Numerical and analytical bounds on threshold error rates for hypergraph-product codes

NASA Astrophysics Data System (ADS)

Kovalev, Alexey A.; Prabhakar, Sanjay; Dumer, Ilya; Pryadko, Leonid P.

2018-06-01

We study analytically and numerically decoding properties of finite-rate hypergraph-product quantum low density parity-check codes obtained from random (3,4)-regular Gallager codes, with a simple model of independent X and Z errors. Several nontrivial lower and upper bounds for the decodable region are constructed analytically by analyzing the properties of the homological difference, equal minus the logarithm of the maximum-likelihood decoding probability for a given syndrome. Numerical results include an upper bound for the decodable region from specific heat calculations in associated Ising models and a minimum-weight decoding threshold of approximately 7 % .

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

Wigner distribution function of Hermite-cosine-Gaussian beams through an apertured optical system.

PubMed

Sun, Dong; Zhao, Daomu

2005-08-01

By introducing the hard-aperture function into a finite sum of complex Gaussian functions, the approximate analytical expressions of the Wigner distribution function for Hermite-cosine-Gaussian beams passing through an apertured paraxial ABCD optical system are obtained. The analytical results are compared with the numerically integrated ones, and the absolute errors are also given. It is shown that the analytical results are proper and that the calculation speed for them is much faster than for the numerical results.

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

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

Solution of the advection-dispersion equation: Continuous load of finite duration

USGS Publications Warehouse

Runkel, R.L.

1996-01-01

Field studies of solute fate and transport in streams and rivers often involve an. experimental release of solutes at an upstream boundary for a finite period of time. A review of several standard references on surface-water-quality modeling indicates that the analytical solution to the constant-parameter advection-dispersion equation for this type of boundary condition has been generally overlooked. Here an exact analytical solution that considers a continuous load of unite duration is compared to an approximate analytical solution presented elsewhere. Results indicate that the exact analytical solution should be used for verification of numerical solutions and other solute-transport problems wherein a high level of accuracy is required. ?? ASCE.

Semi-analytic valuation of stock loans with finite maturity

NASA Astrophysics Data System (ADS)

Lu, Xiaoping; Putri, Endah R. M.

2015-10-01

In this paper we study stock loans of finite maturity with different dividend distributions semi-analytically using the analytical approximation method in Zhu (2006). Stock loan partial differential equations (PDEs) are established under Black-Scholes framework. Laplace transform method is used to solve the PDEs. Optimal exit price and stock loan value are obtained in Laplace space. Values in the original time space are recovered by numerical Laplace inversion. To demonstrate the efficiency and accuracy of our semi-analytic method several examples are presented, the results are compared with those calculated using existing methods. We also present a calculation of fair service fee charged by the lender for different loan parameters.

Reflection and diffraction corrections for nonlinear materials characterization by quasi-static pulse measurement

NASA Astrophysics Data System (ADS)

Nagy, Peter B.; Qu, Jianmin; Jacobs, Laurence J.

2014-02-01

A harmonic acoustic tone burst propagating through an elastic solid with quadratic nonlinearity produces not only a parallel burst of second harmonic but also an often neglected quasi-static pulse associated with the acoustic radiation-induced eigenstrain. Although initial analytical and experimental studies by Yost and Cantrell suggested that the pulse might have a right-angled triangular shape with the peak displacement at the leading edge being proportional to the length of the tone burst, more recent theoretical, analytical, numerical, and experimental studies proved that the pulse has a flat-top shape and the peak displacement is proportional to the propagation length. In this paper, analytical and numerical simulation results are presented to illustrate two types of finite-size effects. First, the finite axial dimension of the specimen cannot be simply accounted for by a linear reflection coefficient that neglects the nonlinear interaction between the combined incident and reflected fields. Second, the quasistatic pulse generated by a transducer of finite aperture suffers more severe divergence than both the fundamental and second harmonic pulses generated by the same transducer. These finite-size effects can make the top of the quasi-static pulse sloped rather than flat and therefore must be taken into consideration in the interpretation of experimental data.

Reflection and diffraction corrections for nonlinear materials characterization by quasi-static pulse measurement

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

Nagy, Peter B.; Qu, Jianmin; Jacobs, Laurence J.

A harmonic acoustic tone burst propagating through an elastic solid with quadratic nonlinearity produces not only a parallel burst of second harmonic but also an often neglected quasi-static pulse associated with the acoustic radiation-induced eigenstrain. Although initial analytical and experimental studies by Yost and Cantrell suggested that the pulse might have a right-angled triangular shape with the peak displacement at the leading edge being proportional to the length of the tone burst, more recent theoretical, analytical, numerical, and experimental studies proved that the pulse has a flat-top shape and the peak displacement is proportional to the propagation length. In thismore » paper, analytical and numerical simulation results are presented to illustrate two types of finite-size effects. First, the finite axial dimension of the specimen cannot be simply accounted for by a linear reflection coefficient that neglects the nonlinear interaction between the combined incident and reflected fields. Second, the quasistatic pulse generated by a transducer of finite aperture suffers more severe divergence than both the fundamental and second harmonic pulses generated by the same transducer. These finite-size effects can make the top of the quasi-static pulse sloped rather than flat and therefore must be taken into consideration in the interpretation of experimental data.« less

Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions

DOE PAGES

Lloyd, Jeffrey T.; Clayton, John D.; Austin, Ryan A.; ...

2015-07-10

Background: The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic-viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Methods: Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine-Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes themore » rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Results: Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). Conclusions: For weak shocks, results of the two numerical methods are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide insight into the shock structure afforded by the numerical methods.« less

International Conference on Numerical Methods in Fluid Dynamics, 7th, Stanford University, Stanford and Moffett Field, CA, June 23-27, 1980, Proceedings

NASA Technical Reports Server (NTRS)

Reynolds, W. C. (Editor); Maccormack, R. W.

1981-01-01

Topics discussed include polygon transformations in fluid mechanics, computation of three-dimensional horseshoe vortex flow using the Navier-Stokes equations, an improved surface velocity method for transonic finite-volume solutions, transonic flow calculations with higher order finite elements, the numerical calculation of transonic axial turbomachinery flows, and the simultaneous solutions of inviscid flow and boundary layer at transonic speeds. Also considered are analytical solutions for the reflection of unsteady shock waves and relevant numerical tests, reformulation of the method of characteristics for multidimensional flows, direct numerical simulations of turbulent shear flows, the stability and separation of freely interacting boundary layers, computational models of convective motions at fluid interfaces, viscous transonic flow over airfoils, and mixed spectral/finite difference approximations for slightly viscous flows.

Purely numerical approach for analyzing flow to a well intercepting a vertical fracture

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

Narasimhan, T.N.; Palen, W.A.

1979-03-01

A numerical method, based on an Integral Finite Difference approach, is presented to investigate wells intercepting fractures in general and vertical fractures in particular. Such features as finite conductivity, wellbore storage, damage, and fracture deformability and its influence as permeability are easily handled. The advantage of the numerical approach is that it is based on fewer assumptions than analytic solutions and hence has greater generality. Illustrative examples are given to validate the method against known solutions. New results are presenteed to demonstrate the applicability of the method to problems not apparently considered in the literature so far.

Properties of finite difference models of non-linear conservative oscillators

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1988-01-01

Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.

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.

Analytical and Numerical Results for an Adhesively Bonded Joint Subjected to Pure Bending

NASA Technical Reports Server (NTRS)

Smeltzer, Stanley S., III; Lundgren, Eric

2006-01-01

A one-dimensional, semi-analytical methodology that was previously developed for evaluating adhesively bonded joints composed of anisotropic adherends and adhesives that exhibit inelastic material behavior is further verified in the present paper. A summary of the first-order differential equations and applied joint loading used to determine the adhesive response from the methodology are also presented. The method was previously verified against a variety of single-lap joint configurations from the literature that subjected the joints to cases of axial tension and pure bending. Using the same joint configuration and applied bending load presented in a study by Yang, the finite element analysis software ABAQUS was used to further verify the semi-analytical method. Linear static ABAQUS results are presented for two models, one with a coarse and one with a fine element meshing, that were used to verify convergence of the finite element analyses. Close agreement between the finite element results and the semi-analytical methodology were determined for both the shear and normal stress responses of the adhesive bondline. Thus, the semi-analytical methodology was successfully verified using the ABAQUS finite element software and a single-lap joint configuration subjected to pure bending.

Lax-Wendroff and TVD finite volume methods for unidimensional thermomechanical numerical simulations of impacts on elastic-plastic solids

NASA Astrophysics Data System (ADS)

Heuzé, Thomas

2017-10-01

We present in this work two finite volume methods for the simulation of unidimensional impact problems, both for bars and plane waves, on elastic-plastic solid media within the small strain framework. First, an extension of Lax-Wendroff to elastic-plastic constitutive models with linear and nonlinear hardenings is presented. Second, a high order TVD method based on flux-difference splitting [1] and Superbee flux limiter [2] is coupled with an approximate elastic-plastic Riemann solver for nonlinear hardenings, and follows that of Fogarty [3] for linear ones. Thermomechanical coupling is accounted for through dissipation heating and thermal softening, and adiabatic conditions are assumed. This paper essentially focuses on one-dimensional problems since analytical solutions exist or can easily be developed. Accordingly, these two numerical methods are compared to analytical solutions and to the explicit finite element method on test cases involving discontinuous and continuous solutions. This allows to study in more details their respective performance during the loading, unloading and reloading stages. Particular emphasis is also paid to the accuracy of the computed plastic strains, some differences being found according to the numerical method used. Lax-Wendoff two-dimensional discretization of a one-dimensional problem is also appended at the end to demonstrate the extensibility of such numerical scheme to multidimensional problems.

Modeling convection-diffusion-reaction systems for microfluidic molecular communications with surface-based receivers in Internet of Bio-Nano Things

PubMed Central

Akan, Ozgur B.

