Nonstrict Feedback Structure.

PubMed

Sun, Yumei; Chen, Bing; Lin, Chong; Wang, Honghong

2017-09-18

This paper focuses on finite-time adaptive neural tracking control for nonlinear systems in nonstrict feedback form. A semiglobal finite-time practical stability criterion is first proposed. Correspondingly, the finite-time adaptive neural control strategy is given by using this criterion. Unlike the existing results on adaptive neural/fuzzy control, the proposed adaptive neural controller guarantees that the tracking error converges to a sufficiently small domain around the origin in finite time, and other closed-loop signals are bounded. At last, two examples are used to test the validity of our results.

Three-dimensional finite element analysis of occipitocervical fixation using an anterior occiput-to-axis locking plate system: a pilot study.

PubMed

Cai, Xianhua; Yu, Yang; Liu, Zhichao; Zhang, Meichao; Huang, Weibing

2014-08-01

Although there are many techniques for occipitocervical fixation, there have been no reports regarding occipitocervical fixation via the use of an anterior anatomical locking plate system. The biomechanics of this new system were analyzed by a three-dimensional finite element to provide a theoretical basis for clinical application. This was a modeling study. We studied a 27-year-old healthy male volunteer in whom cervical disease was excluded via X-ray examination. The states of stress and strain of these two internal fixation devices were analyzed. A three-dimensional finite element model of normal occiput-C2 was established based on the anatomical data from a Chinese population. An unstable model of occipital-cervical region was established by subtracting several unit structures from the normal model. An anterior occiput-to-axis locking titanium plate system was then applied and an anterior occiput-to-axis screw fixation was performed on the unstable model. Limitation of motion was performed on the surface of the fixed model, and physiological loads were imposed on the surface of the skull base. Under various loads from different directions, the peak values of displacement of the anterior occiput-to-axis locking titanium plate system decreased 15.5%, 12.5%, 14.4%, and 23.7%, respectively, under the loads of flexion, extension, lateral bending, and axial rotation. Compared with the anterior occiput-to-axis screw fixation, the peak values of stress of the anterior occiput-to-axis locking titanium plate system also decreased 3.9%, 2.9%, 9.7%, and 7.2%, respectively, under the loads of flexion, extension, lateral bending, and axial rotation. The anterior occiput-to-axis locking titanium plate system proved superior to the anterior occiput-to-axis screw system both in the stress distribution and fixation stability based on finite element analysis. It provides a new clinical option for anterior occipitocervical fixation. Copyright © 2014 Elsevier Inc. All rights reserved.

Minimal measures for Euler-Lagrange flows on finite covering spaces

NASA Astrophysics Data System (ADS)

Wang, Fang; Xia, Zhihong

2016-12-01

In this paper we study the minimal measures for positive definite Lagrangian systems on compact manifolds. We are particularly interested in manifolds with more complicated fundamental groups. Mather’s theory classifies the minimal or action-minimizing measures according to the first (co-)homology group of a given manifold. We extend Mather’s notion of minimal measures to a larger class for compact manifolds with non-commutative fundamental groups, and use finite coverings to study the structure of these extended minimal measures. We also define action-minimizers and minimal measures in the homotopical sense. Our program is to study the structure of homotopical minimal measures by considering Mather’s minimal measures on finite covering spaces. Our goal is to show that, in general, manifolds with a non-commutative fundamental group have a richer set of minimal measures, hence a richer dynamical structure. As an example, we study the geodesic flow on surfaces of higher genus. Indeed, by going to the finite covering spaces, the set of minimal measures is much larger and more interesting.

First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients

NASA Technical Reports Server (NTRS)

Manteuffel, Thomas A.; McCormick, Stephen F.; Starke, Gerhard

1996-01-01

The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.

Dual-quaternion based fault-tolerant control for spacecraft formation flying with finite-time convergence.

PubMed

Dong, Hongyang; Hu, Qinglei; Ma, Guangfu

2016-03-01

Study results of developing control system for spacecraft formation proximity operations between a target and a chaser are presented. In particular, a coupled model using dual quaternion is employed to describe the proximity problem of spacecraft formation, and a nonlinear adaptive fault-tolerant feedback control law is developed to enable the chaser spacecraft to track the position and attitude of the target even though its actuator occurs fault. Multiple-task capability of the proposed control system is further demonstrated in the presence of disturbances and parametric uncertainties as well. In addition, the practical finite-time stability feature of the closed-loop system is guaranteed theoretically under the designed control law. Numerical simulation of the proposed method is presented to demonstrate the advantages with respect to interference suppression, fast tracking, fault tolerant and practical finite-time stability. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Finite element modeling of trolling-mode AFM.

PubMed

Sajjadi, Mohammadreza; Pishkenari, Hossein Nejat; Vossoughi, Gholamreza

2018-06-01

Trolling mode atomic force microscopy (TR-AFM) has overcome many imaging problems in liquid environments by considerably reducing the liquid-resonator interaction forces. The finite element model of the TR-AFM resonator considering the effects of fluid and nanoneedle flexibility is presented in this research, for the first time. The model is verified by ABAQUS software. The effect of installation angle of the microbeam relative to the horizon and the effect of fluid on the system behavior are investigated. Using the finite element model, frequency response curve of the system is obtained and validated around the frequency of the operating mode by the available experimental results, in air and liquid. The changes in the natural frequencies in the presence of liquid are studied. The effects of tip-sample interaction on the excitation of higher order modes of the system are also investigated in air and liquid environments. Copyright © 2018 Elsevier B.V. All rights reserved.

Semi-automatic sparse preconditioners for high-order finite element methods on non-uniform meshes

NASA Astrophysics Data System (ADS)

Austin, Travis M.; Brezina, Marian; Jamroz, Ben; Jhurani, Chetan; Manteuffel, Thomas A.; Ruge, John

2012-05-01

High-order finite elements often have a higher accuracy per degree of freedom than the classical low-order finite elements. However, in the context of implicit time-stepping methods, high-order finite elements present challenges to the construction of efficient simulations due to the high cost of inverting the denser finite element matrix. There are many cases where simulations are limited by the memory required to store the matrix and/or the algorithmic components of the linear solver. We are particularly interested in preconditioned Krylov methods for linear systems generated by discretization of elliptic partial differential equations with high-order finite elements. Using a preconditioner like Algebraic Multigrid can be costly in terms of memory due to the need to store matrix information at the various levels. We present a novel method for defining a preconditioner for systems generated by high-order finite elements that is based on a much sparser system than the original high-order finite element system. We investigate the performance for non-uniform meshes on a cube and a cubed sphere mesh, showing that the sparser preconditioner is more efficient and uses significantly less memory. Finally, we explore new methods to construct the sparse preconditioner and examine their effectiveness for non-uniform meshes. We compare results to a direct use of Algebraic Multigrid as a preconditioner and to a two-level additive Schwarz method.

Finite Element Analysis and Experimental Study on Elbow Vibration Transmission Characteristics

NASA Astrophysics Data System (ADS)

Qing-shan, Dai; Zhen-hai, Zhang; Shi-jian, Zhu

2017-11-01

Pipeline system vibration is one of the significant factors leading to the vibration and noise of vessel. Elbow is widely used in the pipeline system. However, the researches about vibration of elbow are little, and there is no systematic study. In this research, we firstly analysed the relationship between elbow vibration transmission characteristics and bending radius by ABAQUS finite element simulation. Then, we conducted the further vibration test to observe the vibration transmission characteristics of different elbows which have the same diameter and different bending radius under different flow velocity. The results of simulation calculation and experiment both showed that the vibration acceleration levels of the pipeline system decreased with the increase of bending radius of the elbow, which was beneficial to reduce the transmission of vibration in the pipeline system. The results could be used as reference for further studies and designs for the low noise installation of pipeline system.

Nonlinear waves in reaction-diffusion systems: The effect of transport memory

NASA Astrophysics Data System (ADS)

Manne, K. K.; Hurd, A. J.; Kenkre, V. M.

2000-04-01

Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity.

The effects of exercise on blood flow with reference to the human cardiovascular system: a finite element study

NASA Technical Reports Server (NTRS)

Sud, V. K.; Srinivasan, R. S.; Charles, J. B.; Bungo, M. W.

1992-01-01

This paper reports on a theoretical investigation into the effects of vasomotion on blood through the human cardiovascular system. The finite element method has been used to analyse the model. Vasoconstriction and vasodilation may be effected either through the action of the central nervous system or autoregulation. One of the conditions responsible for vasomotion is exercise. The proposed model has been solved and quantitative results of flows and pressures due to changing the conductances of specific networks of arterioles, capillaries and venules comprising the arms, legs, stomach and their combinations have been obtained.

Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul

1993-01-01

We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First, a roper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' (SAT) is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.

Thermalization without eigenstate thermalization hypothesis after a quantum quench.

PubMed

Mori, Takashi; Shiraishi, Naoto

2017-08-01

Nonequilibrium dynamics of a nonintegrable system without the eigenstate thermalization hypothesis is studied. It is shown that, in the thermodynamic limit, this model thermalizes after an arbitrary quantum quench at finite temperature, although it does not satisfy the eigenstate thermalization hypothesis. In contrast, when the system size is finite and the temperature is low enough, the system may not thermalize. In this case, the steady state is well described by the generalized Gibbs ensemble constructed by using highly nonlocal conserved quantities. We also show that this model exhibits prethermalization, in which the prethermalized state is characterized by nonthermal energy eigenstates.

Finite difference and Runge-Kutta methods for solving vibration problems

NASA Astrophysics Data System (ADS)

Lintang Renganis Radityani, Scolastika; Mungkasi, Sudi

2017-11-01

The vibration of a storey building can be modelled into a system of second order ordinary differential equations. If the number of floors of a building is large, then the result is a large scale system of second order ordinary differential equations. The large scale system is difficult to solve, and if it can be solved, the solution may not be accurate. Therefore, in this paper, we seek for accurate methods for solving vibration problems. We compare the performance of numerical finite difference and Runge-Kutta methods for solving large scale systems of second order ordinary differential equations. The finite difference methods include the forward and central differences. The Runge-Kutta methods include the Euler and Heun methods. Our research results show that the central finite difference and the Heun methods produce more accurate solutions than the forward finite difference and the Euler methods do.

Fault detection for singular switched linear systems with multiple time-varying delay in finite frequency domain

NASA Astrophysics Data System (ADS)

Zhai, Ding; Lu, Anyang; Li, Jinghao; Zhang, Qingling

2016-10-01

This paper deals with the problem of the fault detection (FD) for continuous-time singular switched linear systems with multiple time-varying delay. In this paper, the actuator fault is considered. Besides, the systems faults and unknown disturbances are assumed in known frequency domains. Some finite frequency performance indices are initially introduced to design the switched FD filters which ensure that the filtering augmented systems under switching signal with average dwell time are exponentially admissible and guarantee the fault input sensitivity and disturbance robustness. By developing generalised Kalman-Yakubovic-Popov lemma and using Parseval's theorem and Fourier transform, finite frequency delay-dependent sufficient conditions for the existence of such a filter which can guarantee the finite-frequency H- and H∞ performance are derived and formulated in terms of linear matrix inequalities. Four examples are provided to illustrate the effectiveness of the proposed finite frequency method.

Mechanical vibration testing of a tibia in vivo and finite element analysis of the shank resonant properties

NASA Astrophysics Data System (ADS)

Maslov, Leonid B.

2003-10-01

Recent clinical studies clearly indicate that the resonant frequencies can be used to assess the healing state of a fractured long bone. Although these studies clearly show a certain relation between the resonant frequencies and the stiffness of the bone, the nature of this relation has not yet studied very well. The attempt of considering the locomotion system of a human shank in complex is firstly presented in this paper. The finite element model of the soft and hard tissues composed of the human shank is developed and the vibration numerical analysis is performed. The values of the resonant frequencies for the isolated tibia and for the complex biomechanical system formed by tibia, fibula, achilles tendon and principal shank muscles are obtained during finite element analysis. The obtained result can be used as theoretical fundament to developing low-frequency resonant methods for testing and diagnostics of the physiological conditions of soft and hard tissue during medical treatment and rehabilitation time period after surgery operation.

The use of spectral methods in bidomain studies.

PubMed

Trayanova, N; Pilkington, T

1992-01-01

A Fourier transform method is developed for solving the bidomain coupled differential equations governing the intracellular and extracellular potentials on a finite sheet of cardiac cells undergoing stimulation. The spectral formulation converts the system of differential equations into a "diagonal" system of algebraic equations. Solving the algebraic equations directly and taking the inverse transform of the potentials proved numerically less expensive than solving the coupled differential equations by means of traditional numerical techniques, such as finite differences; the comparison between the computer execution times showed that the Fourier transform method was about 40 times faster than the finite difference method. By application of the Fourier transform method, transmembrane potential distributions in the two-dimensional myocardial slice were calculated. For a tissue characterized by a ratio of the intra- to extracellular conductivities that is different in all principal directions, the transmembrane potential distribution exhibits a rather complicated geometrical pattern. The influence of the different anisotropy ratios, the finite tissue size, and the stimuli configuration on the pattern of membrane polarization is investigated.

Observer-based robust finite time H∞ sliding mode control for Markovian switching systems with mode-dependent time-varying delay and incomplete transition rate.

PubMed

Gao, Lijun; Jiang, Xiaoxiao; Wang, Dandan

2016-03-01

This paper investigates the problem of robust finite time H∞ sliding mode control for a class of Markovian switching systems. The system is subjected to the mode-dependent time-varying delay, partly unknown transition rate and unmeasurable state. The main difficulty is that, a sliding mode surface cannot be designed based on the unknown transition rate and unmeasurable state directly. To overcome this obstacle, the set of modes is firstly divided into two subsets standing for known transition rate subset and unknown one, based on which a state observer is established. A component robust finite-time sliding mode controller is also designed to cope with the effect of partially unknown transition rate. It is illustrated that the reachability, finite-time stability, finite-time boundedness, finite-time H∞ state feedback stabilization of sliding mode dynamics can be ensured despite the unknown transition rate. Finally, the simulation results verify the effectiveness of robust finite time control problem. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Toric-boson model: Toward a topological quantum memory at finite temperature

NASA Astrophysics Data System (ADS)

Hamma, Alioscia; Castelnovo, Claudio; Chamon, Claudio

2009-06-01

We discuss the existence of stable topological quantum memory at finite temperature. At stake here is the fundamental question of whether it is, in principle, possible to store quantum information for macroscopic times without the intervention from the external world, that is, without error correction. We study the toric code in two dimensions with an additional bosonic field that couples to the defects, in the presence of a generic environment at finite temperature: the toric-boson model. Although the coupling constants for the bare model are not finite in the thermodynamic limit, the model has a finite spectrum. We show that in the topological phase, there is a finite temperature below which open strings are confined and therefore the lifetime of the memory can be made arbitrarily (polynomially) long in system size. The interaction with the bosonic field yields a long-range attractive force between the end points of open strings but leaves closed strings and topological order intact.

Use of system identification techniques for improving airframe finite element models using test data

NASA Technical Reports Server (NTRS)

Hanagud, Sathya V.; Zhou, Weiyu; Craig, James I.; Weston, Neil J.

1991-01-01

A method for using system identification techniques to improve airframe finite element models was developed and demonstrated. The method uses linear sensitivity matrices to relate changes in selected physical parameters to changes in total system matrices. The values for these physical parameters were determined using constrained optimization with singular value decomposition. The method was confirmed using both simple and complex finite element models for which pseudo-experimental data was synthesized directly from the finite element model. The method was then applied to a real airframe model which incorporated all the complexities and details of a large finite element model and for which extensive test data was available. The method was shown to work, and the differences between the identified model and the measured results were considered satisfactory.

Hybrid finite element and Brownian dynamics method for charged particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huber, Gary A., E-mail: ghuber@ucsd.edu; Miao, Yinglong; Zhou, Shenggao

2016-04-28

Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented usingmore » a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.« less

Further analytical study of hybrid rocket combustion

NASA Technical Reports Server (NTRS)

Hung, W. S. Y.; Chen, C. S.; Haviland, J. K.

1972-01-01

Analytical studies of the transient and steady-state combustion processes in a hybrid rocket system are discussed. The particular system chosen consists of a gaseous oxidizer flowing within a tube of solid fuel, resulting in a heterogeneous combustion. Finite rate chemical kinetics with appropriate reaction mechanisms were incorporated in the model. A temperature dependent Arrhenius type fuel surface regression rate equation was chosen for the current study. The governing mathematical equations employed for the reacting gas phase and for the solid phase are the general, two-dimensional, time-dependent conservation equations in a cylindrical coordinate system. Keeping the simplifying assumptions to a minimum, these basic equations were programmed for numerical computation, using two implicit finite-difference schemes, the Lax-Wendroff scheme for the gas phase, and, the Crank-Nicolson scheme for the solid phase.

The nature of the laning transition in two dimensions

NASA Astrophysics Data System (ADS)

Glanz, T.; Löwen, H.

2012-11-01

If a binary colloidal mixture is oppositely driven by an external field, a transition towards a laned state occurs at sufficiently large drives, where particles driven alike form elongated structures (‘lanes’) characterized by a large correlation length ξ along the drive. Here we perform extensive Brownian dynamics computer simulations on a two-dimensional equimolar binary Yukawa system driven by a constant force that acts oppositely on the two species. We systematically address finite-size effects on lane formation by exploring large systems up to 262 144 particles under various boundary conditions. It is found that the correlation length ξ along the field depends exponentially on the driving force (or Peclet number). Conversely, in a finite system, ξ reaches a fraction of the system size at a driving force which is logarithmic in the system size, implying massive finite-size corrections. For a fixed finite drive, ξ does not diverge in the thermodynamic limit. Therefore, though laning has a signature as a sharp transition in a finite system, it is a smooth crossover in the thermodynamic limit.

Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Aguanno, G.; Mattiucci, N.; C. M. Bowden Facility, Building 7804, RDECOM, Redstone Arsenal, Alabama 35898

2010-01-15

We have investigated and experimentally demonstrated the applicability of the Bloch vector for one-dimensional, nonlinear, finite, dissipative systems. The case studied is the second harmonic generation from metallodielectric multilayer filters. In particular, we have applied the Bloch vector analysis to Ag/Ta{sub 2}O{sub 5} thin-film multilayer samples and shown the importance of the phase matching calculated through the Bloch vector. The nonlinear coefficients extracted from experimental results are consistent with previous studies. Nowadays, metal-based nanostructures play a fundamental role in nonlinear nanophotonics and nanoplasmonics. Our results clearly suggest that even in these forefront fields the Bloch vector continues to play anmore » essential role.« less

Superfluid transition of homogeneous and trapped two-dimensional Bose gases.

PubMed

Holzmann, Markus; Baym, Gordon; Blaizot, Jean-Paul; Laloë, Franck

2007-01-30

Current experiments on atomic gases in highly anisotropic traps present the opportunity to study in detail the low temperature phases of two-dimensional inhomogeneous systems. Although, in an ideal gas, the trapping potential favors Bose-Einstein condensation at finite temperature, interactions tend to destabilize the condensate, leading to a superfluid Kosterlitz-Thouless-Berezinskii phase with a finite superfluid mass density but no long-range order, as in homogeneous fluids. The transition in homogeneous systems is conveniently described in terms of dissociation of topological defects (vortex-antivortex pairs). However, trapped two-dimensional gases are more directly approached by generalizing the microscopic theory of the homogeneous gas. In this paper, we first derive, via a diagrammatic expansion, the scaling structure near the phase transition in a homogeneous system, and then study the effects of a trapping potential in the local density approximation. We find that a weakly interacting trapped gas undergoes a Kosterlitz-Thouless-Berezinskii transition from the normal state at a temperature slightly below the Bose-Einstein transition temperature of the ideal gas. The characteristic finite superfluid mass density of a homogeneous system just below the transition becomes strongly suppressed in a trapped gas.

Numerical simulations of earthquakes and the dynamics of fault systems using the Finite Element method.

NASA Astrophysics Data System (ADS)

Kettle, L. M.; Mora, P.; Weatherley, D.; Gross, L.; Xing, H.

2006-12-01

Simulations using the Finite Element method are widely used in many engineering applications and for the solution of partial differential equations (PDEs). Computational models based on the solution of PDEs play a key role in earth systems simulations. We present numerical modelling of crustal fault systems where the dynamic elastic wave equation is solved using the Finite Element method. This is achieved using a high level computational modelling language, escript, available as open source software from ACcESS (Australian Computational Earth Systems Simulator), the University of Queensland. Escript is an advanced geophysical simulation software package developed at ACcESS which includes parallel equation solvers, data visualisation and data analysis software. The escript library was implemented to develop a flexible Finite Element model which reliably simulates the mechanism of faulting and the physics of earthquakes. Both 2D and 3D elastodynamic models are being developed to study the dynamics of crustal fault systems. Our final goal is to build a flexible model which can be applied to any fault system with user-defined geometry and input parameters. To study the physics of earthquake processes, two different time scales must be modelled, firstly the quasi-static loading phase which gradually increases stress in the system (~100years), and secondly the dynamic rupture process which rapidly redistributes stress in the system (~100secs). We will discuss the solution of the time-dependent elastic wave equation for an arbitrary fault system using escript. This involves prescribing the correct initial stress distribution in the system to simulate the quasi-static loading of faults to failure; determining a suitable frictional constitutive law which accurately reproduces the dynamics of the stick/slip instability at the faults; and using a robust time integration scheme. These dynamic models generate data and information that can be used for earthquake forecasting.

Application of finite-element methods to dynamic analysis of flexible spatial and co-planar linkage systems, part 2

NASA Technical Reports Server (NTRS)

Dubowsky, Steven

1989-01-01

An approach is described to modeling the flexibility effects in spatial mechanisms and manipulator systems. The method is based on finite element representations of the individual links in the system. However, it should be noted that conventional finite element methods and software packages will not handle the highly nonlinear dynamic behavior of these systems which results form their changing geometry. In order to design high-performance lightweight systems and their control systems, good models of their dynamic behavior which include the effects of flexibility are required.

A theoretical analysis and finite element simulation of fixator-bone system stiffness on healing progression.

PubMed

Li, Jianfeng; Zhao, Xia; Hu, Xiaojie; Tao, Chunjing; Ji, Run

2018-03-01

The unilateral external fixator has become a quick and easy application for fracture stabilization of the extremities; the main value for evaluation of mechanical stability of the external fixator is stiffness. The stiffness property of the external fixator affects the local biomechanical environment of fractured bone. In this study, a theoretical model with changing Young's modulus of the callus is established by using the Castigliano's theory, investigating compression stiffness, torsional stiffness and bending stiffness of the fixator-bone system during the healing process. The effects of pin deviation angle on three stiffness methods are also investigated. In addition, finite element simulation is discussed regarding the stress distribution between the fixator and bone. The results reveal the three stiffness evaluation methods are similar for the fixator-bone system. Finite element simulation shows that with increased healing time, the transmission of the load between the fixator and bone are different. In addition, the finite element analyses verify the conclusions obtained from the theoretical model. This work helps orthopedic doctors to monitor the progression of fracture healing and determine the appropriate time for removal of a fixation device and provide important theoretical methodology.

A collocation--Galerkin finite element model of cardiac action potential propagation.

PubMed

Rogers, J M; McCulloch, A D

1994-08-01

A new computational method was developed for modeling the effects of the geometric complexity, nonuniform muscle fiber orientation, and material inhomogeneity of the ventricular wall on cardiac impulse propagation. The method was used to solve a modification to the FitzHugh-Nagumo system of equations. The geometry, local muscle fiber orientation, and material parameters of the domain were defined using linear Lagrange or cubic Hermite finite element interpolation. Spatial variations of time-dependent excitation and recovery variables were approximated using cubic Hermite finite element interpolation, and the governing finite element equations were assembled using the collocation method. To overcome the deficiencies of conventional collocation methods on irregular domains, Galerkin equations for the no-flux boundary conditions were used instead of collocation equations for the boundary degrees-of-freedom. The resulting system was evolved using an adaptive Runge-Kutta method. Converged two-dimensional simulations of normal propagation showed that this method requires less CPU time than a traditional finite difference discretization. The model also reproduced several other physiologic phenomena known to be important in arrhythmogenesis including: Wenckebach periodicity, slowed propagation and unidirectional block due to wavefront curvature, reentry around a fixed obstacle, and spiral wave reentry. In a new result, we observed wavespeed variations and block due to nonuniform muscle fiber orientation. The findings suggest that the finite element method is suitable for studying normal and pathological cardiac activation and has significant advantages over existing techniques.

Diffusion with finite-helicity field tensor: A mechanism of generating heterogeneity

NASA Astrophysics Data System (ADS)

Sato, N.; Yoshida, Z.

2018-02-01

Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are nonholonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological constraints is the subject of this study. Conventional arguments based on phase spaces, Jacobi identity, invariant measure, or the H theorem are no longer applicable since all these notions stem from the symplectic geometry underlying canonical Hamiltonian systems. Remembering that Hamiltonian systems are endowed with field tensors (canonical 2-forms) that have zero helicity, our mission is to extend the scope toward the class of systems governed by finite-helicity field tensors. Here, we introduce a class of field tensors that are characterized by Beltrami vectors. We prove an H theorem for this Beltrami class. The most general class of energy-conserving systems are non-Beltrami, for which we identify the "field charge" that prevents the entropy to maximize, resulting in creation of heterogeneous distributions. The essence of the theory can be delineated by classifying three-dimensional dynamics. We then generalize to arbitrary (finite) dimensions.

Phase Transitions in Finite Systems

NASA Astrophysics Data System (ADS)

Chomaz, Philippe; Gulminelli, Francesca

In this series of lectures we will first review the general theory of phase transition in the framework of information theory and briefly address some of the well known mean field solutions of three dimensional problems. The theory of phase transitions in finite systems will then be discussed, with a special emphasis to the conceptual problems linked to a thermodynamical description for small, short-lived, open systems as metal clusters and data samples coming from nuclear collisions. The concept of negative heat capacity developed in the early seventies in the context of self-gravitating systems will be reinterpreted in the general framework of convexity anomalies of thermostatistical potentials. The connection with the distribution of the order parameter will lead us to a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. Finally a careful study of the thermodynamical limit will provide a bridge with the standard theory of phase transitions and show that in a wide class of physical situations the different statistical ensembles are irreducibly inequivalent.

Early Breakdown of Area-Law Entanglement at the Many-Body Delocalization Transition

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Singh, Rajiv R. P.

2015-10-01

We introduce the numerical linked cluster expansion as a controlled numerical tool for the study of the many-body localization transition in a disordered system with continuous nonperturbative disorder. Our approach works directly in the thermodynamic limit, in any spatial dimension, and does not rely on any finite size scaling procedure. We study the onset of many-body delocalization through the breakdown of area-law entanglement in a generic many-body eigenstate. By looking for initial signs of an instability of the localized phase, we obtain a value for the critical disorder, which we believe should be a lower bound for the true value, that is higher than current best estimates from finite size studies. This implies that most current methods tend to overestimate the extent of the localized phase due to finite size effects making the localized phase appear stable at small length scales. We also study the mobility edge in these systems as a function of energy density, and we find that our conclusion is the same at all examined energies.

Method to study complex systems of mesons in lattice QCD

DOE PAGES

Detmold, William; Savage, Martin J.

2010-07-30

Correlation functions involving many hadrons allow finite density systems to be explored with Lattice QCD. Recently, systems with up to 12more » $$\\pi^+$$'s or $K^+$'s have been studied to determine the the $3$-$$\\pi^+$$ and $3$-$K^+$ interactions and the corresponding chemical potential has been determined as a function of density in each case. We derive recursion relations between correlation functions that allow us to extend this work to systems of arbitrary numbers of mesons and to systems containing arbitrary different types of mesons such as $$\\pi^+$$'s, $K^+$'s, $D^0$'s and $B^+$'s. These relations allow for the study of finite-density systems in arbitrary volumes, and the study of high-density systems. Systems comprised of up to N=12 m mesons can be explored with Lattice QCD calculations utilizing $m$ different sources for the quark propagators. As the recursion relations require only a small, N-independent, number of operations to derive the N+1 meson contractions from the N meson contractions, they are compuationally feasible.« less

Singularity formations for a surface wave model

NASA Astrophysics Data System (ADS)

Castro, Angel; Córdoba, Diego; Gancedo, Francisco

2010-11-01

In this paper we study the Burgers equation with a nonlocal term of the form Hu where H is the Hilbert transform. This system has been considered as a quadratic approximation for the dynamics of a free boundary of a vortex patch (see Biello and Hunter 2010 Commun. Pure Appl. Math. LXIII 0303-36 Marsden and Weinstein 1983 Physica D 7 305-23). We prove blowup in finite time for a large class of initial data with finite energy. Considering a more general nonlocal term, of the form ΛαHu for 0 < α < 1, finite time singularity formation is also shown.

Use of system identification techniques for improving airframe finite element models using test data

NASA Technical Reports Server (NTRS)

Hanagud, Sathya V.; Zhou, Weiyu; Craig, James I.; Weston, Neil J.

1993-01-01

A method for using system identification techniques to improve airframe finite element models using test data was developed and demonstrated. The method uses linear sensitivity matrices to relate changes in selected physical parameters to changes in the total system matrices. The values for these physical parameters were determined using constrained optimization with singular value decomposition. The method was confirmed using both simple and complex finite element models for which pseudo-experimental data was synthesized directly from the finite element model. The method was then applied to a real airframe model which incorporated all of the complexities and details of a large finite element model and for which extensive test data was available. The method was shown to work, and the differences between the identified model and the measured results were considered satisfactory.

A software platform for continuum modeling of ion channels based on unstructured mesh

NASA Astrophysics Data System (ADS)

Tu, B.; Bai, S. Y.; Chen, M. X.; Xie, Y.; Zhang, L. B.; Lu, B. Z.

2014-01-01

Most traditional continuum molecular modeling adopted finite difference or finite volume methods which were based on a structured mesh (grid). Unstructured meshes were only occasionally used, but an increased number of applications emerge in molecular simulations. To facilitate the continuum modeling of biomolecular systems based on unstructured meshes, we are developing a software platform with tools which are particularly beneficial to those approaches. This work describes the software system specifically for the simulation of a typical, complex molecular procedure: ion transport through a three-dimensional channel system that consists of a protein and a membrane. The platform contains three parts: a meshing tool chain for ion channel systems, a parallel finite element solver for the Poisson-Nernst-Planck equations describing the electrodiffusion process of ion transport, and a visualization program for continuum molecular modeling. The meshing tool chain in the platform, which consists of a set of mesh generation tools, is able to generate high-quality surface and volume meshes for ion channel systems. The parallel finite element solver in our platform is based on the parallel adaptive finite element package PHG which wass developed by one of the authors [1]. As a featured component of the platform, a new visualization program, VCMM, has specifically been developed for continuum molecular modeling with an emphasis on providing useful facilities for unstructured mesh-based methods and for their output analysis and visualization. VCMM provides a graphic user interface and consists of three modules: a molecular module, a meshing module and a numerical module. A demonstration of the platform is provided with a study of two real proteins, the connexin 26 and hemolysin ion channels.

Mechanical topological insulator in zero dimensions

NASA Astrophysics Data System (ADS)

Lera, Natalia; Alvarez, J. V.

2018-04-01

We study linear vibrational modes in finite isostatic Maxwell lattices, mechanical systems where the number of degrees of freedom matches the number of constraints. Recent progress in topological mechanics exploits the nontrivial topology of BDI class Hamiltonians in one dimenson and arising topological floppy modes at the edges. A finite frame, or zero-dimensional system, also exhibits a nonzero topological index according to the classification table. We construct mechanical insulating models in zero dimensions that complete the BDI classification in the available real space dimensions. We compute and interpret its nontrivial invariant Z2.

Finite-time consensus for multi-agent systems with globally bounded convergence time under directed communication graphs

NASA Astrophysics Data System (ADS)

Fu, Junjie; Wang, Jin-zhi

2017-09-01

In this paper, we study the finite-time consensus problems with globally bounded convergence time also known as fixed-time consensus problems for multi-agent systems subject to directed communication graphs. Two new distributed control strategies are proposed such that leaderless and leader-follower consensus are achieved with convergence time independent on the initial conditions of the agents. Fixed-time formation generation and formation tracking problems are also solved as the generalizations. Simulation examples are provided to demonstrate the performance of the new controllers.

Eroding dipoles and vorticity growth for Euler flows in {{{R}}}^{3}: the hairpin geometry as a model for finite-time blowup

NASA Astrophysics Data System (ADS)

Childress, Stephen; Gilbert, Andrew D.

2018-02-01

A theory of an eroding ‘hairpin’ vortex dipole structure in three-dimensions is developed, extending our previous study of an axisymmetric eroding dipole without swirl. The axisymmetric toroidal dipole was found to lead to maximal growth of vorticity, as {t}4/3. The hairpin is here similarly proposed as a model to produce large ‘self-stretching’ of vorticity, with the possibility of finite-time blow-up. We derive a system of partial differential equations of ‘generalized’ form, involving contour averaging of a locally two-dimensional Euler flow. We do not attempt here to solve the system exactly, but point out that non-existence of physically acceptable solutions would most probably be a result of the axial flow. Because of the axial flow the vorticity distribution within the dipole eddies is no longer of the simple Sadovskii type (vorticity constant over a cross-section) obtained in the axisymmetric problem. Thus the solution of the system depends upon the existence of a larger class of propagating two-dimensional dipoles. The hairpin model is obtained by formal asymptotic analysis. As in the axisymmetric problem a local transformation to ‘shrinking’ coordinates is introduced, but now in a self-similar form appropriate to the study of a possible finite-time singularity. We discuss some properties of the model, including a study of the helicity and a first step in iterating toward a solution from the Sadovskii structure. We also present examples of two-dimensional propagating dipoles not previously studied, which have a vorticity profile consistent with our model. Although no rigorous results can be given, and analysis of the system is only partial, the formal calculations are consistent with the possibility of a finite time blowup of vorticity at a point of vanishing circulation of the dipole eddies, but depending upon the existence of the necessary two-dimensional propagating dipole. Our results also suggest that conservation of kinetic energy as realized in the eroding hairpin excludes a finite time blowup for the corresponding Navier-Stokes model.

Finite-time H∞ filtering for non-linear stochastic systems

NASA Astrophysics Data System (ADS)

Hou, Mingzhe; Deng, Zongquan; Duan, Guangren

2016-09-01

This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

Viscoelastic finite element analysis of residual stresses in porcelain-veneered zirconia dental crowns.

PubMed

Kim, Jeongho; Dhital, Sukirti; Zhivago, Paul; Kaizer, Marina R; Zhang, Yu

2018-06-01

The main problem of porcelain-veneered zirconia (PVZ) dental restorations is chipping and delamination of veneering porcelain owing to the development of deleterious residual stresses during the cooling phase of veneer firing. The aim of this study is to elucidate the effects of cooling rate, thermal contraction coefficient and elastic modulus on residual stresses developed in PVZ dental crowns using viscoelastic finite element methods (VFEM). A three-dimensional VFEM model has been developed to predict residual stresses in PVZ structures using ABAQUS finite element software and user subroutines. First, the newly established model was validated with experimentally measured residual stress profiles using Vickers indentation on flat PVZ specimens. An excellent agreement between the model prediction and experimental data was found. Then, the model was used to predict residual stresses in more complex anatomically-correct crown systems. Two PVZ crown systems with different thermal contraction coefficients and porcelain moduli were studied: VM9/Y-TZP and LAVA/Y-TZP. A sequential dual-step finite element analysis was performed: heat transfer analysis and viscoelastic stress analysis. Controlled and bench convection cooling rates were simulated by applying different convective heat transfer coefficients 1.7E-5 W/mm 2 °C (controlled cooling) and 0.6E-4 W/mm 2 °C (bench cooling) on the crown surfaces exposed to the air. Rigorous viscoelastic finite element analysis revealed that controlled cooling results in lower maximum stresses in both veneer and core layers for the two PVZ systems relative to bench cooling. Better compatibility of thermal contraction coefficients between porcelain and zirconia and a lower porcelain modulus reduce residual stresses in both layers. Copyright © 2018 Elsevier Ltd. All rights reserved.

PRELIMINARY PROGRESS IN THE DEVELOPMENT OF DUCTILE-PHASE TOUGHENED TUNGSTEN FOR PLASMA-FACING MATERIALS: DUAL-PHASE FINITE ELEMENT DAMAGE MODELS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Henager, Charles H.; Nguyen, Ba Nghiep; Kurtz, Richard J.

The objective of this study is to develop a finite element continuum damage model suitable for modeling deformation, cracking, and crack bridging for W-Cu, W-Ni-Fe, and other ductile phase toughened W-composites, or more generally, any multi-phase composite structure where two or more phases undergo cooperative deformation in a composite system.

Finite-dimensional integrable systems: A collection of research problems

NASA Astrophysics Data System (ADS)

Bolsinov, A. V.; Izosimov, A. M.; Tsonev, D. M.

2017-05-01

This article suggests a series of problems related to various algebraic and geometric aspects of integrability. They reflect some recent developments in the theory of finite-dimensional integrable systems such as bi-Poisson linear algebra, Jordan-Kronecker invariants of finite dimensional Lie algebras, the interplay between singularities of Lagrangian fibrations and compatible Poisson brackets, and new techniques in projective geometry.

Conservative properties of finite difference schemes for incompressible flow

NASA Technical Reports Server (NTRS)

Morinishi, Youhei

1995-01-01

The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.

Role of relaxation and time-dependent formation of x-ray spectra

NASA Astrophysics Data System (ADS)

Privalov, Timofei; Gel'mukhanov, Faris; Ågren, Hans

2001-10-01

A fundamental problem of x-ray spectroscopy is the role of relaxation of the electronic subsystem in the field of the transient core hole. The main intention of the present study is to explore the dynamics due to core-hole relaxation in the whole time domain, and to find out how it is manifested in finite molecular systems in comparison with solids. A technique is developed based on a reduction of the Noziéres-De Dominicis equation to a set of linear algebraic equations. The developed time-dependent formalism is applied to a numerical investigation of a one-dimensional tight-binding model. The formation of the x-ray profiles is explored on the real time scale, and the role of interaction with the core hole, band filling, and the final-state rule are investigated for systems of different size. The formation of spectra of the infinite translational invariant system is studied by extensions of the finite systems. We found that the dynamics of finite systems, like molecules, differs qualitatively from solids: Contrary to the latter the time lapse of the Noziéres-De Dominicis domain for finite systems is squeezed between the inverse bandwidth and the revival time, which is proportional to the system size. For small molecules this means that there is no time for a ``Mahan-Noziéres-De Dominicis singularity'' to develop. Comparison with the strict solution of the Noziéres-De Dominicis equation shows that the adiabatic approximation describes x-ray absorption and emission considerably better than the fast approximation. This explains the suppression of the relaxation effects in x-ray emission of, e.g., gas phase and surface adsorbed molecules, but also that these effects are essential for the absorption case. There is still a quantitative distinction between the adiabatic approximation and the strict approach, which becomes more important for larger systems. Adopting the so-called finite state rule by von Barth and Grossman also for molecules, an almost complete numerical agreement between this rule and the strict x-ray-absorption and emission profiles for systems of different sizes is obtained. The simulations indicate that the final-state rule correction is important mainly near the absorption edge and at the top of the emission band.

[Application of finite element method in spinal biomechanics].

PubMed

Liu, Qiang; Zhang, Jun; Sun, Shu-Chun; Wang, Fei

2017-02-25

The finite element model is one of the most important methods in study of modern spinal biomechanics, according to the needs to simulate the various states of the spine, calculate the stress force and strain distribution of the different groups in the state, and explore its principle of mechanics, mechanism of injury, and treatment effectiveness. In addition, in the study of the pathological state of the spine, the finite element is mainly used in the understanding the mechanism of lesion location, evaluating the effects of different therapeutic tool, assisting and completing the selection and improvement of therapeutic tool, in order to provide a theoretical basis for the rehabilitation of spinal lesions. Finite element method can be more provide the service for the patients suffering from spinal correction, operation and individual implant design. Among the design and performance evaluation of the implant need to pay attention to the individual difference and perfect the evaluation system. At present, how to establish a model which is more close to the real situation has been the focus and difficulty of the study of human body's finite element.Although finite element method can better simulate complex working condition, it is necessary to improve the authenticity of the model and the sharing of the group by using many kinds of methods, such as image science, statistics, kinematics and so on. Copyright© 2017 by the China Journal of Orthopaedics and Traumatology Press.

Stability analysis and backward whirl investigation of cracked rotors with time-varying stiffness

NASA Astrophysics Data System (ADS)

AL-Shudeifat, Mohammad A.