2018-01-01

We consider a microfluidic molecular communication (MC) system, where the concentration-encoded molecular messages are transported via fluid flow-induced convection and diffusion, and detected by a surface-based MC receiver with ligand receptors placed at the bottom of the microfluidic channel. The overall system is a convection-diffusion-reaction system that can only be solved by numerical methods, e.g., finite element analysis (FEA). However, analytical models are key for the information and communication technology (ICT), as they enable an optimisation framework to develop advanced communication techniques, such as optimum detection methods and reliable transmission schemes. In this direction, we develop an analytical model to approximate the expected time course of bound receptor concentration, i.e., the received signal used to decode the transmitted messages. The model obviates the need for computationally expensive numerical methods by capturing the nonlinearities caused by laminar flow resulting in parabolic velocity profile, and finite number of ligand receptors leading to receiver saturation. The model also captures the effects of reactive surface depletion layer resulting from the mass transport limitations and moving reaction boundary originated from the passage of finite-duration molecular concentration pulse over the receiver surface. Based on the proposed model, we derive closed form analytical expressions that approximate the received pulse width, pulse delay and pulse amplitude, which can be used to optimize the system from an ICT perspective. We evaluate the accuracy of the proposed model by comparing model-based analytical results to the numerical results obtained by solving the exact system model with COMSOL Multiphysics. PMID:29415019

Modeling convection-diffusion-reaction systems for microfluidic molecular communications with surface-based receivers in Internet of Bio-Nano Things.

PubMed

Kuscu, Murat; Akan, Ozgur B

2018-01-01

We consider a microfluidic molecular communication (MC) system, where the concentration-encoded molecular messages are transported via fluid flow-induced convection and diffusion, and detected by a surface-based MC receiver with ligand receptors placed at the bottom of the microfluidic channel. The overall system is a convection-diffusion-reaction system that can only be solved by numerical methods, e.g., finite element analysis (FEA). However, analytical models are key for the information and communication technology (ICT), as they enable an optimisation framework to develop advanced communication techniques, such as optimum detection methods and reliable transmission schemes. In this direction, we develop an analytical model to approximate the expected time course of bound receptor concentration, i.e., the received signal used to decode the transmitted messages. The model obviates the need for computationally expensive numerical methods by capturing the nonlinearities caused by laminar flow resulting in parabolic velocity profile, and finite number of ligand receptors leading to receiver saturation. The model also captures the effects of reactive surface depletion layer resulting from the mass transport limitations and moving reaction boundary originated from the passage of finite-duration molecular concentration pulse over the receiver surface. Based on the proposed model, we derive closed form analytical expressions that approximate the received pulse width, pulse delay and pulse amplitude, which can be used to optimize the system from an ICT perspective. We evaluate the accuracy of the proposed model by comparing model-based analytical results to the numerical results obtained by solving the exact system model with COMSOL Multiphysics.

The program FANS-3D (finite analytic numerical simulation 3-dimensional) and its applications

NASA Technical Reports Server (NTRS)

Bravo, Ramiro H.; Chen, Ching-Jen

1992-01-01

In this study, the program named FANS-3D (Finite Analytic Numerical Simulation-3 Dimensional) is presented. FANS-3D was designed to solve problems of incompressible fluid flow and combined modes of heat transfer. It solves problems with conduction and convection modes of heat transfer in laminar flow, with provisions for radiation and turbulent flows. It can solve singular or conjugate modes of heat transfer. It also solves problems in natural convection, using the Boussinesq approximation. FANS-3D was designed to solve heat transfer problems inside one, two and three dimensional geometries that can be represented by orthogonal planes in a Cartesian coordinate system. It can solve internal and external flows using appropriate boundary conditions such as symmetric, periodic and user specified.

Analysis of the sound field in finite length infinite baffled cylindrical ducts with vibrating walls of finite impedance.

PubMed

Shao, Wei; Mechefske, Chris K

2005-04-01

This paper describes an analytical model of finite cylindrical ducts with infinite flanges. This model is used to investigate the sound radiation characteristics of the gradient coil system of a magnetic resonance imaging (MRI) scanner. The sound field in the duct satisfies both the boundary conditions at the wall and at the open ends. The vibrating cylindrical wall of the duct is assumed to be the only sound source. Different acoustic conditions for the wall (rigid and absorptive) are used in the simulations. The wave reflection phenomenon at the open ends of the finite duct is described by general radiation impedance. The analytical model is validated by the comparison with its counterpart in a commercial code based on the boundary element method (BEM). The analytical model shows significant advantages over the BEM model with better numerical efficiency and a direct relation between the design parameters and the sound field inside the duct.

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

Tanizaki, Yuya; Nishimura, Hiromichi; Verbaarschot, Jacobus J. M.

We propose new gradient flows that define Lefschetz thimbles and do not blow up in a finite flow time. Here, we study analytic properties of these gradient flows, and confirm them by numerical tests in simple examples.

Generalized analytical solutions to sequentially coupled multi-species advective-dispersive transport equations in a finite domain subject to an arbitrary time-dependent source boundary condition

NASA Astrophysics Data System (ADS)

Chen, Jui-Sheng; Liu, Chen-Wuing; Liang, Ching-Ping; Lai, Keng-Hsin

2012-08-01

SummaryMulti-species advective-dispersive transport equations sequentially coupled with first-order decay reactions are widely used to describe the transport and fate of the decay chain contaminants such as radionuclide, chlorinated solvents, and nitrogen. Although researchers attempted to present various types of methods for analytically solving this transport equation system, the currently available solutions are mostly limited to an infinite or a semi-infinite domain. A generalized analytical solution for the coupled multi-species transport problem in a finite domain associated with an arbitrary time-dependent source boundary is not available in the published literature. In this study, we first derive generalized analytical solutions for this transport problem in a finite domain involving arbitrary number of species subject to an arbitrary time-dependent source boundary. Subsequently, we adopt these derived generalized analytical solutions to obtain explicit analytical solutions for a special-case transport scenario involving an exponentially decaying Bateman type time-dependent source boundary. We test the derived special-case solutions against the previously published coupled 4-species transport solution and the corresponding numerical solution with coupled 10-species transport to conduct the solution verification. Finally, we compare the new analytical solutions derived for a finite domain against the published analytical solutions derived for a semi-infinite domain to illustrate the effect of the exit boundary condition on coupled multi-species transport with an exponential decaying source boundary. The results show noticeable discrepancies between the breakthrough curves of all the species in the immediate vicinity of the exit boundary obtained from the analytical solutions for a finite domain and a semi-infinite domain for the dispersion-dominated condition.

Preliminary numerical analysis of improved gas chromatograph model

NASA Technical Reports Server (NTRS)

Woodrow, P. T.

1973-01-01

A mathematical model for the gas chromatograph was developed which incorporates the heretofore neglected transport mechanisms of intraparticle diffusion and rates of adsorption. Because a closed-form analytical solution to the model does not appear realizable, techniques for the numerical solution of the model equations are being investigated. Criteria were developed for using a finite terminal boundary condition in place of an infinite boundary condition used in analytical solution techniques. The class of weighted residual methods known as orthogonal collocation is presently being investigated and appears promising.

The Finite-Size Scaling Relation for the Order-Parameter Probability Distribution of the Six-Dimensional Ising Model

NASA Astrophysics Data System (ADS)

Merdan, Ziya; Karakuş, Özlem

2016-11-01

The six dimensional Ising model with nearest-neighbor pair interactions has been simulated and verified numerically on the Creutz Cellular Automaton by using five bit demons near the infinite-lattice critical temperature with the linear dimensions L=4,6,8,10. The order parameter probability distribution for six dimensional Ising model has been calculated at the critical temperature. The constants of the analytical function have been estimated by fitting to probability function obtained numerically at the finite size critical point.

Analytical and finite element simulation of a three-bar torsion spring

NASA Astrophysics Data System (ADS)

Rădoi, M.; Cicone, T.

2016-08-01

The present study is dedicated to the innovative 3-bar torsion spring used as suspension solution for the first time at Lunokhod-1, the first autonomous vehicle sent for the exploration of the Moon in the early 70-ies by the former USSR. The paper describes a simple analytical model for calculation of spring static characteristics, taking into account both torsion and bending effects. Closed form solutions of this model allows quick and elegant parametric analysis. A comparison with a single torsion bar with the same stiffness reveal an increase of the maximum stress with more than 50%. A 3D finite element (FE) simulation is proposed to evaluate the accuracy of the analytical model. The model was meshed in an automated pattern (sweep for hubs and tetrahedrons for bars) with mesh morphing. Very close results between analytical and numerical solutions have been found, concluding that the analytical model is accurate. The 3-D finite element simulation was used to evaluate the effects of design details like fillet radius of the bars or contact stresses in the hex hub.

Sensitivity Analysis of Hydraulic Head to Locations of Model Boundaries

DOE PAGES

Lu, Zhiming

2018-01-30

Sensitivity analysis is an important component of many model activities in hydrology. Numerous studies have been conducted in calculating various sensitivities. Most of these sensitivity analysis focus on the sensitivity of state variables (e.g. hydraulic head) to parameters representing medium properties such as hydraulic conductivity or prescribed values such as constant head or flux at boundaries, while few studies address the sensitivity of the state variables to some shape parameters or design parameters that control the model domain. Instead, these shape parameters are typically assumed to be known in the model. In this study, based on the flow equation, wemore » derive the equation (and its associated initial and boundary conditions) for sensitivity of hydraulic head to shape parameters using continuous sensitivity equation (CSE) approach. These sensitivity equations can be solved numerically in general or analytically in some simplified cases. Finally, the approach has been demonstrated through two examples and the results are compared favorably to those from analytical solutions or numerical finite difference methods with perturbed model domains, while numerical shortcomings of the finite difference method are avoided.« less

Sensitivity Analysis of Hydraulic Head to Locations of Model Boundaries

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

Lu, Zhiming

Sensitivity analysis is an important component of many model activities in hydrology. Numerous studies have been conducted in calculating various sensitivities. Most of these sensitivity analysis focus on the sensitivity of state variables (e.g. hydraulic head) to parameters representing medium properties such as hydraulic conductivity or prescribed values such as constant head or flux at boundaries, while few studies address the sensitivity of the state variables to some shape parameters or design parameters that control the model domain. Instead, these shape parameters are typically assumed to be known in the model. In this study, based on the flow equation, wemore » derive the equation (and its associated initial and boundary conditions) for sensitivity of hydraulic head to shape parameters using continuous sensitivity equation (CSE) approach. These sensitivity equations can be solved numerically in general or analytically in some simplified cases. Finally, the approach has been demonstrated through two examples and the results are compared favorably to those from analytical solutions or numerical finite difference methods with perturbed model domains, while numerical shortcomings of the finite difference method are avoided.« less

Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model

NASA Astrophysics Data System (ADS)

Nemoto, Takahiro; Jack, Robert L.; Lecomte, Vivien

2017-03-01

We analyze large deviations of the time-averaged activity in the one-dimensional Fredrickson-Andersen model, both numerically and analytically. The model exhibits a dynamical phase transition, which appears as a singularity in the large deviation function. We analyze the finite-size scaling of this phase transition numerically, by generalizing an existing cloning algorithm to include a multicanonical feedback control: this significantly improves the computational efficiency. Motivated by these numerical results, we formulate an effective theory for the model in the vicinity of the phase transition, which accounts quantitatively for the observed behavior. We discuss potential applications of the numerical method and the effective theory in a range of more general contexts.