2015-07-01

The dynamic stability of dynamical systems with time-periodic stiffness is addressed here. Cracked rotor systems with time-periodic stiffness are well-known examples of such systems. Time-varying area moments of inertia at the cracked element cross-section of a cracked rotor have been used to formulate the time-periodic finite element stiffness matrix. The semi-infinite coefficient matrix obtained by applying the harmonic balance (HB) solution to the finite element (FE) equations of motion is employed here to study the dynamic stability of the system. Consequently, the sign of the determinant of a scaled version of a sub-matrix of this semi-infinite coefficient matrix at a finite number of harmonics in the HB solution is found to be sufficient for identifying the major unstable zones of the system in the parameter plane. Specifically, it is found that the negative determinant always corresponds to unstable zones in all of the systems considered. This approach is applied to a parametrically excited Mathieu's equation, a two degree-of-freedom linear time-periodic dynamical system, a cracked Jeffcott rotor and a finite element model of the cracked rotor system. Compared to the corresponding results obtained by Floquet's theory, the sign of the determinant of the scaled sub-matrix is found to be an efficient tool for identifying the major unstable zones of the linear time-periodic parametrically excited systems, especially large-scale FE systems. Moreover, it is found that the unstable zones for a FE cracked rotor with an open transverse crack model only appear at the backward whirl. The theoretical and experimental results have been found to agree well for verifying that the open crack model excites the backward whirl amplitudes at the critical backward whirling rotational speeds.

Measuring finite-range phase coherence in an optical lattice using Talbot interferometry

PubMed Central

Santra, Bodhaditya; Baals, Christian; Labouvie, Ralf; Bhattacherjee, Aranya B.; Pelster, Axel; Ott, Herwig

2017-01-01

One of the important goals of present research is to control and manipulate coherence in a broad variety of systems, such as semiconductor spintronics, biological photosynthetic systems, superconducting qubits and complex atomic networks. Over the past decades, interferometry of atoms and molecules has proven to be a powerful tool to explore coherence. Here we demonstrate a near-field interferometer based on the Talbot effect, which allows us to measure finite-range phase coherence of ultracold atoms in an optical lattice. We apply this interferometer to study the build-up of phase coherence after a quantum quench of a Bose–Einstein condensate residing in a one-dimensional optical lattice. Our technique of measuring finite-range phase coherence is generic, easy to adopt and can be applied in practically all lattice experiments without further modifications. PMID:28580941

Excitations in the Yang–Gaudin Bose gas

DOE PAGES

Robinson, Neil J.; Konik, Robert M.

2017-06-01

Here, we study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang–Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at 2k F and a finite-momentum roton-like minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as 1/L for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the 2k F gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang–Gaudin Bose gas is also host to multi-spinon bound states, known asmore » $$\\Lambda$$ -strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length n $$\\Lambda$$-string dressed energies $$\\epsilon_n(\\lambda)$$ and the dressed energy $$\\epsilon(k)$$. We solve the Yang–Yang–Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length n $$\\Lambda$$ -string dressed energy is Lorentzian over a wide range of real string centers λ in the vicinity of $$\\lambda = 0$$ . We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Robinson, Neil J.; Konik, Robert M.

Here, we study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang–Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at 2k F and a finite-momentum roton-like minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as 1/L for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the 2k F gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang–Gaudin Bose gas is also host to multi-spinon bound states, known asmore » $$\\Lambda$$ -strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length n $$\\Lambda$$-string dressed energies $$\\epsilon_n(\\lambda)$$ and the dressed energy $$\\epsilon(k)$$. We solve the Yang–Yang–Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length n $$\\Lambda$$ -string dressed energy is Lorentzian over a wide range of real string centers λ in the vicinity of $$\\lambda = 0$$ . We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations.« less

One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Blackwell, Ben F.; Edwards, Jack R.

2007-01-01

The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.

The dynamics of discrete-time computation, with application to recurrent neural networks and finite state machine extraction.

PubMed

Casey, M

1996-08-15

Recurrent neural networks (RNNs) can learn to perform finite state computations. It is shown that an RNN performing a finite state computation must organize its state space to mimic the states in the minimal deterministic finite state machine that can perform that computation, and a precise description of the attractor structure of such systems is given. This knowledge effectively predicts activation space dynamics, which allows one to understand RNN computation dynamics in spite of complexity in activation dynamics. This theory provides a theoretical framework for understanding finite state machine (FSM) extraction techniques and can be used to improve training methods for RNNs performing FSM computations. This provides an example of a successful approach to understanding a general class of complex systems that has not been explicitly designed, e.g., systems that have evolved or learned their internal structure.

A Finite-Volume "Shaving" Method for Interfacing NASA/DAO''s Physical Space Statistical Analysis System to the Finite-Volume GCM with a Lagrangian Control-Volume Vertical Coordinate

NASA Technical Reports Server (NTRS)

Lin, Shian-Jiann; DaSilva, Arlindo; Atlas, Robert (Technical Monitor)

2001-01-01

Toward the development of a finite-volume Data Assimilation System (fvDAS), a consistent finite-volume methodology is developed for interfacing the NASA/DAO's Physical Space Statistical Analysis System (PSAS) to the joint NASA/NCAR finite volume CCM3 (fvCCM3). To take advantage of the Lagrangian control-volume vertical coordinate of the fvCCM3, a novel "shaving" method is applied to the lowest few model layers to reflect the surface pressure changes as implied by the final analysis. Analysis increments (from PSAS) to the upper air variables are then consistently put onto the Lagrangian layers as adjustments to the volume-mean quantities during the analysis cycle. This approach is demonstrated to be superior to the conventional method of using independently computed "tendency terms" for surface pressure and upper air prognostic variables.

Cranking of Nuclei at Finite Temperature:

NASA Astrophysics Data System (ADS)

Bartel, J.; Bencheikh, K.; Quentin, P.

We present a generalization of the Extended Thomas Fermi (ETF) theory to fermionic systems at finite temperature and finite angular momentum. In fact the present approach is more general in the sense that it is able to treat an excited system of fermions subject to an external vector field which in the case of nuclear rotations, developed more extensively here, is simply ěc{r}×ěc{ω }.

Nonlinear Control Systems

DTIC Science & Technology

2007-03-01

Finite -dimensional regulators for a class of infinite dimensional systems ,” Systems and Control Letters, 3 (1983), 7-12. [11] B...semiglobal stabilizability by encoded state feedback,” to appear in Systems and Control Letters. 22 29. C. De Persis, A. Isidori, “Global stabilization of...nonequilibrium setting, for both finite and infinite dimensional control systems . Our objectives for distributed parameter systems included

Finite-size effects in simulations of electrolyte solutions under periodic boundary conditions

NASA Astrophysics Data System (ADS)

Thompson, Jeffrey; Sanchez, Isaac

The equilibrium properties of charged systems with periodic boundary conditions may exhibit pronounced system-size dependence due to the long range of the Coulomb force. As shown by others, the leading-order finite-size correction to the Coulomb energy of a charged fluid confined to a periodic box of volume V may be derived from sum rules satisfied by the charge-charge correlations in the thermodynamic limit V -> ∞ . In classical systems, the relevant sum rule is the Stillinger-Lovett second-moment (or perfect screening) condition. This constraint implies that for large V, periodicity induces a negative bias of -kB T(2 V) - 1 in the total Coulomb energy density of a homogeneous classical charged fluid of given density and temperature. We present a careful study of the impact of such finite-size effects on the calculation of solute chemical potentials from explicit-solvent molecular simulations of aqueous electrolyte solutions. National Science Foundation Graduate Research Fellowship Program, Grant No. DGE-1610403.

Dynamics of cochlear nonlinearity: Automatic gain control or instantaneous damping?

PubMed

Altoè, Alessandro; Charaziak, Karolina K; Shera, Christopher A

2017-12-01

Measurements of basilar-membrane (BM) motion show that the compressive nonlinearity of cochlear mechanical responses is not an instantaneous phenomenon. For this reason, the cochlear amplifier has been thought to incorporate an automatic gain control (AGC) mechanism characterized by a finite reaction time. This paper studies the effect of instantaneous nonlinear damping on the responses of oscillatory systems. The principal results are that (i) instantaneous nonlinear damping produces a noninstantaneous gain control that differs markedly from typical AGC strategies; (ii) the kinetics of compressive nonlinearity implied by the finite reaction time of an AGC system appear inconsistent with the nonlinear dynamics measured on the gerbil basilar membrane; and (iii) conversely, those nonlinear dynamics can be reproduced using an harmonic oscillator with instantaneous nonlinear damping. Furthermore, existing cochlear models that include instantaneous gain-control mechanisms capture the principal kinetics of BM nonlinearity. Thus, an AGC system with finite reaction time appears neither necessary nor sufficient to explain nonlinear gain control in the cochlea.

A locally conservative stabilized continuous Galerkin finite element method for two-phase flow in poroelastic subsurfaces

NASA Astrophysics Data System (ADS)

Deng, Q.; Ginting, V.; McCaskill, B.; Torsu, P.

2017-10-01

We study the application of a stabilized continuous Galerkin finite element method (CGFEM) in the simulation of multiphase flow in poroelastic subsurfaces. The system involves a nonlinear coupling between the fluid pressure, subsurface's deformation, and the fluid phase saturation, and as such, we represent this coupling through an iterative procedure. Spatial discretization of the poroelastic system employs the standard linear finite element in combination with a numerical diffusion term to maintain stability of the algebraic system. Furthermore, direct calculation of the normal velocities from pressure and deformation does not entail a locally conservative field. To alleviate this drawback, we propose an element based post-processing technique through which local conservation can be established. The performance of the method is validated through several examples illustrating the convergence of the method, the effectivity of the stabilization term, and the ability to achieve locally conservative normal velocities. Finally, the efficacy of the method is demonstrated through simulations of realistic multiphase flow in poroelastic subsurfaces.

Optimal least-squares finite element method for elliptic problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Povinelli, Louis A.

1991-01-01

An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

Adaptive disturbance compensation finite control set optimal control for PMSM systems based on sliding mode extended state observer

NASA Astrophysics Data System (ADS)

Wu, Yun-jie; Li, Guo-fei

2018-01-01

Based on sliding mode extended state observer (SMESO) technique, an adaptive disturbance compensation finite control set optimal control (FCS-OC) strategy is proposed for permanent magnet synchronous motor (PMSM) system driven by voltage source inverter (VSI). So as to improve robustness of finite control set optimal control strategy, a SMESO is proposed to estimate the output-effect disturbance. The estimated value is fed back to finite control set optimal controller for implementing disturbance compensation. It is indicated through theoretical analysis that the designed SMESO could converge in finite time. The simulation results illustrate that the proposed adaptive disturbance compensation FCS-OC possesses better dynamical response behavior in the presence of disturbance.

Charging and hybridization in the finite cluster model

NASA Technical Reports Server (NTRS)

Bauschlicher, C. W., Jr.; Bagus, P. S.; Nelin, C. J.

1984-01-01

Cluster wavefunctions which have appropriate hybridization and polarization lead to reasonable properties for the interaction of an adsorbate with a solid surface. However, for Al clusters, it was found that the atomic change distribution is not uniform. The finite cluster size leads to changes not representative for an extended system. This effect appears to be dependent on the particular materials being studied; it does not occur in all cases.

Finite temperature grand canonical ensemble study of the minimum electrophilicity principle.

PubMed

Miranda-Quintana, Ramón Alain; Chattaraj, Pratim K; Ayers, Paul W

2017-09-28

We analyze the minimum electrophilicity principle of conceptual density functional theory using the framework of the finite temperature grand canonical ensemble. We provide support for this principle, both for the cases of systems evolving from a non-equilibrium to an equilibrium state and for the change from one equilibrium state to another. In doing so, we clearly delineate the cases where this principle can, or cannot, be used.

Lie-Hamilton systems on the plane: Properties, classification and applications

NASA Astrophysics Data System (ADS)

Ballesteros, A.; Blasco, A.; Herranz, F. J.; de Lucas, J.; Sardón, C.

2015-04-01

We study Lie-Hamilton systems on the plane, i.e. systems of first-order differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional real Lie algebra of planar Hamiltonian vector fields with respect to a Poisson structure. We start with the local classification of finite-dimensional real Lie algebras of vector fields on the plane obtained in González-López, Kamran, and Olver (1992) [23] and we interpret their results as a local classification of Lie systems. By determining which of these real Lie algebras consist of Hamiltonian vector fields relative to a Poisson structure, we provide the complete local classification of Lie-Hamilton systems on the plane. We present and study through our results new Lie-Hamilton systems of interest which are used to investigate relevant non-autonomous differential equations, e.g. we get explicit local diffeomorphisms between such systems. We also analyse biomathematical models, the Milne-Pinney equations, second-order Kummer-Schwarz equations, complex Riccati equations and Buchdahl equations.

Study on the adjustment capability of the excitation system located inside superconducting machine electromagnetic shield

NASA Astrophysics Data System (ADS)

Xia, D.; Xia, Z.

2017-12-01

The ability for the excitation system to adjust quickly plays a very important role in maintaining the normal operation of superconducting machines and power systems. However, the eddy currents in the electromagnetic shield of superconducting machines hinder the exciting magnetic field change and weaken the adjustment capability of the excitation system. To analyze this problem, a finite element calculation model for the transient electromagnetic field with moving parts is established. The effects of three different electromagnetic shields on the exciting magnetic field are analyzed using finite element method. The results show that the electromagnetic shield hinders the field changes significantly, the better its conductivity, the greater the effect on the superconducting machine excitation.

A Large Scale Dynamical System Immune Network Modelwith Finite Connectivity

NASA Astrophysics Data System (ADS)

Uezu, T.; Kadono, C.; Hatchett, J.; Coolen, A. C. C.

We study a model of an idiotypic immune network which was introduced by N. K. Jerne. It is known that in immune systems there generally exist several kinds of immune cells which can recognize any particular antigen. Taking this fact into account and assuming that each cell interacts with only a finite number of other cells, we analyze a large scale immune network via both numerical simulations and statistical mechanical methods, and show that the distribution of the concentrations of antibodies becomes non-trivial for a range of values of the strength of the interaction and the connectivity.

Concurrent design of an RTP chamber and advanced control system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spence, P.; Schaper, C.; Kermani, A.

1995-12-31

A concurrent-engineering approach is applied to the development of an axisymmetric rapid-thermal-processing (RTP) reactor and its associated temperature controller. Using a detailed finite-element thermal model as a surrogate for actual hardware, the authors have developed and tested a multi-input multi-output (MIMO) controller. Closed-loop simulations are performed by linking the control algorithm with the finite-element code. Simulations show that good temperature uniformity is maintained on the wafer during both steady and transient conditions. A numerical study shows the effect of ramp rate, feedback gain, sensor placement, and wafer-emissivity patterns on system performance.

Properties of highly frustrated magnetic molecules studied by the finite-temperature Lanczos method

NASA Astrophysics Data System (ADS)

Schnack, J.; Wendland, O.

2010-12-01

The very interesting magnetic properties of frustrated magnetic molecules are often hardly accessible due to the prohibitive size of the related Hilbert spaces. The finite-temperature Lanczos method is able to treat spin systems for Hilbert space sizes up to 109. Here we first demonstrate for exactly solvable systems that the method is indeed accurate. Then we discuss the thermal properties of one of the biggest magnetic molecules synthesized to date, the icosidodecahedron with antiferromagnetically coupled spins of s = 1/2. We show how genuine quantum features such as the magnetization plateau behave as a function of temperature.

Finite-size scaling of eigenstate thermalization

NASA Astrophysics Data System (ADS)

Beugeling, W.; Moessner, R.; Haque, Masudul

2014-04-01

According to the eigenstate thermalization hypothesis (ETH), even isolated quantum systems can thermalize because the eigenstate-to-eigenstate fluctuations of typical observables vanish in the limit of large systems. Of course, isolated systems are by nature finite and the main way of computing such quantities is through numerical evaluation for finite-size systems. Therefore, the finite-size scaling of the fluctuations of eigenstate expectation values is a central aspect of the ETH. In this work, we present numerical evidence that for generic nonintegrable systems these fluctuations scale with a universal power law D-1/2 with the dimension D of the Hilbert space. We provide heuristic arguments, in the same spirit as the ETH, to explain this universal result. Our results are based on the analysis of three families of models and several observables for each model. Each family includes integrable members and we show how the system size where the universal power law becomes visible is affected by the proximity to integrability.

Distributed finite-time trajectory tracking control for multiple nonholonomic mobile robots with uncertainties and external disturbances

NASA Astrophysics Data System (ADS)

Ou, Meiying; Sun, Haibin; Gu, Shengwei; Zhang, Yangyi

2017-11-01

This paper investigates the distributed finite-time trajectory tracking control for a group of nonholonomic mobile robots with time-varying unknown parameters and external disturbances. At first, the tracking error system is derived for each mobile robot with the aid of a global invertible transformation, which consists of two subsystems, one is a first-order subsystem and another is a second-order subsystem. Then, the two subsystems are studied respectively, and finite-time disturbance observers are proposed for each robot to estimate the external disturbances. Meanwhile, distributed finite-time tracking controllers are developed for each mobile robot such that all states of each robot can reach the desired value in finite time, where the desired reference value is assumed to be the trajectory of a virtual leader whose information is available to only a subset of the followers, and the followers are assumed to have only local interaction. The effectiveness of the theoretical results is finally illustrated by numerical simulations.

Post-1906 stress recovery of the San Andreas fault system calculated from three-dimensional finite element analysis

USGS Publications Warehouse

Parsons, T.

2002-01-01

The M = 7.8 1906 San Francisco earthquake cast a stress shadow across the San Andreas fault system, inhibiting other large earthquakes for at least 75 years. The duration of the stress shadow is a key question in San Francisco Bay area seismic hazard assessment. This study presents a three-dimensional (3-D) finite element simulation of post-1906 stress recovery. The model reproduces observed geologic slip rates on major strike-slip faults and produces surface velocity vectors comparable to geodetic measurements. Fault stressing rates calculated with the finite element model are evaluated against numbers calculated using deep dislocation slip. In the finite element model, tectonic stressing is distributed throughout the crust and upper mantle, whereas tectonic stressing calculated with dislocations is focused mostly on faults. In addition, the finite element model incorporates postseismic effects such as deep afterslip and viscoelastic relaxation in the upper mantle. More distributed stressing and postseismic effects in the finite element model lead to lower calculated tectonic stressing rates and longer stress shadow durations (17-74 years compared with 7-54 years). All models considered indicate that the 1906 stress shadow was completely erased by tectonic loading no later than 1980. However, the stress shadow still affects present-day earthquake probability. Use of stressing rate parameters calculated with the finite element model yields a 7-12% reduction in 30-year probability caused by the 1906 stress shadow as compared with calculations not incorporating interactions. The aggregate interaction-based probability on selected segments (not including the ruptured San Andreas fault) is 53-70% versus the noninteraction range of 65-77%.

Ion sound instability driven by the ion flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koshkarov, O., E-mail: koshkarov.alexandr@usask.ca; Smolyakov, A. I.; National Research Centre

2015-05-15

Ion sound instabilities driven by the ion flow in a system of a finite length are considered by analytical and numerical methods. The ion sound waves are modified by the presence of stationary ion flow resulting in negative and positive energy modes. The instability develops due to coupling of negative and positive energy modes mediated by reflections from the boundary. It is shown that the wave dispersion due to deviation from quasineutrality is crucial for the stability. In finite length system, the dispersion is characterized by the length of the system measured in units of the Debye length. The instabilitymore » is studied analytically and the results are compared with direct, initial value numerical simulations.« less

Finite-element solutions for geothermal systems

NASA Technical Reports Server (NTRS)

Chen, J. C.; Conel, J. E.

1977-01-01

Vector potential and scalar potential are used to formulate the governing equations for a single-component and single-phase geothermal system. By assuming an initial temperature field, the fluid velocity can be determined which, in turn, is used to calculate the convective heat transfer. The energy equation is then solved by considering convected heat as a distributed source. Using the resulting temperature to compute new source terms, the final results are obtained by iterations of the procedure. Finite-element methods are proposed for modeling of realistic geothermal systems; the advantages of such methods are discussed. The developed methodology is then applied to a sample problem. Favorable agreement is obtained by comparisons with a previous study.

Nonlinear finite element formulation for the large displacement analysis in multibody system dynamics

NASA Technical Reports Server (NTRS)

Rismantab-Sany, J.; Chang, B.; Shabana, A. A.

1989-01-01

A total Lagrangian finite element formulation for the deformable bodies in multibody mechanical systems that undergo finite relative rotations is developed. The deformable bodies are discretized using finite element methods. The shape functions that are used to describe the displacement field are required to include the rigid body modes that describe only large translational displacements. This does not impose any limitations on the technique because most commonly used shape functions satisfy this requirement. The configuration of an element is defined using four sets of coordinate systems: Body, Element, Intermediate element, Global. The body coordinate system serves as a unique standard for the assembly of the elements forming the deformable body. The element coordinate system is rigidly attached to the element and therefore it translates and rotates with the element. The intermediate element coordinate system, whose axes are initially parallel to the element axes, has an origin which is rigidly attached to the origin of the body coordinate system and is used to conveniently describe the configuration of the element in undeformed state with respect to the body coordinate system.

Structural design, analysis, and modal testing of the petite amateur navy satellite (PANSAT)

NASA Astrophysics Data System (ADS)

Sakoda, Daniel J.

1992-09-01

The Naval Postgraduate School's (NPS) Space Systems Academic Group is developing the Petite Amateur Navy Satellite (PANSAT), a small satellite for digital store-and-forward communication in the amateur frequency band. PANSAT is intended to be a payload of opportunity amendable to a number of launch vehicles. The Shuttle Small Self-Contained Payload (SSCP) program was chosen as a design baseline because of its high margins of safety as a manned system. The PANSAT structure design is presented for the launch requirements of a Shuttle SSCP. A finite element model was developed and studied for the design loads of a SSCP. The results showed the structure to be very robust and likely to accommodate the requirements of other launch vehicles. The finite element analysis was verified by model testing, correlating the fundamental mode of the finite element model with that of an engineering test structure.

Stability of the fluid interface in a Hele-Shaw cell subjected to horizontal vibrations

NASA Astrophysics Data System (ADS)

Lyubimova, T. P.; Lyubimov, D. V.; Sadilov, E. S.; Popov, D. M.

2017-07-01

The stability of the horizontal interface of two immiscible viscous fluids in a Hele-Shaw cell subject to gravity and horizontal vibrations is studied. The problem is reduced to the generalized Hill equation, which is solved analytically by the multiple scale method and numerically. The long-wave instability, the resonance (parametric resonance) excitation of waves at finite frequencies of vibrations (for the first three resonances), and the limit of high-frequency vibrations are studied analytically under the assumption of small amplitudes of vibrations and small viscosity. For finite amplitudes of vibrations, finite wave numbers, and finite viscosity, the study is performed numerically. The influence of the specific natural control parameters and physical parameters of the system on its instability threshold is discussed. The results provide extension to other results [J. Bouchgl, S. Aniss, and M. Souhar, Phys. Rev. E 88, 023027 (2013), 10.1103/PhysRevE.88.023027], where the authors considered a similar problem but took into account viscosity in the basic state and did not consider it in the equations for perturbations.

Finite-time synchronization for second-order nonlinear multi-agent system via pinning exponent sliding mode control.

PubMed

Hou, Huazhou; Zhang, Qingling

2016-11-01

In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Study on fluid-structure interaction in liquid oxygen feeding pipe systems using finite volume method

NASA Astrophysics Data System (ADS)

Wei, Xin; Sun, Bing

2011-10-01

The fluid-structure interaction may occur in space launch vehicles, which would lead to bad performance of vehicles, damage equipments on vehicles, or even affect astronauts' health. In this paper, analysis on dynamic behavior of liquid oxygen (LOX) feeding pipe system in a large scale launch vehicle is performed, with the effect of fluid-structure interaction (FSI) taken into consideration. The pipe system is simplified as a planar FSI model with Poisson coupling and junction coupling. Numerical tests on pipes between the tank and the pump are solved by the finite volume method. Results show that restrictions weaken the interaction between axial and lateral vibrations. The reasonable results regarding frequencies and modes indicate that the FSI affects substantially the dynamic analysis, and thus highlight the usefulness of the proposed model. This study would provide a reference to the pipe test, as well as facilitate further studies on oscillation suppression.

On the continuous dependence with respect to sampling of the linear quadratic regulator problem for distributed parameter systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Wang, C.

1990-01-01

The convergence of solutions to the discrete or sampled time linear quadratic regulator problem and associated Riccati equation for infinite dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero (infinity) is established. Both the finite and infinite time horizon problems are studied. In the finite time horizon case, strong continuity of the operators which define the control system and performance index together with a stability and consistency condition on the sampling scheme are required. For the infinite time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary of delay system, and a flexible beam are presented and discussed.

On the continuous dependence with respect to sampling of the linear quadratic regulator problem for distributed parameter system

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Wang, C.

1992-01-01

The convergence of solutions to the discrete- or sampled-time linear quadratic regulator problem and associated Riccati equation for infinite-dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero(infinity) is established. Both the finite-and infinite-time horizon problems are studied. In the finite-time horizon case, strong continuity of the operators that define the control system and performance index, together with a stability and consistency condition on the sampling scheme are required. For the infinite-time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary or delay system, and a flexible beam are presented and discussed.

Weak Galerkin method for the Biot’s consolidation model

DOE PAGES

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

2017-08-23

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Weak Galerkin method for the Biot’s consolidation model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Electric and magnetic microfields inside and outside space-limited configurations of ions and ionic currents

NASA Astrophysics Data System (ADS)

Romanovsky, M. Yu; Ebeling, W.; Schimansky-Geier, L.

2005-01-01

The problem of electric and magnetic microfields inside finite spherical systems of stochastically moving ions and outside them is studied. The first possible field of applications is high temperature ion clusters created by laser fields [1]. Other possible applications are nearly spherical liquid systems at room-temperature containing electrolytes. Looking for biological applications we may also think about a cell which is a complicated electrolytic system or even a brain which is a still more complicated system of electrolytic currents. The essential model assumption is the random character of charges motion. We assume in our basic model that we have a finite nearly spherical system of randomly moving charges. Even taking into account that this is at best a caricature of any real system, it might be of interest as a limiting case, which admits a full theoretical treatment. For symmetry reasons, a random configuration of moving charges cannot generate a macroscopic magnetic field, but there will be microscopic fluctuating magnetic fields. Distributions for electric and magnetic microfields inside and outside such space- limited systems are calculated. Spherical systems of randomly distributed moving charges are investigated. Starting from earlier results for infinitely large systems, which lead to Holtsmark- type distributions, we show that the fluctuations in finite charge distributions are larger (in comparison to infinite systems of the same charge density).

Finite-Time Stabilization and Adaptive Control of Memristor-Based Delayed Neural Networks.

PubMed

Wang, Leimin; Shen, Yi; Zhang, Guodong

Finite-time stability problem has been a hot topic in control and system engineering. This paper deals with the finite-time stabilization issue of memristor-based delayed neural networks (MDNNs) via two control approaches. First, in order to realize the stabilization of MDNNs in finite time, a delayed state feedback controller is proposed. Then, a novel adaptive strategy is applied to the delayed controller, and finite-time stabilization of MDNNs can also be achieved by using the adaptive control law. Some easily verified algebraic criteria are derived to ensure the stabilization of MDNNs in finite time, and the estimation of the settling time functional is given. Moreover, several finite-time stability results as our special cases for both memristor-based neural networks (MNNs) without delays and neural networks are given. Finally, three examples are provided for the illustration of the theoretical results.Finite-time stability problem has been a hot topic in control and system engineering. This paper deals with the finite-time stabilization issue of memristor-based delayed neural networks (MDNNs) via two control approaches. First, in order to realize the stabilization of MDNNs in finite time, a delayed state feedback controller is proposed. Then, a novel adaptive strategy is applied to the delayed controller, and finite-time stabilization of MDNNs can also be achieved by using the adaptive control law. Some easily verified algebraic criteria are derived to ensure the stabilization of MDNNs in finite time, and the estimation of the settling time functional is given. Moreover, several finite-time stability results as our special cases for both memristor-based neural networks (MNNs) without delays and neural networks are given. Finally, three examples are provided for the illustration of the theoretical results.

A design pathfinder with material correlation points for inflatable systems

NASA Astrophysics Data System (ADS)

Fulcher, Jared Terrell

The incorporation of inflatable structures into aerospace systems can produce significant advantages in stowed volume to mechanical effectiveness and overall weight. Many applications of these ultra-lightweight systems are designed to precisely control internal or external surfaces, or both, to achieve desired performance. The modeling of these structures becomes complex due to the material nonlinearities inherent to the majority of construction materials used in inflatable structures. Furthermore, accurately modeling the response and behavior of the interfacing boundaries that are common to many inflatable systems will lead to better understanding of the entire class of structures. The research presented involved using nonlinear finite element simulations correlated with photogrammetry testing to develop a procedure for defining material properties for commercially available polyurethane-coated woven nylon fabric, which is representative of coated materials that have been proven materials for use in many inflatable systems. Further, the new material model was used to design and develop an inflatable pathfinder system which employs only internal pressure to control an assembly of internal membranes. This canonical inflatable system will be used for exploration and development of general understanding of efficient design methodology and analysis of future systems. Canonical structures are incorporated into the design of the phased pathfinder system to allow for more universal insight. Nonlinear finite element simulations were performed to evaluate the effect of various boundary conditions, loading configurations, and material orientations on the geometric precision of geometries representing typical internal/external surfaces commonly incorporated into inflatable pathfinder system. The response of the inflatable system to possible damage was also studied using nonlinear finite element simulations. Development of a correlated material model for analysis of the inflatable pathfinder system has improved the efficiency of design and analysis techniques of future inflatable structures. KEYWORDS: Nonlinear Finite Element, Inflatable Structures, Gossamer Space Systems, Photogrammetry Measurements, Coated Woven Fabric.

Vibration Transmission through Rolling Element Bearings in Geared Rotor Systems

DTIC Science & Technology

1990-11-01

147 4.8 Concluding Remarks ........................................................... 153 V STATISTICAL ENERGY ANALYSIS ............................................ 155...and dynamic finite element techniques are used to develop the discrete vibration models while statistical energy analysis method is used for the broad...bearing system studies, geared rotor system studies, and statistical energy analysis . Each chapter is self sufficient since it is written in a

A weak Galerkin least-squares finite element method for div-curl systems

NASA Astrophysics Data System (ADS)

Li, Jichun; Ye, Xiu; Zhang, Shangyou

2018-06-01

In this paper, we introduce a weak Galerkin least-squares method for solving div-curl problem. This finite element method leads to a symmetric positive definite system and has the flexibility to work with general meshes such as hybrid mesh, polytopal mesh and mesh with hanging nodes. Error estimates of the finite element solution are derived. The numerical examples demonstrate the robustness and flexibility of the proposed method.

Finite element analysis of two disk rotor system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dixit, Harsh Kumar

A finite element model of simple horizontal rotor system is developed for evaluating its dynamic behaviour. The model is based on Timoshenko beam element and accounts for the effect of gyroscopic couple and other rotational forces. Present rotor system consists of single shaft which is supported by bearings at both ends and two disks are mounted at different locations. The natural frequencies, mode shapes and orbits of rotating system for a specific range of rotation speed are obtained by developing a MATLAB code for solving the finite element equations of rotary system. Consequently, Campbell diagram is plotted for finding amore » relationship between natural whirl frequencies and rotation of the rotor.« less

Development library of finite elements for computer-aided design system of reed sensors

NASA Astrophysics Data System (ADS)

Kozlov, A. S.; Shmakov, N. A.; Tkalich, V. L.; Labkovskaia, R. I.; Kalinkina, M. E.; Pirozhnikova, O. I.

2018-05-01

The article is devoted to the development of a modern highly reliable element base of devices for security and fire alarm systems, in particular, to the improvement of the quality of contact cores (reed and membrane) of reed sensors. Modeling of elastic sensitive elements uses quadrangular elements of plates and shells, considered in the system of curvilinear orthogonal coordinates. The developed mathematical models and the formed finite element library are designed for systems of automated design of reed switch detectors to create competitive devices alarms. The finite element library is used for the automated system production of reed switch detectors both in series production and in the implementation of individual orders.

Very Large Data Volumes Analysis of Collaborative Systems with Finite Number of States

ERIC Educational Resources Information Center

Ivan, Ion; Ciurea, Cristian; Pavel, Sorin

2010-01-01

The collaborative system with finite number of states is defined. A very large database is structured. Operations on large databases are identified. Repetitive procedures for collaborative systems operations are derived. The efficiency of such procedures is analyzed. (Contains 6 tables, 5 footnotes and 3 figures.)

Finite burn maneuver modeling for a generalized spacecraft trajectory design and optimization system.

PubMed

Ocampo, Cesar

2004-05-01

The modeling, design, and optimization of finite burn maneuvers for a generalized trajectory design and optimization system is presented. A generalized trajectory design and optimization system is a system that uses a single unified framework that facilitates the modeling and optimization of complex spacecraft trajectories that may operate in complex gravitational force fields, use multiple propulsion systems, and involve multiple spacecraft. The modeling and optimization issues associated with the use of controlled engine burn maneuvers of finite thrust magnitude and duration are presented in the context of designing and optimizing a wide class of finite thrust trajectories. Optimal control theory is used examine the optimization of these maneuvers in arbitrary force fields that are generally position, velocity, mass, and are time dependent. The associated numerical methods used to obtain these solutions involve either, the solution to a system of nonlinear equations, an explicit parameter optimization method, or a hybrid parameter optimization that combines certain aspects of both. The theoretical and numerical methods presented here have been implemented in copernicus, a prototype trajectory design and optimization system under development at the University of Texas at Austin.

A model to study finite-size and magnetic effects on the phase transition of a fermion interacting system

NASA Astrophysics Data System (ADS)

Corrêa, Emerson B. S.; Linhares, César A.; Malbouisson, Adolfo P. C.

2018-03-01

We present a model to study the effects from external magnetic field, chemical potential and finite size on the phase structures of a massive four- and six-fermion interacting systems. These effects are introduced by a method of compactification of coordinates, a generalization of the standard Matsubara prescription. Through the compactification of the z-coordinate and of imaginary time, we describe a heated system with the shape of a film of thickness L, at temperature β-1 undergoing first- or second-order phase transition. We have found a strong dependence of the temperature transition on the coupling constants λ and η. Besides inverse magnetic catalysis and symmetry breaking for both kinds of transition, we have found an inverse symmetry breaking phenomenon with respect to first-order phase transition.

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Finite-time stabilisation of a class of switched nonlinear systems with state constraints

NASA Astrophysics Data System (ADS)

Huang, Shipei; Xiang, Zhengrong

2018-06-01

This paper investigates the finite-time stabilisation for a class of switched nonlinear systems with state constraints. Some power orders of the system are allowed to be ratios of positive even integers over odd integers. A Barrier Lyapunov function is introduced to guarantee that the state constraint is not violated at any time. Using the convex combination method and a recursive design approach, a state-dependent switching law and state feedback controllers of individual subsystems are constructed such that the closed-loop system is finite-time stable without violation of the state constraint. Two examples are provided to show the effectiveness of the proposed method.

Modelling Polar Self Assembly

NASA Astrophysics Data System (ADS)

Olvera de La Cruz, Monica; Sayar, Mehmet; Solis, Francisco J.; Stupp, Samuel I.

2001-03-01

Recent experimental studies in our group have shown that self assembled thin films of noncentrosymmetric supramolecular objects composed of triblock rodcoil molecules exhibit finite polar order. These aggregates have both long range dipolar and short range Ising-like interactions. We study the ground state of a simple model with these competing interactions. We find that the competition between Ising-like and dipolar forces yield a periodic domain structure, which can be controlled by adjusting the force constants and film thickness. When the surface forces are included in the potential, the system exhibits a finite macroscopic polar order.

Finite-time stabilization of uncertain nonholonomic systems in feedforward-like form by output feedback.

PubMed

Gao, Fangzheng; Wu, Yuqiang; Zhang, Zhongcai

2015-11-01

This paper investigates the problem of finite-time stabilization by output feedback for a class of nonholonomic systems in chained form with uncertainties. Comparing with the existing relevant literature, a distinguishing feature of the systems under investigation is that the x-subsystem is a feedforward-like rather than feedback-like system. This renders the existing control methods inapplicable to the control problems of the systems. A constructive design procedure for output feedback control is given. The designed controller renders that the states of closed-loop system are regulated to zero in a finite time. Two simulation examples are provided to illustrate the effectiveness of the proposed approach. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Matrix-Product-State Algorithm for Finite Fractional Quantum Hall Systems

NASA Astrophysics Data System (ADS)

Liu, Zhao; Bhatt, R. N.

2015-09-01

Exact diagonalization is a powerful tool to study fractional quantum Hall (FQH) systems. However, its capability is limited by the exponentially increasing computational cost. In order to overcome this difficulty, density-matrix-renormalization-group (DMRG) algorithms were developed for much larger system sizes. Very recently, it was realized that some model FQH states have exact matrix-product-state (MPS) representation. Motivated by this, here we report a MPS code, which is closely related to, but different from traditional DMRG language, for finite FQH systems on the cylinder geometry. By representing the many-body Hamiltonian as a matrix-product-operator (MPO) and using single-site update and density matrix correction, we show that our code can efficiently search the ground state of various FQH systems. We also compare the performance of our code with traditional DMRG. The possible generalization of our code to infinite FQH systems and other physical systems is also discussed.

Bose–Einstein condensation temperature of finite systems

NASA Astrophysics Data System (ADS)

Xie, Mi

2018-05-01

In studies of the Bose–Einstein condensation of ideal gases in finite systems, the divergence problem usually arises in the equation of state. In this paper, we present a technique based on the heat kernel expansion and zeta function regularization to solve the divergence problem, and obtain the analytical expression of the Bose–Einstein condensation temperature for general finite systems. The result is represented by the heat kernel coefficients, where the asymptotic energy spectrum of the system is used. Besides the general case, for systems with exact spectra, e.g. ideal gases in an infinite slab or in a three-sphere, the sums of the spectra can be obtained exactly and the calculation of corrections to the critical temperatures is more direct. For a system confined in a bounded potential, the form of the heat kernel is different from the usual heat kernel expansion. We show that as long as the asymptotic form of the global heat kernel can be found, our method works. For Bose gases confined in three- and two-dimensional isotropic harmonic potentials, we obtain the higher-order corrections to the usual results of the critical temperatures. Our method can also be applied to the problem of generalized condensation, and we give the correction of the boundary on the second critical temperature in a highly anisotropic slab.

Local existence of solutions to the Euler-Poisson system, including densities without compact support

NASA Astrophysics Data System (ADS)

Brauer, Uwe; Karp, Lavi

2018-01-01

Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density ρ which either falls off at infinity or has compact support. The solutions have finite mass, finite energy functional and include the static spherical solutions for γ = 6/5. The result is achieved by using weighted Sobolev spaces of fractional order and a new non-linear estimate which allows to estimate the physical density by the regularised non-linear matter variable. Gamblin also has studied this setting but using very different functional spaces. However we believe that the functional setting we use is more appropriate to describe a physical isolated body and more suitable to study the Newtonian limit.

Viewing hybrid systems as products of control systems and automata

NASA Technical Reports Server (NTRS)

Grossman, R. L.; Larson, R. G.

1992-01-01

The purpose of this note is to show how hybrid systems may be modeled as products of nonlinear control systems and finite state automata. By a hybrid system, we mean a network of consisting of continuous, nonlinear control system connected to discrete, finite state automata. Our point of view is that the automata switches between the control systems, and that this switching is a function of the discrete input symbols or letters that it receives. We show how a nonlinear control system may be viewed as a pair consisting of a bialgebra of operators coding the dynamics, and an algebra of observations coding the state space. We also show that a finite automata has a similar representation. A hybrid system is then modeled by taking suitable products of the bialgebras coding the dynamics and the observation algebras coding the state spaces.

Measurement-based quantum teleportation on finite AKLT chains

NASA Astrophysics Data System (ADS)

Fujii, Akihiko; Feder, David

In the measurement-based model of quantum computation, universal quantum operations are effected by making repeated local measurements on resource states which contain suitable entanglement. Resource states include two-dimensional cluster states and the ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) state on the honeycomb lattice. Recent studies suggest that measurements on one-dimensional systems in the Haldane phase teleport perfect single-qubit gates in the correlation space, protected by the underlying symmetry. As laboratory realizations of symmetry-protected states will necessarily be finite, we investigate the potential for quantum gate teleportation in finite chains of a bilinear-biquadratic Hamiltonian which is a generalization of the AKLT model representing the full Haldane phase.

Finite Element Model Characterization Of Nano-Composite Thermal And Environmental Barrier Coatings

NASA Technical Reports Server (NTRS)

Yamada, Yoshiki; Zhu, Dongming

2011-01-01

Thermal and environmental barrier coatings have been applied for protecting Si based ceramic matrix composite components from high temperature environment in advanced gas turbine engines. It has been found that the delamination and lifetime of T/EBC systems generally depend on the initiation and propagation of surface cracks induced by the axial mechanical load in addition to severe thermal loads. In order to prevent T/EBC systems from surface cracking and subsequent delamination due to mechanical and thermal stresses, T/EBC systems reinforced with nano-composite architectures have showed promise to improve mechanical properties and provide a potential crack shielding mechanism such as crack bridging. In this study, a finite element model (FEM) was established to understand the potential beneficial effects of nano-composites systems such as SiC nanotube-reinforced oxide T/EBC systems.

Solid-liquid surface tensions of critical nuclei and nucleation barriers from a phase-field-crystal study of a model binary alloy using finite system sizes.

PubMed

Choudhary, Muhammad Ajmal; Kundin, Julia; Emmerich, Heike; Oettel, Martin

2014-08-01

Phase-field-crystal (PFC) modeling has emerged as a computationally efficient tool to address crystal growth phenomena on atomistic length and diffusive time scales. We use a two-dimensional phase-field-crystal model for a binary system based on Elder et al. [Phys. Rev. B 75, 064107 (2007)] to study critical nuclei and their liquid-solid phase boundaries, in particular the nucleus size dependence of the liquid-solid interface tension as well as of the nucleation barrier. Critical nuclei are stabilized in finite systems of various sizes, however, the extracted interface tension as function of the nucleus radius r is independent of system size. We suggest a phenomenological expression to describe the dependence of the extracted interface tension on the nucleus radius r for the liquid-solid system. Moreover, the numerical PFC results show that this dependency can not be fully described by the nonclassical Tolman formula.

Computing Quantitative Characteristics of Finite-State Real-Time Systems

DTIC Science & Technology

1994-05-04

Current methods for verifying real - time systems are essentially decision procedures that establish whether the system model satisfies a given...specification. We present a general method for computing quantitative information about finite-state real - time systems . We have developed algorithms that...our technique can be extended to a more general representation of real - time systems , namely, timed transition graphs. The algorithms presented in this

Fulde–Ferrell superfluids in spinless ultracold Fermi gases

NASA Astrophysics Data System (ADS)

Zheng, Zhen-Fei; Guo, Guang-Can; Zheng, Zhen; Zou, Xu-Bo

2018-06-01

The Fulde–Ferrell (FF) superfluid phase, in which fermions form finite momentum Cooper pairings, is well studied in spin-singlet superfluids in past decades. Different from previous works that engineer the FF state in spinful cold atoms, we show that the FF state can emerge in spinless Fermi gases confined in optical lattice associated with nearest-neighbor interactions. The mechanism of the spinless FF state relies on the split Fermi surfaces by tuning the chemistry potential, which naturally gives rise to finite momentum Cooper pairings. The phase transition is accompanied by changed Chern numbers, in which, different from the conventional picture, the band gap does not close. By beyond-mean-field calculations, we find the finite momentum pairing is more robust, yielding the system promising for maintaining the FF state at finite temperature. Finally we present the possible realization and detection scheme of the spinless FF state.

Distributed finite-time containment control for double-integrator multiagent systems.

PubMed

Wang, Xiangyu; Li, Shihua; Shi, Peng

2014-09-01

In this paper, the distributed finite-time containment control problem for double-integrator multiagent systems with multiple leaders and external disturbances is discussed. In the presence of multiple dynamic leaders, by utilizing the homogeneous control technique, a distributed finite-time observer is developed for the followers to estimate the weighted average of the leaders' velocities at first. Then, based on the estimates and the generalized adding a power integrator approach, distributed finite-time containment control algorithms are designed to guarantee that the states of the followers converge to the dynamic convex hull spanned by those of the leaders in finite time. Moreover, as a special case of multiple dynamic leaders with zero velocities, the proposed containment control algorithms also work for the case of multiple stationary leaders without using the distributed observer. Simulations demonstrate the effectiveness of the proposed control algorithms.

Focal shift and the axial optical coordinate for high-aperture systems of finite Fresnel number.

PubMed

Sheppard, Colin J R; Török, Peter

2003-11-01

Analytic expressions are given for the on-axis intensity predicted by the Rayleigh-Sommerfeld and Kirchhoff diffraction integrals for a scalar optical system of high numerical aperture and finite value of Fresnel number. A definition of the axial optical coordinate is introduced that is valid for finite values of Fresnel number, for high-aperture systems, and for observation points distant from the focus. The focal shift effect is reexamined. For the case when the focal shift is small, explicit expressions are given for the focal shift and the axial peak in intensity.

Finite-time H∞ control for a class of discrete-time switched time-delay systems with quantized feedback

NASA Astrophysics Data System (ADS)

Song, Haiyu; Yu, Li; Zhang, Dan; Zhang, Wen-An

2012-12-01

This paper is concerned with the finite-time quantized H∞ control problem for a class of discrete-time switched time-delay systems with time-varying exogenous disturbances. By using the sector bound approach and the average dwell time method, sufficient conditions are derived for the switched system to be finite-time bounded and ensure a prescribed H∞ disturbance attenuation level, and a mode-dependent quantized state feedback controller is designed by solving an optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.

Dynamic characterization, monitoring and control of rotating flexible beam-mass structures via piezo-embedded techniques

NASA Technical Reports Server (NTRS)

Lai, Steven H.-Y.

1992-01-01

A variational principle and a finite element discretization technique were used to derive the dynamic equations for a high speed rotating flexible beam-mass system embedded with piezo-electric materials. The dynamic equation thus obtained allows the development of finite element models which accommodate both the original structural element and the piezoelectric element. The solutions of finite element models provide system dynamics needed to design a sensing system. The characterization of gyroscopic effect and damping capacity of smart rotating devices are addressed. Several simulation examples are presented to validate the analytical solution.

Finite-time stabilization of chaotic gyros based on a homogeneous supertwisting-like algorithm

NASA Astrophysics Data System (ADS)

Khamsuwan, Pitcha; Sangpet, Teerawat; Kuntanapreeda, Suwat

2018-01-01

This paper presents a finite-time stabilization scheme for nonlinear chaotic gyros. The scheme utilizes a supertwisting-like continuous control algorithm for the systems of dimension more than one with a Lipschitz disturbance. The algorithm yields finite-time convergence similar to that produces by discontinuous sliding mode control algorithms. To design the controller, the nonlinearities in the gyro are treated as a disturbance in the system. Thanks to the dissipativeness of chaotic systems, the nonlinearities also possess the Lipschitz property. Numerical results are provided to illustrate the effectiveness of the scheme.

Flexible architecture of data acquisition firmware based on multi-behaviors finite state machine

NASA Astrophysics Data System (ADS)

Arpaia, Pasquale; Cimmino, Pasquale

2016-11-01

A flexible firmware architecture for different kinds of data acquisition systems, ranging from high-precision bench instruments to low-cost wireless transducers networks, is presented. The key component is a multi-behaviors finite state machine, easily configurable to both low- and high-performance requirements, to diverse operating systems, as well as to on-line and batch measurement algorithms. The proposed solution was validated experimentally on three case studies with data acquisition architectures: (i) concentrated, in a high-precision instrument for magnetic measurements at CERN, (ii) decentralized, for telemedicine remote monitoring of patients at home, and (iii) distributed, for remote monitoring of building's energy loss.

Finite-size effects and switching times for Moran process with mutation.

PubMed

DeVille, Lee; Galiardi, Meghan

2017-04-01

We consider the Moran process with two populations competing under an iterated Prisoner's Dilemma in the presence of mutation, and concentrate on the case where there are multiple evolutionarily stable strategies. We perform a complete bifurcation analysis of the deterministic system which arises in the infinite population size. We also study the Master equation and obtain asymptotics for the invariant distribution and metastable switching times for the stochastic process in the case of large but finite population. We also show that the stochastic system has asymmetries in the form of a skew for parameter values where the deterministic limit is symmetric.

Possible Many-Body Localization in a Long-Lived Finite-Temperature Ultracold Quasineutral Molecular Plasma

NASA Astrophysics Data System (ADS)

Sous, John; Grant, Edward

2018-03-01

We argue that the quenched ultracold plasma presents an experimental platform for studying the quantum many-body physics of disordered systems in the long-time and finite energy-density limits. We consider an experiment that quenches a plasma of nitric oxide to an ultracold system of Rydberg molecules, ions, and electrons that exhibits a long-lived state of arrested relaxation. The qualitative features of this state fail to conform with classical models. Here, we develop a microscopic quantum description for the arrested phase based on an effective many-body spin Hamiltonian that includes both dipole-dipole and van der Waals interactions. This effective model appears to offer a way to envision the essential quantum disordered nonequilibrium physics of this system.

Finite-Size Effects on the Behavior of the Susceptibility in van der Waals Films Bounded by Strongly Absorbing Substrates

NASA Technical Reports Server (NTRS)

Dantchev, Daniel; Rudnick, Joseph; Barmatz, M.

2007-01-01

We study critical point finite-size effects in the case of the susceptibility of a film in which interactions are characterized by a van der Waals-type power law tail. The geometry is appropriate to a slab-like system with two bounding surfaces. Boundary conditions are consistent with surfaces that both prefer the same phase in the low temperature, or broken symmetry, state. We take into account both interactions within the system and interactions between the constituents of the system and the material surrounding it. Specific predictions are made with respect to the behavior of 3He and 4He films in the vicinity of their respective liquid-vapor critical points.

Cavity-coupled double-quantum dot at finite bias: Analogy with lasers and beyond

NASA Astrophysics Data System (ADS)

Kulkarni, Manas; Cotlet, Ovidiu; Türeci, Hakan E.

2014-09-01

We present a theoretical and experimental study of photonic and electronic transport properties of a voltage biased InAs semiconductor double quantum dot (DQD) that is dipole coupled to a superconducting transmission line resonator. We obtain the master equation for the reduced density matrix of the coupled system of cavity photons and DQD electrons accounting systematically for both the presence of phonons and the effect of leads at finite voltage bias. We subsequently derive analytical expressions for transmission, phase response, photon number, and the nonequilibrium steady-state electron current. We show that the coupled system under finite bias realizes an unconventional version of a single-atom laser and analyze the spectrum and the statistics of the photon flux leaving the cavity. In the transmission mode, the system behaves as a saturable single-atom amplifier for the incoming photon flux. Finally, we show that the back action of the photon emission on the steady-state current can be substantial. Our analytical results are compared to exact master equation results establishing regimes of validity of various analytical models. We compare our findings to available experimental measurements.

Dispersion, spatial growth rate, and start current of a Cherenkov free-electron laser with negative-index material

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Yuanyuan; Wei, Yanyu; Jiang, Xuebing

We present an analysis of a Cherenkov free-electron laser based on a single slab made from negative-index materials. In this system, a flat electron beam with finite thickness travelling close to the surface of the slab interacts with the copropagating electromagnetic surface mode. The dispersion equation for a finitely thick slab is worked out and solved numerically to study the dispersion relation of surface modes supported by negative-index materials, and the calculations are in good agreement with the simulation results from a finite difference time domain code. We find that under suitable conditions there is inherent feedback in such amore » scheme due to the characteristics of negative-index materials, which means that the system can oscillate without external reflectors when the beam current exceeds a threshold value, i.e., start current. Using the hydrodynamic approach, we setup coupled equations for this system, and solve these equations analytically in the small signal regime to obtain formulas for the spatial growth rate and start current.« less

Surface and finite size effect on fluctuations dynamics in nanoparticles with long-range order

NASA Astrophysics Data System (ADS)

Morozovska, A. N.; Eliseev, E. A.

2010-02-01

The influence of surface and finite size on the dynamics of the order parameter fluctuations and critical phenomena in the three-dimensional (3D)-confined systems with long-range order was not considered theoretically. In this paper, we study the influence of surface and finite size on the dynamics of the order parameter fluctuations in the particles of arbitrary shape. We consider concrete examples of the spherical and cylindrical ferroic nanoparticles within Landau-Ginzburg-Devonshire phenomenological approach. Allowing for the strong surface energy contribution in micro and nanoparticles, the analytical expressions derived for the Ornstein-Zernike correlator of the long-range order parameter spatial-temporal fluctuations, dynamic generalized susceptibility, relaxation times, and correlation radii discrete spectra are different from those known for bulk systems. Obtained analytical expressions for the correlation function of the order parameter spatial-temporal fluctuations in micro and nanosized systems can be useful for the quantitative analysis of the dynamical structural factors determined from magnetic resonance diffraction and scattering spectra. Besides the practical importance of the correlation function for the analysis of the experimental data, derived expressions for the fluctuations strength determine the fundamental limits of phenomenological theories applicability for 3D-confined systems.

Finite-time output feedback control of uncertain switched systems via sliding mode design

NASA Astrophysics Data System (ADS)

Zhao, Haijuan; Niu, Yugang; Song, Jun

2018-04-01

The problem of sliding mode control (SMC) is investigated for a class of uncertain switched systems subject to unmeasurable state and assigned finite (possible short) time constraint. A key issue is how to ensure the finite-time boundedness (FTB) of system state during reaching phase and sliding motion phase. To this end, a state observer is constructed to estimate the unmeasured states. And then, a state estimate-based SMC law is designed such that the state trajectories can be driven onto the specified integral sliding surface during the assigned finite time interval. By means of partitioning strategy, the corresponding FTB over reaching phase and sliding motion phase are guaranteed and the sufficient conditions are derived via average dwell time technique. Finally, an illustrative example is given to illustrate the proposed method.

Angular Random Walk Estimation of a Time-Domain Switching Micromachined Gyroscope

DTIC Science & Technology

2016-10-19

1 2. PARAMETRIC SYSTEM IDENTIFICATION BASED ON TIME-DOMAIN SWITCHING ........ 2 3. FINITE ELEMENT MODELING OF RESONATOR...8 3. FINITE ELEMENT MODELING OF RESONATOR This section details basic finite element modeling of the resonator used with the TDSMG. While it...Based on finite element simulations of the employed resonator, it is found that the effects of thermomechanical noise is on par with 10 ps of timing

A study of trends and techniques for space base electronics

NASA Technical Reports Server (NTRS)

Trotter, J. D.; Wade, T. E.; Gassaway, J. D.; Mahmood, Q.

1978-01-01

A sputtering system was developed to deposit aluminum and aluminum alloys by the dc sputtering technique. This system is designed for a high level of cleanliness and for monitoring the deposition parameters during film preparation. This system is now ready for studying the deposition and annealing parameters upon double-level metal preparation. A technique recently applied for semiconductor analysis, the finite element method, was studied for use in the computer modeling of two dimensional MOS transistor structures. It was concluded that the method has not been sufficiently well developed for confident use at this time. An algorithm was developed for confident use at this time. An algorithm was developed for implementing a computer study which is based upon the finite difference method. The program which was developed was modified and used to calculate redistribution data for boron and phosphorous which had been predeposited by ion implantation with range and straggle conditions. Data were generated for 111 oriented SOS films with redistribution in N2, dry O2 and steam ambients.

Coupled Aerodynamic and Structural Sensitivity Analysis of a High-Speed Civil Transport

NASA Technical Reports Server (NTRS)

Mason, B. H.; Walsh, J. L.

2001-01-01

An objective of the High Performance Computing and Communication Program at the NASA Langley Research Center is to demonstrate multidisciplinary shape and sizing optimization of a complete aerospace vehicle configuration by using high-fidelity, finite-element structural analysis and computational fluid dynamics aerodynamic analysis. In a previous study, a multi-disciplinary analysis system for a high-speed civil transport was formulated to integrate a set of existing discipline analysis codes, some of them computationally intensive, This paper is an extension of the previous study, in which the sensitivity analysis for the coupled aerodynamic and structural analysis problem is formulated and implemented. Uncoupled stress sensitivities computed with a constant load vector in a commercial finite element analysis code are compared to coupled aeroelastic sensitivities computed by finite differences. The computational expense of these sensitivity calculation methods is discussed.

Automatic prediction of tongue muscle activations using a finite element model.

PubMed

Stavness, Ian; Lloyd, John E; Fels, Sidney

2012-11-15

Computational modeling has improved our understanding of how muscle forces are coordinated to generate movement in musculoskeletal systems. Muscular-hydrostat systems, such as the human tongue, involve very different biomechanics than musculoskeletal systems, and modeling efforts to date have been limited by the high computational complexity of representing continuum-mechanics. In this study, we developed a computationally efficient tracking-based algorithm for prediction of muscle activations during dynamic 3D finite element simulations. The formulation uses a local quadratic-programming problem at each simulation time-step to find a set of muscle activations that generated target deformations and movements in finite element muscular-hydrostat models. We applied the technique to a 3D finite element tongue model for protrusive and bending movements. Predicted muscle activations were consistent with experimental recordings of tongue strain and electromyography. Upward tongue bending was achieved by recruitment of the superior longitudinal sheath muscle, which is consistent with muscular-hydrostat theory. Lateral tongue bending, however, required recruitment of contralateral transverse and vertical muscles in addition to the ipsilateral margins of the superior longitudinal muscle, which is a new proposition for tongue muscle coordination. Our simulation framework provides a new computational tool for systematic analysis of muscle forces in continuum-mechanics models that is complementary to experimental data and shows promise for eliciting a deeper understanding of human tongue function. Copyright © 2012 Elsevier Ltd. All rights reserved.

Structural Health Monitoring Using High-Density Fiber Optic Strain Sensor and Inverse Finite Element Methods

NASA Technical Reports Server (NTRS)

Vazquez, Sixto L.; Tessler, Alexander; Quach, Cuong C.; Cooper, Eric G.; Parks, Jeffrey; Spangler, Jan L.

2005-01-01

In an effort to mitigate accidents due to system and component failure, NASA s Aviation Safety has partnered with industry, academia, and other governmental organizations to develop real-time, on-board monitoring capabilities and system performance models for early detection of airframe structure degradation. NASA Langley is investigating a structural health monitoring capability that uses a distributed fiber optic strain system and an inverse finite element method for measuring and modeling structural deformations. This report describes the constituent systems that enable this structural monitoring function and discusses results from laboratory tests using the fiber strain sensor system and the inverse finite element method to demonstrate structural deformation estimation on an instrumented test article

Effect of Pumping on Groundwater Levels: A Case Study

NASA Astrophysics Data System (ADS)

Sindhu, G.; Vijayachandran, Lekshmi

2018-03-01

Groundwater is a major source for drinking and domestic purposes. Nowadays, extensive pumping has become a major issue of concern since pumping has led to rapid decline in the groundwater table, thus imposing landward gradient, leading to saline water intrusion especially in coastal areas. Groundwater pumping has seen its utmost effect on coastal aquifer systems, where the sea-ward gradient gets disturbed due to anthropogenic influences. Hence, a groundwater flow modelling of an aquifer system is essential for understanding the various hydro-geologic conditions, which can be used to study the responses of the aquifer system with regard to various pumping scenarios. Besides, a model helps to predict the water levels for the future period with respect to changing environment. In this study, a finite element groundwater flow model of a coastal aquifer system at Aakulam, Trivandrum district is developed, calibrated and simulated using the software Finite Element subsurface Flow system (FEFLOW 6.2).This simulated model is then used to predict the groundwater levels for a future 5 year period during pre monsoon and post monsoon season.

Effect of Pumping on Groundwater Levels: A Case Study

NASA Astrophysics Data System (ADS)

Sindhu, G.; Vijayachandran, Lekshmi

2018-06-01

Groundwater is a major source for drinking and domestic purposes. Nowadays, extensive pumping has become a major issue of concern since pumping has led to rapid decline in the groundwater table, thus imposing landward gradient, leading to saline water intrusion especially in coastal areas. Groundwater pumping has seen its utmost effect on coastal aquifer systems, where the sea-ward gradient gets disturbed due to anthropogenic influences. Hence, a groundwater flow modelling of an aquifer system is essential for understanding the various hydro-geologic conditions, which can be used to study the responses of the aquifer system with regard to various pumping scenarios. Besides, a model helps to predict the water levels for the future period with respect to changing environment. In this study, a finite element groundwater flow model of a coastal aquifer system at Aakulam, Trivandrum district is developed, calibrated and simulated using the software Finite Element subsurface Flow system (FEFLOW 6.2).This simulated model is then used to predict the groundwater levels for a future 5 year period during pre monsoon and post monsoon season.

Insights on finite size effects in ab initio study of CO adsorption and dissociation on Fe 110 surface

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chakrabarty, Aurab, E-mail: aurab.chakrabarty@qatar.tamu.edu; Bouhali, Othmane; Mousseau, Normand

Adsorption and dissociation of hydrocarbons on metallic surfaces represent crucial steps on the path to carburization, eventually leading to dusting corrosion. While adsorption of CO molecules on Fe surface is a barrier-less exothermic process, this is not the case for the dissociation of CO into C and O adatoms and the diffusion of C beneath the surface that are found to be associated with large energy barriers. In practice, these barriers can be affected by numerous factors that combine to favour the CO-Fe reaction such as the abundance of CO and other hydrocarbons as well as the presence of structuralmore » defects. From a numerical point of view, studying these factors is challenging and a step-by-step approach is necessary to assess, in particular, the influence of the finite box size on the reaction parameters for adsorption and dissociation of CO on metal surfaces. Here, we use density functional theory (DFT) total energy calculations with the climbing-image nudged elastic band method to estimate the adsorption energies and dissociation barriers for different CO coverages with surface supercells of different sizes. We further compute the effect of periodic boundary condition for DFT calculations and find that the contribution from van der Waals interaction in the computation of adsorption parameters is important as they contribute to correcting the finite-size error in small systems. The dissociation process involves carbon insertion into the Fe surface causing a lattice deformation that requires a larger surface system for unrestricted relaxation. We show that, in the larger surface systems associated with dilute CO-coverages, C-insertion is energetically more favourable, leading to a significant decrease in the dissociation barrier. This observation suggests that a large surface system with dilute coverage is necessary for all similar metal-hydrocarbon reactions in order to study their fundamental electronic mechanisms, as an isolated phenomenon, free from finite-size effects.« less

Insights on finite size effects in ab initio study of CO adsorption and dissociation on Fe 110 surface

NASA Astrophysics Data System (ADS)

Chakrabarty, Aurab; Bouhali, Othmane; Mousseau, Normand; Becquart, Charlotte S.; El-Mellouhi, Fedwa

2016-08-01

Adsorption and dissociation of hydrocarbons on metallic surfaces represent crucial steps on the path to carburization, eventually leading to dusting corrosion. While adsorption of CO molecules on Fe surface is a barrier-less exothermic process, this is not the case for the dissociation of CO into C and O adatoms and the diffusion of C beneath the surface that are found to be associated with large energy barriers. In practice, these barriers can be affected by numerous factors that combine to favour the CO-Fe reaction such as the abundance of CO and other hydrocarbons as well as the presence of structural defects. From a numerical point of view, studying these factors is challenging and a step-by-step approach is necessary to assess, in particular, the influence of the finite box size on the reaction parameters for adsorption and dissociation of CO on metal surfaces. Here, we use density functional theory (DFT) total energy calculations with the climbing-image nudged elastic band method to estimate the adsorption energies and dissociation barriers for different CO coverages with surface supercells of different sizes. We further compute the effect of periodic boundary condition for DFT calculations and find that the contribution from van der Waals interaction in the computation of adsorption parameters is important as they contribute to correcting the finite-size error in small systems. The dissociation process involves carbon insertion into the Fe surface causing a lattice deformation that requires a larger surface system for unrestricted relaxation. We show that, in the larger surface systems associated with dilute CO-coverages, C-insertion is energetically more favourable, leading to a significant decrease in the dissociation barrier. This observation suggests that a large surface system with dilute coverage is necessary for all similar metal-hydrocarbon reactions in order to study their fundamental electronic mechanisms, as an isolated phenomenon, free from finite-size effects.

Distributed robust finite-time nonlinear consensus protocols for multi-agent systems

NASA Astrophysics Data System (ADS)

Zuo, Zongyu; Tie, Lin

2016-04-01

This paper investigates the robust finite-time consensus problem of multi-agent systems in networks with undirected topology. Global nonlinear consensus protocols augmented with a variable structure are constructed with the aid of Lyapunov functions for each single-integrator agent dynamics in the presence of external disturbances. In particular, it is shown that the finite settling time of the proposed general framework for robust consensus design is upper bounded for any initial condition. This makes it possible for network consensus problems to design and estimate the convergence time offline for a multi-agent team with a given undirected information flow. Finally, simulation results are presented to demonstrate the performance and effectiveness of our finite-time protocols.

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Fast smooth second-order sliding mode control for systems with additive colored noises.

PubMed

Yang, Pengfei; Fang, Yangwang; Wu, Youli; Liu, Yunxia; Zhang, Danxu

2017-01-01

In this paper, a fast smooth second-order sliding mode control is presented for a class of stochastic systems with enumerable Ornstein-Uhlenbeck colored noises. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the controller. The finite-time convergence of the prescribed sliding variable dynamics system is proved by using stochastic Lyapunov-like techniques. Then the proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are presented comparing with smooth second-order sliding mode control to validate the analysis.

Structural weights analysis of advanced aerospace vehicles using finite element analysis

NASA Technical Reports Server (NTRS)

Bush, Lance B.; Lentz, Christopher A.; Rehder, John J.; Naftel, J. Chris; Cerro, Jeffrey A.

1989-01-01

A conceptual/preliminary level structural design system has been developed for structural integrity analysis and weight estimation of advanced space transportation vehicles. The system includes a three-dimensional interactive geometry modeler, a finite element pre- and post-processor, a finite element analyzer, and a structural sizing program. Inputs to the system include the geometry, surface temperature, material constants, construction methods, and aerodynamic and inertial loads. The results are a sized vehicle structure capable of withstanding the static loads incurred during assembly, transportation, operations, and missions, and a corresponding structural weight. An analysis of the Space Shuttle external tank is included in this paper as a validation and benchmark case of the system.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Kumar, Vivek; Raghurama Rao, S. V.

2008-04-01

Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

Adsorption of small hydrocarbon radicals on single walled carbon nanotubes of finite length

NASA Astrophysics Data System (ADS)

Wu, Jianhua; Hagelberg, Frank

2010-04-01

Adsorption of the hydrocarbon radicals CH, CH2 , and CH3 on finite single walled carbon nanotubes (SWNTs) of the (10,0) type is investigated by density-functional theory (DFT). Two classes of finite SWNTs are considered: truncated SWNTs, where admission is made for geometric reconstruction of the tube ends, and those capped with fullerene hemispheres. Both prototypes are characterized by ground states with nonvanishing magnetic moments, where antiferromagnetic coordination between nds is preferred over the ferromagnetic alternative. The focus of this study is on the influence exerted by the adsorbates on the magnetic structure of the system as a whole, as well as the relative impact of both, confinement due to the finite lengths of the considered SWNTs and their magnetic structure on the preferred positions of hydrocarbon adsorbates. In particular, it is shown that the confinement outweighs the magnetic effect in defining the adsorption energy variations among nonequivalent sites of attachment. The SWNT spin-density distributions turn out to affect the nature of the bonding between finite SWNT substrates and hydrocarbon radical adsorbates.

Finite element meshing of ANSYS (trademark) solid models

NASA Technical Reports Server (NTRS)

Kelley, F. S.

1987-01-01

A large scale, general purpose finite element computer program, ANSYS, developed and marketed by Swanson Analysis Systems, Inc. is discussed. ANSYS was perhaps the first commercially available program to offer truly interactive finite element model generation. ANSYS's purpose is for solid modeling. This application is briefly discussed and illustrated.

Inferring the Limit Behavior of Some Elementary Cellular Automata

NASA Astrophysics Data System (ADS)

Ruivo, Eurico L. P.; de Oliveira, Pedro P. B.

Cellular automata locally define dynamical systems, discrete in space, time and in the state variables, capable of displaying arbitrarily complex global emergent behavior. One core question in the study of cellular automata refers to their limit behavior, that is, to the global dynamical features in an infinite time evolution. Previous works have shown that for finite time evolutions, the dynamics of one-dimensional cellular automata can be described by regular languages and, therefore, by finite automata. Such studies have shown the existence of growth patterns in the evolution of such finite automata for some elementary cellular automata rules and also inferred the limit behavior of such rules based upon the growth patterns; however, the results on the limit behavior were obtained manually, by direct inspection of the structures that arise during the time evolution. Here we present the formalization of an automatic method to compute such structures. Based on this, the rules of the elementary cellular automata space were classified according to the existence of a growth pattern in their finite automata. Also, we present a method to infer the limit graph of some elementary cellular automata rules, derived from the analysis of the regular expressions that describe their behavior in finite time. Finally, we analyze some attractors of two rules for which we could not compute the whole limit set.

Rashba and Dresselhaus spin-orbit interactions effects on electronic features of a two dimensional elliptic quantum dot

NASA Astrophysics Data System (ADS)

Mokhtari, P.; Rezaei, G.; Zamani, A.

2017-06-01

In this paper, electronic structure of a two dimensional elliptic quantum dot under the influence of external electric and magnetic fields are studied in the presence of Rashba and Dresselhaus spin-orbit interactions. This investigation is done computationally and to do this, at first, the effective Hamiltonian of the system by considering the spin-orbit coupling is demonstrated in the presence of applied electric and magnetic fields and afterwards the Schrödinger equation is solved using the finite difference approach. Utilizing finite element method, eigenvalues and eigenstates of the system are calculated and the effect of the external fields, the size of the dot as well as the strength of Rashba spin-orbit interaction are studied. Our results indicate that, Spin-orbit interactions, external fields and the dot size have a great influence on the electronic structure of the system.

Unexpected finite size effects in interfacial systems: Why bigger is not always better—Increase in uncertainty of surface tension with bulk phase width

NASA Astrophysics Data System (ADS)

Longford, Francis G. J.; Essex, Jonathan W.; Skylaris, Chris-Kriton; Frey, Jeremy G.

2018-06-01

We present an unexpected finite size effect affecting interfacial molecular simulations that is proportional to the width-to-surface-area ratio of the bulk phase Ll/A. This finite size effect has a significant impact on the variance of surface tension values calculated using the virial summation method. A theoretical derivation of the origin of the effect is proposed, giving a new insight into the importance of optimising system dimensions in interfacial simulations. We demonstrate the consequences of this finite size effect via a new way to estimate the surface energetic and entropic properties of simulated air-liquid interfaces. Our method is based on macroscopic thermodynamic theory and involves comparing the internal energies of systems with varying dimensions. We present the testing of these methods using simulations of the TIP4P/2005 water forcefield and a Lennard-Jones fluid model of argon. Finally, we provide suggestions of additional situations, in which this finite size effect is expected to be significant, as well as possible ways to avoid its impact.

Finite-time synchronization of stochastic coupled neural networks subject to Markovian switching and input saturation.

PubMed

Selvaraj, P; Sakthivel, R; Kwon, O M

2018-06-07

This paper addresses the problem of finite-time synchronization of stochastic coupled neural networks (SCNNs) subject to Markovian switching, mixed time delay, and actuator saturation. In addition, coupling strengths of the SCNNs are characterized by mutually independent random variables. By utilizing a simple linear transformation, the problem of stochastic finite-time synchronization of SCNNs is converted into a mean-square finite-time stabilization problem of an error system. By choosing a suitable mode dependent switched Lyapunov-Krasovskii functional, a new set of sufficient conditions is derived to guarantee the finite-time stability of the error system. Subsequently, with the help of anti-windup control scheme, the actuator saturation risks could be mitigated. Moreover, the derived conditions help to optimize estimation of the domain of attraction by enlarging the contractively invariant set. Furthermore, simulations are conducted to exhibit the efficiency of proposed control scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.

Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.« less

Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity

DOE PAGES

Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel

2018-02-08

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.« less

Distributed Adaptive Finite-Time Approach for Formation-Containment Control of Networked Nonlinear Systems Under Directed Topology.

PubMed

Wang, Yujuan; Song, Yongduan; Ren, Wei

2017-07-06

This paper presents a distributed adaptive finite-time control solution to the formation-containment problem for multiple networked systems with uncertain nonlinear dynamics and directed communication constraints. By integrating the special topology feature of the new constructed symmetrical matrix, the technical difficulty in finite-time formation-containment control arising from the asymmetrical Laplacian matrix under single-way directed communication is circumvented. Based upon fractional power feedback of the local error, an adaptive distributed control scheme is established to drive the leaders into the prespecified formation configuration in finite time. Meanwhile, a distributed adaptive control scheme, independent of the unavailable inputs of the leaders, is designed to keep the followers within a bounded distance from the moving leaders and then to make the followers enter the convex hull shaped by the formation of the leaders in finite time. The effectiveness of the proposed control scheme is confirmed by the simulation.

Solution of a tridiagonal system of equations on the finite element machine

NASA Technical Reports Server (NTRS)

Bostic, S. W.

1984-01-01

Two parallel algorithms for the solution of tridiagonal systems of equations were implemented on the Finite Element Machine. The Accelerated Parallel Gauss method, an iterative method, and the Buneman algorithm, a direct method, are discussed and execution statistics are presented.

Distributed Leader-Following Finite-Time Consensus Control for Linear Multiagent Systems under Switching Topology

PubMed Central

Xu, Xiaole; Chen, Shengyong

2014-01-01

This paper investigates the finite-time consensus problem of leader-following multiagent systems. The dynamical models for all following agents and the leader are assumed the same general form of linear system, and the interconnection topology among the agents is assumed to be switching and undirected. We mostly consider the continuous-time case. By assuming that the states of neighbouring agents are known to each agent, a sufficient condition is established for finite-time consensus via a neighbor-based state feedback protocol. While the states of neighbouring agents cannot be available and only the outputs of neighbouring agents can be accessed, the distributed observer-based consensus protocol is proposed for each following agent. A sufficient condition is provided in terms of linear matrix inequalities to design the observer-based consensus protocol, which makes the multiagent systems achieve finite-time consensus under switching topologies. Then, we discuss the counterparts for discrete-time case. Finally, we provide an illustrative example to show the effectiveness of the design approach. PMID:24883367

Protecting a quantum state from environmental noise by an incompatible finite-time measurement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brasil, Carlos Alexandre; Castro, L. A. de; Napolitano, R. d. J.

We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. For the description of the measurement of an observable that is incompatible with the interaction between system and environment, we have found an approximate analytical expression, valid at zero temperature and weak coupling with the measuring device. We have tested the validity of the analyticalmore » predictions against an exact numerical approach, based on the superoperator-splitting method, that confirms the protection of the initial state of the system. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.« less

Advances in the p and h-p Versions of the Finite Element Method. A survey

DTIC Science & Technology

1988-01-01

p versions is the code PROBE which was developed by NOETIC Technologies, St. Louis, MO [49] [60]. PROBE solves two dimensional problems of linear...p and h-p versions of the finite element method was studied in detail from various point of view. We will mention here some essential illustrative...49] PROBE - Sample Problems. Series of reports, Noetic Technologies, St. Louis, MO 63117. [50] Rank, E., Babu’ka, I., An expert system for the

Application of a data base management system to a finite element model

NASA Technical Reports Server (NTRS)

Rogers, J. L., Jr.

1980-01-01

In today's software market, much effort is being expended on the development of data base management systems (DBMS). Most commercially available DBMS were designed for business use. However, the need for such systems within the engineering and scientific communities is becoming apparent. A potential DBMS application that appears attractive is the handling of data for finite element engineering models. The applications of a commercially available, business-oriented DBMS to a structural engineering, finite element model is explored. The model, DBMS, an approach to using the DBMS, advantages and disadvantages are described. Plans for research on a scientific and engineering DBMS are discussed.

Quantum electron-vibrational dynamics at finite temperature: Thermo field dynamics approach

NASA Astrophysics Data System (ADS)

Borrelli, Raffaele; Gelin, Maxim F.

2016-12-01

Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on the thermo field dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. A comparison with the theoretically equivalent density matrix formulation shows the key numerical advantages of the present approach. The solution of thermo field dynamics equations with a novel technique for the propagation of tensor trains (matrix product states) is discussed. Numerical applications to model spin-boson systems show that the present approach is a promising tool for the description of quantum dynamics of complex molecular systems at finite temperature.

Cooperative combinatorial optimization: evolutionary computation case study.

PubMed

Burgin, Mark; Eberbach, Eugene

2008-01-01

This paper presents a formalization of the notion of cooperation and competition of multiple systems that work toward a common optimization goal of the population using evolutionary computation techniques. It is proved that evolutionary algorithms are more expressive than conventional recursive algorithms, such as Turing machines. Three classes of evolutionary computations are introduced and studied: bounded finite, unbounded finite, and infinite computations. Universal evolutionary algorithms are constructed. Such properties of evolutionary algorithms as completeness, optimality, and search decidability are examined. A natural extension of evolutionary Turing machine (ETM) model is proposed to properly reflect phenomena of cooperation and competition in the whole population.

The finite element method in low speed aerodynamics

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1975-01-01

The finite element procedure is shown to be of significant impact in design of the 'computational wind tunnel' for low speed aerodynamics. The uniformity of the mathematical differential equation description, for viscous and/or inviscid, multi-dimensional subsonic flows about practical aerodynamic system configurations, is utilized to establish the general form of the finite element algorithm. Numerical results for inviscid flow analysis, as well as viscous boundary layer, parabolic, and full Navier Stokes flow descriptions verify the capabilities and overall versatility of the fundamental algorithm for aerodynamics. The proven mathematical basis, coupled with the distinct user-orientation features of the computer program embodiment, indicate near-term evolution of a highly useful analytical design tool to support computational configuration studies in low speed aerodynamics.

Finite key analysis for symmetric attacks in quantum key distribution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meyer, Tim; Kampermann, Hermann; Kleinmann, Matthias

2006-10-15

We introduce a constructive method to calculate the achievable secret key rate for a generic class of quantum key distribution protocols, when only a finite number n of signals is given. Our approach is applicable to all scenarios in which the quantum state shared by Alice and Bob is known. In particular, we consider the six state protocol with symmetric eavesdropping attacks, and show that for a small number of signals, i.e., below n{approx}10{sup 4}, the finite key rate differs significantly from the asymptotic value for n{yields}{infinity}. However, for larger n, a good approximation of the asymptotic value is found.more » We also study secret key rates for protocols using higher-dimensional quantum systems.« less

Finite-element analysis of NiTi wire deflection during orthodontic levelling treatment

NASA Astrophysics Data System (ADS)

Razali, M. F.; Mahmud, A. S.; Mokhtar, N.; Abdullah, J.

2016-02-01

Finite-element analysis is an important product development tool in medical devices industry for design and failure analysis of devices. This tool helps device designers to quickly explore various design options, optimizing specific designs and providing a deeper insight how a device is actually performing. In this study, three-dimensional finite-element models of superelastic nickel-titanium arch wire engaged in a three brackets system were developed. The aim was to measure the effect of binding friction developed on wire-bracket interaction towards the remaining recovery force available for tooth movement. Uniaxial and three brackets bending test were modelled and validated against experimental works. The prediction made by the three brackets bending models shows good agreement with the experimental results.

A high-accuracy optical linear algebra processor for finite element applications

NASA Technical Reports Server (NTRS)

Casasent, D.; Taylor, B. K.

1984-01-01

Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced.

Adiabatic and nonadiabatic perturbation theory for coherence vector description of neutrino oscillations

NASA Astrophysics Data System (ADS)

Hollenberg, Sebastian; Päs, Heinrich

2012-01-01

The standard wave function approach for the treatment of neutrino oscillations fails in situations where quantum ensembles at a finite temperature with or without an interacting background plasma are encountered. As a first step to treat such phenomena in a novel way, we propose a unified approach to both adiabatic and nonadiabatic two-flavor oscillations in neutrino ensembles with finite temperature and generic (e.g., matter) potentials. Neglecting effects of ensemble decoherence for now, we study the evolution of a neutrino ensemble governed by the associated quantum kinetic equations, which apply to systems with finite temperature. The quantum kinetic equations are solved formally using the Magnus expansion and it is shown that a convenient choice of the quantum mechanical picture (e.g., the interaction picture) reveals suitable parameters to characterize the physics of the underlying system (e.g., an effective oscillation length). It is understood that this method also provides a promising starting point for the treatment of the more general case in which decoherence is taken into account.

Patient-specific finite element modeling for femoral bone augmentation

PubMed Central

Basafa, Ehsan; Armiger, Robert S.; Kutzer, Michael D.; Belkoff, Stephen M.; Mears, Simon C.; Armand, Mehran

2015-01-01

The aim of this study was to provide a fast and accurate finite element (FE) modeling scheme for predicting bone stiffness and strength suitable for use within the framework of a computer-assisted osteoporotic femoral bone augmentation surgery system. The key parts of the system, i.e. preoperative planning and intraoperative assessment of the augmentation, demand the finite element model to be solved and analyzed rapidly. Available CT scans and mechanical testing results from nine pairs of osteoporotic femur bones, with one specimen from each pair augmented by polymethylmethacrylate (PMMA) bone cement, were used to create FE models and compare the results with experiments. Correlation values of R2 = 0.72–0.95 were observed between the experiments and FEA results which, combined with the fast model convergence (~3 min for ~250,000 degrees of freedom), makes the presented modeling approach a promising candidate for the intended application of preoperative planning and intraoperative assessment of bone augmentation surgery. PMID:23375663

Computational Methods for Structural Mechanics and Dynamics

NASA Technical Reports Server (NTRS)

Stroud, W. Jefferson (Editor); Housner, Jerrold M. (Editor); Tanner, John A. (Editor); Hayduk, Robert J. (Editor)

1989-01-01

Topics addressed include: transient dynamics; transient finite element method; transient analysis in impact and crash dynamic studies; multibody computer codes; dynamic analysis of space structures; multibody mechanics and manipulators; spatial and coplanar linkage systems; flexible body simulation; multibody dynamics; dynamical systems; and nonlinear characteristics of joints.