Fourier/Chebyshev methods for the incompressible Navier-Stokes equations in finite domains

NASA Technical Reports Server (NTRS)

Corral, Roque; Jimenez, Javier

1992-01-01

A fully spectral numerical scheme for the incompressible Navier-Stokes equations in domains which are infinite or semi-infinite in one dimension. The domain is not mapped, and standard Fourier or Chebyshev expansions can be used. The handling of the infinite domain does not introduce any significant overhead. The scheme assumes that the vorticity in the flow is essentially concentrated in a finite region, which is represented numerically by standard spectral collocation methods. To accomodate the slow exponential decay of the velocities at infinity, extra expansion functions are introduced, which are handled analytically. A detailed error analysis is presented, and two applications to Direct Numerical Simulation of turbulent flows are discussed in relation with the numerical performance of the scheme.

Analytical validation of an explicit finite element model of a rolling element bearing with a localised line spall

NASA Astrophysics Data System (ADS)

Singh, Sarabjeet; Howard, Carl Q.; Hansen, Colin H.; Köpke, Uwe G.

2018-03-01

In this paper, numerically modelled vibration response of a rolling element bearing with a localised outer raceway line spall is presented. The results were obtained from a finite element (FE) model of the defective bearing solved using an explicit dynamics FE software package, LS-DYNA. Time domain vibration signals of the bearing obtained directly from the FE modelling were processed further to estimate time-frequency and frequency domain results, such as spectrogram and power spectrum, using standard signal processing techniques pertinent to the vibration-based monitoring of rolling element bearings. A logical approach to analyses of the numerically modelled results was developed with an aim to presenting the analytical validation of the modelled results. While the time and frequency domain analyses of the results show that the FE model generates accurate bearing kinematics and defect frequencies, the time-frequency analysis highlights the simulation of distinct low- and high-frequency characteristic vibration signals associated with the unloading and reloading of the rolling elements as they move in and out of the defect, respectively. Favourable agreement of the numerical and analytical results demonstrates the validation of the results from the explicit FE modelling of the bearing.

Stochastic coalescence in finite systems: an algorithm for the numerical solution of the multivariate master equation.

NASA Astrophysics Data System (ADS)

Alfonso, Lester; Zamora, Jose; Cruz, Pedro

2015-04-01

The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.

Controlling Reflections from Mesh Refinement Interfaces in Numerical Relativity

NASA Technical Reports Server (NTRS)

Baker, John G.; Van Meter, James R.

2005-01-01

A leading approach to improving the accuracy on numerical relativity simulations of black hole systems is through fixed or adaptive mesh refinement techniques. We describe a generic numerical error which manifests as slowly converging, artificial reflections from refinement boundaries in a broad class of mesh-refinement implementations, potentially limiting the effectiveness of mesh- refinement techniques for some numerical relativity applications. We elucidate this numerical effect by presenting a model problem which exhibits the phenomenon, but which is simple enough that its numerical error can be understood analytically. Our analysis shows that the effect is caused by variations in finite differencing error generated across low and high resolution regions, and that its slow convergence is caused by the presence of dramatic speed differences among propagation modes typical of 3+1 relativity. Lastly, we resolve the problem, presenting a class of finite-differencing stencil modifications which eliminate this pathology in both our model problem and in numerical relativity examples.

Testing density-dependent groundwater models: Two-dimensional steady state unstable convection in infinite, finite and inclined porous layers

USGS Publications Warehouse

Weatherill, D.; Simmons, C.T.; Voss, C.I.; Robinson, N.I.

2004-01-01

This study proposes the use of several problems of unstable steady state convection with variable fluid density in a porous layer of infinite horizontal extent as two-dimensional (2-D) test cases for density-dependent groundwater flow and solute transport simulators. Unlike existing density-dependent model benchmarks, these problems have well-defined stability criteria that are determined analytically. These analytical stability indicators can be compared with numerical model results to test the ability of a code to accurately simulate buoyancy driven flow and diffusion. The basic analytical solution is for a horizontally infinite fluid-filled porous layer in which fluid density decreases with depth. The proposed test problems include unstable convection in an infinite horizontal box, in a finite horizontal box, and in an infinite inclined box. A dimensionless Rayleigh number incorporating properties of the fluid and the porous media determines the stability of the layer in each case. Testing the ability of numerical codes to match both the critical Rayleigh number at which convection occurs and the wavelength of convection cells is an addition to the benchmark problems currently in use. The proposed test problems are modelled in 2-D using the SUTRA [SUTRA-A model for saturated-unsaturated variable-density ground-water flow with solute or energy transport. US Geological Survey Water-Resources Investigations Report, 02-4231, 2002. 250 p] density-dependent groundwater flow and solute transport code. For the case of an infinite horizontal box, SUTRA results show a distinct change from stable to unstable behaviour around the theoretical critical Rayleigh number of 4??2 and the simulated wavelength of unstable convection agrees with that predicted by the analytical solution. The effects of finite layer aspect ratio and inclination on stability indicators are also tested and numerical results are in excellent agreement with theoretical stability criteria and with numerical results previously reported in traditional fluid mechanics literature. ?? 2004 Elsevier Ltd. All rights reserved.

ULTRASONIC STUDIES OF THE FUNDAMENTAL MECHANISMS OF RECRYSTALLIZATION AND SINTERING OF METALS

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

TURNER, JOSEPH A.

2005-11-30

The purpose of this project was to develop a fundamental understanding of the interaction of an ultrasonic wave with complex media, with specific emphases on recrystallization and sintering of metals. A combined analytical, numerical, and experimental research program was implemented. Theoretical models of elastic wave propagation through these complex materials were developed using stochastic wave field techniques. The numerical simulations focused on finite element wave propagation solutions through complex media. The experimental efforts were focused on corroboration of the models developed and on the development of new experimental techniques. The analytical and numerical research allows the experimental results to bemore » interpreted quantitatively.« less

Semi-analytical discontinuous Galerkin finite element method for the calculation of dispersion properties of guided waves in plates.

PubMed

Hebaz, Salah-Eddine; Benmeddour, Farouk; Moulin, Emmanuel; Assaad, Jamal

2018-01-01

The development of reliable guided waves inspection systems is conditioned by an accurate knowledge of their dispersive properties. The semi-analytical finite element method has been proven to be very practical for modeling wave propagation in arbitrary cross-section waveguides. However, when it comes to computations on complex geometries to a given accuracy, it still has a major drawback: the high consumption of resources. Recently, discontinuous Galerkin finite element method (DG-FEM) has been found advantageous over the standard finite element method when applied as well in the frequency domain. In this work, a high-order method for the computation of Lamb mode characteristics in plates is proposed. The problem is discretised using a class of DG-FEM, namely, the interior penalty methods family. The analytical validation is performed through the homogeneous isotropic case with traction-free boundary conditions. Afterwards, functionally graded material plates are analysed and a numerical example is presented. It was found that the obtained results are in good agreement with those found in the literature.

User's manual for the one-dimensional hypersonic experimental aero-thermodynamic (1DHEAT) data reduction code

NASA Technical Reports Server (NTRS)

Hollis, Brian R.

1995-01-01

A FORTRAN computer code for the reduction and analysis of experimental heat transfer data has been developed. This code can be utilized to determine heat transfer rates from surface temperature measurements made using either thin-film resistance gages or coaxial surface thermocouples. Both an analytical and a numerical finite-volume heat transfer model are implemented in this code. The analytical solution is based on a one-dimensional, semi-infinite wall thickness model with the approximation of constant substrate thermal properties, which is empirically corrected for the effects of variable thermal properties. The finite-volume solution is based on a one-dimensional, implicit discretization. The finite-volume model directly incorporates the effects of variable substrate thermal properties and does not require the semi-finite wall thickness approximation used in the analytical model. This model also includes the option of a multiple-layer substrate. Fast, accurate results can be obtained using either method. This code has been used to reduce several sets of aerodynamic heating data, of which samples are included in this report.

Composite material bend-twist coupling for wind turbine blade applications

NASA Astrophysics Data System (ADS)

Walsh, Justin M.

Current efforts in wind turbine blade design seek to employ bend-twist coupling of composite materials for passive power control by twisting blades to feather. Past efforts in this area of study have proved to be problematic, especially in formulation of the bend-twist coupling coefficient alpha. Kevlar/epoxy, carbon/epoxy and glass/epoxy specimens were manufactured to study bend-twist coupling, from which numerical and analytical models could be verified. Finite element analysis was implemented to evaluate fiber orientation and material property effects on coupling magnitude. An analytical/empirical model was then derived to describe numerical results and serve as a replacement for the commonly used coupling coefficient alpha. Through the results from numerical and analytical models, a foundation for aeroelastic design of wind turbines blades utilizing biased composite materials is provided.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

Fiber-reinforced materials: finite elements for the treatment of the inextensibility constraint

NASA Astrophysics Data System (ADS)

Auricchio, Ferdinando; Scalet, Giulia; Wriggers, Peter

2017-12-01

The present paper proposes a numerical framework for the analysis of problems involving fiber-reinforced anisotropic materials. Specifically, isotropic linear elastic solids, reinforced by a single family of inextensible fibers, are considered. The kinematic constraint equation of inextensibility in the fiber direction leads to the presence of an undetermined fiber stress in the constitutive equations. To avoid locking-phenomena in the numerical solution due to the presence of the constraint, mixed finite elements based on the Lagrange multiplier, perturbed Lagrangian, and penalty method are proposed. Several boundary-value problems under plane strain conditions are solved and numerical results are compared to analytical solutions, whenever the derivation is possible. The performed simulations allow to assess the performance of the proposed finite elements and to discuss several features of the developed formulations concerning the effective approximation for the displacement and fiber stress fields, mesh convergence, and sensitivity to penalty parameters.