Higher-Order Adaptive Finite-Element Methods for Kohn-Sham Density Functional Theory

DTIC Science & Technology

2012-07-03

systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemi- cal accuracy...calculations. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of materials systems contain- ing a...benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy

Hierarchy of Certain Types of DNA Splicing Systems

NASA Astrophysics Data System (ADS)

Yusof, Yuhani; Sarmin, Nor Haniza; Goode, T. Elizabeth; Mahmud, Mazri; Heng, Fong Wan

A Head splicing system (H-system)consists of a finite set of strings (words) written over a finite alphabet, along with a finite set of rules that acts on the strings by iterated cutting and pasting to create a splicing language. Any interpretation that is aligned with Tom Head's original idea is one in which the strings represent double-stranded deoxyribonucleic acid (dsDNA) and the rules represent the cutting and pasting action of restriction enzymes and ligase, respectively. A new way of writing the rule sets is adopted so as to make the biological interpretation transparent. This approach is used in a formal language- theoretic analysis of the hierarchy of certain classes of splicing systems, namely simple, semi-simple and semi-null splicing systems. The relations between such systems and their associated languages are given as theorems, corollaries and counterexamples.

Obtaining manufactured geometries of deep-drawn components through a model updating procedure using geometric shape parameters

NASA Astrophysics Data System (ADS)

Balla, Vamsi Krishna; Coox, Laurens; Deckers, Elke; Plyumers, Bert; Desmet, Wim; Marudachalam, Kannan

2018-01-01

The vibration response of a component or system can be predicted using the finite element method after ensuring numerical models represent realistic behaviour of the actual system under study. One of the methods to build high-fidelity finite element models is through a model updating procedure. In this work, a novel model updating method of deep-drawn components is demonstrated. Since the component is manufactured with a high draw ratio, significant deviations in both profile and thickness distributions occurred in the manufacturing process. A conventional model updating, involving Young's modulus, density and damping ratios, does not lead to a satisfactory match between simulated and experimental results. Hence a new model updating process is proposed, where geometry shape variables are incorporated, by carrying out morphing of the finite element model. This morphing process imitates the changes that occurred during the deep drawing process. An optimization procedure that uses the Global Response Surface Method (GRSM) algorithm to maximize diagonal terms of the Modal Assurance Criterion (MAC) matrix is presented. This optimization results in a more accurate finite element model. The advantage of the proposed methodology is that the CAD surface of the updated finite element model can be readily obtained after optimization. This CAD model can be used for carrying out analysis, as it represents the manufactured part more accurately. Hence, simulations performed using this updated model with an accurate geometry, will therefore yield more reliable results.

Finite-time containment control of perturbed multi-agent systems based on sliding-mode control

NASA Astrophysics Data System (ADS)

Yu, Di; Ji, Xiang Yang

2018-01-01

Aimed at faster convergence rate, this paper investigates finite-time containment control problem for second-order multi-agent systems with norm-bounded non-linear perturbation. When topology between the followers are strongly connected, the nonsingular fast terminal sliding-mode error is defined, corresponding discontinuous control protocol is designed and the appropriate value range of control parameter is obtained by applying finite-time stability analysis, so that the followers converge to and move along the desired trajectories within the convex hull formed by the leaders in finite time. Furthermore, on the basis of the sliding-mode error defined, the corresponding distributed continuous control protocols are investigated with fast exponential reaching law and double exponential reaching law, so as to make the followers move to the small neighbourhoods of their desired locations and keep within the dynamic convex hull formed by the leaders in finite time to achieve practical finite-time containment control. Meanwhile, we develop the faster control scheme according to comparison of the convergence rate of these two different reaching laws. Simulation examples are given to verify the correctness of theoretical results.

3-d finite element model development for biomechanics: a software demonstration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hollerbach, K.; Hollister, A.M.; Ashby, E.

1997-03-01

Finite element analysis is becoming an increasingly important part of biomechanics and orthopedic research, as computational resources become more powerful, and data handling algorithms become more sophisticated. Until recently, tools with sufficient power did not exist or were not accessible to adequately model complicated, three-dimensional, nonlinear biomechanical systems. In the past, finite element analyses in biomechanics have often been limited to two-dimensional approaches, linear analyses, or simulations of single tissue types. Today, we have the resources to model fully three-dimensional, nonlinear, multi-tissue, and even multi-joint systems. The authors will present the process of developing these kinds of finite element models,more » using human hand and knee examples, and will demonstrate their software tools.« less

Study of hypervelocity meteoroid impact on orbital space stations

NASA Technical Reports Server (NTRS)

Leimbach, K. R.; Prozan, R. J.

1973-01-01

Structural damage resulting in hypervelocity impact of a meteorite on a spacecraft is discussed. Of particular interest is the backside spallation caused by such a collision. To treat this phenomenon two numerical schemes were developed in the course of this study to compute the elastic-plastic flow fracture of a solid. The numerical schemes are a five-point finite difference scheme and a four-node finite element scheme. The four-node finite element scheme proved to be less sensitive to the type of boundary conditions and loadings. Although further development work is needed to improve the program versatility (generalization of the network topology, secondary storage for large systems, improving of the coding to reduce the run time, etc.), the basic framework is provided for a utilitarian computer program which may be used in a wide variety of situations. Analytic results showing the program output are given for several test cases.

Collective Surfing of Chemically Active Particles

NASA Astrophysics Data System (ADS)

Masoud, Hassan; Shelley, Michael J.

2014-03-01

We study theoretically the collective dynamics of immotile particles bound to a 2D surface atop a 3D fluid layer. These particles are chemically active and produce a chemical concentration field that creates surface-tension gradients along the surface. The resultant Marangoni stresses create flows that carry the particles, possibly concentrating them. For a 3D diffusion-dominated concentration field and Stokesian fluid we show that the surface dynamics of active particle density can be determined using nonlocal 2D surface operators. Remarkably, we also show that for both deep or shallow fluid layers this surface dynamics reduces to the 2D Keller-Segel model for the collective chemotactic aggregation of slime mold colonies. Mathematical analysis has established that the Keller-Segel model can yield finite-time, finite-mass concentration singularities. We show that such singular behavior occurs in our finite-depth system, and study the associated 3D flow structures.

Nonlocal gradient corrections to the exchange free energy of an inhomogeneous many-fermion system at finite temperature

NASA Astrophysics Data System (ADS)

Geldart, D. J. W.; Dunlap, E.; Glasser, M. L.; Shegelski, Mark R. A.

1993-10-01

A general exact result is derived for the coefficient B x( n; T) which determines the first gradient correction to the leading exchange contribution to the free energy at finite temperature of a weakly inhomogeneous extended many fermion system having arbitrary two-body interactions. Explicit analytical results are given in the case of bare Coulomb interactions, and the case of statically screened Coulomb interactions is studied numerically. It is shown that nonanalytical structure leads to different limiting values of B x( n; T) when the inverse screening length and the temperature are both small. Some implications for physical many-electron systems are discussed, including the reasons for discrepancies between the first principles and semiempirical gradient coefficients for atomic exchange energies.

Buyer-vendor coordination for fixed lifetime product with quantity discount under finite production rate

NASA Astrophysics Data System (ADS)

Zhang, Qinghong; Luo, Jianwen; Duan, Yongrui

2016-03-01

Buyer-vendor coordination has been widely addressed; however, the fixed lifetime of the product is seldom considered. In this paper, we study the coordination of an integrated production-inventory system with quantity discount for a fixed lifetime product under finite production rate and deterministic demand. We first derive the buyer's ordering policy and the vendor's production batch size in decentralised and centralised systems. We then compare the two systems and show the non-coordination of the ordering policies and the production batch sizes. To improve the supply chain efficiency, we propose quantity discount contract and prove that the contract can coordinate the buyer-vendor supply chain. Finally, we present analytically tractable solutions and give a numerical example to illustrate the benefits of the proposed quantity discount strategy.

Hypermatrix scheme for finite element systems on CDC STAR-100 computer

NASA Technical Reports Server (NTRS)

Noor, A. K.; Voigt, S. J.

1975-01-01

A study is made of the adaptation of the hypermatrix (block matrix) scheme for solving large systems of finite element equations to the CDC STAR-100 computer. Discussion is focused on the organization of the hypermatrix computation using Cholesky decomposition and the mode of storage of the different submatrices to take advantage of the STAR pipeline (streaming) capability. Consideration is also given to the associated data handling problems and the means of balancing the I/Q and cpu times in the solution process. Numerical examples are presented showing anticipated gain in cpu speed over the CDC 6600 to be obtained by using the proposed algorithms on the STAR computer.

Matrix Sturm-Liouville equation with a Bessel-type singularity on a finite interval

NASA Astrophysics Data System (ADS)

Bondarenko, Natalia

2017-03-01

The matrix Sturm-Liouville equation on a finite interval with a Bessel-type singularity in the end of the interval is studied. Special fundamental systems of solutions for this equation are constructed: analytic Bessel-type solutions with the prescribed behavior at the singular point and Birkhoff-type solutions with the known asymptotics for large values of the spectral parameter. The asymptotic formulas for Stokes multipliers, connecting these two fundamental systems of solutions, are derived. We also set boundary conditions and obtain asymptotic formulas for the spectral data (the eigenvalues and the weight matrices) of the boundary value problem. Our results will be useful in the theory of direct and inverse spectral problems.

Computational methods for the control of distributed parameter systems

NASA Technical Reports Server (NTRS)

Burns, J. A.; Cliff, E. M.; Powers, R. K.

1985-01-01

It is shown that care must be taken to ensure that finite dimensional approximations of distributed parameter systems preserve important system properties (i.e., controllability, observability, stabilizability, detectability, etc.). It is noted that, if the particular scheme used to construct the finite dimensional model does not take into account these system properties, the model may not be suitable for control design and analysis. These ideas are illustrated by a simple example, i.e., a cable-spring-mass system.

Transient hydrodynamic finite-size effects in simulations under periodic boundary conditions

NASA Astrophysics Data System (ADS)

Asta, Adelchi J.; Levesque, Maximilien; Vuilleumier, Rodolphe; Rotenberg, Benjamin

2017-06-01

We use lattice-Boltzmann and analytical calculations to investigate transient hydrodynamic finite-size effects induced by the use of periodic boundary conditions. These effects are inevitable in simulations at the molecular, mesoscopic, or continuum levels of description. We analyze the transient response to a local perturbation in the fluid and obtain the local velocity correlation function via linear response theory. This approach is validated by comparing the finite-size effects on the steady-state velocity with the known results for the diffusion coefficient. We next investigate the full time dependence of the local velocity autocorrelation function. We find at long times a crossover between the expected t-3 /2 hydrodynamic tail and an oscillatory exponential decay, and study the scaling with the system size of the crossover time, exponential rate and amplitude, and oscillation frequency. We interpret these results from the analytic solution of the compressible Navier-Stokes equation for the slowest modes, which are set by the system size. The present work not only provides a comprehensive analysis of hydrodynamic finite-size effects in bulk fluids, which arise regardless of the level of description and simulation algorithm, but also establishes the lattice-Boltzmann method as a suitable tool to investigate such effects in general.

Retrieving the ground state of spin glasses using thermal noise: Performance of quantum annealing at finite temperatures.

PubMed

Nishimura, Kohji; Nishimori, Hidetoshi; Ochoa, Andrew J; Katzgraber, Helmut G

2016-09-01

We study the problem to infer the ground state of a spin-glass Hamiltonian using data from another Hamiltonian with interactions disturbed by noise from the original Hamiltonian, motivated by the ground-state inference in quantum annealing on a noisy device. It is shown that the average Hamming distance between the inferred spin configuration and the true ground state is minimized when the temperature of the noisy system is kept at a finite value, and not at zero temperature. We present a spin-glass generalization of a well-established result that the ground state of a purely ferromagnetic Hamiltonian is best inferred at a finite temperature in the sense of smallest Hamming distance when the original ferromagnetic interactions are disturbed by noise. We use the numerical transfer-matrix method to establish the existence of an optimal finite temperature in one- and two-dimensional systems. Our numerical results are supported by mean-field calculations, which give an explicit expression of the optimal temperature to infer the spin-glass ground state as a function of variances of the distributions of the original interactions and the noise. The mean-field prediction is in qualitative agreement with numerical data. Implications on postprocessing of quantum annealing on a noisy device are discussed.

Numeric simulation model for long-term orthodontic tooth movement with contact boundary conditions using the finite element method.

PubMed

Hamanaka, Ryo; Yamaoka, Satoshi; Anh, Tuan Nguyen; Tominaga, Jun-Ya; Koga, Yoshiyuki; Yoshida, Noriaki

2017-11-01

Although many attempts have been made to simulate orthodontic tooth movement using the finite element method, most were limited to analyses of the initial displacement in the periodontal ligament and were insufficient to evaluate the effect of orthodontic appliances on long-term tooth movement. Numeric simulation of long-term tooth movement was performed in some studies; however, neither the play between the brackets and archwire nor the interproximal contact forces were considered. The objectives of this study were to simulate long-term orthodontic tooth movement with the edgewise appliance by incorporating those contact conditions into the finite element model and to determine the force system when the space is closed with sliding mechanics. We constructed a 3-dimensional model of maxillary dentition with 0.022-in brackets and 0.019 × 0.025-in archwire. Forces of 100 cN simulating sliding mechanics were applied. The simulation was accomplished on the assumption that bone remodeling correlates with the initial tooth displacement. This method could successfully represent the changes in the moment-to-force ratio: the tooth movement pattern during space closure. We developed a novel method that could simulate the long-term orthodontic tooth movement and accurately determine the force system in the course of time by incorporating contact boundary conditions into finite element analysis. It was also suggested that friction is progressively increased during space closure in sliding mechanics. Copyright © 2017. Published by Elsevier Inc.

Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight. [atmospheric general circulation experiment, convection in a float zone, and the Bridgman-Stockbarger crystal growing system

NASA Technical Reports Server (NTRS)

Roberts, G. O.; Fowlis, W. W.; Miller, T. L.

1984-01-01

Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface.

The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Long, Wen; Yang, Zhaoqing; Copping, Andrea E.

: As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3Dmore » sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.« less

Optimization of the Conical Angle Design in Conical Implant-Abutment Connections: A Pilot Study Based on the Finite Element Method.

PubMed

Yao, Kuang-Ta; Chen, Chen-Sheng; Cheng, Cheng-Kung; Fang, Hsu-Wei; Huang, Chang-Hung; Kao, Hung-Chan; Hsu, Ming-Lun

2018-02-01

Conical implant-abutment connections are popular for their excellent connection stability, which is attributable to frictional resistance in the connection. However, conical angles, the inherent design parameter of conical connections, exert opposing effects on 2 influencing factors of the connection stability: frictional resistance and abutment rigidity. This pilot study employed an optimization approach through the finite element method to obtain an optimal conical angle for the highest connection stability in an Ankylos-based conical connection system. A nonlinear 3-dimensional finite element parametric model was developed according to the geometry of the Ankylos system (conical half angle = 5.7°) by using the ANSYS 11.0 software. Optimization algorithms were conducted to obtain the optimal conical half angle and achieve the minimal value of maximum von Mises stress in the abutment, which represents the highest connection stability. The optimal conical half angle obtained was 10.1°. Compared with the original design (5.7°), the optimal design demonstrated an increased rigidity of abutment (36.4%) and implant (25.5%), a decreased microgap at the implant-abutment interface (62.3%), a decreased contact pressure (37.9%) with a more uniform stress distribution in the connection, and a decreased stress in the cortical bone (4.5%). In conclusion, the methodology of design optimization to determine the optimal conical angle of the Ankylos-based system is feasible. Because of the heterogeneity of different systems, more studies should be conducted to define the optimal conical angle in various conical connection designs.

Electronic excitations in finite and infinite polyenes

NASA Astrophysics Data System (ADS)

Tavan, Paul; Schulten, Klaus

1987-09-01

We study electronic excitations in long polyenes, i.e., in one-dimensional strongly correlated electron systems which are neither infinite nor small. The excitations are described within Hubbard and Pariser-Parr-Pople (PPP) models by means of a multiple-reference double-excitation expansion [P. Tavan and K. Schulten, J. Chem. Phys. 85, 6602 (1986)]. We find that quantized ``transition'' momenta can be assigned to electronic excitations in finite chains. These momenta link excitation energies of finite chains to dispersion relations of infinite chains, i.e., they bridge the gap between finite and infinite systems. A key result is the following: Excitation energies E in polyenes with N carbon atoms are described very accurately by the formula Eβ=ΔEβ0+αβk(N)q, q=1,2,..., where β denotes the excitation class, ΔEβ0 the energy gap in the infinite system [αβk(N)>0], and k(N) the elementary transition momentum. The parameters ΔEβ0 and αβ are determined for covalent and ionic excitations in alternating and nonalternating polyenes. The covalent excitations are combinations of triplet excitations T, i.e., T, TT, TTT, . . . . The lowest singlet excitations in the infinite polyene, e.g., in polyacetylene or polydiacetylene, are TT states. Available evidence proves that these states can dissociate into separate triplets. The bond structure of TT states is that of a neutral soliton-antisoliton pair. The level density of TT states in long polyenes is high enough to allow dissociation into separate solitons.

Pseudo-simple heteroclinic cycles in R4

NASA Astrophysics Data System (ADS)

Chossat, Pascal; Lohse, Alexander; Podvigina, Olga

2018-06-01

We study pseudo-simple heteroclinic cycles for a Γ-equivariant system in R4 with finite Γ ⊂ O(4) , and their nearby dynamics. In particular, in a first step towards a full classification - analogous to that which exists already for the class of simple cycles - we identify all finite subgroups of O(4) admitting pseudo-simple cycles. To this end we introduce a constructive method to build equivariant dynamical systems possessing a robust heteroclinic cycle. Extending a previous study we also investigate the existence of periodic orbits close to a pseudo-simple cycle, which depends on the symmetry groups of equilibria in the cycle. Moreover, we identify subgroups Γ ⊂ O(4) , Γ ⊄ SO(4) , admitting fragmentarily asymptotically stable pseudo-simple heteroclinic cycles. (It has been previously shown that for Γ ⊂ SO(4) pseudo-simple cycles generically are completely unstable.) Finally, we study a generalized heteroclinic cycle, which involves a pseudo-simple cycle as a subset.

Complexity multiscale asynchrony measure and behavior for interacting financial dynamics

NASA Astrophysics Data System (ADS)

Yang, Ge; Wang, Jun; Niu, Hongli

2016-08-01

A stochastic financial price process is proposed and investigated by the finite-range multitype contact dynamical system, in an attempt to study the nonlinear behaviors of real asset markets. The viruses spreading process in a finite-range multitype system is used to imitate the interacting behaviors of diverse investment attitudes in a financial market, and the empirical research on descriptive statistics and autocorrelation behaviors of return time series is performed for different values of propagation rates. Then the multiscale entropy analysis is adopted to study several different shuffled return series, including the original return series, the corresponding reversal series, the random shuffled series, the volatility shuffled series and the Zipf-type shuffled series. Furthermore, we propose and compare the multiscale cross-sample entropy and its modification algorithm called composite multiscale cross-sample entropy. We apply them to study the asynchrony of pairs of time series under different time scales.

Evaluation of β-blocker gel and effect of dosing volume for topical delivery.

PubMed

Zhang, Qian; Chantasart, Doungdaw; Li, S Kevin

2015-05-01

Although topical administration of β-blockers is desired because of the improved therapeutic efficacy and reduced systemic adverse effects compared with systemic administration in the treatment of infantile hemangioma, the permeation of β-blockers across skin under finite dose conditions has not been systematically studied and an effective topical β-blocker formulation for skin application is not available. The present study evaluated the permeation of β-blockers propranolol, betaxolol, and timolol across human epidermal membrane (HEM) from a topical gel in Franz diffusion cells in vitro under various dosing conditions. The effects of occlusion and dosing volume on percutaneous absorption of β-blockers from the gel were studied. The permeation data were compared with those of finite dose diffusion theory. The results showed that skin permeation of β-blockers generally could be enhanced two to three times by skin occlusion. The cumulative amounts of β-blockers permeated across HEM increased with increasing dosing volume. An adequate fit was obtained between the theoretical curve and experimental permeation data, indicating that the experimental results of the gel are consistent with finite dose diffusion theory. In conclusion, the findings suggest the feasibility of using topical gels of β-blockers for infantile hemangioma treatment and topical application with skin occlusion is preferred. © 2015 Wiley Periodicals, Inc. and the American Pharmacists Association.

A Numerical Study of Scalable Cardiac Electro-Mechanical Solvers on HPC Architectures

PubMed Central

Colli Franzone, Piero; Pavarino, Luca F.; Scacchi, Simone

2018-01-01

We introduce and study some scalable domain decomposition preconditioners for cardiac electro-mechanical 3D simulations on parallel HPC (High Performance Computing) architectures. The electro-mechanical model of the cardiac tissue is composed of four coupled sub-models: (1) the static finite elasticity equations for the transversely isotropic deformation of the cardiac tissue; (2) the active tension model describing the dynamics of the intracellular calcium, cross-bridge binding and myofilament tension; (3) the anisotropic Bidomain model describing the evolution of the intra- and extra-cellular potentials in the deforming cardiac tissue; and (4) the ionic membrane model describing the dynamics of ionic currents, gating variables, ionic concentrations and stretch-activated channels. This strongly coupled electro-mechanical model is discretized in time with a splitting semi-implicit technique and in space with isoparametric finite elements. The resulting scalable parallel solver is based on Multilevel Additive Schwarz preconditioners for the solution of the Bidomain system and on BDDC preconditioned Newton-Krylov solvers for the non-linear finite elasticity system. The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks. PMID:29674971

Immune networks: multitasking capabilities near saturation

NASA Astrophysics Data System (ADS)

Agliari, E.; Annibale, A.; Barra, A.; Coolen, A. C. C.; Tantari, D.

2013-10-01

Pattern-diluted associative networks were recently introduced as models for the immune system, with nodes representing T-lymphocytes and stored patterns representing signalling protocols between T- and B-lymphocytes. It was shown earlier that in the regime of extreme pattern dilution, a system with NT T-lymphocytes can manage a number N_B={ {O}}(N_T^\\delta ) of B-lymphocytes simultaneously, with δ < 1. Here we study this model in the extensive load regime NB = αNT, with a high degree of pattern dilution, in agreement with immunological findings. We use graph theory and statistical mechanical analysis based on replica methods to show that in the finite-connectivity regime, where each T-lymphocyte interacts with a finite number of B-lymphocytes as NT → ∞, the T-lymphocytes can coordinate effective immune responses to an extensive number of distinct antigen invasions in parallel. As α increases, the system eventually undergoes a second order transition to a phase with clonal cross-talk interference, where the system’s performance degrades gracefully. Mathematically, the model is equivalent to a spin system on a finitely connected graph with many short loops, so one would expect the available analytical methods, which all assume locally tree-like graphs, to fail. Yet it turns out to be solvable. Our results are supported by numerical simulations.

Finite-time H∞ control for linear continuous system with norm-bounded disturbance

NASA Astrophysics Data System (ADS)

Meng, Qingyi; Shen, Yanjun

2009-04-01

In this paper, the definition of finite-time H∞ control is presented. The system under consideration is subject to time-varying norm-bounded exogenous disturbance. The main aim of this paper is focused on the design a state feedback controller which ensures that the closed-loop system is finite-time bounded (FTB) and reduces the effect of the disturbance input on the controlled output to a prescribed level. A sufficient condition is presented for the solvability of this problem, which can be reduced to a feasibility problem involving linear matrix inequalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints

NASA Astrophysics Data System (ADS)

Manukure, Solomon

2018-04-01

We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.

From Finite Time to Finite Physical Dimensions Thermodynamics: The Carnot Engine and Onsager's Relations Revisited

NASA Astrophysics Data System (ADS)

Feidt, Michel; Costea, Monica

2018-04-01

Many works have been devoted to finite time thermodynamics since the Curzon and Ahlborn [1] contribution, which is generally considered as its origin. Nevertheless, previous works in this domain have been revealed [2], [3], and recently, results of the attempt to correlate Finite Time Thermodynamics with Linear Irreversible Thermodynamics according to Onsager's theory were reported [4]. The aim of the present paper is to extend and improve the approach relative to thermodynamic optimization of generic objective functions of a Carnot engine with linear response regime presented in [4]. The case study of the Carnot engine is revisited within the steady state hypothesis, when non-adiabaticity of the system is considered, and heat loss is accounted for by an overall heat leak between the engine heat reservoirs. The optimization is focused on the main objective functions connected to engineering conditions, namely maximum efficiency or power output, except the one relative to entropy that is more fundamental. Results given in reference [4] relative to the maximum power output and minimum entropy production as objective function are reconsidered and clarified, and the change from finite time to finite physical dimension was shown to be done by the heat flow rate at the source. Our modeling has led to new results of the Carnot engine optimization and proved that the primary interest for an engineer is mainly connected to what we called Finite Physical Dimensions Optimal Thermodynamics.

Adaptive sliding mode control for finite-time stability of quad-rotor UAVs with parametric uncertainties.

PubMed

Mofid, Omid; Mobayen, Saleh

2018-01-01

Adaptive control methods are developed for stability and tracking control of flight systems in the presence of parametric uncertainties. This paper offers a design technique of adaptive sliding mode control (ASMC) for finite-time stabilization of unmanned aerial vehicle (UAV) systems with parametric uncertainties. Applying the Lyapunov stability concept and finite-time convergence idea, the recommended control method guarantees that the states of the quad-rotor UAV are converged to the origin with a finite-time convergence rate. Furthermore, an adaptive-tuning scheme is advised to guesstimate the unknown parameters of the quad-rotor UAV at any moment. Finally, simulation results are presented to exhibit the helpfulness of the offered technique compared to the previous methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Fourier heat conduction as a strong kinetic effect in one-dimensional hard-core gases

NASA Astrophysics Data System (ADS)

Zhao, Hanqing; Wang, Wen-ge

2018-01-01

For a one-dimensional (1D) momentum conserving system, intensive studies have shown that generally its heat current autocorrelation function (HCAF) tends to decay in a power-law manner and results in the breakdown of the Fourier heat conduction law in the thermodynamic limit. This has been recognized to be a dominant hydrodynamic effect. Here we show that, instead, the kinetic effect can be dominant in some cases and leads to the Fourier law for finite-size systems. Usually the HCAF undergoes a fast decaying kinetic stage followed by a long slowly decaying hydrodynamic tail. In a finite range of the system size, we find that whether the system follows the Fourier law depends on whether the kinetic stage dominates. Our Rapid Communication is illustrated by the 1D hard-core gas models with which the HCAF is derived analytically and verified numerically by molecular dynamics simulations.

A one-dimensional nonlinear problem of thermoelasticity in extended thermodynamics

NASA Astrophysics Data System (ADS)

Rawy, E. K.

2018-06-01

We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system is clarified through a study of the characteristic curves. Progressive wave solutions with two finite speeds are noted. A numerical treatment is presented for the nonlinear system using a three-step, quasi-linearization, iterative finite-difference scheme for which the linear system of equations is the initial step in the iteration. The obtained results are discussed in detail. They clearly show the hyperbolic nature of the system, and may be of interest in investigating thermoelastic materials, not only at low temperatures, but also during high temperature processes involving rapid changes in temperature as in laser treatment of surfaces.

Parallel Computation and Visualization of Three-dimensional, Time-dependent, Thermal Convective Flows

NASA Technical Reports Server (NTRS)

Wang, P.; Li, P.

1998-01-01

A high-resolution numerical study on parallel systems is reported on three-dimensional, time-dependent, thermal convective flows. A parallel implentation on the finite volume method with a multigrid scheme is discussed, and a parallel visualization systemm is developed on distributed systems for visualizing the flow.

On conforming mixed finite element methods for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.

1982-01-01

The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.

Statistical field theory with constraints: Application to critical Casimir forces in the canonical ensemble.

PubMed

Gross, Markus; Gambassi, Andrea; Dietrich, S

2017-08-01

The effect of imposing a constraint on a fluctuating scalar order parameter field in a system of finite volume is studied within statistical field theory. The canonical ensemble, corresponding to a fixed total integrated order parameter (e.g., the total number of particles), is obtained as a special case of the theory. A perturbative expansion is developed which allows one to systematically determine the constraint-induced finite-volume corrections to the free energy and to correlation functions. In particular, we focus on the Landau-Ginzburg model in a film geometry (i.e., in a rectangular parallelepiped with a small aspect ratio) with periodic, Dirichlet, or Neumann boundary conditions in the transverse direction and periodic boundary conditions in the remaining, lateral directions. Within the expansion in terms of ε=4-d, where d is the spatial dimension of the bulk, the finite-size contribution to the free energy of the confined system and the associated critical Casimir force are calculated to leading order in ε and are compared to the corresponding expressions for an unconstrained (grand canonical) system. The constraint restricts the fluctuations within the system and it accordingly modifies the residual finite-size free energy. The resulting critical Casimir force is shown to depend on whether it is defined by assuming a fixed transverse area or a fixed total volume. In the former case, the constraint is typically found to significantly enhance the attractive character of the force as compared to the grand canonical case. In contrast to the grand canonical Casimir force, which, for supercritical temperatures, vanishes in the limit of thick films, in the canonical case with fixed transverse area the critical Casimir force attains for thick films a negative value for all boundary conditions studied here. Typically, the dependence of the critical Casimir force both on the temperaturelike and on the fieldlike scaling variables is different in the two ensembles.

Statistical field theory with constraints: Application to critical Casimir forces in the canonical ensemble

NASA Astrophysics Data System (ADS)

Gross, Markus; Gambassi, Andrea; Dietrich, S.

2017-08-01

The effect of imposing a constraint on a fluctuating scalar order parameter field in a system of finite volume is studied within statistical field theory. The canonical ensemble, corresponding to a fixed total integrated order parameter (e.g., the total number of particles), is obtained as a special case of the theory. A perturbative expansion is developed which allows one to systematically determine the constraint-induced finite-volume corrections to the free energy and to correlation functions. In particular, we focus on the Landau-Ginzburg model in a film geometry (i.e., in a rectangular parallelepiped with a small aspect ratio) with periodic, Dirichlet, or Neumann boundary conditions in the transverse direction and periodic boundary conditions in the remaining, lateral directions. Within the expansion in terms of ɛ =4 -d , where d is the spatial dimension of the bulk, the finite-size contribution to the free energy of the confined system and the associated critical Casimir force are calculated to leading order in ɛ and are compared to the corresponding expressions for an unconstrained (grand canonical) system. The constraint restricts the fluctuations within the system and it accordingly modifies the residual finite-size free energy. The resulting critical Casimir force is shown to depend on whether it is defined by assuming a fixed transverse area or a fixed total volume. In the former case, the constraint is typically found to significantly enhance the attractive character of the force as compared to the grand canonical case. In contrast to the grand canonical Casimir force, which, for supercritical temperatures, vanishes in the limit of thick films, in the canonical case with fixed transverse area the critical Casimir force attains for thick films a negative value for all boundary conditions studied here. Typically, the dependence of the critical Casimir force both on the temperaturelike and on the fieldlike scaling variables is different in the two ensembles.

Recursive Inversion By Finite-Impulse-Response Filters

NASA Technical Reports Server (NTRS)

Bach, Ralph E., Jr.; Baram, Yoram

1991-01-01

Recursive approximation gives least-squares best fit to exact response. Algorithm yields finite-impulse-response approximation of unknown single-input/single-output, causal, time-invariant, linear, real system, response of which is sequence of impulses. Applicable to such system-inversion problems as suppression of echoes and identification of target from its scatter response to incident impulse.

THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

EPA Science Inventory

A three-point backward finite-difference method has been derived for a system of mixed hyperbolic_¯¯parabolic (convection_¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

A Novel Finite-Sum Inequality-Based Method for Robust H∞ Control of Uncertain Discrete-Time Takagi-Sugeno Fuzzy Systems With Interval-Like Time-Varying Delays.

PubMed

Zhang, Xian-Ming; Han, Qing-Long; Ge, Xiaohua

2017-09-22

This paper is concerned with the problem of robust H∞ control of an uncertain discrete-time Takagi-Sugeno fuzzy system with an interval-like time-varying delay. A novel finite-sum inequality-based method is proposed to provide a tighter estimation on the forward difference of certain Lyapunov functional, leading to a less conservative result. First, an auxiliary vector function is used to establish two finite-sum inequalities, which can produce tighter bounds for the finite-sum terms appearing in the forward difference of the Lyapunov functional. Second, a matrix-based quadratic convex approach is employed to equivalently convert the original matrix inequality including a quadratic polynomial on the time-varying delay into two boundary matrix inequalities, which delivers a less conservative bounded real lemma (BRL) for the resultant closed-loop system. Third, based on the BRL, a novel sufficient condition on the existence of suitable robust H∞ fuzzy controllers is derived. Finally, two numerical examples and a computer-simulated truck-trailer system are provided to show the effectiveness of the obtained results.

Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2005-01-01

A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.

Advances and trends in structures and dynamics; Proceedings of the Symposium, Washington, DC, October 22-25, 1984

NASA Technical Reports Server (NTRS)

Noor, A. K. (Editor); Hayduk, R. J. (Editor)

1985-01-01

Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.

Logics for Coalgebras of Finitary Set Functors

NASA Astrophysics Data System (ADS)

Sprunger, David

In this thesis, we present a collection of results about coalgebras of finitary Set functors. Our chief contribution is a logic for behavioral equivalence for states in these coalgebras. This proof system is intended to formalize a common pattern of reasoning in the study of coalgebra commonly called proof by bisimulation or bisimulation up-to. The approach in this thesis combine these up-to techniques with a concept very close to bisimulation to show the proof system is sound and complete with respect to behavioral equivalence. Our second category of contributions revolves around applications of coalgebra to the study of sequences and power series. The culmination of this work is a new approach to Christol's Theorem, a classic result characterizing the algebraic power series in finite characteristic rings as those whose coefficients can be produced by finite automata.

Compositeness of hadron resonances in finite volume

NASA Astrophysics Data System (ADS)

Tsuchida, Yujiro; Hyodo, Tetsuo

2018-05-01

We develop a theoretical framework to quantify the structure of unstable hadron resonances. With the help of the corresponding system in a finite volume, we define the compositeness of resonance states which can be interpreted as a probability. This framework is used to study the structure of the scalar mesons f0(980 ) and a0(980 ) . In both mesons, the K ¯K component dominates about a half of the wave function. The method is also applied to the Λ (1405 ) resonance. We argue that a single energy level in finite volume represents the two eigenstates in infinite volume. The K ¯N component of Λ (1405 ) , including contributions from both eigenstates, is found to be 58%, and the rest is composed of the π Σ and other channels.

Topological footprints of the Kitaev chain with long-range superconducting pairings at a finite temperature

NASA Astrophysics Data System (ADS)

Bhattacharya, Utso; Dutta, Amit

2018-06-01

We study the one-dimensional Kitaev chain with long-range superconductive pairing terms at a finite temperature where the system is prepared in a mixed state in equilibrium with a heat reservoir maintained at a constant temperature T . In order to probe the footprint of the ground-state topological behavior of the model at finite temperature, we look at two global quantities extracted out of two geometrical constructions: the Uhlmann and the interferometric phase. Interestingly, when the long-range effect dominates, the Uhlmann phase approach fails to reproduce the topological aspects of the model in the pure-state limit; on the other hand, the interferometric phase which has a proper pure state reduction, shows a behavior independent of the ambient temperature.

Higher order cumulants in colorless partonic plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cherif, S.; Laboratoire de Physique et de Mathématiques Appliquées; Ahmed, M. A. A.

2016-06-10

Any physical system considered to study the QCD deconfinement phase transition certainly has a finite volume, so the finite size effects are inevitably present. This renders the location of the phase transition and the determination of its order as an extremely difficult task, even in the simplest known cases. In order to identify and locate the colorless QCD deconfinement transition point in finite volume T{sub 0}(V), a new approach based on the finite-size cumulant expansion of the order parameter and the ℒ{sub m,n}-Method is used. We have shown that both cumulants of higher order and their ratios, associated to themore » thermodynamical fluctuations of the order parameter, in QCD deconfinement phase transition behave in a particular enough way revealing pronounced oscillations in the transition region. The sign structure and the oscillatory behavior of these in the vicinity of the deconfinement phase transition point might be a sensitive probe and may allow one to elucidate their relation to the QCD phase transition point. In the context of our model, we have shown that the finite volume transition point is always associated to the appearance of a particular point in whole higher order cumulants under consideration.« less

An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Sebastian, J. D.; Weatherill, W. H.

1979-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.

Verus: A Tool for Quantitative Analysis of Finite-State Real-Time Systems.

DTIC Science & Technology

1996-08-12

Symbolic model checking is a technique for verifying finite-state concurrent systems that has been extended to handle real - time systems . Models with...up to 10(exp 30) states can often be verified in minutes. In this paper, we present a new tool to analyze real - time systems , based on this technique...We have designed a language, called Verus, for the description of real - time systems . Such a description is compiled into a state-transition graph and

Design approach of an aquaculture cage system for deployment in the constructed channel flow environments of a power plant

PubMed Central

Lee, Jihoon; Fredriksson, David W.; DeCew, Judson; Drach, Andrew; Yim, Solomon C.

2018-01-01

This study provides an engineering approach for designing an aquaculture cage system for use in constructed channel flow environments. As sustainable aquaculture has grown globally, many novel techniques have been introduced such as those implemented in the global Atlantic salmon industry. The advent of several highly sophisticated analysis software systems enables the development of such novel engineering techniques. These software systems commonly include three-dimensional (3D) drafting, computational fluid dynamics, and finite element analysis. In this study, a combination of these analysis tools is applied to evaluate a conceptual aquaculture system for potential deployment in a power plant effluent channel. The channel is supposedly clean; however, it includes elevated water temperatures and strong currents. The first portion of the analysis includes the design of a fish cage system with specific net solidities using 3D drafting techniques. Computational fluid dynamics is then applied to evaluate the flow reduction through the system from the previously generated solid models. Implementing the same solid models, a finite element analysis is performed on the critical components to assess the material stresses produced by the drag force loads that are calculated from the fluid velocities. PMID:29897954

A hybrid finite element-transfer matrix model for vibroacoustic systems with flat and homogeneous acoustic treatments.

PubMed

Alimonti, Luca; Atalla, Noureddine; Berry, Alain; Sgard, Franck

2015-02-01

Practical vibroacoustic systems involve passive acoustic treatments consisting of highly dissipative media such as poroelastic materials. The numerical modeling of such systems at low to mid frequencies typically relies on substructuring methodologies based on finite element models. Namely, the master subsystems (i.e., structural and acoustic domains) are described by a finite set of uncoupled modes, whereas condensation procedures are typically preferred for the acoustic treatments. However, although accurate, such methodology is computationally expensive when real life applications are considered. A potential reduction of the computational burden could be obtained by approximating the effect of the acoustic treatment on the master subsystems without introducing physical degrees of freedom. To do that, the treatment has to be assumed homogeneous, flat, and of infinite lateral extent. Under these hypotheses, simple analytical tools like the transfer matrix method can be employed. In this paper, a hybrid finite element-transfer matrix methodology is proposed. The impact of the limiting assumptions inherent within the analytical framework are assessed for the case of plate-cavity systems involving flat and homogeneous acoustic treatments. The results prove that the hybrid model can capture the qualitative behavior of the vibroacoustic system while reducing the computational effort.

Finite element methods for the biomechanics of soft hydrated tissues: nonlinear analysis and adaptive control of meshes.