Surface response of a viscoelastic medium to subsurface acoustic sources with application to medical diagnosis

NASA Astrophysics Data System (ADS)

Royston, Thomas J.; Yazicioglu, Yigit; Loth, Francis

2003-02-01

The response at the surface of an isotropic viscoelastic medium to buried fundamental acoustic sources is studied theoretically, computationally and experimentally. Finite and infinitesimal monopole and dipole sources within the low audible frequency range (40-400 Hz) are considered. Analytical and numerical integral solutions that account for compression, shear and surface wave response to the buried sources are formulated and compared with numerical finite element simulations and experimental studies on finite dimension phantom models. It is found that at low audible frequencies, compression and shear wave propagation from point sources can both be significant, with shear wave effects becoming less significant as frequency increases. Additionally, it is shown that simple closed-form analytical approximations based on an infinite medium model agree well with numerically obtained ``exact'' half-space solutions for the frequency range and material of interest in this study. The focus here is on developing a better understanding of how biological soft tissue affects the transmission of vibro-acoustic energy from biological acoustic sources below the skin surface, whose typical spectral content is in the low audible frequency range. Examples include sound radiated from pulmonary, gastro-intestinal and cardiovascular system functions, such as breath sounds, bowel sounds and vascular bruits, respectively.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result.

PubMed

Wu, Yang; Kelly, Damien P

2014-12-12

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of [Formula: see text] and [Formula: see text] type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of [Formula: see text] and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by [Formula: see text], where [Formula: see text] is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result

NASA Astrophysics Data System (ADS)

Wu, Yang; Kelly, Damien P.

2014-12-01

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of ? and ? type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of ? and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by ?, where ? is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

Bäcklund transformation, analytic soliton solutions and numerical simulation for a (2+1)-dimensional complex Ginzburg-Landau equation in a nonlinear fiber

NASA Astrophysics Data System (ADS)

Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong

2017-10-01

In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere

NASA Astrophysics Data System (ADS)

Swidinsky, Andrei; Liu, Lifei

2017-11-01

We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.

Finite-difference time-domain modelling of through-the-Earth radio signal propagation

NASA Astrophysics Data System (ADS)

Ralchenko, M.; Svilans, M.; Samson, C.; Roper, M.

2015-12-01

This research seeks to extend the knowledge of how a very low frequency (VLF) through-the-Earth (TTE) radio signal behaves as it propagates underground, by calculating and visualizing the strength of the electric and magnetic fields for an arbitrary geology through numeric modelling. To achieve this objective, a new software tool has been developed using the finite-difference time-domain method. This technique is particularly well suited to visualizing the distribution of electromagnetic fields in an arbitrary geology. The frequency range of TTE radio (400-9000 Hz) and geometrical scales involved (1 m resolution for domains a few hundred metres in size) involves processing a grid composed of millions of cells for thousands of time steps, which is computationally expensive. Graphics processing unit acceleration was used to reduce execution time from days and weeks, to minutes and hours. Results from the new modelling tool were compared to three cases for which an analytic solution is known. Two more case studies were done featuring complex geologic environments relevant to TTE communications that cannot be solved analytically. There was good agreement between numeric and analytic results. Deviations were likely caused by numeric artifacts from the model boundaries; however, in a TTE application in field conditions, the uncertainty in the conductivity of the various geologic formations will greatly outweigh these small numeric errors.

Numerical calculations of velocity and pressure distribution around oscillating airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Ecer, A.; Kobiske, M.

1974-01-01

An analytical procedure based on the Navier-Stokes equations was developed for analyzing and representing properties of unsteady viscous flow around oscillating obstacles. A variational formulation of the vorticity transport equation was discretized in finite element form and integrated numerically. At each time step of the numerical integration, the velocity field around the obstacle was determined for the instantaneous vorticity distribution from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints, using the Lagrangian Multiplier Technique, at each time step of the numerical integration. The procedure was then applied for determining pressures around obstacles oscillating in unsteady flow. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.

Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver

DOE PAGES

Vincenti, H.; Vay, J. -L.

2015-11-22

Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the result. Such modifications for instance occur when Perfectly Matched Layers (PMLs) are used at simulation domain boundaries to simulate open media. Another example is the use of arbitrary order Maxwell solver with domain decomposition technique that may under some condition involve stencil truncations at subdomain boundaries, resulting in small spurious errors that do eventually build up. In each case, a careful evaluation of the characteristics and magnitude of themore » errors resulting from these approximations, and their impact at any frequency and angle, requires detailed analytical and numerical studies. To this end, we present a general analytical approach that enables the evaluation of numerical discretization errors of fully three-dimensional arbitrary order finite-difference Maxwell solver, with arbitrary modification of the local stencil in the simulation domain. The analytical model is validated against simulations of domain decomposition technique and PMLs, when these are used with very high-order Maxwell solver, as well as in the infinite order limit of pseudo-spectral solvers. Results confirm that the new analytical approach enables exact predictions in each case. It also confirms that the domain decomposition technique can be used with very high-order Maxwell solver and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.« less

Gradient flows without blow-up for Lefschetz thimbles

DOE PAGES

Tanizaki, Yuya; Nishimura, Hiromichi; Verbaarschot, Jacobus J. M.

2017-10-16

We propose new gradient flows that define Lefschetz thimbles and do not blow up in a finite flow time. Here, we study analytic properties of these gradient flows, and confirm them by numerical tests in simple examples.

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.

On the superposition principle in interference experiments.

PubMed

Sinha, Aninda; H Vijay, Aravind; Sinha, Urbasi

2015-05-14

The superposition principle is usually incorrectly applied in interference experiments. This has recently been investigated through numerics based on Finite Difference Time Domain (FDTD) methods as well as the Feynman path integral formalism. In the current work, we have derived an analytic formula for the Sorkin parameter which can be used to determine the deviation from the application of the principle. We have found excellent agreement between the analytic distribution and those that have been earlier estimated by numerical integration as well as resource intensive FDTD simulations. The analytic handle would be useful for comparing theory with future experiments. It is applicable both to physics based on classical wave equations as well as the non-relativistic Schrödinger equation.

Implicit finite difference methods on composite grids

NASA Technical Reports Server (NTRS)

Mastin, C. Wayne

1987-01-01

Techniques for eliminating time lags in the implicit finite-difference solution of partial differential equations are investigated analytically, with a focus on transient fluid dynamics problems on overlapping multicomponent grids. The fundamental principles of the approach are explained, and the method is shown to be applicable to both rectangular and curvilinear grids. Numerical results for sample problems are compared with exact solutions in graphs, and good agreement is demonstrated.

Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code.

PubMed

Predoi, Mihai Valentin

2014-09-01

The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method. Copyright © 2014 Elsevier B.V. All rights reserved.

Microstructured optical fibers for terahertz waveguiding regime by using an analytical field model

NASA Astrophysics Data System (ADS)

Sharma, Dinesh Kumar; Sharma, Anurag; Tripathi, Saurabh Mani

2017-12-01

Microstructured optical fibres (MOFs) are seen as novel optical waveguide for the potential applications in the terahertz (THz) band as they provide a flexible route towards THz waveguiding. Using the analytical field model (Sharma et al., 2014) developed for index-guiding MOFs with hexagonal lattice of circular air-holes in the photonic crystal cladding; we aim to study the propagation characteristics such as effective index, near and the far-field radiation patterns and its evolution from near-to-far-field domain, spot size, effective mode area, and the numerical aperture at the THz regime. Further, we present an analytical field expression for the next higher-order mode of the MOF for studying the modal properties at terahertz frequencies. Also, we investigate the mode cut-off conditions for identifying the single-mode operation range at THz frequencies. Emphasis is put on studying the coupling characteristics of MOF geometries for efficient mode coupling. Comparisons with available experimental and numerical simulation results, e.g., those based on the full-vector finite element method (FEM) and the finite-difference frequency-domain (FDFD) method have been included.

Skin friction enhancement in a model problem of undulatory swimming

NASA Astrophysics Data System (ADS)

Ehrenstein, Uwe; Eloy, Christophe

2013-10-01

To calculate the energy costs of swimming, it is crucial to evaluate the drag force originating from skin friction. In this paper we examine the assumption, known as the 'Bone-Lighthill boundary-layer thinning hypothesis', that undulatory swimming motions induce a drag increase because of the compression of the boundary layer. Studying analytically an incoming flow along a flat plate moving at a normal velocity as a limit case of a yawed cylinder in uniform flow under the laminar boundary layer assumption, we demonstrate that the longitudinal drag scales as the square root of the normal velocity component. This analytical prediction is interpreted in the light of a three-dimensional numerical simulation result for a plate of finite length and width. An analogous two-dimensional Navier-Stokes problem by artificially accelerating the flow in a channel of finite height is proposed and solved numerically, showing the robustness of the analytical results. Solving the problem for an undulatory plate motion similar to fish swimming, we find a drag enhancement which can be estimated to be of the order of 20 %.

Fokker-Planck Equations of Stochastic Acceleration: A Study of Numerical Methods

NASA Astrophysics Data System (ADS)

Park, Brian T.; Petrosian, Vahe

1996-03-01

Stochastic wave-particle acceleration may be responsible for producing suprathermal particles in many astrophysical situations. The process can be described as a diffusion process through the Fokker-Planck equation. If the acceleration region is homogeneous and the scattering mean free path is much smaller than both the energy change mean free path and the size of the acceleration region, then the Fokker-Planck equation reduces to a simple form involving only the time and energy variables. in an earlier paper (Park & Petrosian 1995, hereafter Paper 1), we studied the analytic properties of the Fokker-Planck equation and found analytic solutions for some simple cases. In this paper, we study the numerical methods which must be used to solve more general forms of the equation. Two classes of numerical methods are finite difference methods and Monte Carlo simulations. We examine six finite difference methods, three fully implicit and three semi-implicit, and a stochastic simulation method which uses the exact correspondence between the Fokker-Planck equation and the it5 stochastic differential equation. As discussed in Paper I, Fokker-Planck equations derived under the above approximations are singular, causing problems with boundary conditions and numerical overflow and underflow. We evaluate each method using three sample equations to test its stability, accuracy, efficiency, and robustness for both time-dependent and steady state solutions. We conclude that the most robust finite difference method is the fully implicit Chang-Cooper method, with minor extensions to account for the escape and injection terms. Other methods suffer from stability and accuracy problems when dealing with some Fokker-Planck equations. The stochastic simulation method, although simple to implement, is susceptible to Poisson noise when insufficient test particles are used and is computationally very expensive compared to the finite difference method.

Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models

NASA Astrophysics Data System (ADS)

Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.

2010-10-01

Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.

Fourier analysis of finite element preconditioned collocation schemes

NASA Technical Reports Server (NTRS)

Deville, Michel O.; Mund, Ernest H.

1990-01-01

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

Analytical and numerical treatment of drift-tearing modes in plasma slab

NASA Astrophysics Data System (ADS)

Mirnov, V. V.; Hegna, C. C.; Sovinec, C. R.; Howell, E. C.

2016-10-01

Two-fluid corrections to linear tearing modes includes 1) diamagnetic drifts that reduce the growth rate and 2) electron and ion decoupling on short scales that can lead to fast reconnection. We have recently developed an analytical model that includes effects 1) and 2) and important contribution from finite electron parallel thermal conduction. Both the tendencies 1) and 2) are confirmed by an approximate analytic dispersion relation that is derived using a perturbative approach of small ion-sound gyroradius ρs. This approach is only valid at the beginning of the transition from the collisional to semi-collisional regimes. Further analytical and numerical work is performed to cover the full interval of ρs connecting these two limiting cases. Growth rates are computed from analytic theory with a shooting method. They match the resistive MHD regime with the dispersion relations known at asymptotically large ion-sound gyroradius. A comparison between this analytical treatment and linear numerical simulations using the NIMROD code with cold ions and hot electrons in plasma slab is reported. The material is based on work supported by the U.S. DOE and NSF.

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.

A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

DOE PAGES

Gao, Kai; Chung, Eric T.; Gibson, Richard L.; ...

2015-06-05

The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elasticmore » wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.« less

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: Stationary modes

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1988-01-01

Spatially discrete difference approximations for hyperbolic initial-boundary-value problems (IBVPs) require numerical boundary conditions in addition to the analytical boundary conditions specified for the differential equations. Improper treatment of a numerical boundary condition can cause instability of the discrete IBVP even though the approximation is stable for the pure initial-value or Cauchy problem. In the discrete IBVP stability literature there exists a small class of discrete approximations called borderline cases. For nondissipative approximations, borderline cases are unstable according to the theory of the Gustafsson, Kreiss, and Sundstrom (GKS) but they may be Lax-Richtmyer stable or unstable in the L sub 2 norm on a finite domain. It is shown that borderline approximation can be characterized by the presence of a stationary mode for the finite-domain problem. A stationary mode has the property that it does not decay with time and a nontrivial stationary mode leads to algebraic growth of the solution norm with mesh refinement. An analytical condition is given which makes it easy to detect a stationary mode; several examples of numerical boundary conditions are investigated corresponding to borderline cases.

Modeling of heat flow and effective thermal conductivity of fractured media: Analytical and numerical methods

NASA Astrophysics Data System (ADS)

Nguyen, S. T.; Vu, M.-H.; Vu, M. N.; Tang, A. M.

2017-05-01

The present work aims to modeling the thermal conductivity of fractured materials using homogenization-based analytical and pattern-based numerical methods. These materials are considered as a network of cracks distributed inside a solid matrix. Heat flow through such media is perturbed by the crack system. The problem of heat flow across a single crack is firstly investigated. The classical Eshelby's solution, extended to the thermal conduction problem of an ellipsoidal inclusion embedding in an infinite homogeneous matrix, gives an analytical solution of temperature discontinuity across a non-conducting penny-shaped crack. This solution is then validated by the numerical simulation based on the finite elements method. The numerical simulation allows analyzing the effect of crack conductivity. The problem of a single crack is then extended to a medium containing multiple cracks. Analytical estimations for effective thermal conductivity, that take into account the interaction between cracks and their spatial distribution, are developed for the case of non-conducting cracks. Pattern-based numerical method is then employed for both cases non-conducting and conducting cracks. In the case of non-conducting cracks, numerical and analytical methods, both account for the spatial distribution of the cracks, fit perfectly. In the case of conducting cracks, the numerical analyzing of crack conductivity effect shows that highly conducting cracks weakly affect heat flow and the effective thermal conductivity of fractured media.

Analytical, Numerical and Experimental Examination of Reinforced Composites Beams Covered with Carbon Fiber Reinforced Plastic

NASA Astrophysics Data System (ADS)

Kasimzade, A. A.; Tuhta, S.

2012-03-01

In the article, analytical, numerical (Finite Element Method) and experimental investigation results of beam that was strengthened with fiber reinforced plastic-FRP composite has been given as comparative, the effect of FRP wrapping number to the maximum load and moment capacity has been evaluated depending on this results. Carbon FRP qualitative dependences have been occurred between wrapping number and beam load and moment capacity for repair-strengthen the reinforced concrete beams with carbon fiber. Shown possibilities of application traditional known analysis programs, for the analysis of Carbon Fiber Reinforced Plastic (CFRP) strengthened structures.

Theory and Circuit Model for Lossy Coaxial Transmission Line

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

Genoni, T. C.; Anderson, C. N.; Clark, R. E.

2017-04-01

The theory of signal propagation in lossy coaxial transmission lines is revisited and new approximate analytic formulas for the line impedance and attenuation are derived. The accuracy of these formulas from DC to 100 GHz is demonstrated by comparison to numerical solutions of the exact field equations. Based on this analysis, a new circuit model is described which accurately reproduces the line response over the entire frequency range. Circuit model calculations are in excellent agreement with the numerical and analytic results, and with finite-difference-time-domain simulations which resolve the skindepths of the conducting walls.

Modelling migration in multilayer systems by a finite difference method: the spherical symmetry case

NASA Astrophysics Data System (ADS)

Hojbotǎ, C. I.; Toşa, V.; Mercea, P. V.

2013-08-01

We present a numerical model based on finite differences to solve the problem of chemical impurity migration within a multilayer spherical system. Migration here means diffusion of chemical species in conditions of concentration partitioning at layer interfaces due to different solubilities of the migrant in different layers. We detail here the numerical model and discuss the results of its implementation. To validate the method we compare it with cases where an analytic solution exists. We also present an application of our model to a practical problem in which we compute the migration of caprolactam from the packaging multilayer foil into the food.

A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions: FULLY COUPLED PARALLEL SIMULATION OF HYDRAULIC FRACTURES IN 3-D

DOE PAGES

Settgast, Randolph R.; Fu, Pengcheng; Walsh, Stuart D. C.; ...

2016-09-18

This study describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions.

A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions: FULLY COUPLED PARALLEL SIMULATION OF HYDRAULIC FRACTURES IN 3-D

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

Settgast, Randolph R.; Fu, Pengcheng; Walsh, Stuart D. C.

This study describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions.

An improved 3D MoF method based on analytical partial derivatives

NASA Astrophysics Data System (ADS)

Chen, Xiang; Zhang, Xiong

2016-12-01

MoF (Moment of Fluid) method is one of the most accurate approaches among various surface reconstruction algorithms. As other second order methods, MoF method needs to solve an implicit optimization problem to obtain the optimal approximate surface. Therefore, the partial derivatives of the objective function have to be involved during the iteration for efficiency and accuracy. However, to the best of our knowledge, the derivatives are currently estimated numerically by finite difference approximation because it is very difficult to obtain the analytical derivatives of the object function for an implicit optimization problem. Employing numerical derivatives in an iteration not only increase the computational cost, but also deteriorate the convergence rate and robustness of the iteration due to their numerical error. In this paper, the analytical first order partial derivatives of the objective function are deduced for 3D problems. The analytical derivatives can be calculated accurately, so they are incorporated into the MoF method to improve its accuracy, efficiency and robustness. Numerical studies show that by using the analytical derivatives the iterations are converged in all mixed cells with the efficiency improvement of 3 to 4 times.

A numerical study of the steady scalar convective diffusion equation for small viscosity

NASA Technical Reports Server (NTRS)

Giles, M. B.; Rose, M. E.

1983-01-01

A time-independent convection diffusion equation is studied by means of a compact finite difference scheme and numerical solutions are compared to the analytic inviscid solutions. The correct internal and external boundary layer behavior is observed, due to an inherent feature of the scheme which automatically produces upwind differencing in inviscid regions and the correct viscous behavior in viscous regions.

Analytical and numerical solutions of the potential and electric field generated by different electrode arrays in a tumor tissue under electrotherapy.

PubMed

Bergues Pupo, Ana E; Reyes, Juan Bory; Bergues Cabrales, Luis E; Bergues Cabrales, Jesús M

2011-09-24

Electrotherapy is a relatively well established and efficient method of tumor treatment. In this paper we focus on analytical and numerical calculations of the potential and electric field distributions inside a tumor tissue in a two-dimensional model (2D-model) generated by means of electrode arrays with shapes of different conic sections (ellipse, parabola and hyperbola). Analytical calculations of the potential and electric field distributions based on 2D-models for different electrode arrays are performed by solving the Laplace equation, meanwhile the numerical solution is solved by means of finite element method in two dimensions. Both analytical and numerical solutions reveal significant differences between the electric field distributions generated by electrode arrays with shapes of circle and different conic sections (elliptic, parabolic and hyperbolic). Electrode arrays with circular, elliptical and hyperbolic shapes have the advantage of concentrating the electric field lines in the tumor. The mathematical approach presented in this study provides a useful tool for the design of electrode arrays with different shapes of conic sections by means of the use of the unifying principle. At the same time, we verify the good correspondence between the analytical and numerical solutions for the potential and electric field distributions generated by the electrode array with different conic sections.

Tidal Dissipation Within the Jupiter Moon Io - A Numerical Approach

NASA Astrophysics Data System (ADS)

Steinke, Teresa; van der Wal, Wouter; Hu, Haiyang; Vermeersen, Bert

2017-04-01

Satellite images and recent Earth-based observations of the innermost of the Galilean moons reveal a conspicuous pattern of volcanic hotspots and paterae on its surface. This pattern is associated with the heat flux originating from tidal dissipation in Io's mantle and asthenosphere. As shown by many analytical studies [e.g. Segatz et al. 1988], the local heat flux pattern depends on the rheology and structure of the satellite's interior and therefore could reveal constraints on Io's present interior. However, non-linear processes, different rheologies, and in particular lateral variations arising from the spatial heating pattern are difficult to incorporate in analytical 1D models but might be crucial. This motivates the development of a 3D finite element model of a layered body disturbed by a tidal potential. As a first step of this project we present a 3D finite element model of a spherically stratified body of linear viscoelastic rheology. For validation, we compare the resulting tidal deformation and local heating patterns with the results obtained by analytical models. Numerical errors increase with lower values of the asthenosphere viscosity. Currently, the numerical model allows realistic simulation down to viscosities of 1018 Pa s. Furthermore, we investigate an adequate way to deal with the relaxation of false modes that arise at the onset of the periodic tidal potential series in the numerical approach. Segatz, M., Spohn, T., Ross, M. N., Schubert, G. (1988). Tidal dissipation, surface heat flow, and figure of viscoelastic models of Io. Icarus, 75(2), 187-206.