PubMed

Spilker, R L; de Almeida, E S; Donzelli, P S

1992-01-01

This chapter addresses computationally demanding numerical formulations in the biomechanics of soft tissues. The theory of mixtures can be used to represent soft hydrated tissues in the human musculoskeletal system as a two-phase continuum consisting of an incompressible solid phase (collagen and proteoglycan) and an incompressible fluid phase (interstitial water). We first consider the finite deformation of soft hydrated tissues in which the solid phase is represented as hyperelastic. A finite element formulation of the governing nonlinear biphasic equations is presented based on a mixed-penalty approach and derived using the weighted residual method. Fluid and solid phase deformation, velocity, and pressure are interpolated within each element, and the pressure variables within each element are eliminated at the element level. A system of nonlinear, first-order differential equations in the fluid and solid phase deformation and velocity is obtained. In order to solve these equations, the contributions of the hyperelastic solid phase are incrementally linearized, a finite difference rule is introduced for temporal discretization, and an iterative scheme is adopted to achieve equilibrium at the end of each time increment. We demonstrate the accuracy and adequacy of the procedure using a six-node, isoparametric axisymmetric element, and we present an example problem for which independent numerical solution is available. Next, we present an automated, adaptive environment for the simulation of soft tissue continua in which the finite element analysis is coupled with automatic mesh generation, error indicators, and projection methods. Mesh generation and updating, including both refinement and coarsening, for the two-dimensional examples examined in this study are performed using the finite quadtree approach. The adaptive analysis is based on an error indicator which is the L2 norm of the difference between the finite element solution and a projected finite element solution. Total stress, calculated as the sum of the solid and fluid phase stresses, is used in the error indicator. To allow the finite difference algorithm to proceed in time using an updated mesh, solution values must be transferred to the new nodal locations. This rezoning is accomplished using a projected field for the primary variables. The accuracy and effectiveness of this adaptive finite element analysis is demonstrated using a linear, two-dimensional, axisymmetric problem corresponding to the indentation of a thin sheet of soft tissue. The method is shown to effectively capture the steep gradients and to produce solutions in good agreement with independent, converged, numerical solutions.

A study on thermal barrier coatings including thermal expansion mismatch and bond coat oxidation

NASA Technical Reports Server (NTRS)

Chang, George C.; Phucharoen, Woraphat; Miller, Robert A.

1986-01-01

The present investigation deals with a plasma-sprayed thermal barrier coating (TBC) intended for high temperature applications to advanced gas turbine blades. Typically, this type of coating system consists of a zirconia-yttria ceramic layer with a nickel-chromium-aluminum bond coat on a superalloy substrate. The problem on hand is a complex one due to the fact that bond coat oxidation and thermal mismatch occur in the TBC. Cracking in the TBC has also been experimentally illustrated. A clearer understanding of the mechanical behavior of the TBC is investigated. The stress states in a model thermal barrier coating as it cools down in air is studied. The powerful finite element method was utilized to model a coating cylindrical specimen. Four successively refined finite element models were developed. Some results obtained using the first two models have been reported previously. The major accomplishment is the successful development of an elastic TBC finite element model known as TBCG with interface geometry between the ceramic layer and the bond coat. An equally important milestone is the near-completion of the new elastic-plastic TBC finite element model called TBCGEP which yielded initial results. Representative results are presented.

Stable and unstable singularities in the unforced Hele-Shaw cell

DOE Office of Scientific and Technical Information (OSTI.GOV)

Almgren, R.; Bertozzi, A.; Brenner, M.P.

We study singularity formation in the lubrication model for the unforced Hele-Shaw system, describing the breaking in two of a fluid droplet confined between two narrowly spaced glass plates. By varying the initial data, we exhibit four different scenarios: (1) the droplet breaks in finite time, with two pinch points moving toward each other and merging at the singular time; (2) the droplet breaks in finite time, with two asymmetric pinch points propagating away from each other; (3) the droplet breaks in finite time, with a single symmetric pinch point; or (4) the droplet relaxes to a stable equilibrium shapemore » without a finite time breakup. Each of the three singular scenarios has a self-similar structure with different scaling laws; the first scenario has not been observed before in other Hele-Shaw studies. We demonstrate instabilities of the second and third scenarios, in which the solution changes its behavior at a thickness that can be arbitrarily small depending on the initial condition. These transitions can be identified by examining the structure of the solution in the intermediate scaling region. {copyright} {ital 1996 American Institute of Physics.}« less

Entanglement entropy in Fermi gases and Anderson's orthogonality catastrophe.

PubMed

Ossipov, A

2014-09-26

We study the ground-state entanglement entropy of a finite subsystem of size L of an infinite system of noninteracting fermions scattered by a potential of finite range a. We derive a general relation between the scattering matrix and the overlap matrix and use it to prove that for a one-dimensional symmetric potential the von Neumann entropy, the Rényi entropies, and the full counting statistics are robust against potential scattering, provided that L/a≫1. The results of numerical calculations support the validity of this conclusion for a generic potential.

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.

Vibration suppression with approximate finite dimensional compensators for distributed systems: Computational methods and experimental results

NASA Technical Reports Server (NTRS)

Banks, H. T.; Smith, Ralph C.; Wang, Yun

1994-01-01

Based on a distributed parameter model for vibrations, an approximate finite dimensional dynamic compensator is designed to suppress vibrations (multiple modes with a broad band of frequencies) of a circular plate with Kelvin-Voigt damping and clamped boundary conditions. The control is realized via piezoceramic patches bonded to the plate and is calculated from information available from several pointwise observed state variables. Examples from computational studies as well as use in laboratory experiments are presented to demonstrate the effectiveness of this design.

Finite-Size Effects in Single Chain Magnets: An Experimental and Theoretical Study

NASA Astrophysics Data System (ADS)

Bogani, L.; Caneschi, A.; Fedi, M.; Gatteschi, D.; Massi, M.; Novak, M. A.; Pini, M. G.; Rettori, A.; Sessoli, R.; Vindigni, A.

2004-05-01

The problem of finite-size effects in s=1/2 Ising systems showing slow dynamics of the magnetization is investigated introducing diamagnetic impurities in a Co2+-radical chain. The static magnetic properties have been measured and analyzed considering the peculiarities induced by the ferrimagnetic character of the compound. The dynamic susceptibility shows that an Arrhenius law is observed with the same energy barrier for the pure and the doped compounds while the prefactor decreases, as theoretically predicted. Multiple spin reversal has also been investigated.

Expansion and improvement of the FORMA system for response and load analysis. Volume 2C: Listings, finite element FORMA subroutines

NASA Technical Reports Server (NTRS)

Wohlen, R. L.

1976-01-01

A listing of the source deck of each finite element FORMA subroutine is given to remove the 'black-box' aura of the subroutines so that the analyst may better understand the detailed operations of each subroutine. The FORTRAN 4 programming language is used in all finite element FORMA subroutines.

Toward automatic finite element analysis

NASA Technical Reports Server (NTRS)

Kela, Ajay; Perucchio, Renato; Voelcker, Herbert

1987-01-01

Two problems must be solved if the finite element method is to become a reliable and affordable blackbox engineering tool. Finite element meshes must be generated automatically from computer aided design databases and mesh analysis must be made self-adaptive. The experimental system described solves both problems in 2-D through spatial and analytical substructuring techniques that are now being extended into 3-D.

Review of literature on the finite-element solution of the equations of two-dimensional surface-water flow in the horizontal plane

USGS Publications Warehouse

Lee, Jonathan K.; Froehlich, David C.

1987-01-01

Published literature on the application of the finite-element method to solving the equations of two-dimensional surface-water flow in the horizontal plane is reviewed in this report. The finite-element method is ideally suited to modeling two-dimensional flow over complex topography with spatially variable resistance. A two-dimensional finite-element surface-water flow model with depth and vertically averaged velocity components as dependent variables allows the user great flexibility in defining geometric features such as the boundaries of a water body, channels, islands, dikes, and embankments. The following topics are reviewed in this report: alternative formulations of the equations of two-dimensional surface-water flow in the horizontal plane; basic concepts of the finite-element method; discretization of the flow domain and representation of the dependent flow variables; treatment of boundary conditions; discretization of the time domain; methods for modeling bottom, surface, and lateral stresses; approaches to solving systems of nonlinear equations; techniques for solving systems of linear equations; finite-element alternatives to Galerkin's method of weighted residuals; techniques of model validation; and preparation of model input data. References are listed in the final chapter.

Quantum spectral curve for arbitrary state/operator in AdS5/CFT4

NASA Astrophysics Data System (ADS)

Gromov, Nikolay; Kazakov, Vladimir; Leurent, Sébastien; Volin, Dmytro

2015-09-01

We give a derivation of quantum spectral curve (QSC) — a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys. Rev. Lett. 112 (2014). We also generalize this construction to all local single trace operators of the theory, in contrast to the TBA-like approaches worked out only for a limited class of states. We reveal a rich algebraic and analytic structure of the QSC in terms of a so called Q-system — a finite set of Baxter-like Q-functions. This new point of view on the finite size spectral problem is shown to be completely compatible, though in a far from trivial way, with already known exact equations (analytic Y-system/TBA, or FiNLIE). We use the knowledge of this underlying Q-system to demonstrate how the classical finite gap solutions and the asymptotic Bethe ansatz emerge from our formalism in appropriate limits.

GEMPIC: geometric electromagnetic particle-in-cell methods

NASA Astrophysics Data System (ADS)

Kraus, Michael; Kormann, Katharina; Morrison, Philip J.; Sonnendrücker, Eric

2017-08-01

We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss' law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.

System-Integrated Finite Element Analysis of a Full-Scale Helicopter Crash Test with Deployable Energy Absorbers

NASA Technical Reports Server (NTRS)

Annett, Martin S.; Polanco, Michael A.

2010-01-01

A full-scale crash test of an MD-500 helicopter was conducted in December 2009 at NASA Langley's Landing and Impact Research facility (LandIR). The MD-500 helicopter was fitted with a composite honeycomb Deployable Energy Absorber (DEA) and tested under vertical and horizontal impact velocities of 26-ft/sec and 40-ft/sec, respectively. The objectives of the test were to evaluate the performance of the DEA concept under realistic crash conditions and to generate test data for validation of a system integrated finite element model. In preparation for the full-scale crash test, a series of sub-scale and MD-500 mass simulator tests was conducted to evaluate the impact performances of various components, including a new crush tube and the DEA blocks. Parameters defined within the system integrated finite element model were determined from these tests. The objective of this paper is to summarize the finite element models developed and analyses performed, beginning with pre-test predictions and continuing through post-test validation.

Rigorous joining of advanced reduced-dimensional beam models to three-dimensional finite element models

NASA Astrophysics Data System (ADS)

Song, Huimin

In the aerospace and automotive industries, many finite element analyses use lower-dimensional finite elements such as beams, plates and shells, to simplify the modeling. These simplified models can greatly reduce the computation time and cost; however, reduced-dimensional models may introduce inaccuracies, particularly near boundaries and near portions of the structure where reduced-dimensional models may not apply. Another factor in creation of such models is that beam-like structures frequently have complex geometry, boundaries and loading conditions, which may make them unsuitable for modeling with single type of element. The goal of this dissertation is to develop a method that can accurately and efficiently capture the response of a structure by rigorous combination of a reduced-dimensional beam finite element model with a model based on full two-dimensional (2D) or three-dimensional (3D) finite elements. The first chapter of the thesis gives the background of the present work and some related previous work. The second chapter is focused on formulating a system of equations that govern the joining of a 2D model with a beam model for planar deformation. The essential aspect of this formulation is to find the transformation matrices to achieve deflection and load continuity on the interface. Three approaches are provided to obtain the transformation matrices. An example based on joining a beam to a 2D finite element model is examined, and the accuracy of the analysis is studied by comparing joint results with the full 2D analysis. The third chapter is focused on formulating the system of equations for joining a beam to a 3D finite element model for static and free-vibration problems. The transition between the 3D elements and beam elements is achieved by use of the stress recovery technique of the variational-asymptotic method as implemented in VABS (the Variational Asymptotic Beam Section analysis). The formulations for an interface transformation matrix and the generalized Timoshenko beam are discussed in this chapter. VABS is also used to obtain the beam constitutive properties and warping functions for stress recovery. Several 3D-beam joint examples are presented to show the convergence and accuracy of the analysis. Accuracy is accessed by comparing the joint results with the full 3D analysis. The fourth chapter provides conclusions from present studies and recommendations for future work.

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Nonautonomous ultradiscrete hungry Toda lattice and a generalized box-ball system

NASA Astrophysics Data System (ADS)

Maeda, Kazuki

2017-09-01

A nonautonomous version of the ultradiscrete hungry Toda lattice with a finite lattice boundary condition is derived by applying reduction and ultradiscretization to a nonautonomous two-dimensional discrete Toda lattice. It is shown that the derived ultradiscrete system has a direct connection to the box-ball system with many kinds of balls and finite carrier capacity. Particular solutions to the ultradiscrete system are constructed by using the theory of some sort of discrete biorthogonal polynomials.

Effect of curvature squared corrections to gravitational action on viscosity-to-entropy ratio of the dual gauge theory

NASA Astrophysics Data System (ADS)

Petrov, Pavel

In this thesis we study the properties of strongly-coupled large-N conformal field theories (CFT's) using AdS/CFT correspondence. Chapter 1 serves as an introduction. In Chapter 2 we study the shear viscosity of strongly-coupled large-N conformal field theories. We find that it is affected by R2 corrections to the AdS action and present an example of 4D theory in which the the conjectured universal lower bound on viscosity-to-entropy ratio η/s > 1/4π is violated by 1/N corrections. This fact proves that there is no universal lower bound of 1/4π on viscosity-to-entropy ratio and may be relevant for the studies of QCD quark-gluon plasma for which this ratio is experimentally found to be close to 1/4π. In Chapter 3 we study the formation of the electron star in 4D AdS space. We show that in a gravity theory with charged fermions a layer of charged fermion fluid may form at a finite distance from the charged black hole. We show that these “electron stars” are candidate gravity duals for strongly interacting fermion systems at finite density and finite temperature. Entropy density for such systems scales as s ˜ T2/z at low temperatures as expected from IR criticality of electron stars solutions.

Experimental and numerical analysis of stress wave propagation in polymers and the role of interfaces in armour systems

NASA Astrophysics Data System (ADS)

Gorwade, Chandragupt V.; Ashcroft, Ian A.; Silberschmidt, Vadim V.; Hughes, Foz T. R.; Swallowe, Gerry M.

2012-12-01

Advanced polymeric materials are finding an increasing range of industrial and defence applications. These materials have the potential to improve combat survivability, whilst reducing the cost and weight of armour systems. In this paper the results from a split Hopkinson pressure bar (SHPB) test of a high density polyethylene (HDPE) sample involving multiple stress waves is discussed with aid of a finite element model of the test. It is seen that the phenomenon of impedance mismatch at interfaces plays an important role in the levels of stress and deformation seen in the sample. A multi-layer armour system is then investigated using the finite element model. This case study illustrates the role of impedance mismatch and interface engineering in the design and optimisation of armour solutions.

Quantum key distribution for composite dimensional finite systems

NASA Astrophysics Data System (ADS)

Shalaby, Mohamed; Kamal, Yasser

2017-06-01

The application of quantum mechanics contributes to the field of cryptography with very important advantage as it offers a mechanism for detecting the eavesdropper. The pioneering work of quantum key distribution uses mutually unbiased bases (MUBs) to prepare and measure qubits (or qudits). Weak mutually unbiased bases (WMUBs) have weaker properties than MUBs properties, however, unlike MUBs, a complete set of WMUBs can be constructed for systems with composite dimensions. In this paper, we study the use of weak mutually unbiased bases (WMUBs) in quantum key distribution for composite dimensional finite systems. We prove that the security analysis of using a complete set of WMUBs to prepare and measure the quantum states in the generalized BB84 protocol, gives better results than using the maximum number of MUBs that can be constructed, when they are analyzed against the intercept and resend attack.

SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.

1999-03-01

This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples ofmore » the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.« less

Rapid finite-fault inversions in Southern California using Cybershake Green's functions

NASA Astrophysics Data System (ADS)

Thio, H. K.; Polet, J.

2017-12-01

We have developed a system for rapid finite fault inversion for intermediate and large Southern California earthquakes using local, regional and teleseismic seismic waveforms as well as geodetic data. For modeling the local seismic data, we use 3D Green's functions from the Cybershake project, which were made available to us courtesy of the Southern California Earthquake Center (SCEC). The use of 3D Green's functions allows us to extend the inversion to higher frequency waveform data and smaller magnitude earthquakes, in addition to achieving improved solutions in general. The ultimate aim of this work is to develop the ability to provide high quality finite fault models within a few hours after any damaging earthquake in Southern California, so that they may be used as input to various post-earthquake assessment tools such as ShakeMap, as well as by the scientific community and other interested parties. Additionally, a systematic determination of finite fault models has value as a resource for scientific studies on detailed earthquake processes, such as rupture dynamics and scaling relations. We are using an established least-squares finite fault inversion method that has been applied extensively both on large as well as smaller regional earthquakes, in conjunction with the 3D Green's functions, where available, as well as 1D Green's functions for areas for which the Cybershake library has not yet been developed. We are carrying out validation and calibration of this system using significant earthquakes that have occurred in the region over the last two decades, spanning a range of locations and magnitudes (5.4 and higher).

Finite element based electric motor design optimization

NASA Technical Reports Server (NTRS)

Campbell, C. Warren

1993-01-01

The purpose of this effort was to develop a finite element code for the analysis and design of permanent magnet electric motors. These motors would drive electromechanical actuators in advanced rocket engines. The actuators would control fuel valves and thrust vector control systems. Refurbishing the hydraulic systems of the Space Shuttle after each flight is costly and time consuming. Electromechanical actuators could replace hydraulics, improve system reliability, and reduce down time.

Transient Finite Element Computations on a Variable Transputer System

NASA Technical Reports Server (NTRS)

Smolinski, Patrick J.; Lapczyk, Ireneusz

1993-01-01

A parallel program to analyze transient finite element problems was written and implemented on a system of transputer processors. The program uses the explicit time integration algorithm which eliminates the need for equation solving, making it more suitable for parallel computations. An interprocessor communication scheme was developed for arbitrary two dimensional grid processor configurations. Several 3-D problems were analyzed on a system with a small number of processors.

Digitizing for Computer-Aided Finite Element Model Generation.

DTIC Science & Technology

1979-10-10

this approach is a collection of programs developed over the last eight years at the University of Arizona, and called the GIFTS system. This paper...briefly describes the latest version of the system, GIFTS -5, and demonstrates its suitability in a design environment by simple examples. The programs...constituting the GIFTS system were used as a tool for research in many areas, including mesh generation, finite element data base design, interactive

Finite-mode analysis by means of intensity information in fractional optical systems.

PubMed

Alieva, Tatiana; Bastiaans, Martin J

2002-03-01

It is shown how a coherent optical signal that contains only a finite number of Hermite-Gauss modes can be reconstructed from the knowledge of its Radon-Wigner transform-associated with the intensity distribution in a fractional-Fourier-transform optical system-at only two transversal points. The proposed method can be generalized to any fractional system whose generator transform has a complete orthogonal set of eigenfunctions.

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

A robust model predictive control algorithm for uncertain nonlinear systems that guarantees resolvability

NASA Technical Reports Server (NTRS)

Acikmese, Ahmet Behcet; Carson, John M., III

2006-01-01

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees resolvability. With resolvability, initial feasibility of the finite-horizon optimal control problem implies future feasibility in a receding-horizon framework. The control consists of two components; (i) feed-forward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives and derivatives in polytopes. An illustrative numerical example is also provided.

Modeling of a reinforced concrete beam using shape memory alloy as reinforcement bars

NASA Astrophysics Data System (ADS)

Bajoria, Kamal M.; Kaduskar, Shreya S.

2017-04-01

In this paper the structural behavior of reinforced concrete (RC) beams with smart rebars under three point loading system has been numerically studied, using Finite Element Method. The material used in this study is Superelastic Shape Memory Alloy (SE SMA) which contains nickel and titanium. Shape memory alloys (SMAs) are a unique class of materials which have ability to undergo large deformation and also regain their un-deformed shape by removal of stress or by heating. In this study, a uniaxial SMA model is able to reproduce the pseudo-elastic behavior for the reinforcing SMA wires. Finite element simulation is developed in order to study the load-deflection behavior of smart concrete beams subjected to three-point bending tests.

Theoretical foundations for finite-time transient stability and sensitivity analysis of power systems

NASA Astrophysics Data System (ADS)

Dasgupta, Sambarta

Transient stability and sensitivity analysis of power systems are problems of enormous academic and practical interest. These classical problems have received renewed interest, because of the advancement in sensor technology in the form of phasor measurement units (PMUs). The advancement in sensor technology has provided unique opportunity for the development of real-time stability monitoring and sensitivity analysis tools. Transient stability problem in power system is inherently a problem of stability analysis of the non-equilibrium dynamics, because for a short time period following a fault or disturbance the system trajectory moves away from the equilibrium point. The real-time stability decision has to be made over this short time period. However, the existing stability definitions and hence analysis tools for transient stability are asymptotic in nature. In this thesis, we discover theoretical foundations for the short-term transient stability analysis of power systems, based on the theory of normally hyperbolic invariant manifolds and finite time Lyapunov exponents, adopted from geometric theory of dynamical systems. The theory of normally hyperbolic surfaces allows us to characterize the rate of expansion and contraction of co-dimension one material surfaces in the phase space. The expansion and contraction rates of these material surfaces can be computed in finite time. We prove that the expansion and contraction rates can be used as finite time transient stability certificates. Furthermore, material surfaces with maximum expansion and contraction rate are identified with the stability boundaries. These stability boundaries are used for computation of stability margin. We have used the theoretical framework for the development of model-based and model-free real-time stability monitoring methods. Both the model-based and model-free approaches rely on the availability of high resolution time series data from the PMUs for stability prediction. The problem of sensitivity analysis of power system, subjected to changes or uncertainty in load parameters and network topology, is also studied using the theory of normally hyperbolic manifolds. The sensitivity analysis is used for the identification and rank ordering of the critical interactions and parameters in the power network. The sensitivity analysis is carried out both in finite time and in asymptotic. One of the distinguishing features of the asymptotic sensitivity analysis is that the asymptotic dynamics of the system is assumed to be a periodic orbit. For asymptotic sensitivity analysis we employ combination of tools from ergodic theory and geometric theory of dynamical systems.

Efimov effect for heteronuclear three-body systems at positive scattering length and finite temperature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Emmons, Samuel B.; Kang, Daekyoung; Acharya, Bijaya

2017-09-08

Here, we study the recombination process of three atoms scattering into an atom and diatomic molecule in heteronuclear mixtures of ultracold atomic gases with large and positive interspecies scattering length at finite temperature. We calculate the temperature dependence of the three-body recombination rates by extracting universal scaling functions that parametrize the energy dependence of the scattering matrix. We compare our results to experimental data for the 40K– 87Rb mixture and make a prediction for 6Li– 87Rb. We find that contributions from higher partial wave channels significantly impact the total rate and, in systems with particularly large mass imbalance, can evenmore » obliterate the recombination minima associated with the Efimov effect.« less

Computational methods for the identification of spatially varying stiffness and damping in beams

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rosen, I. G.

1986-01-01

A numerical approximation scheme for the estimation of functional parameters in Euler-Bernoulli models for the transverse vibration of flexible beams with tip bodies is developed. The method permits the identification of spatially varying flexural stiffness and Voigt-Kelvin viscoelastic damping coefficients which appear in the hybrid system of ordinary and partial differential equations and boundary conditions describing the dynamics of such structures. An inverse problem is formulated as a least squares fit to data subject to constraints in the form of a vector system of abstract first order evolution equations. Spline-based finite element approximations are used to finite dimensionalize the problem. Theoretical convergence results are given and numerical studies carried out on both conventional (serial) and vector computers are discussed.

Noise-driven neuromorphic tuned amplifier.

PubMed

Fanelli, Duccio; Ginelli, Francesco; Livi, Roberto; Zagli, Niccoló; Zankoc, Clement

2017-12-01

We study a simple stochastic model of neuronal excitatory and inhibitory interactions. The model is defined on a directed lattice and internodes couplings are modulated by a nonlinear function that mimics the process of synaptic activation. We prove that such a system behaves as a fully tunable amplifier: the endogenous component of noise, stemming from finite size effects, seeds a coherent (exponential) amplification across the chain generating giant oscillations with tunable frequencies, a process that the brain could exploit to enhance, and eventually encode, different signals. On a wider perspective, the characterized amplification process could provide a reliable pacemaking mechanism for biological systems. The device extracts energy from the finite size bath and operates as an out of equilibrium thermal machine, under stationary conditions.

Dynamical decoupling of unbounded Hamiltonians

NASA Astrophysics Data System (ADS)

Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin

2018-03-01

We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.

Books and monographs on finite element technology

NASA Technical Reports Server (NTRS)

Noor, A. K.

1985-01-01

The present paper proviees a listing of all of the English books and some of the foreign books on finite element technology, taking into account also a list of the conference proceedings devoted solely to finite elements. The references are divided into categories. Attention is given to fundamentals, mathematical foundations, structural and solid mechanics applications, fluid mechanics applications, other applied science and engineering applications, computer implementation and software systems, computational and modeling aspects, special topics, boundary element methods, proceedings of symmposia and conferences on finite element technology, bibliographies, handbooks, and historical accounts.

Characterization of the structural collapse undergone by an unstable system of ultrasoft particles

NASA Astrophysics Data System (ADS)

Prestipino, Santi; Malescio, Gianpietro

2016-09-01

The effective repulsion between macromolecules such as polymer chains or dendrimers is everywhere finite, implying that interaction centers can even coincide. If, in addition, the large-distance attraction is sufficiently strong, then the system is driven unstable. An unstable system lacks a conventional thermodynamics since, in the infinite-size limit, it eventually collapses to a finite-size cluster (for instance, a polymer dispersion undergoes irreversible coagulation when increasing the amount of dissolved salt beyond a certain limit). Using a double-Gaussian (DG) potential for demonstration, we study the phase behavior of a system of ultrasoft particles as a function of the attraction strength η. Above a critical threshold ηc, the DG system is unstable but its collective behavior is far from trivial since two separate regions of the thermodynamic plane can be identified, based on the value taken by the average waiting time for collapse: this is finite and small on one side of the boundary, while presumably infinite in the other region. In order to make sense of this evidence, we consider a stable system of particles interacting through a DG potential augmented with a hard core (stabilized DG, or SDG potential). We provide arguments supporting the view that the boundary line of the unstable DG model is the remnant of the spinodal line of a fluid-fluid phase transition occurring in the SDG model when the hard-core diameter is sent to zero.

Groups graded by root systems and property (T)

PubMed Central

Ershov, Mikhail; Jaikin-Zapirain, Andrei; Kassabov, Martin; Zhang, Zezhou

2014-01-01

We establish property (T) for a large class of groups graded by root systems, including elementary Chevalley groups and Steinberg groups of rank at least 2 over finitely generated commutative rings with 1. We also construct a group with property (T) which surjects onto all finite simple groups of Lie type and rank at least two. PMID:25425669

Experimental analysis and simulation calculation of the inductances of loosely coupled transformer

NASA Astrophysics Data System (ADS)

Kerui, Chen; Yang, Han; Yan, Zhang; Nannan, Gao; Ying, Pei; Hongbo, Li; Pei, Li; Liangfeng, Guo

2017-11-01

The experimental design of iron-core wireless power transmission system is designed, and an experimental model of loosely coupled transformer is built. Measuring the air gap on both sides of the transformer 15mm inductor under the parameters. The feasibility and feasibility of using the finite element method to calculate the coil inductance parameters of the loosely coupled transformer are analyzed. The system was modeled by ANSYS, and the magnetic field was calculated by finite element method, and the inductance parameters were calculated. The finite element method is used to calculate the inductive parameters of the loosely coupled transformer, and the basis for the accurate compensation of the capacitance of the wireless power transmission system is established.

Metriplectic integrators for the Landau collision operator

DOE PAGES

Kraus, Michael; Hirvijoki, Eero

2017-10-02

Here, we present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau collision integral and, using a Galerkin discretization for the velocity space, we transform the infinite-dimensional system into a finite-dimensional, time-continuous metriplectic system. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of energy, momentum, and particle densities, as well as the production of entropy is demonstrated algebraically for the fully discrete system. Due to the generality of our approach, the conservation properties and the monotonicmore » behavior of entropy are guaranteed for finite element discretizations, in general, independently of the mesh configuration.« less

Two-Nucleon Systems in a Finite Volume

DOE Office of Scientific and Technical Information (OSTI.GOV)

Briceno, Raul

2014-11-01

I present the formalism and methodology for determining the nucleon-nucleon scattering parameters from the finite volume spectra obtained from lattice quantum chromodynamics calculations. Using the recently derived energy quantization conditions and the experimentally determined scattering parameters, the bound state spectra for finite volume systems with overlap with the 3S1-3D3 channel are predicted for a range of volumes. It is shown that the extractions of the infinite-volume deuteron binding energy and the low-energy scattering parameters, including the S-D mixing angle, are possible from Lattice QCD calculations of two-nucleon systems with boosts of |P| <= 2pi sqrt{3}/L in volumes with spatial extentsmore » L satisfying fm <~ L <~ 14 fm.« less

Fast smooth second-order sliding mode control for stochastic systems with enumerable coloured noises

NASA Astrophysics Data System (ADS)

Yang, Peng-fei; Fang, Yang-wang; Wu, You-li; Zhang, Dan-xu; Xu, Yang

2018-01-01

A fast smooth second-order sliding mode control is presented for a class of stochastic systems driven by enumerable Ornstein-Uhlenbeck coloured noises with time-varying coefficients. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the control. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Then the prescribed sliding variable dynamic is presented. The sufficient condition guaranteeing its finite-time convergence is given and proved using stochastic Lyapunov-like techniques. The proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are given comparing with smooth second-order sliding mode control to validate the analysis.

Reductions in finite-dimensional integrable systems and special points of classical r-matrices

NASA Astrophysics Data System (ADS)

Skrypnyk, T.

2016-12-01

For a given 𝔤 ⊗ 𝔤-valued non-skew-symmetric non-dynamical classical r-matrices r(u, v) with spectral parameters, we construct the general form of 𝔤-valued Lax matrices of finite-dimensional integrable systems satisfying linear r-matrix algebra. We show that the reduction in the corresponding finite-dimensional integrable systems is connected with "the special points" of the classical r-matrices in which they become degenerated. We also propose a systematic way of the construction of additional integrals of the Lax-integrable systems associated with the symmetries of the corresponding r-matrices. We consider examples of the Lax matrices and integrable systems that are obtained in the framework of the general scheme. Among them there are such physically important systems as generalized Gaudin systems in an external magnetic field, ultimate integrable generalization of Toda-type chains (including "modified" or "deformed" Toda chains), generalized integrable Jaynes-Cummings-Dicke models, integrable boson models generalizing Bose-Hubbard dimer models, etc.

Time-dependent density functional theory with twist-averaged boundary conditions

NASA Astrophysics Data System (ADS)

Schuetrumpf, B.; Nazarewicz, W.; Reinhard, P.-G.

2016-05-01

Background: Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, three-dimensional (3D) coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a spatial box. For finite quantum systems (atoms, molecules, nuclei, hadrons), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. Purpose: The finite-volume artifacts for finite systems can be practically cured by invoking an absorbing potential in a certain boundary region sufficiently far from the described system. However, such absorption cannot be applied in the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust), which suffer from unphysical effects stemming from a finite computational box used. Here, twist-averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we extend TABC to time-dependent modes. Method: We use the 3D time-dependent density functional framework with the Skyrme energy density functional. The practical calculations are carried out for small- and large-amplitude electric dipole and quadrupole oscillations of 16O. We apply and compare three kinds of boundary conditions: periodic, absorbing, and twist-averaged. Results: Calculations employing absorbing boundary conditions (ABC) and TABC are superior to those based on periodic boundary conditions. For low-energy excitations, TABC and ABC variants yield very similar results. With only four twist phases per spatial direction in TABC, one obtains an excellent reduction of spurious fluctuations. In the nonlinear regime, one has to deal with evaporated particles. In TABC, the floating nucleon gas remains in the box; the amount of nucleons in the gas is found to be roughly the same as the number of absorbed particles in ABC. Conclusion: We demonstrate that by using TABC, one can reduce finite-volume effects drastically without adding any additional parameters associated with absorption at large distances. Moreover, TABC are an obvious choice for time-dependent calculations for infinite systems. Since TABC calculations for different twists can be performed independently, the method is trivially adapted to parallel computing.

The GPRIME approach to finite element modeling

NASA Technical Reports Server (NTRS)

Wallace, D. R.; Mckee, J. H.; Hurwitz, M. M.

1983-01-01

GPRIME, an interactive modeling system, runs on the CDC 6000 computers and the DEC VAX 11/780 minicomputer. This system includes three components: (1) GPRIME, a user friendly geometric language and a processor to translate that language into geometric entities, (2) GGEN, an interactive data generator for 2-D models; and (3) SOLIDGEN, a 3-D solid modeling program. Each component has a computer user interface of an extensive command set. All of these programs make use of a comprehensive B-spline mathematics subroutine library, which can be used for a wide variety of interpolation problems and other geometric calculations. Many other user aids, such as automatic saving of the geometric and finite element data bases and hidden line removal, are available. This interactive finite element modeling capability can produce a complete finite element model, producing an output file of grid and element data.

Finite element analysis of low speed viscous and inviscid aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1977-01-01

A weak interaction solution algorithm was established for aerodynamic flow about an isolated airfoil. Finite element numerical methodology was applied to solution of each of differential equations governing potential flow, and viscous and turbulent boundary layer and wake flow downstream of the sharp trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. Closure for turbulence was accomplished using both first and second order models. The COMOC finite element fluid mechanics computer program was modified to solve the identified equation systems for two dimensional flows. A numerical program was completed to determine factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems. Good accuracy and convergence are demonstrated. Each solution is obtained within the identical finite element framework of COMOC.

Finite element method for optimal guidance of an advanced launch vehicle

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.; Calise, Anthony J.; Leung, Martin

1992-01-01

A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.

Finite-time blow-up for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type

NASA Astrophysics Data System (ADS)

Hashira, Takahiro; Ishida, Sachiko; Yokota, Tomomi

2018-05-01

This paper deals with the quasilinear degenerate Keller-Segel systems of parabolic-parabolic type in a ball of RN (N ≥ 2). In the case of non-degenerate diffusion, Cieślak-Stinner [3,4] proved that if q > m + 2/N, where m denotes the intensity of diffusion and q denotes the nonlinearity, then there exist initial data such that the corresponding solution blows up in finite time. As to the case of degenerate diffusion, it is known that a solution blows up if q > m + 2/N (see Ishida-Yokota [13]); however, whether the blow-up time is finite or infinite has been unknown. This paper gives an answer to the unsolved problem. Indeed, the finite-time blow-up of energy solutions is established when q > m + 2/N.

Topology optimization of finite strain viscoplastic systems under transient loads

DOE PAGES

Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel

2018-02-08

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.« less

A finite element-boundary integral method for cavities in a circular cylinder

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.

1992-01-01

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. However, due to a lack of rigorous mathematical models for conformal antenna arrays, antenna designers resort to measurement and planar antenna concepts for designing non-planar conformal antennas. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We extend this formulation to conformal arrays on large metallic cylinders. In this report, we develop the mathematical formulation. In particular, we discuss the shape functions, the resulting finite elements and the boundary integral equations, and the solution of the conformal finite element-boundary integral system. Some validation results are presented and we further show how this formulation can be applied with minimal computational and memory resources.

Quantum number theoretic transforms on multipartite finite systems.

PubMed

Vourdas, A; Zhang, S

2009-06-01

A quantum system composed of p-1 subsystems, each of which is described with a p-dimensional Hilbert space (where p is a prime number), is considered. A quantum number theoretic transform on this system, which has properties similar to those of a Fourier transform, is studied. A representation of the Heisenberg-Weyl group in this context is also discussed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Møller, Jacob Schach

These notes provide an introduction to the spectral analysis of Pauli-Fierz systems at zero and positive temperature. More precisely, we study finite dimensional quantum systems linearly coupled to a single reservoir, a massless scalar quantum field. We emphasize structure results valid at arbitrary system-reservoir coupling strength. The notes contain a mixture of known, refined, and new results and each section ends with a discussion of open problems.

Convergence to equilibrium of renormalised solutions to nonlinear chemical reaction–diffusion systems

NASA Astrophysics Data System (ADS)

Fellner, Klemens; Tang, Bao Quoc

2018-06-01

The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the so-called entropy method, we show that if the system does not have boundary equilibria, i.e. equilibrium states lying on the boundary of R_+^N, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite-dimensional inequality. This inequality is proven via a contradiction argument and thus not explicitly. An explicit method of proof, however, is provided for a specific application modelling a reversible enzyme reaction by exploiting the specific structure of the conservation laws. Our approach is also useful to study the trend to equilibrium for systems possessing boundary equilibria. More precisely, to show the convergence to equilibrium for systems with boundary equilibria, we establish a sufficient condition in terms of a modified finite-dimensional inequality along trajectories of the system. By assuming this condition, which roughly means that the system produces too much entropy to stay close to a boundary equilibrium for infinite time, the entropy method shows exponential convergence to equilibrium for renormalised solutions to complex balanced systems with boundary equilibria.

A simple finite element method for linear hyperbolic problems

DOE PAGES

Mu, Lin; Ye, Xiu

2017-09-14

Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

A simple finite element method for linear hyperbolic problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mu, Lin; Ye, Xiu

Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

Kicking atoms with finite duration pulses

NASA Astrophysics Data System (ADS)

Fekete, Julia; Chai, Shijie; Daszuta, Boris; Andersen, Mikkel F.

2016-05-01

The atom optics delta-kicked particle is a paradigmatic system for experimental studies of quantum chaos and classical-quantum correspondence. It consists of a cloud of laser cooled atoms exposed to a periodically pulsed standing wave of far off-resonant laser light. A purely quantum phenomena in such systems are quantum resonances which transfers the atoms into a coherent superposition of largely separated momentum states. Using such large momentum transfer ``beamsplitters'' in atom interferometers may have applications in high precision metrology. The growth in momentum separation cannot be maintained indefinitely due to finite laser power. The largest momentum transfer is achieved by violating the usual delta-kick assumption. Therefore we explore the behavior of the atom optics kicked particle with finite pulse duration. We have developed a semi-classical model which shows good agreement with the full quantum description as well as our experiments. Furthermore we have found a simple scaling law that helps to identify optimal parameters for an atom interferometer. We verify this by measurements of the ``Talbot time'' (a measurement of h/m) which together with other well-known constants constitute a measurement of the fine structure constant.

On the ab initio calculation of vibrational formation entropy of point defect: the case of the silicon vacancy

NASA Astrophysics Data System (ADS)

Seeberger, Pia; Vidal, Julien

2017-08-01

Formation entropy of point defects is one of the last crucial elements required to fully describe the temperature dependence of point defect formation. However, while many attempts have been made to compute them for very complicated systems, very few works have been carried out such as to assess the different effects of finite size effects and precision on such quantity. Large discrepancies can be found in the literature for a system as primitive as the silicon vacancy. In this work, we have proposed a systematic study of formation entropy for silicon vacancy in its 3 stable charge states: neutral, +2 and -2 for supercells with size not below 432 atoms. Rationalization of the formation entropy is presented, highlighting importance of finite size error and the difficulty to compute such quantities due to high numerical requirement. It is proposed that the direct calculation of formation entropy of VSi using first principles methods will be plagued by very high computational workload (or large numerical errors) and finite size dependent results.

Analysis of wave motion in one-dimensional structures through fast-Fourier-transform-based wavelet finite element method

NASA Astrophysics Data System (ADS)

Shen, Wei; Li, Dongsheng; Zhang, Shuaifang; Ou, Jinping

2017-07-01

This paper presents a hybrid method that combines the B-spline wavelet on the interval (BSWI) finite element method and spectral analysis based on fast Fourier transform (FFT) to study wave propagation in One-Dimensional (1D) structures. BSWI scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high-accuracy dynamic stiffness matrix. Dynamic reduction on element level is applied to eliminate the interior degrees of freedom of BSWI elements and substantially reduce the size of the system matrix. The dynamic equations of the system are then transformed and solved in the frequency domain through FFT-based spectral analysis which is especially suitable for parallel computation. A comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high-frequency wave problems. Other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1D rods and beams. Finally, the errors caused by FFT and their corresponding solutions are presented.

Magnetic-field-induced mixed-level Kondo effect in two-level systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wong, Arturo; Ngo, Anh T.; Ulloa, Sergio E.

2016-10-17

We consider a two-orbital impurity system with intra-and interlevel Coulomb repulsion that is coupled to a single conduction channel. This situation can generically occur in multilevel quantum dots or in systems of coupled quantum dots. For finite energy spacing between spin-degenerate orbitals, an in-plane magnetic field drives the system from a local-singlet ground state to a "mixed-level" Kondo regime, where the Zeeman-split levels are degenerate for opposite-spin states. We use the numerical renormalization group approach to fully characterize this mixed-level Kondo state and discuss its properties in terms of the applied Zeeman field, temperature, and system parameters. Under suitable conditions,more » the total spectral function is shown to develop a Fermi-level resonance, so that the linear conductance of the system peaks at a finite Zeeman field while it decreases as a function of temperature. These features, as well as the local moment and entropy contribution of the impurity system, are commensurate with Kondo physics, which can be studied in suitably tuned quantum dot systems.« less

A training rule which guarantees finite-region stability for a class of closed-loop neural-network control systems.