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 synchronization of complex networks with non-identical nodes and impulsive disturbances

NASA Astrophysics Data System (ADS)

Zhang, Wanli; Li, Chuandong; He, Xing; Li, Hongfei

2018-01-01

This paper investigates the finite-time synchronization of complex networks (CNs) with non-identical nodes and impulsive disturbances. By utilizing stability theories, new 1-norm-based analytical techniques and suitable comparison, systems, several sufficient conditions are obtained to realize the synchronization goal in finite time. State feedback controllers with and without the sign function are designed. Results show that the controllers with sign function can reduce the conservativeness of control gains and the controllers without sign function can overcome the chattering phenomenon. Numerical simulations are offered to verify the effectiveness of the theoretical analysis.

Numerical simulation for solution of space-time fractional telegraphs equations with local fractional derivatives via HAFSTM

NASA Astrophysics Data System (ADS)

Pandey, Rishi Kumar; Mishra, Hradyesh Kumar

2017-11-01

In this paper, the semi-analytic numerical technique for the solution of time-space fractional telegraph equation is applied. This numerical technique is based on coupling of the homotopy analysis method and sumudu transform. It shows the clear advantage with mess methods like finite difference method and also with polynomial methods similar to perturbation and Adomian decomposition methods. It is easily transform the complex fractional order derivatives in simple time domain and interpret the results in same meaning.

An Artificial Neural Networks Method for Solving Partial Differential Equations

NASA Astrophysics Data System (ADS)

Alharbi, Abir

2010-09-01

While there already exists many analytical and numerical techniques for solving PDEs, this paper introduces an approach using artificial neural networks. The approach consists of a technique developed by combining the standard numerical method, finite-difference, with the Hopfield neural network. The method is denoted Hopfield-finite-difference (HFD). The architecture of the nets, energy function, updating equations, and algorithms are developed for the method. The HFD method has been used successfully to approximate the solution of classical PDEs, such as the Wave, Heat, Poisson and the Diffusion equations, and on a system of PDEs. The software Matlab is used to obtain the results in both tabular and graphical form. The results are similar in terms of accuracy to those obtained by standard numerical methods. In terms of speed, the parallel nature of the Hopfield nets methods makes them easier to implement on fast parallel computers while some numerical methods need extra effort for parallelization.

Numerical Solution of the Kzk Equation for Pulsed Finite Amplitude Sound Beams in Thermoviscous Fluids

NASA Astrophysics Data System (ADS)

Lee, Yang-Sub

A time-domain numerical algorithm for solving the KZK (Khokhlov-Zabolotskaya-Kuznetsov) nonlinear parabolic wave equation is developed for pulsed, axisymmetric, finite amplitude sound beams in thermoviscous fluids. The KZK equation accounts for the combined effects of diffraction, absorption, and nonlinearity at the same order of approximation. The accuracy of the algorithm is established via comparison with analytical solutions for several limiting cases, and with numerical results obtained from a widely used algorithm for solving the KZK equation in the frequency domain. The time domain algorithm is used to investigate waveform distortion and shock formation in directive sound beams radiated by pulsed circular piston sources. New results include predictions for the entire process of self-demodulation, and for the effect of frequency modulation on pulse envelope distortion. Numerical results are compared with measurements, and focused sources are investigated briefly.

Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

NASA Astrophysics Data System (ADS)

Malakar, Kanaya; Jemseena, V.; Kundu, Anupam; Vijay Kumar, K.; Sabhapandit, Sanjib; Majumdar, Satya N.; Redner, S.; Dhar, Abhishek

2018-04-01

We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady-state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady-state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain with an absorbing boundary condition at the origin. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verification of our analytical results.

Analytic-continuation approach to the resummation of divergent series in Rayleigh-Schrödinger perturbation theory

NASA Astrophysics Data System (ADS)

Mihálka, Zsuzsanna É.; Surján, Péter R.

2017-12-01

The method of analytic continuation is applied to estimate eigenvalues of linear operators from finite order results of perturbation theory even in cases when the latter is divergent. Given a finite number of terms E(k ),k =1 ,2 ,⋯M resulting from a Rayleigh-Schrödinger perturbation calculation, scaling these numbers by μk (μ being the perturbation parameter) we form the sum E (μ ) =∑kμkE(k ) for small μ values for which the finite series is convergent to a certain numerical accuracy. Extrapolating the function E (μ ) to μ =1 yields an estimation of the exact solution of the problem. For divergent series, this procedure may serve as resummation tool provided the perturbation problem has a nonzero radius of convergence. As illustrations, we treat the anharmonic (quartic) oscillator and an example from the many-electron correlation problem.

Finite-temperature dynamics of the Mott insulating Hubbard chain

NASA Astrophysics Data System (ADS)

Nocera, Alberto; Essler, Fabian H. L.; Feiguin, Adrian E.

2018-01-01

We study the dynamical response of the half-filled one-dimensional Hubbard model for a range of interaction strengths U and temperatures T by a combination of numerical and analytical techniques. Using time-dependent density matrix renormalization group computations we find that the single-particle spectral function undergoes a crossover to a spin-incoherent Luttinger liquid regime at temperatures T ˜J =4 t2/U for sufficiently large U >4 t . At smaller values of U and elevated temperatures the spectral function is found to exhibit two thermally broadened bands of excitations, reminiscent of what is found in the Hubbard-I approximation. The dynamical density-density response function is shown to exhibit a finite-temperature resonance at low frequencies inside the Mott gap, with a physical origin similar to the Villain mode in gapped quantum spin chains. We complement our numerical computations by developing an analytic strong-coupling approach to the low-temperature dynamics in the spin-incoherent regime.

Modal element method for potential flow in non-uniform ducts: Combining closed form analysis with CFD

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Baumeister, Joseph F.

1994-01-01

An analytical procedure is presented, called the modal element method, that combines numerical grid based algorithms with eigenfunction expansions developed by separation of variables. A modal element method is presented for solving potential flow in a channel with two-dimensional cylindrical like obstacles. The infinite computational region is divided into three subdomains; the bounded finite element domain, which is characterized by the cylindrical obstacle and the surrounding unbounded uniform channel entrance and exit domains. The velocity potential is represented approximately in the grid based domain by a finite element solution and is represented analytically by an eigenfunction expansion in the uniform semi-infinite entrance and exit domains. The calculated flow fields are in excellent agreement with exact analytical solutions. By eliminating the grid surrounding the obstacle, the modal element method reduces the numerical grid size, employs a more precise far field boundary condition, as well as giving theoretical insight to the interaction of the obstacle with the mean flow. Although the analysis focuses on a specific geometry, the formulation is general and can be applied to a variety of problems as seen by a comparison to companion theories in aeroacoustics and electromagnetics.

Nonlinear resonances in the ABC-flow

NASA Astrophysics Data System (ADS)

Didov, A. A.; Uleysky, M. Yu.

2018-01-01

In this paper, we study resonances of the ABC-flow in the near integrable case ( C ≪1 ). This is an interesting example of a Hamiltonian system with 3/2 degrees of freedom in which simultaneous existence of two resonances of the same order is possible. Analytical conditions of the resonance existence are received. It is shown numerically that the largest n :1 (n = 1, 2, 3) resonances exist, and their energies are equal to theoretical energies in the near integrable case. We provide analytical and numerical evidences for existence of two branches of the two largest n :1 (n = 1, 2) resonances in the region of finite motion.

Curved Thermopiezoelectric Shell Structures Modeled by Finite Element Analysis

NASA Technical Reports Server (NTRS)

Lee, Ho-Jun

2000-01-01

"Smart" structures composed of piezoelectric materials may significantly improve the performance of aeropropulsion systems through a variety of vibration, noise, and shape-control applications. The development of analytical models for piezoelectric smart structures is an ongoing, in-house activity at the NASA Glenn Research Center at Lewis Field focused toward the experimental characterization of these materials. Research efforts have been directed toward developing analytical models that account for the coupled mechanical, electrical, and thermal response of piezoelectric composite materials. Current work revolves around implementing thermal effects into a curvilinear-shell finite element code. This enhances capabilities to analyze curved structures and to account for coupling effects arising from thermal effects and the curved geometry. The current analytical model implements a unique mixed multi-field laminate theory to improve computational efficiency without sacrificing accuracy. The mechanics can model both the sensory and active behavior of piezoelectric composite shell structures. Finite element equations are being implemented for an eight-node curvilinear shell element, and numerical studies are being conducted to demonstrate capabilities to model the response of curved piezoelectric composite structures (see the figure).

Large-amplitude nonlinear normal modes of the discrete sine lattices.

PubMed

Smirnov, Valeri V; Manevitch, Leonid I

2017-02-01

We present an analytical description of the large-amplitude stationary oscillations of the finite discrete system of harmonically coupled pendulums without any restrictions on their amplitudes (excluding a vicinity of π). Although this model has numerous applications in different fields of physics, it was studied earlier in the infinite limit only. The discrete chain with a finite length can be considered as a well analytical analog of the coarse-grain models of flexible polymers in the molecular dynamics simulations. The developed approach allows to find the dispersion relations for arbitrary amplitudes of the nonlinear normal modes. We emphasize that the long-wavelength approximation, which is described by well-known sine-Gordon equation, leads to an inadequate zone structure for the amplitudes of about π/2 even if the chain is long enough. An extremely complex zone structure at the large amplitudes corresponds to multiple resonances between nonlinear normal modes even with strongly different wave numbers. Due to the complexity of the dispersion relations the modes with shorter wavelengths may have smaller frequencies. The stability of the nonlinear normal modes under condition of the resonant interaction are discussed. It is shown that this interaction of the modes in the vicinity of the long wavelength edge of the spectrum leads to the localization of the oscillations. The thresholds of instability and localization are determined explicitly. The numerical simulation of the dynamics of a finite-length chain is in a good agreement with obtained analytical predictions.

Rotational degree-of-freedom synthesis: An optimised finite difference method for non-exact data

NASA Astrophysics Data System (ADS)

Gibbons, T. J.; Öztürk, E.; Sims, N. D.

2018-01-01

Measuring the rotational dynamic behaviour of a structure is important for many areas of dynamics such as passive vibration control, acoustics, and model updating. Specialist and dedicated equipment is often needed, unless the rotational degree-of-freedom is synthesised based upon translational data. However, this involves numerically differentiating the translational mode shapes to approximate the rotational modes, for example using a finite difference algorithm. A key challenge with this approach is choosing the measurement spacing between the data points, an issue which has often been overlooked in the published literature. The present contribution will for the first time prove that the use of a finite difference approach can be unstable when using non-exact measured data and a small measurement spacing, for beam-like structures. Then, a generalised analytical error analysis is used to propose an optimised measurement spacing, which balances the numerical error of the finite difference equation with the propagation error from the perturbed data. The approach is demonstrated using both numerical and experimental investigations. It is shown that by obtaining a small number of test measurements it is possible to optimise the measurement accuracy, without any further assumptions on the boundary conditions of the structure.