PubMed

Kuntanapreeda, S; Fullmer, R R

1996-01-01

A training method for a class of neural network controllers is presented which guarantees closed-loop system stability. The controllers are assumed to be nonlinear, feedforward, sampled-data, full-state regulators implemented as single hidden-layer neural networks. The controlled systems must be locally hermitian and observable. Stability of the closed-loop system is demonstrated by determining a Lyapunov function, which can be used to identify a finite stability region about the regulator point.

Potential of minicomputer/array-processor system for nonlinear finite-element analysis

NASA Technical Reports Server (NTRS)

Strohkorb, G. A.; Noor, A. K.

1983-01-01

The potential of using a minicomputer/array-processor system for the efficient solution of large-scale, nonlinear, finite-element problems is studied. A Prime 750 is used as the host computer, and a software simulator residing on the Prime is employed to assess the performance of the Floating Point Systems AP-120B array processor. Major hardware characteristics of the system such as virtual memory and parallel and pipeline processing are reviewed, and the interplay between various hardware components is examined. Effective use of the minicomputer/array-processor system for nonlinear analysis requires the following: (1) proper selection of the computational procedure and the capability to vectorize the numerical algorithms; (2) reduction of input-output operations; and (3) overlapping host and array-processor operations. A detailed discussion is given of techniques to accomplish each of these tasks. Two benchmark problems with 1715 and 3230 degrees of freedom, respectively, are selected to measure the anticipated gain in speed obtained by using the proposed algorithms on the array processor.

Computational Nonlinear Morphology with Emphasis on Semitic Languages. Studies in Natural Language Processing.

ERIC Educational Resources Information Center

Kiraz, George Anton

This book presents a tractable computational model that can cope with complex morphological operations, especially in Semitic languages, and less complex morphological systems present in Western languages. It outlines a new generalized regular rewrite rule system that uses multiple finite-state automata to cater to root-and-pattern morphology,…

Nonlinear stability in reaction-diffusion systems via optimal Lyapunov functions

NASA Astrophysics Data System (ADS)

Lombardo, S.; Mulone, G.; Trovato, M.

2008-06-01

We define optimal Lyapunov functions to study nonlinear stability of constant solutions to reaction-diffusion systems. A computable and finite radius of attraction for the initial data is obtained. Applications are given to the well-known Brusselator model and a three-species model for the spatial spread of rabies among foxes.

Magnetic Actuator Modelling for Rotating Machinery Analysis

NASA Astrophysics Data System (ADS)

Mendes, Ricardo Ugliara; de Castro, Hélio Fiori; Cavalca, Kátia Lucchesi; Ferreira, Luiz Otávio Saraiva

Rotating machines have a wide range of application such as airplanes, factories, laboratories and power plants. Lately, with computer aid design, shafts finite element models including bearings, discs, seals and couplings have been developed, allowing the prediction of the machine behavior. In order to keep confidence during operation, it is necessary to monitor these systems, trying to predict future failures. One of the most applied technique for this purpose is the modal analysis. It consists of applying a perturbation force into the system and then to measure its response. However, there is a difficulty that brings limitations to the excitation of systems with rotating shafts when using impact hammers or shakers, once due to friction, undesired tangential forces and noise can be present in the measurements. Therefore, the study of a non-contact technique of external excitation becomes of high interest. In this sense, the present work deals with the study and development of a finite element model for rotating machines using a magnetic actuator as an external excitation source. This work also brings numerical simulations where the magnetic actuator was used to obtain the frequency response function of the rotating system.

Numerical computation of transonic flows by finite-element and finite-difference methods

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.

1978-01-01

Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.

Construction and validation of a three-dimensional finite element model of degenerative scoliosis.

PubMed

Zheng, Jie; Yang, Yonghong; Lou, Shuliang; Zhang, Dongsheng; Liao, Shenghui

2015-12-24

With the aging of the population, degenerative scoliosis (DS) incidence rate is increasing. In recent years, increasing research on this topic has been carried out, yet biomechanical research on the subject is seldom seen and in vitro biomechanical model of DS nearly cannot be available. The objective of this study was to develop and validate a complete three-dimensional finite element model of DS in order to build the digital platform for further biomechanical study. A 55-year-old female DS patient (Suer Pan, ID number was P141986) was selected for this study. This study was performed in accordance with the ethical standards of Declaration of Helsinki and its amendments and was approved by the local ethics committee (117 hospital of PLA ethics committee). Spiral computed tomography (CT) scanning was conducted on the patient's lumbar spine from the T12 to S1. CT images were then imported into a finite element modeling system. A three-dimensional solid model was then formed from segmentation of the CT scan. The three-dimensional model of each vertebra was then meshed, and material properties were assigned to each element according to the pathological characteristics of DS. Loads and boundary conditions were then applied in such a manner as to simulate in vitro biomechanical experiments conducted on lumbar segments. The results of the model were then compared with experimental results in order to validate the model. An integral three-dimensional finite element model of DS was built successfully, consisting of 113,682 solid elements, 686 cable elements, 33,329 shell elements, 4968 target elements, 4968 contact elements, totaling 157,635 elements, and 197,374 nodes. The model accurately described the physical features of DS and was geometrically similar to the object of study. The results of analysis with the finite element model agreed closely with in vitro experiments, validating the accuracy of the model. The three-dimensional finite element model of DS built in this study is clear, reliable, and effective for further biomechanical simulation study of DS.

Neutron star mergers as a probe of modifications of general relativity with finite-range scalar forces

NASA Astrophysics Data System (ADS)

Sagunski, Laura; Zhang, Jun; Johnson, Matthew C.; Lehner, Luis; Sakellariadou, Mairi; Liebling, Steven L.; Palenzuela, Carlos; Neilsen, David

2018-03-01

Observations of gravitational radiation from compact binary systems provide an unprecedented opportunity to test general relativity in the strong field dynamical regime. In this paper, we investigate how future observations of gravitational radiation from binary neutron star mergers might provide constraints on finite-range forces from a universally coupled massive scalar field. Such scalar degrees of freedom (d.o.f.) are a characteristic feature of many extensions of general relativity. For concreteness, we work in the context of metric f (R ) gravity, which is equivalent to general relativity and a universally coupled scalar field with a nonlinear potential whose form is fixed by the choice of f (R ). In theories where neutron stars (or other compact objects) obtain a significant scalar charge, the resulting attractive finite-range scalar force has implications for both the inspiral and merger phases of binary systems. We first present an analysis of the inspiral dynamics in Newtonian limit, and forecast the constraints on the mass of the scalar and charge of the compact objects for the Advanced LIGO gravitational wave observatory. We then perform a comparative study of binary neutron star mergers in general relativity with those of a one-parameter model of f (R ) gravity using fully relativistic hydrodynamical simulations. These simulations elucidate the effects of the scalar on the merger and postmerger dynamics. We comment on the utility of the full waveform (inspiral, merger, postmerger) to probe different regions of parameter space for both the particular model of f (R ) gravity studied here and for finite-range scalar forces more generally.

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle

NASA Astrophysics Data System (ADS)

Evans, Denis J.; Searles, Debra J.; Mittag, Emil

2001-05-01

For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.

Relative position finite-time coordinated tracking control of spacecraft formation without velocity measurements.

PubMed

Hu, Qinglei; Zhang, Jian

2015-01-01

This paper investigates finite-time relative position coordinated tracking problem by output feedback for spacecraft formation flying without velocity measurement. By employing homogeneous system theory, a finite-time relative position coordinated tracking controller by state feedback is firstly developed, where the desired time-varying trajectory given in advance can be tracked by the formation. Then, to address the problem of lack of velocity measurements, a finite-time output feedback controller is proposed by involving a novel filter to recover unknown velocity information in a finite time. Rigorous proof shows that the proposed control law ensures global stability and guarantees the position of spacecraft formation to track a time-varying reference in finite time. Finally, simulation results are presented to illustrate the performance of the proposed controller. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1976-01-01

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Exact solution of two interacting run-and-tumble random walkers with finite tumble duration

NASA Astrophysics Data System (ADS)

Slowman, A. B.; Evans, M. R.; Blythe, R. A.

2017-09-01

We study a model of interacting run-and-tumble random walkers operating under mutual hardcore exclusion on a one-dimensional lattice with periodic boundary conditions. We incorporate a finite, poisson-distributed, tumble duration so that a particle remains stationary whilst tumbling, thus generalising the persistent random walker model. We present the exact solution for the nonequilibrium stationary state of this system in the case of two random walkers. We find this to be characterised by two lengthscales, one arising from the jamming of approaching particles, and the other from one particle moving when the other is tumbling. The first of these lengthscales vanishes in a scaling limit where the continuous-space dynamics is recovered whilst the second remains finite. Thus the nonequilibrium stationary state reveals a rich structure of attractive, jammed and extended pieces.

Numerical evaluation of discontinuous and nonconforming finite element methods in nonlinear solid mechanics

NASA Astrophysics Data System (ADS)

Bayat, Hamid Reza; Krämer, Julian; Wunderlich, Linus; Wulfinghoff, Stephan; Reese, Stefanie; Wohlmuth, Barbara; Wieners, Christian

2018-03-01

This work presents a systematic study of discontinuous and nonconforming finite element methods for linear elasticity, finite elasticity, and small strain plasticity. In particular, we consider new hybrid methods with additional degrees of freedom on the skeleton of the mesh and allowing for a local elimination of the element-wise degrees of freedom. We show that this process leads to a well-posed approximation scheme. The quality of the new methods with respect to locking and anisotropy is compared with standard and in addition locking-free conforming methods as well as established (non-) symmetric discontinuous Galerkin methods with interior penalty. For several benchmark configurations, we show that all methods converge asymptotically for fine meshes and that in many cases the hybrid methods are more accurate for a fixed size of the discrete system.

Quantum Monte Carlo calculations of two neutrons in finite volume

DOE PAGES

Klos, P.; Lynn, J. E.; Tews, I.; ...

2016-11-18

Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground state and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial formore » determining observables from the calculated energies. Finally, using the Lüscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes.« less

Emergence of currents as a transient quantum effect in nonequilibrium systems

NASA Astrophysics Data System (ADS)

Granot, Er'El; Marchewka, Avi

2011-09-01

Most current calculations are based on equilibrium or semi-equilibrium models. However, except for very special scenarios (like ring configuration), the current cannot exist in equilibrium. Moreover, unlike with equilibrium scenarios, there is no generic approach to confront out-of-equilibrium currents. In this paper we used recent studies on transient quantum mechanics to solve the current, which appears in the presence of very high density gradients and fast transients. It shows that the emerging current appears instantaneously, and although the density beyond the discontinuity is initially negligible the currents there have a finite value, and remain constant for a finite period. It is shown that this nonequilibrium effect can be measured in real experiments (such as cooled rubidium atoms), where the discontinuity is replaced with a finite width (hundreds of nanometers) gradient.

Parametric Instability of Static Shafts-Disk System Using Finite Element Method

NASA Astrophysics Data System (ADS)

Wahab, A. M.; Rasid, Z. A.; Abu, A.

2017-10-01

Parametric instability condition is an important consideration in design process as it can cause failure in machine elements. In this study, parametric instability behaviour was studied for a simple shaft and disk system that was subjected to axial load under pinned-pinned boundary condition. The shaft was modelled based on the Nelson’s beam model, which considered translational and rotary inertias, transverse shear deformation and torsional effect. The Floquet’s method was used to estimate the solution for Mathieu equation. Finite element codes were developed using MATLAB to establish the instability chart. The effect of additional disk mass on the stability chart was investigated for pinned-pinned boundary conditions. Numerical results and illustrative examples are given. It is found that the additional disk mass decreases the instability region during static condition. The location of the disk as well has significant effect on the instability region of the shaft.

Active muscle response using feedback control of a finite element human arm model.

PubMed

Östh, Jonas; Brolin, Karin; Happee, Riender

2012-01-01

Mathematical human body models (HBMs) are important research tools that are used to study the human response in car crash situations. Development of automotive safety systems requires the implementation of active muscle response in HBM, as novel safety systems also interact with vehicle occupants in the pre-crash phase. In this study, active muscle response was implemented using feedback control of a nonlinear muscle model in the right upper extremity of a finite element (FE) HBM. Hill-type line muscle elements were added, and the active and passive properties were assessed. Volunteer tests with low impact loading resulting in elbow flexion motions were performed. Simulations of posture maintenance in a gravity field and the volunteer tests were successfully conducted. It was concluded that feedback control of a nonlinear musculoskeletal model can be used to obtain posture maintenance and human-like reflexive responses in an FE HBM.

Pinching solutions of slender cylindrical jets

NASA Technical Reports Server (NTRS)

Papageorgiou, Demetrios T.; Orellana, Oscar

1993-01-01

Simplified equations for slender jets are derived for a circular jet of one fluid flowing into an ambient second fluid, the flow being confined in a circular tank. Inviscid flows are studied which include both surface tension effects and Kelvin-Helmholtz instability. For slender jets a coupled nonlinear system of equations is found for the jet shape and the axial velocity jump across it. The equations can break down after a finite time and similarity solutions are constructed, and studied analytically and numerically. The break-ups found pertain to the jet pinching after a finite time, without violation of the slender jet ansatz. The system is conservative and admissible singular solutions are those which conserve the total energy, mass, and momentum. Such solutions are constructed analytically and numerically, and in the case of vortex sheets with no surface tension certain solutions are given in closed form.

Conductance of finite systems and scaling in localization theory

NASA Astrophysics Data System (ADS)

Suslov, I. M.

2012-11-01

The conductance of finite systems plays a central role in the scaling theory of localization (Abrahams et al., Phys. Rev. Lett. 42, 673 (1979)). Usually it is defined by the Landauer-type formulas, which remain open the following questions: (a) exclusion of the contact resistance in the many-channel case; (b) correspondence of the Landauer conductance with internal properties of the system; (c) relation with the diffusion coefficient D(ω, q) of an infinite system. The answers to these questions are obtained below in the framework of two approaches: (1) self-consistent theory of localization by Vollhardt and Wölfle, and (2) quantum mechanical analysis based on the shell model. Both approaches lead to the same definition for the conductance of a finite system, closely related to the Thouless definition. In the framework of the self-consistent theory, the relations of finite-size scaling are derived and the Gell-Mann-Low functions β( g) for space dimensions d = 1, 2, 3 are calculated. In contrast to the previous attempt by Vollhardt and Wölfle (1982), the metallic and localized phase are considered from the same standpoint, and the conductance of a finite system has no singularity at the critical point. In the 2D case, the expansion of β( g) in 1/ g coincides with results of the σ-model approach on the two-loop level and depends on the renormalization scheme in higher loops; the use of dimensional regularization for transition to dimension d = 2 + ɛ looks incompatible with the physical essence of the problem. The results are compared with numerical and physical experiments. A situation in higher dimensions and the conditions for observation of the localization law σ(ω) ∝ - iω for conductivity are discussed.

A genuine nonlinear approach for controller design of a boiler-turbine system.

PubMed

Yang, Shizhong; Qian, Chunjiang; Du, Haibo

2012-05-01

This paper proposes a genuine nonlinear approach for controller design of a drum-type boiler-turbine system. Based on a second order nonlinear model, a finite-time convergent controller is first designed to drive the states to their setpoints in a finite time. In the case when the state variables are unmeasurable, the system will be regulated using a constant controller or an output feedback controller. An adaptive controller is also designed to stabilize the system since the model parameters may vary under different operating points. The novelty of the proposed controller design approach lies in fully utilizing the system nonlinearities instead of linearizing or canceling them. In addition, the newly developed techniques for finite-time convergent controller are used to guarantee fast convergence of the system. Simulations are conducted under different cases and the results are presented to illustrate the performance of the proposed controllers. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

A quantum Otto engine with finite heat baths: energy, correlations, and degradation

NASA Astrophysics Data System (ADS)

Pozas-Kerstjens, Alejandro; Brown, Eric G.; Hovhannisyan, Karen V.

2018-04-01

We study a driven harmonic oscillator operating an Otto cycle by strongly interacting with two thermal baths of finite size. Using the tools of Gaussian quantum mechanics, we directly simulate the dynamics of the engine as a whole, without the need to make any approximations. This allows us to understand the non-equilibrium thermodynamics of the engine not only from the perspective of the working medium, but also as it is seen from the thermal baths’ standpoint. For sufficiently large baths, our engine is capable of running a number of perfect cycles, delivering finite power while operating very close to maximal efficiency. Thereafter, having traversed the baths, the perturbations created by the interaction abruptly deteriorate the engine’s performance. We additionally study the correlations generated in the system, and, in particular, we find a direct connection between the build up of bath–bath correlations and the degradation of the engine’s performance over the course of many cycles.

Stress and efficiency studies in EFG

NASA Technical Reports Server (NTRS)

1986-01-01

The goals of this program were: (1) to define minimum stress configurations for silicon sheet growth at high speeds; (2) to quantify dislocation electrical activity and their limits on minority carrier diffusion length in deformed silicon; and (3) to study reasons for degradation of lifetime with increases in doping level in edge-defined film-fed growth (EFG) materials. A finite element model was developed for calculating residual stress with plastic deformation. A finite element model was verified for EFG control variable relationships to temperature field of the sheet to permit prediction of profiles and stresses encountered in EFG systems. A residual stress measurement technique was developed for finite size EFG material blanks using shadow Moire interferometry. Transient creep response of silicon was investigated in the temperature range between 800 and 1400 C in strain and strain regimes of interest in stress analysis of sheet growth. Quantitative relationships were established between minority carrier diffusion length and dislocation densities using Electron Beam Induced Current (EBIC) measurement in FZ silicon deformed in four point bending tests.

Experimental study and finite element analysis based on equivalent load method for laser ultrasonic measurement of elastic constants.

PubMed

Zhan, Yu; Liu, Changsheng; Zhang, Fengpeng; Qiu, Zhaoguo

2016-07-01

The laser ultrasonic generation of Rayleigh surface wave and longitudinal wave in an elastic plate is studied by experiment and finite element method. In order to eliminate the measurement error and the time delay of the experimental system, the linear fitting method of experimental data is applied. The finite element analysis software ABAQUS is used to simulate the propagation of Rayleigh surface wave and longitudinal wave caused by laser excitation on a sheet metal sample surface. The equivalent load method is proposed and applied. The pulsed laser is equivalent to the surface load in time and space domain to meet the Gaussian profile. The relationship between the physical parameters of the laser and the load is established by the correction factor. The numerical solution is in good agreement with the experimental result. The simple and effective numerical and experimental methods for laser ultrasonic measurement of the elastic constants are demonstrated. Copyright © 2016. Published by Elsevier B.V.

Sudden spreading of infections in an epidemic model with a finite seed fraction

NASA Astrophysics Data System (ADS)

Hasegawa, Takehisa; Nemoto, Koji

2018-03-01

We study a simple case of the susceptible-weakened-infected-removed model in regular random graphs in a situation where an epidemic starts from a finite fraction of initially infected nodes (seeds). Previous studies have shown that, assuming a single seed, this model exhibits a kind of discontinuous transition at a certain value of infection rate. Performing Monte Carlo simulations and evaluating approximate master equations, we find that the present model has two critical infection rates for the case with a finite seed fraction. At the first critical rate the system shows a percolation transition of clusters composed of removed nodes, and at the second critical rate, which is larger than the first one, a giant cluster suddenly grows and the order parameter jumps even though it has been already rising. Numerical evaluation of the master equations shows that such sudden epidemic spreading does occur if the degree of the underlying network is large and the seed fraction is small.

A structurally oriented simulation system

NASA Technical Reports Server (NTRS)

Aran, Z.

1973-01-01

The computer program SOSS (Structurally Oriented Simulation System) is designed to be used as an experimental aid in the study of reliable systems. Basically, SOSS can simulate the structure and behavior of a discrete-time, finite-state, time-invariant system at various levels of structural definition. A general description of the program is given along with its modes of operation, command language of the basic system, future features to be incorporated in SOSS, and an example of usage.

Analysis of Flexible Bars and Frames with Large Displacements of Nodes By Finite Element Method in the Form of Classical Mixed Method

NASA Astrophysics Data System (ADS)

Ignatyev, A. V.; Ignatyev, V. A.; Onischenko, E. V.

2017-11-01

This article is the continuation of the work made bt the authors on the development of the algorithms that implement the finite element method in the form of a classical mixed method for the analysis of geometrically nonlinear bar systems [1-3]. The paper describes an improved algorithm of the formation of the nonlinear governing equations system for flexible plane frames and bars with large displacements of nodes based on the finite element method in a mixed classical form and the use of the procedure of step-by-step loading. An example of the analysis is given.

Implementation of structural response sensitivity calculations in a large-scale finite-element analysis system

NASA Technical Reports Server (NTRS)

Giles, G. L.; Rogers, J. L., Jr.

1982-01-01

The methodology used to implement structural sensitivity calculations into a major, general-purpose finite-element analysis system (SPAR) is described. This implementation includes a generalized method for specifying element cross-sectional dimensions as design variables that can be used in analytically calculating derivatives of output quantities from static stress, vibration, and buckling analyses for both membrane and bending elements. Limited sample results for static displacements and stresses are presented to indicate the advantages of analytically calculating response derivatives compared to finite difference methods. Continuing developments to implement these procedures into an enhanced version of SPAR are also discussed.

On some theoretical and practical aspects of multigrid methods. [to solve finite element systems from elliptic equations

NASA Technical Reports Server (NTRS)

Nicolaides, R. A.

1979-01-01

A description and explanation of a simple multigrid algorithm for solving finite element systems is given. Numerical results for an implementation are reported for a number of elliptic equations, including cases with singular coefficients and indefinite equations. The method shows the high efficiency, essentially independent of the grid spacing, predicted by the theory.

A Hybrid Numerical Analysis Method for Structural Health Monitoring

NASA Technical Reports Server (NTRS)

Forth, Scott C.; Staroselsky, Alexander

2001-01-01

A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.

Finite-SNR analysis for partial relaying cooperation with channel coding and opportunistic relay selection

NASA Astrophysics Data System (ADS)

Vu, Thang X.; Duhamel, Pierre; Chatzinotas, Symeon; Ottersten, Bjorn

2017-12-01

This work studies the performance of a cooperative network which consists of two channel-coded sources, multiple relays, and one destination. To achieve high spectral efficiency, we assume that a single time slot is dedicated to relaying. Conventional network-coded-based cooperation (NCC) selects the best relay which uses network coding to serve the two sources simultaneously. The bit error rate (BER) performance of NCC with channel coding, however, is still unknown. In this paper, we firstly study the BER of NCC via a closed-form expression and analytically show that NCC only achieves diversity of order two regardless of the number of available relays and the channel code. Secondly, we propose a novel partial relaying-based cooperation (PARC) scheme to improve the system diversity in the finite signal-to-noise ratio (SNR) regime. In particular, closed-form expressions for the system BER and diversity order of PARC are derived as a function of the operating SNR value and the minimum distance of the channel code. We analytically show that the proposed PARC achieves full (instantaneous) diversity order in the finite SNR regime, given that an appropriate channel code is used. Finally, numerical results verify our analysis and demonstrate a large SNR gain of PARC over NCC in the SNR region of interest.

Revisiting of Multiscale Static Analysis of Notched Laminates Using the Generalized Method of Cells

NASA Technical Reports Server (NTRS)

Naghipour Ghezeljeh, Paria; Arnold, Steven M.; Pineda, Evan J.

2016-01-01

Composite material systems generally exhibit a range of behavior on different length scales (from constituent level to macro); therefore, a multiscale framework is beneficial for the design and engineering of these material systems. The complex nature of the observed composite failure during experiments suggests the need for a three-dimensional (3D) multiscale model to attain a reliable prediction. However, the size of a multiscale three-dimensional finite element model can become prohibitively large and computationally costly. Two-dimensional (2D) models are preferred due to computational efficiency, especially if many different configurations have to be analyzed for an in-depth damage tolerance and durability design study. In this study, various 2D and 3D multiscale analyses will be employed to conduct a detailed investigation into the tensile failure of a given multidirectional, notched carbon fiber reinforced polymer laminate. Threedimensional finite element analysis is typically considered more accurate than a 2D finite element model, as compared with experiments. Nevertheless, in the absence of adequate mesh refinement, large differences may be observed between a 2D and 3D analysis, especially for a shear-dominated layup. This observed difference has not been widely addressed in previous literature and is the main focus of this paper.

Efficient partitioning and assignment on programs for multiprocessor execution

NASA Technical Reports Server (NTRS)

Standley, Hilda M.

1993-01-01

The general problem studied is that of segmenting or partitioning programs for distribution across a multiprocessor system. Efficient partitioning and the assignment of program elements are of great importance since the time consumed in this overhead activity may easily dominate the computation, effectively eliminating any gains made by the use of the parallelism. In this study, the partitioning of sequentially structured programs (written in FORTRAN) is evaluated. Heuristics, developed for similar applications are examined. Finally, a model for queueing networks with finite queues is developed which may be used to analyze multiprocessor system architectures with a shared memory approach to the problem of partitioning. The properties of sequentially written programs form obstacles to large scale (at the procedure or subroutine level) parallelization. Data dependencies of even the minutest nature, reflecting the sequential development of the program, severely limit parallelism. The design of heuristic algorithms is tied to the experience gained in the parallel splitting. Parallelism obtained through the physical separation of data has seen some success, especially at the data element level. Data parallelism on a grander scale requires models that accurately reflect the effects of blocking caused by finite queues. A model for the approximation of the performance of finite queueing networks is developed. This model makes use of the decomposition approach combined with the efficiency of product form solutions.

A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains

NASA Technical Reports Server (NTRS)

Kandil, Osama A.

1998-01-01

Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.

Object Toolkit Version 4.3 User’s Manual

DTIC Science & Technology

2016-12-31

unlimited. (OPS-17-12855 dtd 19 Jan 2017) 13. SUPPLEMENTARY NOTES 14. ABSTRACT Object Toolkit is a finite - element model builder specifically designed for...INTRODUCTION 1 What Is Object Toolkit? Object Toolkit is a finite - element model builder specifically designed for creating representations of spacecraft...Nascap-2k and EPIC, the user is not required to purchase or learn expensive finite element generators to create system models. Second, Object Toolkit

Computing Finite-Time Lyapunov Exponents with Optimally Time Dependent Reduction

NASA Astrophysics Data System (ADS)

Babaee, Hessam; Farazmand, Mohammad; Sapsis, Themis; Haller, George

2016-11-01

We present a method to compute Finite-Time Lyapunov Exponents (FTLE) of a dynamical system using Optimally Time-Dependent (OTD) reduction recently introduced by H. Babaee and T. P. Sapsis. The OTD modes are a set of finite-dimensional, time-dependent, orthonormal basis {ui (x , t) } |i=1N that capture the directions associated with transient instabilities. The evolution equation of the OTD modes is derived from a minimization principle that optimally approximates the most unstable directions over finite times. To compute the FTLE, we evolve a single OTD mode along with the nonlinear dynamics. We approximate the FTLE from the reduced system obtained from projecting the instantaneous linearized dynamics onto the OTD mode. This results in a significant reduction in the computational cost compared to conventional methods for computing FTLE. We demonstrate the efficiency of our method for double Gyre and ABC flows. ARO project 66710-EG-YIP.

Testing Linear Temporal Logic Formulae on Finite Execution Traces

NASA Technical Reports Server (NTRS)

Havelund, Klaus; Rosu, Grigore; Norvig, Peter (Technical Monitor)

2001-01-01

We present an algorithm for efficiently testing Linear Temporal Logic (LTL) formulae on finite execution traces. The standard models of LTL are infinite traces, reflecting the behavior of reactive and concurrent systems which conceptually may be continuously alive. In most past applications of LTL. theorem provers and model checkers have been used to formally prove that down-scaled models satisfy such LTL specifications. Our goal is instead to use LTL for up-scaled testing of real software applications. Such tests correspond to analyzing the conformance of finite traces against LTL formulae. We first describe what it means for a finite trace to satisfy an LTL property. We then suggest an optimized algorithm based on transforming LTL formulae. The work is done using the Maude rewriting system. which turns out to provide a perfect notation and an efficient rewriting engine for performing these experiments.

A Design of Finite Memory Residual Generation Filter for Sensor Fault Detection

NASA Astrophysics Data System (ADS)

Kim, Pyung Soo

2017-04-01

In the current paper, a residual generation filter with finite memory structure is proposed for sensor fault detection. The proposed finite memory residual generation filter provides the residual by real-time filtering of fault vector using only the most recent finite measurements and inputs on the window. It is shown that the residual given by the proposed residual generation filter provides the exact fault for noisefree systems. The proposed residual generation filter is specified to the digital filter structure for the amenability to hardware implementation. Finally, to illustrate the capability of the proposed residual generation filter, extensive simulations are performed for the discretized DC motor system with two types of sensor faults, incipient soft bias-type fault and abrupt bias-type fault. In particular, according to diverse noise levels and windows lengths, meaningful simulation results are given for the abrupt bias-type fault.

On some methods of discrete systems behaviour simulation

NASA Astrophysics Data System (ADS)

Sytnik, Alexander A.; Posohina, Natalia I.

1998-07-01

The project is solving one of the fundamental problems of mathematical cybernetics and discrete mathematics, the one connected with synthesis and analysis of managing systems, depending on the research of their functional opportunities and reliable behaviour. This work deals with the case of finite-state machine behaviour restoration when the structural redundancy is not available and the direct updating of current behaviour is impossible. The described below method, uses number theory to build a special model of finite-state machine, it is simulating the transition between the states of the finite-state machine using specially defined functions of exponential type with the help of several methods of number theory and algebra it is easy to determine, whether there is an opportunity to restore the behaviour (with the help of this method) in the given case or not and also derive the class of finite-state machines, admitting such restoration.

Probabilistic Structural Analysis Theory Development

NASA Technical Reports Server (NTRS)

Burnside, O. H.

1985-01-01

The objective of the Probabilistic Structural Analysis Methods (PSAM) project is to develop analysis techniques and computer programs for predicting the probabilistic response of critical structural components for current and future space propulsion systems. This technology will play a central role in establishing system performance and durability. The first year's technical activity is concentrating on probabilistic finite element formulation strategy and code development. Work is also in progress to survey critical materials and space shuttle mian engine components. The probabilistic finite element computer program NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) is being developed. The final probabilistic code will have, in the general case, the capability of performing nonlinear dynamic of stochastic structures. It is the goal of the approximate methods effort to increase problem solving efficiency relative to finite element methods by using energy methods to generate trial solutions which satisfy the structural boundary conditions. These approximate methods will be less computer intensive relative to the finite element approach.

Volume dependence of baryon number cumulants and their ratios

DOE PAGES

Almási, Gábor A.; Pisarski, Robert D.; Skokov, Vladimir V.

2017-03-17

Here, we explore the influence of finite-volume effects on cumulants of baryon/quark number fluctuations in a nonperturbative chiral model. In order to account for soft modes, we use the functional renormalization group in a finite volume, using a smooth regulator function in momentum space. We compare the results for a smooth regulator with those for a sharp (or Litim) regulator, and show that in a finite volume, the latter produces spurious artifacts. In a finite volume there are only apparent critical points, about which we compute the ratio of the fourth- to the second-order cumulant of quark number fluctuations. Finally,more » when the volume is sufficiently small the system has two apparent critical points; as the system size decreases, the location of the apparent critical point can move to higher temperature and lower chemical potential.« less

A novel modelling approach to energy transport in a respiratory system.

PubMed

Nithiarasu, Perumal; Sazonov, Igor

2017-10-01

In this paper, energy transport in a respiratory tract is modelled using the finite element method for the first time. The upper and lower respiratory tracts are approximated as a 1-dimensional domain with varying cross-sectional and surface areas, and the radial heat conduction in the tissue is approximated using the 1-dimensional cylindrical coordinate system. The governing equations are solved using 1-dimensional linear finite elements with convective and evaporative boundary conditions on the wall. The results obtained for the exhalation temperature of the respiratory system have been compared with the available animal experiments. The study of a full breathing cycle indicates that evaporation is the main mode of heat transfer, and convection plays almost negligible role in the energy transport. This is in-line with the results obtained from animal experiments. Copyright © 2016 John Wiley & Sons, Ltd.

Large-Scale First-Principles Molecular Dynamics Simulations with Electrostatic Embedding: Application to Acetylcholinesterase Catalysis

DOE PAGES

Fattebert, Jean-Luc; Lau, Edmond Y.; Bennion, Brian J.; ...

2015-10-22

Enzymes are complicated solvated systems that typically require many atoms to simulate their function with any degree of accuracy. We have recently developed numerical techniques for large scale First-Principles molecular dynamics simulations and applied them to study the enzymatic reaction catalyzed by acetylcholinesterase. We carried out Density functional theory calculations for a quantum mechanical (QM) sub- system consisting of 612 atoms with an O(N) complexity finite-difference approach. The QM sub-system is embedded inside an external potential field representing the electrostatic effect due to the environment. We obtained finite temperature sampling by First-Principles molecular dynamics for the acylation reaction of acetylcholinemore » catalyzed by acetylcholinesterase. Our calculations shows two energies barriers along the reaction coordinate for the enzyme catalyzed acylation of acetylcholine. In conclusion, the second barrier (8.5 kcal/mole) is rate-limiting for the acylation reaction and in good agreement with experiment.« less

Finite-size effects on current correlation functions

NASA Astrophysics Data System (ADS)

Chen, Shunda; Zhang, Yong; Wang, Jiao; Zhao, Hong

2014-02-01

We study why the calculation of current correlation functions (CCFs) still suffers from finite-size effects even when the periodic boundary condition is taken. Two important one-dimensional, momentum-conserving systems are investigated as examples. Intriguingly, it is found that the state of a system recurs in the sense of microcanonical ensemble average, and such recurrence may result in oscillations in CCFs. Meanwhile, we find that the sound mode collisions induce an extra time decay in a current so that its correlation function decays faster (slower) in a smaller (larger) system. Based on these two unveiled mechanisms, a procedure for correctly evaluating the decay rate of a CCF is proposed, with which our analysis suggests that the global energy CCF decays as ˜t-2/3 in the diatomic hard-core gas model and in a manner close to ˜t-1/2 in the Fermi-Pasta-Ulam-β model.

Dynamic Analysis of Geared Rotors by Finite Elements

NASA Technical Reports Server (NTRS)

Kahraman, A.; Ozguven, H. Nevzat; Houser, D. R.; Zakrajsek, J. J.

1992-01-01

A finite element model of a geared rotor system on flexible bearings has been developed. The model includes the rotary inertia of on shaft elements, the axial loading on shafts, flexibility and damping of bearings, material damping of shafts and the stiffness and the damping of gear mesh. The coupling between the torsional and transverse vibrations of gears were considered in the model. A constant mesh stiffness was assumed. The analysis procedure can be used for forced vibration analysis geared rotors by calculating the critical speeds and determining the response of any point on the shafts to mass unbalances, geometric eccentricities of gears, and displacement transmission error excitation at the mesh point. The dynamic mesh forces due to these excitations can also be calculated. The model has been applied to several systems for the demonstration of its accuracy and for studying the effect of bearing compliances on system dynamics.

Exchange-driven growth.

PubMed

Ben-Naim, E; Krapivsky, P L

2003-09-01

We study a class of growth processes in which clusters evolve via exchange of particles. We show that depending on the rate of exchange there are three possibilities: (I) Growth-clusters grow indefinitely, (II) gelation-all mass is transformed into an infinite gel in a finite time, and (III) instant gelation. In regimes I and II, the cluster size distribution attains a self-similar form. The large size tail of the scaling distribution is Phi(x) approximately exp(-x(2-nu)), where nu is a homogeneity degree of the rate of exchange. At the borderline case nu=2, the distribution exhibits a generic algebraic tail, Phi(x) approximately x(-5). In regime III, the gel nucleates immediately and consumes the entire system. For finite systems, the gelation time vanishes logarithmically, T approximately [lnN](-(nu-2)), in the large system size limit N--> infinity. The theory is applied to coarsening in the infinite range Ising-Kawasaki model and in electrostatically driven granular layers.

Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with ε-error bound.

PubMed

Wang, Fei-Yue; Jin, Ning; Liu, Derong; Wei, Qinglai

2011-01-01

In this paper, we study the finite-horizon optimal control problem for discrete-time nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an ε-error bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method.

Tan's contact and the phase distribution of repulsive Fermi gases: Insights from quantum chromodynamics noise analyses

NASA Astrophysics Data System (ADS)

Porter, William J.; Drut, Joaquín E.

2017-05-01

Path-integral analyses originally pioneered in the study of the complex-phase problem afflicting lattice calculations of finite-density quantum chromodynamics are generalized to nonrelativistic Fermi gases with repulsive interactions. Using arguments similar to those previously applied to relativistic theories, we show that the analogous problem in nonrelativistic systems manifests itself naturally in Tan's contact as a nontrivial cancellation between terms with varied dependence on extensive thermodynamic quantities. We analyze that case under the assumption of a Gaussian phase distribution, which is supported by our Monte Carlo calculations and perturbative considerations. We further generalize these results to observables other than the contact, as well as to polarized systems and systems with fixed particle number. Our results are quite general in that they apply to repulsive multicomponent fermions, they are independent of dimensionality or trapping potential, and they hold in the ground state as well as at finite temperature.

GPS/INS Sensor Fusion Using GPS Wind up Model

NASA Technical Reports Server (NTRS)

Williamson, Walton R. (Inventor)

2013-01-01

A method of stabilizing an inertial navigation system (INS), includes the steps of: receiving data from an inertial navigation system; and receiving a finite number of carrier phase observables using at least one GPS receiver from a plurality of GPS satellites; calculating a phase wind up correction; correcting at least one of the finite number of carrier phase observables using the phase wind up correction; and calculating a corrected IMU attitude or velocity or position using the corrected at least one of the finite number of carrier phase observables; and performing a step selected from the steps consisting of recording, reporting, or providing the corrected IMU attitude or velocity or position to another process that uses the corrected IMU attitude or velocity or position. A GPS stabilized inertial navigation system apparatus is also described.

The aggregated unfitted finite element method for elliptic problems

NASA Astrophysics Data System (ADS)

Badia, Santiago; Verdugo, Francesc; Martín, Alberto F.

2018-07-01

Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use of iterative Krylov methods and, in consequence, hinders the practical usage of unfitted methods for realistic large scale applications. In this work, we present a technique that addresses such conditioning problems by constructing enhanced finite element spaces based on a cell aggregation technique. The presented method, called aggregated unfitted finite element method, is easy to implement, and can be used, in contrast to previous works, in Galerkin approximations of coercive problems with conforming Lagrangian finite element spaces. The mathematical analysis of the new method states that the condition number of the resulting linear system matrix scales as in standard finite elements for body-fitted meshes, without being affected by small cut cells, and that the method leads to the optimal finite element convergence order. These theoretical results are confirmed with 2D and 3D numerical experiments.

Gapless Spin-Liquid Ground State in the S =1 /2 Kagome Antiferromagnet

NASA Astrophysics Data System (ADS)

Liao, H. J.; Xie, Z. Y.; Chen, J.; Liu, Z. Y.; Xie, H. D.; Huang, R. Z.; Normand, B.; Xiang, T.

2017-03-01

The defining problem in frustrated quantum magnetism, the ground state of the nearest-neighbor S =1 /2 antiferromagnetic Heisenberg model on the kagome lattice, has defied all theoretical and numerical methods employed to date. We apply the formalism of tensor-network states, specifically the method of projected entangled simplex states, which combines infinite system size with a correct accounting for multipartite entanglement. By studying the ground-state energy, the finite magnetic order appearing at finite tensor bond dimensions, and the effects of a next-nearest-neighbor coupling, we demonstrate that the ground state is a gapless spin liquid. We discuss the comparison with other numerical studies and the physical interpretation of this result.

NASTRAN data generation of helicopter fuselages using interactive graphics. [preprocessor system for finite element analysis using IBM computer

NASA Technical Reports Server (NTRS)

Sainsbury-Carter, J. B.; Conaway, J. H.

1973-01-01

The development and implementation of a preprocessor system for the finite element analysis of helicopter fuselages is described. The system utilizes interactive graphics for the generation, display, and editing of NASTRAN data for fuselage models. It is operated from an IBM 2250 cathode ray tube (CRT) console driven by an IBM 370/145 computer. Real time interaction plus automatic data generation reduces the nominal 6 to 10 week time for manual generation and checking of data to a few days. The interactive graphics system consists of a series of satellite programs operated from a central NASTRAN Systems Monitor. Fuselage structural models including the outer shell and internal structure may be rapidly generated. All numbering systems are automatically assigned. Hard copy plots of the model labeled with GRID or elements ID's are also available. General purpose programs for displaying and editing NASTRAN data are included in the system. Utilization of the NASTRAN interactive graphics system has made possible the multiple finite element analysis of complex helicopter fuselage structures within design schedules.

Probabilistic structural analysis methods for select space propulsion system components

NASA Technical Reports Server (NTRS)

Millwater, H. R.; Cruse, T. A.

1989-01-01

The Probabilistic Structural Analysis Methods (PSAM) project developed at the Southwest Research Institute integrates state-of-the-art structural analysis techniques with probability theory for the design and analysis of complex large-scale engineering structures. An advanced efficient software system (NESSUS) capable of performing complex probabilistic analysis has been developed. NESSUS contains a number of software components to perform probabilistic analysis of structures. These components include: an expert system, a probabilistic finite element code, a probabilistic boundary element code and a fast probability integrator. The NESSUS software system is shown. An expert system is included to capture and utilize PSAM knowledge and experience. NESSUS/EXPERT is an interactive menu-driven expert system that provides information to assist in the use of the probabilistic finite element code NESSUS/FEM and the fast probability integrator (FPI). The expert system menu structure is summarized. The NESSUS system contains a state-of-the-art nonlinear probabilistic finite element code, NESSUS/FEM, to determine the structural response and sensitivities. A broad range of analysis capabilities and an extensive element library is present.

Inertial Manifold and Large Deviations Approach to Reduced PDE Dynamics

NASA Astrophysics Data System (ADS)

Cardin, Franco; Favretti, Marco; Lovison, Alberto

2017-09-01

In this paper a certain type of reaction-diffusion equation—similar to the Allen-Cahn equation—is the starting point for setting up a genuine thermodynamic reduction i.e. involving a finite number of parameters or collective variables of the initial system. We firstly operate a finite Lyapunov-Schmidt reduction of the cited reaction-diffusion equation when reformulated as a variational problem. In this way we gain a finite-dimensional ODE description of the initial system which preserves the gradient structure of the original one and that is exact for the static case and only approximate for the dynamic case. Our main concern is how to deal with this approximate reduced description of the initial PDE. To start with, we note that our approximate reduced ODE is similar to the approximate inertial manifold introduced by Temam and coworkers for Navier-Stokes equations. As a second approach, we take into account the uncertainty (loss of information) introduced with the above mentioned approximate reduction by considering the stochastic version of the ODE. We study this reduced stochastic system using classical tools from large deviations, viscosity solutions and weak KAM Hamilton-Jacobi theory. In the last part we suggest a possible use of a result of our approach in the comprehensive treatment non equilibrium thermodynamics given by Macroscopic Fluctuation Theory.

Finite element simulations of the head-brain responses to the top impacts of a construction helmet: Effects of the neck and body mass.

PubMed

Wu, John Z; Pan, Christopher S; Wimer, Bryan M; Rosen, Charles L

2017-01-01

Traumatic brain injuries are among the most common severely disabling injuries in the United States. Construction helmets are considered essential personal protective equipment for reducing traumatic brain injury risks at work sites. In this study, we proposed a practical finite element modeling approach that would be suitable for engineers to optimize construction helmet design. The finite element model includes all essential anatomical structures of a human head (i.e. skin, scalp, skull, cerebrospinal fluid, brain, medulla, spinal cord, cervical vertebrae, and discs) and all major engineering components of a construction helmet (i.e. shell and suspension system). The head finite element model has been calibrated using the experimental data in the literature. It is technically difficult to precisely account for the effects of the neck and body mass on the dynamic responses, because the finite element model does not include the entire human body. An approximation approach has been developed to account for the effects of the neck and body mass on the dynamic responses of the head-brain. Using the proposed model, we have calculated the responses of the head-brain during a top impact when wearing a construction helmet. The proposed modeling approach would provide a tool to improve the helmet design on a biomechanical basis.

A finite element analysis of a 3D auxetic textile structure for composite reinforcement

NASA Astrophysics Data System (ADS)

Ge, Zhaoyang; Hu, Hong; Liu, Yanping

2013-08-01

This paper reports the finite element analysis of an innovative 3D auxetic textile structure consisting of three yarn systems (weft, warp and stitch yarns). Different from conventional 3D textile structures, the proposed structure exhibits an auxetic behaviour under compression and can be used as a reinforcement to manufacture auxetic composites. The geometry of the structure is first described. Then a 3D finite element model is established using ANSYS software and validated by the experimental results. The deformation process of the structure at different compression strains is demonstrated, and the validated finite element model is finally used to simulate the auxetic behaviour of the structure with different structural parameters and yarn properties. The results show that the auxetic behaviour of the proposed structure increases with increasing compression strain, and all the structural parameters and yarn properties have significant effects on the auxetic behaviour of the structure. It is expected that the study could provide a better understanding of 3D auxetic textile structures and could promote their application in auxetic composites.

Quantifying matrix product state

NASA Astrophysics Data System (ADS)

Bhatia, Amandeep Singh; Kumar, Ajay

2018-03-01

Motivated by the concept of quantum finite-state machines, we have investigated their relation with matrix product state of quantum spin systems. Matrix product states play a crucial role in the context of quantum information processing and are considered as a valuable asset for quantum information and communication purpose. It is an effective way to represent states of entangled systems. In this paper, we have designed quantum finite-state machines of one-dimensional matrix product state representations for quantum spin systems.

Iterative algorithms for large sparse linear systems on parallel computers

NASA Technical Reports Server (NTRS)

Adams, L. M.

1982-01-01

Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

Performance of Minicomputers in Finite Element Analysis Pre and Post Processing.

DTIC Science & Technology

1980-07-29

points, and 78 rectangular plate elements. It was generated using the BULKM mesh generation program, which is a part of the GIFTS -5 system [3]. c...The program used, DECOM, is part of the GIFTS system. It uses a hyper-(partitioned) matrix generalization of the Cholesky decomposition algorithm. d...Pub. 2018, Oct. 77. 3. Kamel, H.A. and McCabe, M.W., GIFTS : Graphics Oriented Interactive Finite Element Time-Sharing System. Structural Mechanics

Equilibration in finite Bose systems

NASA Astrophysics Data System (ADS)

Wolschin, Georg

2018-06-01

The equilibration of a finite Bose system is modeled using a gradient expansion of the collision integral that leads to a nonlinear transport equation. For constant transport coefficients, it is solved in closed form through a nonlinear transformation. Using schematic initial conditions, the exact solution and the equilibration time are derived and compared to the corresponding case for fermions. Applications to the fast equilibration of the gluon system created initially in relativistic heavy-ion collisions, and to cold quantum gases are envisaged.

Annual Review of Research Under the Joint Services Electronics Program.

DTIC Science & Technology

1983-12-01

Total Number of Professionals: PI 2 RA 2 (1/2 time ) 6. Sunmmary: Our research into the theory of nonlinear control systems and appli- * cations to...known that all linear time -invariant controllable systems can be transformed to Brunovsky canonical form by a transformation consist- ing only of...estimating the impulse response ( = transfer matrix) of a discrete- time linear system x(t+l) = Fx(t) + Gu(t) y(t) = Hx(t) from a finite set of finite

Small Body GN&C Research Report: A Robust Model Predictive Control Algorithm with Guaranteed Resolvability

NASA Technical Reports Server (NTRS)

Acikmese, Behcet A.; Carson, John M., III

2005-01-01

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees the resolvability of the associated finite-horizon optimal control problem in a receding-horizon implementation. The control consists of two components; (i) feedforward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives, and derivatives in polytopes. An illustrative numerical example is also provided.

Two Universality Classes for the Many-Body Localization Transition

NASA Astrophysics Data System (ADS)

Khemani, Vedika; Sheng, D. N.; Huse, David A.

2017-08-01

We provide a systematic comparison of the many-body localization (MBL) transition in spin chains with nonrandom quasiperiodic versus random fields. We find evidence suggesting that these belong to two separate universality classes: the first dominated by "intrinsic" intrasample randomness, and the second dominated by external intersample quenched randomness. We show that the effects of intersample quenched randomness are strongly growing, but not yet dominant, at the system sizes probed by exact-diagonalization studies on random models. Thus, the observed finite-size critical scaling collapses in such studies appear to be in a preasymptotic regime near the nonrandom universality class, but showing signs of the initial crossover towards the external-randomness-dominated universality class. Our results provide an explanation for why exact-diagonalization studies on random models see an apparent scaling near the transition while also obtaining finite-size scaling exponents that strongly violate Harris-Chayes bounds that apply to disorder-driven transitions. We also show that the MBL phase is more stable for the quasiperiodic model as compared to the random one, and the transition in the quasiperiodic model suffers less from certain finite-size effects.

Liquid Rocket Booster (LRB) for the Space Transportation System (STS) systems study. Appendix A: Stress analysis report for the pump-fed and pressure-fed liquid rocket booster

NASA Technical Reports Server (NTRS)

1989-01-01

Pressure effects on the pump-fed Liquid Rocket Booster (LRB) of the Space Transportation System are examined. Results from the buckling tests; bending moments tests; barrel, propellant tanks, frame XB1513, nose cone, and intertank tests; and finite element examination of forward and aft skirts are presented.

Bistable traveling waves for a competitive-cooperative system with nonlocal delays

NASA Astrophysics Data System (ADS)

Tian, Yanling; Zhao, Xiao-Qiang

2018-04-01

This paper is devoted to the study of bistable traveling waves for a competitive-cooperative reaction and diffusion system with nonlocal time delays. The existence of bistable waves is established by appealing to the theory of monotone semiflows and the finite-delay approximations. Then the global stability of such traveling waves is obtained via a squeezing technique and a dynamical systems approach.

GTX Reference Vehicle Structural Verification Methods and Weight Summary

NASA Technical Reports Server (NTRS)

Hunter, J. E.; McCurdy, D. R.; Dunn, P. W.

2002-01-01

The design of a single-stage-to-orbit air breathing propulsion system requires the simultaneous development of a reference launch vehicle in order to achieve the optimal mission performance. Accordingly, for the GTX study a 300-lb payload reference vehicle was preliminary sized to a gross liftoff weight (GLOW) of 238,000 lb. A finite element model of the integrated vehicle/propulsion system was subjected to the trajectory environment and subsequently optimized for structural efficiency. This study involved the development of aerodynamic loads mapped to finite element models of the integrated system in order to assess vehicle margins of safety. Commercially available analysis codes were used in the process along with some internally developed spread-sheets and FORTRAN codes specific to the GTX geometry for mapping of thermal and pressure loads. A mass fraction of 0.20 for the integrated system dry weight has been the driver for a vehicle design consisting of state-of-the-art composite materials in order to meet the rigid weight requirements. This paper summarizes the methodology used for preliminary analyses and presents the current status of the weight optimization for the structural components of the integrated system.

GTX Reference Vehicle Structural Verification Methods and Weight Summary

NASA Technical Reports Server (NTRS)

Hunter, J. E.; McCurdy, D. R.; Dunn, P. W.

2002-01-01

The design of a single-stage-to-orbit air breathing propulsion system requires the simultaneous development of a reference launch vehicle in order to achieve the optimal mission performance. Accordingly, for the GTX study a 300-lb payload reference vehicle was preliminarily sized to a gross liftoff weight (GLOW) of 238,000 lb. A finite element model of the integrated vehicle/propulsion system was subjected to the trajectory environment and subsequently optimized for structural efficiency. This study involved the development of aerodynamic loads mapped to finite element models of the integrated system in order to assess vehicle margins of safety. Commercially available analysis codes were used in the process along with some internally developed spreadsheets and FORTRAN codes specific to the GTX geometry for mapping of thermal and pressure loads. A mass fraction of 0.20 for the integrated system dry weight has been the driver for a vehicle design consisting of state-of-the-art composite materials in order to meet the rigid weight requirements. This paper summarizes the methodology used for preliminary analyses and presents the current status of the weight optimization for the structural components of the integrated system.

Large Angle Transient Dynamics (LATDYN) user's manual

NASA Technical Reports Server (NTRS)

Abrahamson, A. Louis; Chang, Che-Wei; Powell, Michael G.; Wu, Shih-Chin; Bingel, Bradford D.; Theophilos, Paula M.

1991-01-01

A computer code for modeling the large angle transient dynamics (LATDYN) of structures was developed to investigate techniques for analyzing flexible deformation and control/structure interaction problems associated with large angular motions of spacecraft. This type of analysis is beyond the routine capability of conventional analytical tools without simplifying assumptions. In some instances, the motion may be sufficiently slow and the spacecraft (or component) sufficiently rigid to simplify analyses of dynamics and controls by making pseudo-static and/or rigid body assumptions. The LATDYN introduces a new approach to the problem by combining finite element structural analysis, multi-body dynamics, and control system analysis in a single tool. It includes a type of finite element that can deform and rotate through large angles at the same time, and which can be connected to other finite elements either rigidly or through mechanical joints. The LATDYN also provides symbolic capabilities for modeling control systems which are interfaced directly with the finite element structural model. Thus, the nonlinear equations representing the structural model are integrated along with the equations representing sensors, processing, and controls as a coupled system.

Generalized epidemic process on modular networks.

PubMed

Chung, Kihong; Baek, Yongjoo; Kim, Daniel; Ha, Meesoon; Jeong, Hawoong

2014-05-01

Social reinforcement and modular structure are two salient features observed in the spreading of behavior through social contacts. In order to investigate the interplay between these two features, we study the generalized epidemic process on modular networks with equal-sized finite communities and adjustable modularity. Using the analytical approach originally applied to clique-based random networks, we show that the system exhibits a bond-percolation type continuous phase transition for weak social reinforcement, whereas a discontinuous phase transition occurs for sufficiently strong social reinforcement. Our findings are numerically verified using the finite-size scaling analysis and the crossings of the bimodality coefficient.

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

This paper considers several topics arising in the finite element solution of the incompressible Navier-Stokes equations. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. Following this, the role of artificial viscosity in viscous flow calculations is studied, emphasizing recent work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some recent modifications are mentioned.

A Variational Formulation for the Finite Element Analysis of Sound Wave Propagation in a Spherical Shell

NASA Technical Reports Server (NTRS)

Lebiedzik, Catherine

1995-01-01

Development of design tools to furnish optimal acoustic environments for lightweight aircraft demands the ability to simulate the acoustic system on a workstation. In order to form an effective mathematical model of the phenomena at hand, we have begun by studying the propagation of acoustic waves inside closed spherical shells. Using a fully-coupled fluid-structure interaction model based upon variational principles, we have written a finite element analysis program and are in the process of examining several test cases. Future investigations are planned to increase model accuracy by incorporating non-linear and viscous effects.

Quality-assurance study of the special - purpose finite-element program - SPECTROM: I. Thermal, thermoelastic, and viscoelastic problems. [Comparison with MARC-CDC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wagner, R.A.

1980-12-01

This comparison study involves a preliminary verification of finite element calculations. The methodology of the comparison study consists of solving four example problems with both the SPECTROM finite element program and the MARC-CDC general purpose finite element program. The results show close agreement for all example problems.

Trends and techniques for space base electronics. [mathematical models, ion implantation, and semiconductors

NASA Technical Reports Server (NTRS)

Gassaway, J. D.; Mahmood, Q.; Trotter, J. D.

1978-01-01

A system was developed for depositing aluminum and aluminum alloys by the D.C. sputtering technique. This system which was designed for a high level of cleanliness and ion monitoring the deposition parameters during film preparation is ready for studying the deposition and annealing parameters upon double level metal preparation. The finite element method was studied for use in the computer modeling of two dimensional MOS transistor structures. An algorithm was developed for implementing a computer study which is based upon the finite difference method. The program was modified and used to calculate redistribution data for boron and phosphorous which had been predeposited by ion implantation with range and straggle conditions typical of those used at MSFC. Data were generated for 111 oriented SOS films with redistribution in N2, dry O2 and steam ambients. Data are given showing both two dimensional effects and the evolution of the junction depth, sheet resistance and integrated dose with redistribution time.

Lack of a thermodynamic finite-temperature spin-glass phase in the two-dimensional randomly coupled ferromagnet

NASA Astrophysics Data System (ADS)

Zhu, Zheng; Ochoa, Andrew J.; Katzgraber, Helmut G.

2018-05-01

The search for problems where quantum adiabatic optimization might excel over classical optimization techniques has sparked a recent interest in inducing a finite-temperature spin-glass transition in quasiplanar topologies. We have performed large-scale finite-temperature Monte Carlo simulations of a two-dimensional square-lattice bimodal spin glass with next-nearest ferromagnetic interactions claimed to exhibit a finite-temperature spin-glass state for a particular relative strength of the next-nearest to nearest interactions [Phys. Rev. Lett. 76, 4616 (1996), 10.1103/PhysRevLett.76.4616]. Our results show that the system is in a paramagnetic state in the thermodynamic limit, despite zero-temperature simulations [Phys. Rev. B 63, 094423 (2001), 10.1103/PhysRevB.63.094423] suggesting the existence of a finite-temperature spin-glass transition. Therefore, deducing the finite-temperature behavior from zero-temperature simulations can be dangerous when corrections to scaling are large.

Finite-strain large-deflection elastic-viscoplastic finite-element transient response analysis of structures

NASA Technical Reports Server (NTRS)

Rodal, J. J. A.; Witmer, E. A.

1979-01-01

A method of analysis for thin structures that incorporates finite strain, elastic-plastic, strain hardening, time dependent material behavior implemented with respect to a fixed configuration and is consistently valid for finite strains and finite rotations is developed. The theory is formulated systematically in a body fixed system of convected coordinates with materially embedded vectors that deform in common with continuum. Tensors are considered as linear vector functions and use is made of the dyadic representation. The kinematics of a deformable continuum is treated in detail, carefully defining precisely all quantities necessary for the analysis. The finite strain theory developed gives much better predictions and agreement with experiment than does the traditional small strain theory, and at practically no additional cost. This represents a very significant advance in the capability for the reliable prediction of nonlinear transient structural responses, including the reliable prediction of strains large enough to produce ductile metal rupture.

The new finite temperature Schrödinger equations with strong or weak interaction

NASA Astrophysics Data System (ADS)

Li, Heling; Yang, Bin; Shen, Hongjun

2017-07-01

Implanting the thoughtway of thermostatistics into quantum mechanics, we formulate new Schrödinger equations of multi-particle and single-particle respectively at finite temperature. To get it, the pure-state free energies and the microscopic entropy operators are introduced and meantime the pure-state free energies take the places of mechanical energies at finite temperature. The definition of microscopic entropy introduced by Wu was also revised, and the strong or weak interactions dependent on temperature are considered in multi-particle Schrödinger Equations. Based on the new Schrödinger equation at finite temperature, two simple cases were analyzed. The first one is concerning some identical harmonic oscillators in N lattice points and the other one is about N unrelated particles in three dimensional in finite potential well. From the results gotten, we conclude that the finite temperature Schrödinger equation is particularly important for mesoscopic systems.

Electrically tunable Dicke effect in a double-ring resonator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cetin, A. E.; Muestecaplioglu, Oe. E.; Department of Physics, Koc University, Sariyer, Istanbul 34450

We study the finite-element method analysis of the Dicke effect using numerical simulations in an all-optical system of an optical waveguide side-coupled to two interacting ring resonators in a liquid crystal environment. The system is shown to exhibit all the signatures of the Dicke effect under active and reversible control by an applied voltage.

Comparative study of state-of-the-art myoelectric controllers for multigrasp prosthetic hands.

PubMed

Segil, Jacob L; Controzzi, Marco; Weir, Richard F ff; Cipriani, Christian

2014-01-01

A myoelectric controller should provide an intuitive and effective human-machine interface that deciphers user intent in real-time and is robust enough to operate in daily life. Many myoelectric control architectures have been developed, including pattern recognition systems, finite state machines, and more recently, postural control schemes. Here, we present a comparative study of two types of finite state machines and a postural control scheme using both virtual and physical assessment procedures with seven nondisabled subjects. The Southampton Hand Assessment Procedure (SHAP) was used in order to compare the effectiveness of the controllers during activities of daily living using a multigrasp artificial hand. Also, a virtual hand posture matching task was used to compare the controllers when reproducing six target postures. The performance when using the postural control scheme was significantly better (p < 0.05) than the finite state machines during the physical assessment when comparing within-subject averages using the SHAP percent difference metric. The virtual assessment results described significantly greater completion rates (97% and 99%) for the finite state machines, but the movement time tended to be faster (2.7 s) for the postural control scheme. Our results substantiate that postural control schemes rival other state-of-the-art myoelectric controllers.

Adjacent level effects of bi level disc replacement, bi level fusion and disc replacement plus fusion in cervical spine--a finite element based study.

PubMed

Faizan, Ahmad; Goel, Vijay K; Biyani, Ashok; Garfin, Steven R; Bono, Christopher M

2012-03-01

Studies delineating the adjacent level effect of single level disc replacement systems have been reported in literature. The aim of this study was to compare the adjacent level biomechanics of bi-level disc replacement, bi-level fusion and a construct having adjoining level disc replacement and fusion system. In total, biomechanics of four models- intact, bi level disc replacement, bi level fusion and fusion plus disc replacement at adjoining levels- was studied to gain insight into the effects of various instrumentation systems on cranial and caudal adjacent levels using finite element analysis (73.6N+varying moment). The bi-level fusion models are more than twice as stiff as compared to the intact model during flexion-extension, lateral bending and axial rotation. Bi-level disc replacement model required moments lower than intact model (1.5Nm). Fusion plus disc replacement model required moment 10-25% more than intact model, except in extension. Adjacent level motions, facet loads and endplate stresses increased substantially in the bi-level fusion model. On the other hand, adjacent level motions, facet loads and endplate stresses were similar to intact for the bi-level disc replacement model. For the fusion plus disc replacement model, adjacent level motions, facet loads and endplate stresses were closer to intact model rather than the bi-level fusion model, except in extension. Based on our finite element analysis, fusion plus disc replacement procedure has less severe biomechanical effects on adjacent levels when compared to bi-level fusion procedure. Bi-level disc replacement procedure did not have any adverse mechanical effects on adjacent levels. Copyright © 2011 Elsevier Ltd. All rights reserved.

Non-linear dynamic analysis of geared systems, part 2

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

Finite Element Analysis of Flexural Vibrations in Hard Disk Drive Spindle Systems

NASA Astrophysics Data System (ADS)

LIM, SEUNGCHUL

2000-06-01

This paper is concerned with the flexural vibration analysis of the hard disk drive (HDD) spindle system by means of the finite element method. In contrast to previous research, every system component is here analytically modelled taking into account its structural flexibility and also the centrifugal effect particularly on the disk. To prove the effectiveness and accuracy of the formulated models, commercial HDD systems with two and three identical disks are selected as examples. Then their major natural modes are computed with only a small number of element meshes as the shaft rotational speed is varied, and subsequently compared with the existing numerical results obtained using other methods and newly acquired experimental ones. Based on such a series of studies, the proposed method can be concluded as a very promising tool for the design of HDDs and various other high-performance computer disk drives such as floppy disk drives, CD ROM drives, and their variations having spindle mechanisms similar to those of HDDs.

Cooperative Solutions in Multi-Person Quadratic Decision Problems: Finite-Horizon and State-Feedback Cost-Cumulant Control Paradigm

DTIC Science & Technology

2007-01-01

CONTRACT NUMBER Problems: Finite -Horizon and State-Feedback Cost-Cumulant Control Paradigm (PREPRINT) 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER...cooperative cost-cumulant control regime for the class of multi-person single-objective decision problems characterized by quadratic random costs and... finite -horizon integral quadratic cost associated with a linear stochastic system . Since this problem formation is parameterized by the number of cost

Numerical algorithms for computations of feedback laws arising in control of flexible systems

NASA Technical Reports Server (NTRS)

Lasiecka, Irena

1989-01-01

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

US Marine Corps assault amphibious vehicle suspension system analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hammonds, C.J.; Jones, J.K.; Mayhall, J.A.

1988-11-01

In response to a request from the US Marine Corps (USMC), the Oak Ridge National Laboratory investigated a problem with the suspension system of the assault amphibious vehicle (AAV), Personnel Model 7A1. In the course of the investigation, drawings of the AAV and field survey data on bearing failures provided by VSE Corporation were used. The analysis approach taken was to model the suspension system and the vehicle hull and support structure using finite element techniques. This provided stress and deflection information for the system. To determine the loads imparted to the system as the AAV traversed terrain features, amore » dynamics model was developed to provide loads to the finite element analysis (FEA). Because the primary indication of a problem was frequent suspension-system bearing failure, an analysis of the suspension-system bearings was conducted. Finally, to check the accuracy of the models and to provide actual load data for bearing analysis, an instrumented AAV was tested over a surveyed course at Camp Pendleton, California. Initially the dynamics model assumed the interface between the hull and the suspension system to be fixed. Later improvements incorporating the flexibility of the vehicle hull into the analysis by linking the two models resulted in improved accuracy. Actual measurements of the front road-arm displacement and vertical acceleration of the chassis are compared with predictions from the model. The correlation is quite good and indicates that the model can accurately predict the dynamic load on each road wheel for input into finite element analyses. The dynamics model can be expanded to study the effects of adding weight to the vehicle, traversing other terrains, or evaluating inputs such as weapons firing or drop tests. 7 refs., 75 figs., 10 tabs.« less

A systematic study of finite BRST-BFV transformations in generalized Hamiltonian formalism

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2014-09-01

We study systematically finite BRST-BFV transformations in the generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate an arbitrary finite change of gauge-fixing functions in the path integral.

Optimal control of first order distributed systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Johnson, T. L.

1972-01-01

The problem of characterizing optimal controls for a class of distributed-parameter systems is considered. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables, which are constrained at the boundary by a finite number of algebraic relations. Multiple control inputs, extending over the entire spatial region occupied by the system ("distributed controls') are to be designed so that the response of the system is optimal. A major example involving boundary control of an unstable low-density plasma is developed from physical laws.

Many-body delocalization in a strongly disordered system with long-range interactions: Finite-size scaling

NASA Astrophysics Data System (ADS)

Burin, Alexander L.

2015-03-01

Many-body localization in a disordered system of interacting spins coupled by the long-range interaction 1 /Rα is investigated combining analytical theory considering resonant interactions and a finite-size scaling of exact numerical solutions with number of spins N . The numerical results for a one-dimensional system are consistent with the general expectations of analytical theory for a d -dimensional system including the absence of localization in the infinite system at α <2 d and a universal scaling of a critical energy disordering Wc∝N2/d -α d .

Finite Energy and Bounded Attacks on Control System Sensor Signals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Djouadi, Seddik M; Melin, Alexander M; Ferragut, Erik M

Control system networks are increasingly being connected to enterprise level networks. These connections leave critical industrial controls systems vulnerable to cyber-attacks. Most of the effort in protecting these cyber-physical systems (CPS) has been in securing the networks using information security techniques and protection and reliability concerns at the control system level against random hardware and software failures. However, besides these failures the inability of information security techniques to protect against all intrusions means that the control system must be resilient to various signal attacks for which new analysis and detection methods need to be developed. In this paper, sensor signalmore » attacks are analyzed for observer-based controlled systems. The threat surface for sensor signal attacks is subdivided into denial of service, finite energy, and bounded attacks. In particular, the error signals between states of attack free systems and systems subject to these attacks are quantified. Optimal sensor and actuator signal attacks for the finite and infinite horizon linear quadratic (LQ) control in terms of maximizing the corresponding cost functions are computed. The closed-loop system under optimal signal attacks are provided. Illustrative numerical examples are provided together with an application to a power network with distributed LQ controllers.« less

On the Stability of Jump-Linear Systems Driven by Finite-State Machines with Markovian Inputs

NASA Technical Reports Server (NTRS)

Patilkulkarni, Sudarshan; Herencia-Zapana, Heber; Gray, W. Steven; Gonzalez, Oscar R.

2004-01-01

This paper presents two mean-square stability tests for a jump-linear system driven by a finite-state machine with a first-order Markovian input process. The first test is based on conventional Markov jump-linear theory and avoids the use of any higher-order statistics. The second test is developed directly using the higher-order statistics of the machine s output process. The two approaches are illustrated with a simple model for a recoverable computer control system.

Experimental investigation of moving surfaces for boundary layer and circulation control of airfoils and wings

NASA Astrophysics Data System (ADS)

Vets, Robert

An experimental study was conducted to assess the application of a moving surface to affect boundary layers and circulation around airfoils for the purpose of altering and enhancing aerodynamic performance of finite wings at moderate Reynolds numbers. The moving surface was established by a wide, lightweight, nylon belt that enveloped a wing's symmetric airfoil profile articulated via a friction drive cylinder such that the direction of the upper surface was in the direction of the free stream. A water tunnel visualization study accompanied wind tunnel testing at the University of Washington, Kirsten Wind Tunnel of finite wings. An experimental study was conducted to assess the application of a moving surface to affect boundary layers and circulation around airfoils for the purpose of altering and enhancing aerodynamic performance of finite wings at moderate Reynolds numbers. The moving surface was established by a wide, lightweight, nylon belt that enveloped a wing's symmetric airfoil profile articulated via a friction drive cylinder such that the direction of the upper surface was in the direction of the free stream. A water tunnel visualization study accompanied wind tunnel testing at the University of Washington, Kirsten Wind Tunnel of finite wings. The defining non-dimensional parameter for the system is the ratio of the surface velocity to the free stream velocity, us/Uo. Results show a general increase in lift with increasing us/Uo. The endurance parameter served as an additional metric for the system's performance. Examining the results of the endurance parameter shows general increase in endurance and lift with the moving surface activated. Peak performance in terms of increased endurance along with increased lift occurs at or slightly above us/Uo = 1. Water tunnel visualization showed a marked difference in the downwash for velocity ratios greater than 1, supporting the measured data. Reynolds numbers for this investigation were 1.9E5 and 4.3E5, relevant to the class of fixed wing, Tier-1, Unmanned Aerial Vehicles (UAV).

Accuracy of topological entanglement entropy on finite cylinders.

PubMed

Jiang, Hong-Chen; Singh, Rajiv R P; Balents, Leon

2013-09-06

Topological phases are unique states of matter which support nonlocal excitations which behave as particles with fractional statistics. A universal characterization of gapped topological phases is provided by the topological entanglement entropy (TEE). We study the finite size corrections to the TEE by focusing on systems with a Z2 topological ordered state using density-matrix renormalization group and perturbative series expansions. We find that extrapolations of the TEE based on the Renyi entropies with a Renyi index of n≥2 suffer from much larger finite size corrections than do extrapolations based on the von Neumann entropy. In particular, when the circumference of the cylinder is about ten times the correlation length, the TEE obtained using von Neumann entropy has an error of order 10(-3), while for Renyi entropies it can even exceed 40%. We discuss the relevance of these findings to previous and future searches for topological ordered phases, including quantum spin liquids.

Finite element thermal analysis of multispectral coatings for the ABL

NASA Astrophysics Data System (ADS)

Shah, Rashmi S.; Bettis, Jerry R.; Stewart, Alan F.; Bonsall, Lynn; Copland, James; Hughes, William; Echeverry, Juan C.

1999-04-01

The thermal response of a coated optical surface is an important consideration in the design of any high average power system. Finite element temperature distribution were calculated for both coating witness samples and calorimetry wafers and were compared to actual measured data under tightly controlled conditions. Coatings for ABL were deposited on various substrates including fused silica, ULE, Zerodur, and silicon. The witness samples were irradiate data high power levels at 1.315micrometers to evaluate laser damage thresholds and study absorption levels. Excellent agreement was obtained between temperature predictions and measured thermal response curves. When measured absorption values were not available, the code was used to predict coating absorption based on the measured temperature rise on the back surface. Using the finite element model, the damaging temperature rise can be predicted for a coating with known absorption based on run time, flux, and substrate material.

Dispersion and viscous attenuation of capillary waves with finite amplitude

NASA Astrophysics Data System (ADS)

Denner, Fabian; Paré, Gounséti; Zaleski, Stéphane

2017-04-01

We present a comprehensive study of the dispersion of capillary waves with finite amplitude, based on direct numerical simulations. The presented results show an increase of viscous attenuation and, consequently, a smaller frequency of capillary waves with increasing initial wave amplitude. Interestingly, however, the critical wavenumber as well as the wavenumber at which the maximum frequency is observed remain the same for a given two-phase system, irrespective of the wave amplitude. By devising an empirical correlation that describes the effect of the wave amplitude on the viscous attenuation, the dispersion of capillary waves with finite initial amplitude is shown to be, in very good approximation, self-similar throughout the entire underdamped regime and independent of the fluid properties. The results also shown that analytical solutions for capillary waves with infinitesimal amplitude are applicable with reasonable accuracy for capillary waves with moderate amplitude.

Chiral Luttinger liquids and a generalized Luttinger's theorem in fractional quantum Hall edges via finite-entanglement scaling

NASA Astrophysics Data System (ADS)

Varjas, Daniel; Zaletel, Michael; Moore, Joel

2014-03-01

We use bosonic field theories and the infinite system density matrix renormalization group (iDMRG) method to study infinite strips of fractional quantum Hall (FQH) states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge mode exponents and momenta without finite-size errors. We analyze states in the first and second level of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid (χLL) theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the non-chiral case. We prove a generalized Luttinger's theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in 1D.

Chiral Luttinger liquids and a generalized Luttinger theorem in fractional quantum Hall edges via finite-entanglement scaling

NASA Astrophysics Data System (ADS)

Varjas, Dániel; Zaletel, Michael P.; Moore, Joel E.

2013-10-01

We use bosonic field theories and the infinite system density matrix renormalization group method to study infinite strips of fractional quantum Hall states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge-mode exponents, and momenta without finite-size errors. We analyze states in the first and second levels of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the nonchiral case. We prove a generalized Luttinger theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in one dimension.

A new class of finite-time nonlinear consensus protocols for multi-agent systems

NASA Astrophysics Data System (ADS)

Zuo, Zongyu; Tie, Lin

2014-02-01

This paper is devoted to investigating the finite-time consensus problem for a multi-agent system in networks with undirected topology. A new class of global continuous time-invariant consensus protocols is constructed for each single-integrator agent dynamics with the aid of Lyapunov functions. In particular, it is shown that the settling time of the proposed new class of finite-time consensus protocols is upper bounded for arbitrary initial conditions. This makes it possible for network consensus problems that the convergence time is designed and estimated offline for a given undirected information flow and a group volume of agents. Finally, a numerical simulation example is presented as a proof of concept.

Static and dynamic structural-sensitivity derivative calculations in the finite-element-based Engineering Analysis Language (EAL) system

NASA Technical Reports Server (NTRS)

Camarda, C. J.; Adelman, H. M.

1984-01-01

The implementation of static and dynamic structural-sensitivity derivative calculations in a general purpose, finite-element computer program denoted the Engineering Analysis Language (EAL) System is described. Derivatives are calculated with respect to structural parameters, specifically, member sectional properties including thicknesses, cross-sectional areas, and moments of inertia. Derivatives are obtained for displacements, stresses, vibration frequencies and mode shapes, and buckling loads and mode shapes. Three methods for calculating derivatives are implemented (analytical, semianalytical, and finite differences), and comparisons of computer time and accuracy are made. Results are presented for four examples: a swept wing, a box beam, a stiffened cylinder with a cutout, and a space radiometer-antenna truss.

AUTOMATIC CALIBRATION OF A STOCHASTIC-LAGRANGIAN TRANSPORT MODEL (SLAM)

EPA Science Inventory

Numerical models are a useful tool in evaluating and designing NAPL remediation systems. Traditional constitutive finite difference and finite element models are complex and expensive to apply. For this reason, this paper presents the application of a simplified stochastic-Lagran...

A comparative finite elemental analysis of glass abutment supported and unsupported cantilever fixed partial denture.

PubMed

Ramakrishaniah, Ravikumar; Al Kheraif, Abdulaziz A; Elsharawy, Mohamed A; Alsaleh, Ayman K; Ismail Mohamed, Karem M; Rehman, Ihtesham Ur

2015-05-01

The purpose of this study was to investigate and compare the load distribution and displacement of cantilever prostheses with and without glass abutment by three dimensional finite element analysis. Micro-computed tomography was used to study the relationship between the glass abutment and the ridge. The external surface of the maxilla was scanned, and a simplified finite element model was constructed. The ZX-27 glass abutment and the maxillary first and second premolars were created and modified. The solid model of the three-unit cantilever fixed partial denture was scanned, and the fitting surface was modified with reference to the created abutments using the 3D CAD system. The finite element analysis was completed in ANSYS. The fit and total gap volume between the glass abutment and dental model were determined by Skyscan 1173 high-energy spiral micro-CT scan. The results of the finite element analysis in this study showed that the cantilever prosthesis supported by the glass abutment demonstrated significantly less stress on the terminal abutment and overall deformation of the prosthesis under vertical and oblique load. Micro-computed tomography determined a gap volume of 6.74162 mm(3). By contacting the mucosa, glass abutments transfer some amount of masticatory load to the residual alveolar ridge, thereby preventing damage to the periodontal microstructures of the terminal abutment. The passive contact of the glass abutment with the mucosa not only preserves the health of the mucosa covering the ridge but also permits easy cleaning. It is possible to increase the success rate of cantilever FPDs by supporting the cantilevered pontic with glass abutments. Copyright © 2015 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Electron-phonon interaction in quantum transport through quantum dots and molecular systems

NASA Astrophysics Data System (ADS)

Ojeda, J. H.; Duque, C. A.; Laroze, D.

2016-12-01

The quantum transport and effects of decoherence properties are studied in quantum dots systems and finite homogeneous chains of aromatic molecules connected to two semi-infinite leads. We study these systems based on the tight-binding approach through Green's function technique within a real space renormalization and polaron transformation schemes. In particular, we calculate the transmission probability following the Landauer-Büttiker formalism, the I - V characteristics and the noise power of current fluctuations taken into account the decoherence. Our results may explain the inelastic effects through nanoscopic systems.

Time-optimal control with finite bandwidth

NASA Astrophysics Data System (ADS)

Hirose, M.; Cappellaro, P.

2018-04-01

Time-optimal control theory provides recipes to achieve quantum operations with high fidelity and speed, as required in quantum technologies such as quantum sensing and computation. While technical advances have achieved the ultrastrong driving regime in many physical systems, these capabilities have yet to be fully exploited for the precise control of quantum systems, as other limitations, such as the generation of higher harmonics or the finite response time of the control apparatus, prevent the implementation of theoretical time-optimal control. Here we present a method to achieve time-optimal control of qubit systems that can take advantage of fast driving beyond the rotating wave approximation. We exploit results from time-optimal control theory to design driving protocols that can be implemented with realistic, finite-bandwidth control fields, and we find a relationship between bandwidth limitations and achievable control fidelity.

Evaluation of Kirkwood-Buff integrals via finite size scaling: a large scale molecular dynamics study

NASA Astrophysics Data System (ADS)

Dednam, W.; Botha, A. E.

2015-01-01

Solvation of bio-molecules in water is severely affected by the presence of co-solvent within the hydration shell of the solute structure. Furthermore, since solute molecules can range from small molecules, such as methane, to very large protein structures, it is imperative to understand the detailed structure-function relationship on the microscopic level. For example, it is useful know the conformational transitions that occur in protein structures. Although such an understanding can be obtained through large-scale molecular dynamic simulations, it is often the case that such simulations would require excessively large simulation times. In this context, Kirkwood-Buff theory, which connects the microscopic pair-wise molecular distributions to global thermodynamic properties, together with the recently developed technique, called finite size scaling, may provide a better method to reduce system sizes, and hence also the computational times. In this paper, we present molecular dynamics trial simulations of biologically relevant low-concentration solvents, solvated by aqueous co-solvent solutions. In particular we compare two different methods of calculating the relevant Kirkwood-Buff integrals. The first (traditional) method computes running integrals over the radial distribution functions, which must be obtained from large system-size NVT or NpT simulations. The second, newer method, employs finite size scaling to obtain the Kirkwood-Buff integrals directly by counting the particle number fluctuations in small, open sub-volumes embedded within a larger reservoir that can be well approximated by a much smaller simulation cell. In agreement with previous studies, which made a similar comparison for aqueous co-solvent solutions, without the additional solvent, we conclude that the finite size scaling method is also applicable to the present case, since it can produce computationally more efficient results which are equivalent to the more costly radial distribution function method.

Finite Energy and Bounded Actuator Attacks on Cyber-Physical Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Djouadi, Seddik M; Melin, Alexander M; Ferragut, Erik M

As control system networks are being connected to enterprise level networks for remote monitoring, operation, and system-wide performance optimization, these same connections are providing vulnerabilities that can be exploited by malicious actors for attack, financial gain, and theft of intellectual property. Much effort in cyber-physical system (CPS) protection has focused on protecting the borders of the system through traditional information security techniques. Less effort has been applied to the protection of cyber-physical systems from intelligent attacks launched after an attacker has defeated the information security protections to gain access to the control system. In this paper, attacks on actuator signalsmore » are analyzed from a system theoretic context. The threat surface is classified into finite energy and bounded attacks. These two broad classes encompass a large range of potential attacks. The effect of theses attacks on a linear quadratic (LQ) control are analyzed, and the optimal actuator attacks for both finite and infinite horizon LQ control are derived, therefore the worst case attack signals are obtained. The closed-loop system under the optimal attack signals is given and a numerical example illustrating the effect of an optimal bounded attack is provided.« less

A finite element conjugate gradient FFT method for scattering

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.