Analytical Modeling of a Novel Transverse Flux Machine for Direct Drive Wind Turbine Applications: Preprint

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

Hasan, IIftekhar; Husain, Tausif; Uddin, Md Wasi

2015-08-24

This paper presents a nonlinear analytical model of a novel double-sided flux concentrating Transverse Flux Machine (TFM) based on the Magnetic Equivalent Circuit (MEC) model. The analytical model uses a series-parallel combination of flux tubes to predict the flux paths through different parts of the machine including air gaps, permanent magnets, stator, and rotor. The two-dimensional MEC model approximates the complex three-dimensional flux paths of the TFM and includes the effects of magnetic saturation. The model is capable of adapting to any geometry that makes it a good alternative for evaluating prospective designs of TFM compared to finite element solversmore » that are numerically intensive and require more computation time. A single-phase, 1-kW, 400-rpm machine is analytically modeled, and its resulting flux distribution, no-load EMF, and torque are verified with finite element analysis. The results are found to be in agreement, with less than 5% error, while reducing the computation time by 25 times.« less

Analytical Modeling of a Novel Transverse Flux Machine for Direct Drive Wind Turbine Applications

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

Hasan, IIftekhar; Husain, Tausif; Uddin, Md Wasi

2015-09-02

This paper presents a nonlinear analytical model of a novel double sided flux concentrating Transverse Flux Machine (TFM) based on the Magnetic Equivalent Circuit (MEC) model. The analytical model uses a series-parallel combination of flux tubes to predict the flux paths through different parts of the machine including air gaps, permanent magnets (PM), stator, and rotor. The two-dimensional MEC model approximates the complex three-dimensional flux paths of the TFM and includes the effects of magnetic saturation. The model is capable of adapting to any geometry which makes it a good alternative for evaluating prospective designs of TFM as compared tomore » finite element solvers which are numerically intensive and require more computation time. A single phase, 1 kW, 400 rpm machine is analytically modeled and its resulting flux distribution, no-load EMF and torque, verified with Finite Element Analysis (FEA). The results are found to be in agreement with less than 5% error, while reducing the computation time by 25 times.« less

Approximate Solutions for Ideal Dam-Break Sediment-Laden Flows on Uniform Slopes

NASA Astrophysics Data System (ADS)

Ni, Yufang; Cao, Zhixian; Borthwick, Alistair; Liu, Qingquan

2018-04-01

Shallow water hydro-sediment-morphodynamic (SHSM) models have been applied increasingly widely in hydraulic engineering and geomorphological studies over the past few decades. Analytical and approximate solutions are usually sought to verify such models and therefore confirm their credibility. Dam-break flows are often evoked because such flows normally feature shock waves and contact discontinuities that warrant refined numerical schemes to solve. While analytical and approximate solutions to clear-water dam-break flows have been available for some time, such solutions are rare for sediment transport in dam-break flows. Here we aim to derive approximate solutions for ideal dam-break sediment-laden flows resulting from the sudden release of a finite volume of frictionless, incompressible water-sediment mixture on a uniform slope. The approximate solutions are presented for three typical sediment transport scenarios, i.e., pure advection, pure sedimentation, and concurrent entrainment and deposition. Although the cases considered in this paper are not real, the approximate solutions derived facilitate suitable benchmark tests for evaluating SHSM models, especially presently when shock waves can be numerically resolved accurately with a suite of finite volume methods, while the accuracy of the numerical solutions of contact discontinuities in sediment transport remains generally poorer.

Hybrid Numerical-Analytical Scheme for Calculating Elastic Wave Diffraction in Locally Inhomogeneous Waveguides

NASA Astrophysics Data System (ADS)

Glushkov, E. V.; Glushkova, N. V.; Evdokimov, A. A.

2018-01-01

Numerical simulation of traveling wave excitation, propagation, and diffraction in structures with local inhomogeneities (obstacles) is computationally expensive due to the need for mesh-based approximation of extended domains with the rigorous account for the radiation conditions at infinity. Therefore, hybrid numerical-analytic approaches are being developed based on the conjugation of a numerical solution in a local vicinity of the obstacle and/or source with an explicit analytic representation in the remaining semi-infinite external domain. However, in standard finite-element software, such a coupling with the external field, moreover, in the case of multimode expansion, is generally not provided. This work proposes a hybrid computational scheme that allows realization of such a conjugation using a standard software. The latter is used to construct a set of numerical solutions used as the basis for the sought solution in the local internal domain. The unknown expansion coefficients on this basis and on normal modes in the semi-infinite external domain are then determined from the conditions of displacement and stress continuity at the boundary between the two domains. We describe the implementation of this approach in the scalar and vector cases. To evaluate the reliability of the results and the efficiency of the algorithm, we compare it with a semianalytic solution to the problem of traveling wave diffraction by a horizontal obstacle, as well as with a finite-element solution obtained for a limited domain artificially restricted using absorbing boundaries. As an example, we consider the incidence of a fundamental antisymmetric Lamb wave onto surface and partially submerged elastic obstacles. It is noted that the proposed hybrid scheme can also be used to determine the eigenfrequencies and eigenforms of resonance scattering, as well as the characteristics of traveling waves in embedded waveguides.

Aerodynamic parameter studies and sensitivity analysis for rotor blades in axial flight

NASA Technical Reports Server (NTRS)

Chiu, Y. Danny; Peters, David A.

1991-01-01

The analytical capability is offered for aerodynamic parametric studies and sensitivity analyses of rotary wings in axial flight by using a 3-D undistorted wake model in curved lifting line theory. The governing equations are solved by both the Multhopp Interpolation technique and the Vortex Lattice method. The singularity from the bound vortices is eliminated through the Hadamard's finite part concept. Good numerical agreement between both analytical methods and finite differences methods are found. Parametric studies were made to assess the effects of several shape variables on aerodynamic loads. It is found, e.g., that a rotor blade with out-of-plane and inplane curvature can theoretically increase lift in the inboard and outboard regions respectively without introducing an additional induced drag.

Analytical and numerical solutions of the potential and electric field generated by different electrode arrays in a tumor tissue under electrotherapy

PubMed Central

2011-01-01

Background Electrotherapy is a relatively well established and efficient method of tumor treatment. In this paper we focus on analytical and numerical calculations of the potential and electric field distributions inside a tumor tissue in a two-dimensional model (2D-model) generated by means of electrode arrays with shapes of different conic sections (ellipse, parabola and hyperbola). Methods Analytical calculations of the potential and electric field distributions based on 2D-models for different electrode arrays are performed by solving the Laplace equation, meanwhile the numerical solution is solved by means of finite element method in two dimensions. Results Both analytical and numerical solutions reveal significant differences between the electric field distributions generated by electrode arrays with shapes of circle and different conic sections (elliptic, parabolic and hyperbolic). Electrode arrays with circular, elliptical and hyperbolic shapes have the advantage of concentrating the electric field lines in the tumor. Conclusion The mathematical approach presented in this study provides a useful tool for the design of electrode arrays with different shapes of conic sections by means of the use of the unifying principle. At the same time, we verify the good correspondence between the analytical and numerical solutions for the potential and electric field distributions generated by the electrode array with different conic sections. PMID:21943385

Thermodynamic analysis of journal bearings operating under steady state loading in laminar regime. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Khonsari, M. M.

1983-01-01

Thermohydrodynamic effects in journal bearings operating under steady load in laminar regime are investigated. An analytical model for the finite and infinitely long journal bearings is formulated. The model includes correction factors for the cavitation effects in the unloaded region of the bearing and the mixing of the recirculating oil and supply oil at the oil inlet. A finite difference computer program is developed to numerically solve the governing equations of the continuity, Reynolds, energy, Laplace heat conduction, and a viscosity-temperature relation simultaneously. The program includes a numerical technique for obtaining an isothermal shaft temperature. The numerical results of temperature distribution and the heat effects on the bearing load carrying capacity agree closely with those of experimental findings. Several different sets of simpler boundary conditions for the energy equation are studied.

Arbitrary-order corrections for finite-time drift and diffusion coefficients

NASA Astrophysics Data System (ADS)

Anteneodo, C.; Riera, R.

2009-09-01

We address a standard class of diffusion processes with linear drift and quadratic diffusion coefficients. These contributions to dynamic equations can be directly drawn from data time series. However, real data are constrained to finite sampling rates and therefore it is crucial to establish a suitable mathematical description of the required finite-time corrections. Based on Itô-Taylor expansions, we present the exact corrections to the finite-time drift and diffusion coefficients. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments that furnish extra theoretical checks for this class of diffusion models. The analytical predictions are compared with the numerical outcomes of representative artificial time series.

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.

Nature of self-diffusion in two-dimensional fluids

NASA Astrophysics Data System (ADS)

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; Talkner, Peter; Kidera, Akinori; Lee, Eok Kyun

2017-12-01

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. We numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(t\\sqrt{{ln}t}), however with a rescaled time.

Geodynamics for Everyone: Robust Finite-Difference Heat Transfer Models using MS Excel 2007 Spreadsheets

NASA Astrophysics Data System (ADS)

Grose, C. J.

2008-05-01

Numerical geodynamics models of heat transfer are typically thought of as specialized topics of research requiring knowledge of specialized modelling software, linux platforms, and state-of-the-art finite-element codes. I have implemented analytical and numerical finite-difference techniques with Microsoft Excel 2007 spreadsheets to solve for complex solid-earth heat transfer problems for use by students, teachers, and practicing scientists without specialty in geodynamics modelling techniques and applications. While implementation of equations for use in Excel spreadsheets is occasionally cumbersome, once case boundary structure and node equations are developed, spreadsheet manipulation becomes routine. Model experimentation by modifying parameter values, geometry, and grid resolution makes Excel a useful tool whether in the classroom at the undergraduate or graduate level or for more engaging student projects. Furthermore, the ability to incorporate complex geometries and heat-transfer characteristics makes it ideal for first and occasionally higher order geodynamics simulations to better understand and constrain the results of professional field research in a setting that does not require the constraints of state-of-the-art modelling codes. The straightforward expression and manipulation of model equations in excel can also serve as a medium to better understand the confusing notations of advanced mathematical problems. To illustrate the power and robustness of computation and visualization in spreadsheet models I focus primarily on one-dimensional analytical and two-dimensional numerical solutions to two case problems: (i) the cooling of oceanic lithosphere and (ii) temperatures within subducting slabs. Excel source documents will be made available.