1991-01-01

Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.

Finite-element reentry heat-transfer analysis of space shuttle Orbiter

NASA Technical Reports Server (NTRS)

Ko, William L.; Quinn, Robert D.; Gong, Leslie

1986-01-01

A structural performance and resizing (SPAR) finite-element thermal analysis computer program was used in the heat-transfer analysis of the space shuttle orbiter subjected to reentry aerodynamic heating. Three wing cross sections and one midfuselage cross section were selected for the thermal analysis. The predicted thermal protection system temperatures were found to agree well with flight-measured temperatures. The calculated aluminum structural temperatures also agreed reasonably well with the flight data from reentry to touchdown. The effects of internal radiation and of internal convection were found to be significant. The SPAR finite-element solutions agreed reasonably well with those obtained from the conventional finite-difference method.

Computer animation of modal and transient vibrations

NASA Technical Reports Server (NTRS)

Lipman, Robert R.

1987-01-01

An interactive computer graphics processor is described that is capable of generating input to animate modal and transient vibrations of finite element models on an interactive graphics system. The results from NASTRAN can be postprocessed such that a three dimensional wire-frame picture, in perspective, of the finite element mesh is drawn on the graphics display. Modal vibrations of any mode shape or transient motions over any range of steps can be animated. The finite element mesh can be color-coded by any component of displacement. Viewing parameters and the rate of vibration of the finite element model can be interactively updated while the structure is vibrating.

Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms

NASA Technical Reports Server (NTRS)

Kurdila, Andrew J.; Sharpley, Robert C.

1999-01-01

This paper presents a final report on Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms. The focus of this research is to derive and implement: 1) Wavelet based methodologies for the compression, transmission, decoding, and visualization of three dimensional finite element geometry and simulation data in a network environment; 2) methodologies for interactive algorithm monitoring and tracking in computational mechanics; and 3) Methodologies for interactive algorithm steering for the acceleration of large scale finite element simulations. Also included in this report are appendices describing the derivation of wavelet based Particle Image Velocity algorithms and reduced order input-output models for nonlinear systems by utilizing wavelet approximations.

Finite elements: Theory and application

NASA Technical Reports Server (NTRS)

Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)

1988-01-01

Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.

Modelling robot's behaviour using finite automata

NASA Astrophysics Data System (ADS)

Janošek, Michal; Žáček, Jaroslav

2017-07-01

This paper proposes a model of a robot's behaviour described by finite automata. We split robot's knowledge into several knowledge bases which are used by the inference mechanism of the robot's expert system to make a logic deduction. Each knowledgebase is dedicated to the particular behaviour domain and the finite automaton helps us switching among these knowledge bases with the respect of actual situation. Our goal is to simplify and reduce complexity of one big knowledgebase splitting it into several pieces. The advantage of this model is that we can easily add new behaviour by adding new knowledgebase and add this behaviour into the finite automaton and define necessary states and transitions.

A systematic study of finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2014-09-01

We study systematically finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.

A locally conservative non-negative finite element formulation for anisotropic advective-diffusive-reactive systems

NASA Astrophysics Data System (ADS)

Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.

2015-12-01

Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties. Several representative numerical examples are discussed to illustrate the importance of the proposed numerical formulations to accurately describe various aspects of mixing process in chaotic flows and to simulate transport in highly heterogeneous anisotropic media.

The control data "GIRAFFE" system for interactive graphic finite element analysis

NASA Technical Reports Server (NTRS)

Park, S.; Brandon, D. M., Jr.

1975-01-01

The Graphical Interface for Finite Elements (GIRAFFE) general purpose interactive graphics application package was described. This system may be used as a pre/post processor for structural analysis computer programs. It facilitates the operations of creating, editing, or reviewing all the structural input/output data on a graphics terminal in a time-sharing mode of operation. An application program for a simple three-dimensional plate problem was illustrated.

Further Results on Finite-Time Partial Stability and Stabilization. Applications to Nonlinear Control Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jammazi, Chaker

2009-03-05

The paper gives Lyapunov type sufficient conditions for partial finite-time and asymptotic stability in which some state variables converge to zero while the rest converge to constant values that possibly depend on the initial conditions. The paper then presents partially asymptotically stabilizing controllers for many nonlinear control systems for which continuous asymptotically stabilizing (in the usual sense) controllers are known not to exist.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saha, Sourabh K.

Although geometric imperfections have a detrimental effect on buckling, imperfection sensitivity has not been well studied in the past during design of sinusoidal micro and nano-scale structures via wrinkling of supported thin films. This is likely because one is more interested in predicting the shape/size of the resultant patterns than the buckling bifurcation onset strain during fabrication of such wrinkled structures. Herein, I have demonstrated that even modest geometric imperfections alter the final wrinkled mode shapes via the mode locking phenomenon wherein the imperfection mode grows in exclusion to the natural mode of the system. To study the effect ofmore » imperfections on mode locking, I have (i) developed a finite element mesh perturbation scheme to generate arbitrary geometric imperfections in the system and (ii) performed a parametric study via finite element methods to link the amplitude and period of the sinusoidal imperfections to the observed wrinkle mode shape and size. Based on this, a non-dimensional geometric parameter has been identified that characterizes the effect of imperfection on the mode locking phenomenon – the equivalent imperfection size. An upper limit for this equivalent imperfection size has been identified via a combination of analytical and finite element modeling. During compression of supported thin films, the system gets “locked” into the imperfection mode if its equivalent imperfection size is above this critical limit. For the polydimethylsiloxane/glass bilayer with a wrinkle period of 2 µm, this mode lock-in limit corresponds to an imperfection amplitude of 32 nm for an imperfection period of 5 µm and 8 nm for an imperfection period of 0.8 µm. Interestingly, when the non-dimensional critical imperfection size is scaled by the bifurcation onset strain, the scaled critical size depends solely on the ratio of the imperfection to natural periods. Furthermore, the computational data generated here can be generalized beyond the specific natural periods and bilayer systems studied to enable deterministic design of a variety of wrinkled micro and nano-scale structures.« less

Study of a Compression-Molding Process for Ultraviolet Light-Emitting Diode Exposure Systems via Finite-Element Analysis

PubMed Central

Wu, Kuo-Tsai; Hwang, Sheng-Jye; Lee, Huei-Huang

2017-01-01

Although wafer-level camera lenses are a very promising technology, problems such as warpage with time and non-uniform thickness of products still exist. In this study, finite element simulation was performed to simulate the compression molding process for acquiring the pressure distribution on the product on completion of the process and predicting the deformation with respect to the pressure distribution. Results show that the single-gate compression molding process significantly increases the pressure at the center of the product, whereas the multi-gate compressing molding process can effectively distribute the pressure. This study evaluated the non-uniform thickness of product and changes in the process parameters through computer simulations, which could help to improve the compression molding process. PMID:28617315

A Spectral Finite Element Approach to Modeling Soft Solids Excited with High-Frequency Harmonic Loads

PubMed Central

Brigham, John C.; Aquino, Wilkins; Aguilo, Miguel A.; Diamessis, Peter J.

2010-01-01

An approach for efficient and accurate finite element analysis of harmonically excited soft solids using high-order spectral finite elements is presented and evaluated. The Helmholtz-type equations used to model such systems suffer from additional numerical error known as pollution when excitation frequency becomes high relative to stiffness (i.e. high wave number), which is the case, for example, for soft tissues subject to ultrasound excitations. The use of high-order polynomial elements allows for a reduction in this pollution error, but requires additional consideration to counteract Runge's phenomenon and/or poor linear system conditioning, which has led to the use of spectral element approaches. This work examines in detail the computational benefits and practical applicability of high-order spectral elements for such problems. The spectral elements examined are tensor product elements (i.e. quad or brick elements) of high-order Lagrangian polynomials with non-uniformly distributed Gauss-Lobatto-Legendre nodal points. A shear plane wave example is presented to show the dependence of the accuracy and computational expense of high-order elements on wave number. Then, a convergence study for a viscoelastic acoustic-structure interaction finite element model of an actual ultrasound driven vibroacoustic experiment is shown. The number of degrees of freedom required for a given accuracy level was found to consistently decrease with increasing element order. However, the computationally optimal element order was found to strongly depend on the wave number. PMID:21461402

A superlinear iteration method for calculation of finite length journal bearing's static equilibrium position.

PubMed

Zhou, Wenjie; Wei, Xuesong; Wang, Leqin; Wu, Guangkuan

2017-05-01

Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method-twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length.

A superlinear iteration method for calculation of finite length journal bearing's static equilibrium position

PubMed Central

Zhou, Wenjie; Wei, Xuesong; Wang, Leqin

2017-01-01

Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method—twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length. PMID:28572997

Design, development and use of the finite element machine

NASA Technical Reports Server (NTRS)

Adams, L. M.; Voigt, R. C.

1983-01-01

Some of the considerations that went into the design of the Finite Element Machine, a research asynchronous parallel computer are described. The present status of the system is also discussed along with some indication of the type of results that were obtained.

The Master Equation for Two-Level Accelerated Systems at Finite Temperature

NASA Astrophysics Data System (ADS)

Tomazelli, J. L.; Cunha, R. O.

2016-10-01

In this work, we study the behaviour of two weakly coupled quantum systems, described by a separable density operator; one of them is a single oscillator, representing a microscopic system, while the other is a set of oscillators which perform the role of a reservoir in thermal equilibrium. From the Liouville-Von Neumann equation for the reduced density operator, we devise the master equation that governs the evolution of the microscopic system, incorporating the effects of temperature via Thermofield Dynamics formalism by suitably redefining the vacuum of the macroscopic system. As applications, we initially investigate the behaviour of a Fermi oscillator in the presence of a heat bath consisting of a set of Fermi oscillators and that of an atomic two-level system interacting with a scalar radiation field, considered as a reservoir, by constructing the corresponding master equation which governs the time evolution of both sub-systems at finite temperature. Finally, we calculate the energy variation rates for the atom and the field, as well as the atomic population levels, both in the inertial case and at constant proper acceleration, considering the two-level system as a prototype of an Unruh detector, for admissible couplings of the radiation field.

Localized Single Frequency Lasing States in a Finite Parity-Time Symmetric Resonator Chain

PubMed Central

Phang, Sendy; Vukovic, Ana; Creagh, Stephen C.; Sewell, Phillip D.; Gradoni, Gabriele; Benson, Trevor M.

2016-01-01

In this paper a practical case of a finite periodic Parity Time chain made of resonant dielectric cylinders is considered. The paper analyzes a more general case where PT symmetry is achieved by modulating both the real and imaginary part of the material refractive index along the resonator chain. The band-structure of the finite periodic PT resonator chains is compared to infinite chains in order to understand the complex interdependence of the Bloch phase and the amount of the gain/loss in the system that causes the PT symmetry to break. The results show that the type of the modulation along the unit cell can significantly affect the position of the threshold point of the PT system. In all cases the lowest threshold is achieved near the end of the Brillouin zone. In the case of finite PT-chains, and for a particular type of modulation, early PT symmetry breaking is observed and shown to be caused by the presence of termination states localized at the edges of the finite chain resulting in localized lasing and dissipative modes at each end of the chain. PMID:26848095

Second-Order Consensus in Multiagent Systems via Distributed Sliding Mode Control.

PubMed

Yu, Wenwu; Wang, He; Cheng, Fei; Yu, Xinghuo; Wen, Guanghui

2016-11-22

In this paper, the new decoupled distributed sliding-mode control (DSMC) is first proposed for second-order consensus in multiagent systems, which finally solves the fundamental unknown problem for sliding-mode control (SMC) design of coupled networked systems. A distributed full-order sliding-mode surface is designed based on the homogeneity with dilation for reaching second-order consensus in multiagent systems, under which the sliding-mode states are decoupled. Then, the SMC is applied to the decoupled sliding-mode states to reach their origin in finite time, which is the sliding-mode surface. The states of agents can first reach the designed sliding-mode surface in finite time and then move to the second-order consensus state along the surface in finite time as well. The DSMC designed in this paper can eliminate the influence of singularity problems and weaken the influence of chattering, which is still very difficult in the SMC systems. In addition, DSMC proposes a general decoupling framework for designing SMC in networked multiagent systems. Simulations are presented to verify the theoretical results in this paper.

Studies of finite element analysis of composite material structures

NASA Technical Reports Server (NTRS)

Douglas, D. O.; Holzmacher, D. E.; Lane, Z. C.; Thornton, E. A.

1975-01-01

Research in the area of finite element analysis is summarized. Topics discussed include finite element analysis of a picture frame shear test, BANSAP (a bandwidth reduction program for SAP IV), FEMESH (a finite element mesh generation program based on isoparametric zones), and finite element analysis of a composite bolted joint specimens.

Finite-size scaling in the system of coupled oscillators with heterogeneity in coupling strength

NASA Astrophysics Data System (ADS)

Hong, Hyunsuk

2017-07-01

We consider a mean-field model of coupled phase oscillators with random heterogeneity in the coupling strength. The system that we investigate here is a minimal model that contains randomness in diverse values of the coupling strength, and it is found to return to the original Kuramoto model [Y. Kuramoto, Prog. Theor. Phys. Suppl. 79, 223 (1984), 10.1143/PTPS.79.223] when the coupling heterogeneity disappears. According to one recent paper [H. Hong, H. Chaté, L.-H. Tang, and H. Park, Phys. Rev. E 92, 022122 (2015), 10.1103/PhysRevE.92.022122], when the natural frequency of the oscillator in the system is "deterministically" chosen, with no randomness in it, the system is found to exhibit the finite-size scaling exponent ν ¯=5 /4 . Also, the critical exponent for the dynamic fluctuation of the order parameter is found to be given by γ =1 /4 , which is different from the critical exponents for the Kuramoto model with the natural frequencies randomly chosen. Originally, the unusual finite-size scaling behavior of the Kuramoto model was reported by Hong et al. [H. Hong, H. Chaté, H. Park, and L.-H. Tang, Phys. Rev. Lett. 99, 184101 (2007), 10.1103/PhysRevLett.99.184101], where the scaling behavior is found to be characterized by the unusual exponent ν ¯=5 /2 . On the other hand, if the randomness in the natural frequency is removed, it is found that the finite-size scaling behavior is characterized by a different exponent, ν ¯=5 /4 [H. Hong, H. Chaté, L.-H. Tang, and H. Park, Phys. Rev. E 92, 022122 (2015), 10.1103/PhysRevE.92.022122]. Those findings brought about our curiosity and led us to explore the effects of the randomness on the finite-size scaling behavior. In this paper, we pay particular attention to investigating the finite-size scaling and dynamic fluctuation when the randomness in the coupling strength is considered.

Assessment of carbon fibre composite fracture fixation plate using finite element analysis.

PubMed

Saidpour, Seyed H

2006-07-01

In the internal fixation of fractured bone by means of bone-plates fastened to the bone on its tensile surface, an on-going concern has been the excessive stress shielding of the bone by the excessively-stiff stainless-steel plate. The compressive stress shielding at the fracture-interface immediately after fracture-fixation delays callus formation and bone healing. Likewise, the tensile stress shielding in the layer of bone underneath the plate can cause osteoporosis and decrease in tensile strength of this layer. In this study a novel forearm internal fracture fixation plate made from short carbon fibre reinforced plastic (CFRP) was used in an attempt to address the problem. Accordingly, it has been possible to analyse the stress distribution in the composite plates using finite-element modelling. A three-dimensional, quarter-symmetric finite element model was generated for the plate system. The stress state in the underlying bone was examined for several loading conditions. Based on the analytical results the composite plate system is likely to reduce stress-shielding effects at the fracture site when subjected to bending and torsional loads. The design of the plate was further optimised by reducing the width around the innermost holes.

Vectorial finite elements for solving the radiative transfer equation

NASA Astrophysics Data System (ADS)

Badri, M. A.; Jolivet, P.; Rousseau, B.; Le Corre, S.; Digonnet, H.; Favennec, Y.

2018-06-01

The discrete ordinate method coupled with the finite element method is often used for the spatio-angular discretization of the radiative transfer equation. In this paper we attempt to improve upon such a discretization technique. Instead of using standard finite elements, we reformulate the radiative transfer equation using vectorial finite elements. In comparison to standard finite elements, this reformulation yields faster timings for the linear system assemblies, as well as for the solution phase when using scattering media. The proposed vectorial finite element discretization for solving the radiative transfer equation is cross-validated against a benchmark problem available in literature. In addition, we have used the method of manufactured solutions to verify the order of accuracy for our discretization technique within different absorbing, scattering, and emitting media. For solving large problems of radiation on parallel computers, the vectorial finite element method is parallelized using domain decomposition. The proposed domain decomposition method scales on large number of processes, and its performance is unaffected by the changes in optical thickness of the medium. Our parallel solver is used to solve a large scale radiative transfer problem of the Kelvin-cell radiation.

Finite Time Control Design for Bilateral Teleoperation System With Position Synchronization Error Constrained.

PubMed

Yang, Yana; Hua, Changchun; Guan, Xinping

2016-03-01

Due to the cognitive limitations of the human operator and lack of complete information about the remote environment, the work performance of such teleoperation systems cannot be guaranteed in most cases. However, some practical tasks conducted by the teleoperation system require high performances, such as tele-surgery needs satisfactory high speed and more precision control results to guarantee patient' health status. To obtain some satisfactory performances, the error constrained control is employed by applying the barrier Lyapunov function (BLF). With the constrained synchronization errors, some high performances, such as, high convergence speed, small overshoot, and an arbitrarily predefined small residual constrained synchronization error can be achieved simultaneously. Nevertheless, like many classical control schemes only the asymptotic/exponential convergence, i.e., the synchronization errors converge to zero as time goes infinity can be achieved with the error constrained control. It is clear that finite time convergence is more desirable. To obtain a finite-time synchronization performance, the terminal sliding mode (TSM)-based finite time control method is developed for teleoperation system with position error constrained in this paper. First, a new nonsingular fast terminal sliding mode (NFTSM) surface with new transformed synchronization errors is proposed. Second, adaptive neural network system is applied for dealing with the system uncertainties and the external disturbances. Third, the BLF is applied to prove the stability and the nonviolation of the synchronization errors constraints. Finally, some comparisons are conducted in simulation and experiment results are also presented to show the effectiveness of the proposed method.

Nondestructive evaluation of pavement structural condition for rehabilitation design : final report.

DOT National Transportation Integrated Search

2016-05-31

Falling Weight Deflectometer (FWD) is the common non-destructive testing method for in-situ evaluation of pavement condition. : This study aims to develop finite element (FE) models that can simulate FWD loading on pavement system and capture the : c...

The Frequency and Distribution of the X-Finite Verb Clauses in the Second Book of the Psalter

ERIC Educational Resources Information Center

Stewart, Joshua E.

2014-01-01

The Hebrew verbal system is riddled with difficulties that have caused Hebraist much consternation for centuries. The study of the Hebrew verb system is complicated further because no living informant of the language exists. Without a living witness of the language, uncovering the nuances has been limited to the corpus of written material…

Electric-field induced spin accumulation in the Landau level states of topological insulator thin films

NASA Astrophysics Data System (ADS)

Siu, Zhuo Bin; Chowdhury, Debashree; Basu, Banasri; Jalil, Mansoor B. A.

2017-08-01

A topological insulator (TI) thin film differs from the more typically studied thick TI system in that the former has both a top and a bottom surface where the states localized at both surfaces can couple to one other across the finite thickness. An out-of-plane magnetic field leads to the formation of discrete Landau level states in the system, whereas an in-plane magnetization breaks the angular momentum symmetry of the system. In this work, we study the spin accumulation induced by the application of an in-plane electric field to the TI thin film system where the Landau level states and inter-surface coupling are simultaneously present. We show, via Kubo formula calculations, that the in-plane spin accumulation perpendicular to the magnetization due to the electric field vanishes for a TI thin film with symmetric top and bottom surfaces. A finite in-plane spin accumulation perpendicular to both the electric field and magnetization emerges upon applying either a differential magnetization coupling or a potential difference between the two film surfaces. This spin accumulation results from the breaking of the antisymmetry of the spin accumulation around the k-space equal-energy contours.

Floquet states of a kicked particle in a singular potential: Exponential and power-law profiles

NASA Astrophysics Data System (ADS)

Paul, Sanku; Santhanam, M. S.

2018-03-01

It is well known that, in the chaotic regime, all the Floquet states of kicked rotor system display an exponential profile resulting from dynamical localization. If the kicked rotor is placed in an additional stationary infinite potential well, its Floquet states display power-law profile. It has also been suggested in general that the Floquet states of periodically kicked systems with singularities in the potential would have power-law profile. In this work, we study the Floquet states of a kicked particle in finite potential barrier. By varying the height of finite potential barrier, the nature of transition in the Floquet state from exponential to power-law decay profile is studied. We map this system to a tight-binding model and show that the nature of decay profile depends on energy band spanned by the Floquet states (in unperturbed basis) relative to the potential height. This property can also be inferred from the statistics of Floquet eigenvalues and eigenvectors. This leads to an unusual scenario in which the level spacing distribution, as a window in to the spectral correlations, is not a unique characteristic for the entire system.

Rocket thrust chamber thermal barrier coatings

NASA Technical Reports Server (NTRS)

Batakis, A. P.; Vogan, J. W.

1985-01-01

A research program was conducted to generate data and develop analytical techniques to predict the performance and reliability of ceramic thermal barrier coatings in high heat flux environments. A finite element model was used to analyze the thermomechanical behavior of coating systems in rocket thrust chambers. Candidate coating systems (using a copper substrate, NiCrAlY bond coat and ZrO2.8Y2O3 ceramic overcoat) were selected for detailed study based on photomicrographic evaluations of experimental test specimens. The effects of plasma spray application parameters on the material properties of these coatings were measured and the effects on coating performance evaluated using the finite element model. Coating design curves which define acceptable operating envelopes for seleted coating systems were constructed based on temperature and strain limitations. Spray gun power levels was found to have the most significant effect on coating structure. Three coating systems were selected for study using different power levels. Thermal conductivity, strain tolerance, density, and residual stress were measured for these coatings. Analyses indicated that extremely thin coatings ( 0.02 mm) are required to accommodate the high heat flux of a rocket thrust chamber and ensure structural integrity.

Numerical study of slip system activity and crystal lattice rotation under wedge nanoindents in tungsten single crystals

NASA Astrophysics Data System (ADS)

Volz, T.; Schwaiger, R.; Wang, J.; Weygand, S. M.

2018-05-01

Tungsten is a promising material for plasma facing components in future nuclear fusion reactors. In the present work, we numerically investigate the deformation behavior of unirradiated tungsten (a body-centered cubic (bcc) single crystal) underneath nanoindents. A finite element (FE) model is presented to simulate wedge indentation. Crystal plasticity finite element (CPFE) simulations were performed for face-centered and body-centered single crystals accounting for the slip system family {110} <111> in the bcc crystal system and the {111} <110> slip family in the fcc system. The 90° wedge indenter was aligned parallel to the [1 ¯01 ]-direction and indented the crystal in the [0 1 ¯0 ]-direction up to a maximum indentation depth of 2 µm. In both, the fcc and bcc single crystals, the activity of slip systems was investigated and compared. Good agreement with the results from former investigations on fcc single crystals was observed. Furthermore, the in-plane lattice rotation in the material underneath an indent was determined and compared for the fcc and bcc single crystals.

Microphysics of liquid complex plasmas in equilibrium and non-equilibrium systems

NASA Astrophysics Data System (ADS)

Piel, Alexander; Block, Dietmar; Melzer, André; Mulsow, Matthias; Schablinski, Jan; Schella, André; Wieben, Frank; Wilms, Jochen

2018-05-01

The dynamic evolution of the microscopic structure of solid and liquid phases of complex plasmas is studied experimentally and by means of molecular dynamics (MD) simulations. In small finite systems, the cooperative motion can be described in terms of discrete modes. These modes are studied with different experimental approaches. Using diffuse scattered laser light, applying laser tweezer forces to individual particles, and periodic laser pulses, the excitation of modes is investigated. The instantaneous normal mode analysis of experimental data from two-dimensional liquid clusters gives access to the local dynamics of the liquid phase. Our investigations shed light on the role of compressional and shear modes as well as the determination of diffusion constants and melting temperatures in finite systems. Special attention is paid to hydrodynamic situations with a stationary inhomogeneous dust flow. MD simulations allow to study the collective motion in the shell of nearest neighbors, which can be linked to smooth and sudden changes of the macroscopic flow. Finally, the observed micro-motion in all situations above allows to shed light on the preference of shear-like over compressional motion in terms of a minimized potential energy and a dynamic incompressibility.

Computer-aided modeling and prediction of performance of the modified Lundell class of alternators in space station solar dynamic power systems

NASA Technical Reports Server (NTRS)

Demerdash, Nabeel A. O.; Wang, Ren-Hong

1988-01-01

The main purpose of this project is the development of computer-aided models for purposes of studying the effects of various design changes on the parameters and performance characteristics of the modified Lundell class of alternators (MLA) as components of a solar dynamic power system supplying electric energy needs in the forthcoming space station. Key to this modeling effort is the computation of magnetic field distribution in MLAs. Since the nature of the magnetic field is three-dimensional, the first step in the investigation was to apply the finite element method to discretize volume, using the tetrahedron as the basic 3-D element. Details of the stator 3-D finite element grid are given. A preliminary look at the early stage of a 3-D rotor grid is presented.

Numerical study of supersonic combustion using a finite rate chemistry model

NASA Technical Reports Server (NTRS)

Chitsomboon, T.; Tiwari, S. N.; Kumar, A.; Drummond, J. P.

1986-01-01

The governing equations of two-dimensional chemically reacting flows are presented together with a global two-step chemistry model for H2-air combustion. The explicit unsplit MacCormack finite difference algorithm is used to advance the discrete system of the governing equations in time until convergence is attained. The source terms in the species equations are evaluated implicitly to alleviate stiffness associated with fast reactions. With implicit source terms, the species equations give rise to a block-diagonal system which can be solved very efficiently on vector-processing computers. A supersonic reacting flow in an inlet-combustor configuration is calculated for the case where H2 is injected into the flow from the side walls and the strut. Results of the calculation are compared against the results obtained by using a complete reaction model.

A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES

EPA Science Inventory

A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromagnetic properties of the model are symmetric with respect ...

ANALYTICAL SOLUTION TO SATURATED FLOW IN A FINITE STRATIFIED AQUIFER

EPA Science Inventory

An analytical solution for the flow of water in a saturated-stratified aquitard-aquifer-aquitard system of finite length is presented. The analytical solution assumes one-dimensional horizontal flow in the aquifer and two-dimensional flow in the aquitards. Several examples are gi...

On the finite element modeling of the asymmetric cracked rotor

NASA Astrophysics Data System (ADS)

AL-Shudeifat, Mohammad A.

2013-05-01

The advanced phase of the breathing crack in the heavy duty horizontal rotor system is expected to be dominated by the open crack state rather than the breathing state after a short period of operation. The reason for this scenario is the expected plastic deformation in crack location due to a large compression stress field appears during the continuous shaft rotation. Based on that, the finite element modeling of a cracked rotor system with a transverse open crack is addressed here. The cracked rotor with the open crack model behaves as an asymmetric shaft due to the presence of the transverse edge crack. Hence, the time-varying area moments of inertia of the cracked section are employed in formulating the periodic finite element stiffness matrix which yields a linear time-periodic system. The harmonic balance method (HB) is used for solving the finite element (FE) equations of motion for studying the dynamic behavior of the system. The behavior of the whirl orbits during the passage through the subcritical rotational speeds of the open crack model is compared to that for the breathing crack model. The presence of the open crack with the unbalance force was found only to excite the 1/2 and 1/3 of the backward critical whirling speed. The whirl orbits in the neighborhood of these subcritical speeds were found to have nearly similar behavior for both open and breathing crack models. While unlike the breathing crack model, the subcritical forward whirling speeds have not been observed for the open crack model in the response to the unbalance force. As a result, the behavior of the whirl orbits during the passage through the forward subcritical rotational speeds is found to be enough to distinguish the breathing crack from the open crack model. These whirl orbits with inner loops that appear in the neighborhood of the forward subcritical speeds are then a unique property for the breathing crack model.

An efficient finite element method for simulation of droplet spreading on a topologically rough surface

NASA Astrophysics Data System (ADS)

Luo, Li; Wang, Xiao-Ping; Cai, Xiao-Chuan

2017-11-01

We study numerically the dynamics of a three-dimensional droplet spreading on a rough solid surface using a phase-field model consisting of the coupled Cahn-Hilliard and Navier-Stokes equations with a generalized Navier boundary condition (GNBC). An efficient finite element method on unstructured meshes is introduced to cope with the complex geometry of the solid surfaces. We extend the GNBC to surfaces with complex geometry by including its weak form along different normal and tangential directions in the finite element formulation. The semi-implicit time discretization scheme results in a decoupled system for the phase function, the velocity, and the pressure. In addition, a mass compensation algorithm is introduced to preserve the mass of the droplet. To efficiently solve the decoupled systems, we present a highly parallel solution strategy based on domain decomposition techniques. We validate the newly developed solution method through extensive numerical experiments, particularly for those phenomena that can not be achieved by two-dimensional simulations. On a surface with circular posts, we study how wettability of the rough surface depends on the geometry of the posts. The contact line motion for a droplet spreading over some periodic rough surfaces are also efficiently computed. Moreover, we study the spreading process of an impacting droplet on a microstructured surface, a qualitative agreement is achieved between the numerical and experimental results. The parallel performance suggests that the proposed solution algorithm is scalable with over 4,000 processors cores with tens of millions of unknowns.

Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR line shape

NASA Astrophysics Data System (ADS)

Zschocke, Fabian; Vojta, Matthias

2015-07-01

Kitaev's compass model on the honeycomb lattice realizes a spin liquid whose emergent excitations are dispersive Majorana fermions and static Z2 gauge fluxes. We discuss the proper selection of physical states for finite-size simulations in the Majorana representation, based on a recent paper by F. L. Pedrocchi, S. Chesi, and D. Loss [Phys. Rev. B 84, 165414 (2011), 10.1103/PhysRevB.84.165414]. Certain physical observables acquire large finite-size effects, in particular if the ground state is not fermion-free, which we prove to generally apply to the system in the gapless phase and with periodic boundary conditions. To illustrate our findings, we compute the static and dynamic spin susceptibilities for finite-size systems. Specifically, we consider random-bond disorder (which preserves the solubility of the model), calculate the distribution of local flux gaps, and extract the NMR line shape. We also predict a transition to a random-flux state with increasing disorder.

Unified control/structure design and modeling research

NASA Technical Reports Server (NTRS)

Mingori, D. L.; Gibson, J. S.; Blelloch, P. A.; Adamian, A.

1986-01-01

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

The accuracy of the Gaussian-and-finite-element-Coulomb (GFC) method for the calculation of Coulomb integrals.

PubMed

Przybytek, Michal; Helgaker, Trygve

2013-08-07

We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (γ(H) = 2) and eight (γ(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (αmin (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems; however, this scaling can be reduced to linear by introducing more effective techniques for recognizing significant three-center overlap distributions.

Local structural ordering in surface-confined liquid crystals

NASA Astrophysics Data System (ADS)

Śliwa, I.; Jeżewski, W.; Zakharov, A. V.

2017-06-01

The effect of the interplay between attractive nonlocal surface interactions and attractive pair long-range intermolecular couplings on molecular structures of liquid crystals confined in thin cells with flat solid surfaces has been studied. Extending the McMillan mean field theory to include finite systems, it has been shown that confining surfaces can induce complex orientational and translational ordering of molecules. Typically, local smectic A, nematic, and isotropic phases have been shown to coexist in certain temperature ranges, provided that confining cells are sufficiently thick, albeit finite. Due to the nonlocality of surface interactions, the spatial arrangement of these local phases can display, in general, an unexpected complexity along the surface normal direction. In particular, molecules located in the vicinity of surfaces can still be organized in smectic layers, even though nematic and/or isotropic order can simultaneously appear in the interior of cells. The resulting surface freezing of smectic layers has been confirmed to occur even for rather weak surface interactions. The surface interactions cannot, however, prevent smectic layers from melting relatively close to system boundaries, even when molecules are still arranged in layers within the central region of the system. The internal interfaces, separating individual liquid-crystal phases, are demonstrated here to form fronts of local finite-size transitions that move across cells under temperature changes. Although the complex molecular ordering in surface confined liquid-crystal systems can essentially be controlled by temperature variations, specific thermal properties of these systems, especially the nature of the local transitions, are argued to be strongly conditioned to the degree of molecular packing.

Prediction of the thermal environment and thermal response of simple panels exposed to radiant heat

NASA Technical Reports Server (NTRS)

Turner, Travis L.; Ash, Robert L.

1989-01-01

A method of predicting the radiant heat flux distribution produced by a bank of tubular quartz heaters was applied to a radiant system consisting of a single unreflected lamp irradiating a flat metallic incident surface. In this manner, the method was experimentally verified for various radiant system parameter settings and used as a source of input for a finite element thermal analysis. Two finite element thermal analyses were applied to a thermal system consisting of a thin metallic panel exposed to radiant surface heating. A two-dimensional steady-state finite element thermal analysis algorithm, based on Galerkin's Method of Weighted Residuals (GFE), was formulated specifically for this problem and was used in comparison to the thermal analyzers of the Engineering Analysis Language (EAL). Both analyses allow conduction, convection, and radiation boundary conditions. Differences in the respective finite element formulation are discussed in terms of their accuracy and resulting comparison discrepancies. The thermal analyses are shown to perform well for the comparisons presented here with some important precautions about the various boundary condition models. A description of the experiment, corresponding analytical modeling, and resulting comparisons are presented.

Geodetic Finite-Fault-based Earthquake Early Warning Performance for Great Earthquakes Worldwide

NASA Astrophysics Data System (ADS)

Ruhl, C. J.; Melgar, D.; Grapenthin, R.; Allen, R. M.

2017-12-01

GNSS-based earthquake early warning (EEW) algorithms estimate fault-finiteness and unsaturated moment magnitude for the largest, most damaging earthquakes. Because large events are infrequent, algorithms are not regularly exercised and insufficiently tested on few available datasets. The Geodetic Alarm System (G-larmS) is a GNSS-based finite-fault algorithm developed as part of the ShakeAlert EEW system in the western US. Performance evaluations using synthetic earthquakes offshore Cascadia showed that G-larmS satisfactorily recovers magnitude and fault length, providing useful alerts 30-40 s after origin time and timely warnings of ground motion for onshore urban areas. An end-to-end test of the ShakeAlert system demonstrated the need for GNSS data to accurately estimate ground motions in real-time. We replay real data from several subduction-zone earthquakes worldwide to demonstrate the value of GNSS-based EEW for the largest, most damaging events. We compare predicted ground acceleration (PGA) from first-alert-solutions with those recorded in major urban areas. In addition, where applicable, we compare observed tsunami heights to those predicted from the G-larmS solutions. We show that finite-fault inversion based on GNSS-data is essential to achieving the goals of EEW.

Fast mean and variance computation of the diffuse sound transmission through finite-sized thick and layered wall and floor systems

NASA Astrophysics Data System (ADS)

Decraene, Carolina; Dijckmans, Arne; Reynders, Edwin P. B.

2018-05-01

A method is developed for computing the mean and variance of the diffuse field sound transmission loss of finite-sized layered wall and floor systems that consist of solid, fluid and/or poroelastic layers. This is achieved by coupling a transfer matrix model of the wall or floor to statistical energy analysis subsystem models of the adjacent room volumes. The modal behavior of the wall is approximately accounted for by projecting the wall displacement onto a set of sinusoidal lateral basis functions. This hybrid modal transfer matrix-statistical energy analysis method is validated on multiple wall systems: a thin steel plate, a polymethyl methacrylate panel, a thick brick wall, a sandwich panel, a double-leaf wall with poro-elastic material in the cavity, and a double glazing. The predictions are compared with experimental data and with results obtained using alternative prediction methods such as the transfer matrix method with spatial windowing, the hybrid wave based-transfer matrix method, and the hybrid finite element-statistical energy analysis method. These comparisons confirm the prediction accuracy of the proposed method and the computational efficiency against the conventional hybrid finite element-statistical energy analysis method.

H∞ filter design for nonlinear systems with quantised measurements in finite frequency domain

NASA Astrophysics Data System (ADS)

El Hellani, D.; El Hajjaji, A.; Ceschi, R.

2017-04-01

This paper deals with the problem of finite frequency (FF) H∞ full-order fuzzy filter design for nonlinear discrete-time systems with quantised measurements, described by Takagi-Sugeno models. The measured signals are assumed to be quantised with a logarithmic quantiser. Using a fuzzy-basis-dependent Lyapunov function, the finite frequency ℓ2 gain definition, the generalised S-procedure, and Finsler's lemma, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H∞ attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. With the aid of Finsler's lemma, a large number of slack variables are introduced to the design conditions, which provides extra degrees of freedom in optimising the guaranteed H∞ performance. This directly leads to performance improvement and reduction of conservatism. Finally, we give a simulation example to demonstrate the efficiency of the proposed design method, and we show that a lower H∞ attenuation level can be obtained by our developed approach in comparison with another result in the literature.

A Finite Speed Curzon-Ahlborn Engine

ERIC Educational Resources Information Center

Agrawal, D. C.

2009-01-01

Curzon and Ahlborn achieved finite power output by introducing the concept of finite rate of heat transfer in a Carnot engine. The finite power can also be achieved through a finite speed of the piston on the four branches of the Carnot cycle. The present paper combines these two approaches to study the behaviour of output power in terms of…

Quantitative Imaging of Young's Modulus of Soft Tissues from Ultrasound Water Jet Indentation: A Finite Element Study

PubMed Central

Lu, Min-Hua; Mao, Rui; Lu, Yin; Liu, Zheng; Wang, Tian-Fu; Chen, Si-Ping

2012-01-01

Indentation testing is a widely used approach to evaluate mechanical characteristics of soft tissues quantitatively. Young's modulus of soft tissue can be calculated from the force-deformation data with known tissue thickness and Poisson's ratio using Hayes' equation. Our group previously developed a noncontact indentation system using a water jet as a soft indenter as well as the coupling medium for the propagation of high-frequency ultrasound. The novel system has shown its ability to detect the early degeneration of articular cartilage. However, there is still lack of a quantitative method to extract the intrinsic mechanical properties of soft tissue from water jet indentation. The purpose of this study is to investigate the relationship between the loading-unloading curves and the mechanical properties of soft tissues to provide an imaging technique of tissue mechanical properties. A 3D finite element model of water jet indentation was developed with consideration of finite deformation effect. An improved Hayes' equation has been derived by introducing a new scaling factor which is dependent on Poisson's ratios v, aspect ratio a/h (the radius of the indenter/the thickness of the test tissue), and deformation ratio d/h. With this model, the Young's modulus of soft tissue can be quantitatively evaluated and imaged with the error no more than 2%. PMID:22927890

A validated finite element model of a soft artificial muscle motor

NASA Astrophysics Data System (ADS)

Tse, Tony Chun H.; O'Brien, Benjamin; McKay, Thomas; Anderson, Iain A.

2011-04-01

The Biomimetics Laboratory has developed a soft artificial muscle motor based on Dielectric Elastomers. The motor, 'Flexidrive', is light-weight and has low system complexity. It works by gripping and turning a shaft with a soft gear, like we would with our fingers. The motor's performance depends on many factors, such as actuation waveform, electrode patterning, geometries and contact tribology between the shaft and gear. We have developed a finite element model (FEM) of the motor as a study and design tool. Contact interaction was integrated with previous material and electromechanical coupling models in ABAQUS. The model was experimentally validated through a shape and blocked force analysis.

Finite element analysis of electromagnetic propagation in an absorbing wave guide

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.

1986-01-01

Wave guides play a significant role in microwave space communication systems. The attenuation per unit length of the guide depends on its construction and design frequency range. A finite element Galerkin formulation has been developed to study TM electromagnetic propagation in complex two-dimensional absorbing wave guides. The analysis models the electromagnetic absorptive characteristics of a general wave guide which could be used to determine wall losses or simulate resistive terminations fitted into the ends of a guide. It is believed that the general conclusions drawn by using this simpler two-dimensional geometry will be fundamentally the same for other geometries.

Optimal protocols for slowly driven quantum systems.

PubMed

Zulkowski, Patrick R; DeWeese, Michael R

2015-09-01

The design of efficient quantum information processing will rely on optimal nonequilibrium transitions of driven quantum systems. Building on a recently developed geometric framework for computing optimal protocols for classical systems driven in finite time, we construct a general framework for optimizing the average information entropy for driven quantum systems. Geodesics on the parameter manifold endowed with a positive semidefinite metric correspond to protocols that minimize the average information entropy production in finite time. We use this framework to explicitly compute the optimal entropy production for a simple two-state quantum system coupled to a heat bath of bosonic oscillators, which has applications to quantum annealing.