Flow through three-dimensional arrangements of cylinders with alternating streamwise planar tilt

NASA Astrophysics Data System (ADS)

Sahraoui, M.; Marshall, H.; Kaviany, M.

1993-09-01

In this report, fluid flow through a three-dimensional model for the fibrous filters is examined. In this model, the three-dimensional Stokes equation with the appropriate periodic boundary conditions is solved using the finite volume method. In addition to the numerical solution, we attempt to model this flow analytically by using the two-dimensional extended analytic solution in each of the unit cells of the three-dimensional structure. Particle trajectories computed using the superimposed analytic solution of the flow field are closed to those computed using the numerical solution of the flow field. The numerical results show that the pressure drop is not affected significantly by the relative angle of rotation of the cylinders for the high porosity used in this study (epsilon = 0.8 and epsilon = 0.95). The numerical solution and the superimposed analytic solution are also compared in terms of the particle capture efficiency. The results show that the efficiency predictions using the two methods are within 10% for St = 0.01 and 5% for St = 100. As the the porosity decreases, the three-dimensional effect becomes more significant and a difference of 35% is obtained for epsilon = 0.8.

Inertia-gravity wave radiation from the elliptical vortex in the f-plane shallow water system

NASA Astrophysics Data System (ADS)

Sugimoto, Norihiko

2017-04-01

Inertia-gravity wave (IGW) radiation from the elliptical vortex is investigated in the f-plane shallow water system. The far field of IGW is analytically derived for the case of an almost circular Kirchhoff vortex with a small aspect ratio. Cyclone-anticyclone asymmetry appears at finite values of the Rossby number (Ro) caused by the source originating in the Coriolis acceleration. While the intensity of IGWs from the cyclone monotonically decreases as f increases, that from the anticyclone increases as f increases for relatively smaller f and has a local maximum at intermediate f. A numerical experiment is conducted on a model using a spectral method in an unbounded domain. The numerical results agree quite well with the analytical ones for elliptical vortices with small aspect ratios, implying that the derived analytical forms are useful for the verification of the numerical model. For elliptical vortices with larger aspect ratios, however, significant deviation from the analytical estimates appears. The intensity of IGWs radiated in the numerical simulation is larger than that estimated analytically. The reason is that the source of IGWs is amplified during the time evolution because the shape of the vortex changes from ideal ellipse to elongated with filaments. Nevertheless, cyclone-anticyclone asymmetry similar to the analytical estimate appears in all the range of aspect ratios, suggesting that this asymmetry is a robust feature.

Analytical solution of a stochastic model of risk spreading with global coupling

NASA Astrophysics Data System (ADS)

Morita, Satoru; Yoshimura, Jin

2013-11-01

We study a stochastic matrix model to understand the mechanics of risk spreading (or bet hedging) by dispersion. Up to now, this model has been mostly dealt with numerically, except for the well-mixed case. Here, we present an analytical result that shows that optimal dispersion leads to Zipf's law. Moreover, we found that the arithmetic ensemble average of the total growth rate converges to the geometric one, because the sample size is finite.

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

Vincenti, H.; Vay, J. -L.

Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the result. Such modifications for instance occur when Perfectly Matched Layers (PMLs) are used at simulation domain boundaries to simulate open media. Another example is the use of arbitrary order Maxwell solver with domain decomposition technique that may under some condition involve stencil truncations at subdomain boundaries, resulting in small spurious errors that do eventually build up. In each case, a careful evaluation of the characteristics and magnitude of themore » errors resulting from these approximations, and their impact at any frequency and angle, requires detailed analytical and numerical studies. To this end, we present a general analytical approach that enables the evaluation of numerical discretization errors of fully three-dimensional arbitrary order finite-difference Maxwell solver, with arbitrary modification of the local stencil in the simulation domain. The analytical model is validated against simulations of domain decomposition technique and PMLs, when these are used with very high-order Maxwell solver, as well as in the infinite order limit of pseudo-spectral solvers. Results confirm that the new analytical approach enables exact predictions in each case. It also confirms that the domain decomposition technique can be used with very high-order Maxwell solver and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.« less

Loading-unloading response of circular GLARE fiber-metal laminates under lateral indentation

NASA Astrophysics Data System (ADS)

Tsamasphyros, George J.; Bikakis, George S.

2015-01-01

GLARE is a Fiber-Metal laminated material used in aerospace structures which are frequently subjected to various impact damages. Hence, the response of GLARE plates subjected to lateral indentation is very important. In this paper, analytical expressions are derived and a non-linear finite element modeling procedure is proposed in order to predict the static load-indentation curves of circular GLARE plates during loading and unloading by a hemispherical indentor. We have recently published analytical formulas and a finite element procedure for the static indentation of circular GLARE plates which are now used during the loading stage. Here, considering that aluminum layers are in a state of membrane yield and employing energy balance during unloading, the unloading path is determined. Using this unloading path, an algebraic equation is derived for calculating the permanent dent depth of the GLARE plate after the indentor's withdrawal. Furthermore, our finite element procedure is modified in order to simulate the unloading stage as well. The derived formulas and the proposed finite element modeling procedure are applied successfully to GLARE 2-2/1-0.3 and to GLARE 3-3/2-0.4 circular plates. The analytical results are compared with corresponding FEM results and a good agreement is found. The analytically calculated permanent dent depth is within 6 % for the GLARE 2 plate, and within 7 % for the GLARE 3 plate, of the corresponding numerically calculated result. No other solution of this problem is known to the authors.

Numerical solution of potential flow about arbitrary 2-dimensional multiple bodies

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Thames, F. C.

1982-01-01

A procedure for the finite-difference numerical solution of the lifting potential flow about any number of arbitrarily shaped bodies is given. The solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having coordinate lines coincident with the contours of all bodies in the field, regardless of their shapes and number. The effects of all numerical parameters involved are analyzed and appropriate values are recommended. Comparisons with analytic solutions for single Karman-Trefftz airfoils and a circular cylinder pair show excellent agreement. The technique of application of the boundary-fitted coordinate systems to the numerical solution of partial differential equations is illustrated.

Three-dimensional finite amplitude electroconvection in dielectric liquids

NASA Astrophysics Data System (ADS)

Luo, Kang; Wu, Jian; Yi, Hong-Liang; Tan, He-Ping

2018-02-01

Charge injection induced electroconvection in a dielectric liquid lying between two parallel plates is numerically simulated in three dimensions (3D) using a unified lattice Boltzmann method (LBM). Cellular flow patterns and their subcritical bifurcation phenomena of 3D electroconvection are numerically investigated for the first time. A unit conversion is also derived to connect the LBM system to the real physical system. The 3D LBM codes are validated by three carefully chosen cases and all results are found to be highly consistent with the analytical solutions or other numerical studies. For strong injection, the steady state roll, polygon, and square flow patterns are observed under different initial disturbances. Numerical results show that the hexagonal cell with the central region being empty of charge and centrally downward flow is preferred in symmetric systems under random initial disturbance. For weak injection, the numerical results show that the flow directly passes from the motionless state to turbulence once the system loses its linear stability. In addition, the numerically predicted linear and finite amplitude stability criteria of different flow patterns are discussed.

Estimation of the curvature of the solid liquid interface during Bridgman crystal growth

NASA Astrophysics Data System (ADS)

Barat, Catherine; Duffar, Thierry; Garandet, Jean-Paul

1998-11-01

An approximate solution for the solid/liquid interface curvature due to the crucible effect in crystal growth is derived from simple heat flux considerations. The numerical modelling of the problem carried out with the help of the finite element code FIDAP supports the predictions of our analytical expression and allows to identify its range of validity. Experimental interface curvatures, measured in gallium antimonide samples grown by the vertical Bridgman method, are seen to compare satisfactorily to analytical and numerical results. Other literature data are also in fair agreement with the predictions of our models in the case where the amount of heat carried by the crucible is small compared to the overall heat flux.

Transient well flow in layered aquifer systems: the uniform well-face drawdown solution

NASA Astrophysics Data System (ADS)

Hemker, C. J.

1999-11-01

Previously a hybrid analytical-numerical solution for the general problem of computing transient well flow in vertically heterogeneous aquifers was proposed by the author. The radial component of flow was treated analytically, while the finite-difference technique was used for the vertical flow component only. In the present work the hybrid solution has been modified by replacing the previously assumed uniform well-face gradient (UWG) boundary condition in such a way that the drawdown remains uniform along the well screen. The resulting uniform well-face drawdown (UWD) solution also includes the effects of a finite diameter well, wellbore storage and a thin skin, while partial penetration and vertical heterogeneity are accommodated by the one-dimensional discretization. Solutions are proposed for well flow caused by constant, variable and slug discharges. The model was verified by comparing wellbore drawdowns and well-face flux distributions with published numerical solutions. Differences between UWG and UWD well flow will occur in all situations with vertical flow components near the well, which is demonstrated by considering: (1) partially penetrating wells in confined aquifers, (2) fully penetrating wells in unconfined aquifers with delayed response and (3) layered aquifers and leaky multiaquifer systems. The presented solution can be a powerful tool for solving many well-hydraulic problems, including well tests, flowmeter tests, slug tests and pumping tests. A computer program for the analysis of pumping tests, based on the hybrid analytical-numerical technique and UWG or UWD conditions, is available from the author.

Torsional vibration of a cracked rod by variational formulation and numerical analysis

NASA Astrophysics Data System (ADS)

Chondros, T. G.; Labeas, G. N.

2007-04-01

The torsional vibration of a circumferentially cracked cylindrical shaft is studied through an "exact" analytical solution and a numerical finite element (FE) analysis. The Hu-Washizu-Barr variational formulation is used to develop the differential equation and the boundary conditions of the cracked rod. The equations of motion for a uniform cracked rod in torsional vibration are derived and solved, and the Rayleigh quotient is used to further approximate the natural frequencies of the cracked rod. Results for the problem of the torsional vibration of a cylindrical shaft with a peripheral crack are provided through an analytical solution based on variational formulation to derive the equation of motion and a numerical analysis utilizing a parametric three-dimensional (3D) solid FE model of the cracked rod. The crack is modelled as a continuous flexibility based on fracture mechanics principles. The variational formulation results are compared with the FE alternative. The sensitivity of the FE discretization with respect to the analytical results is assessed.

Novel permanent magnet linear motor with isolated movers: analytical, numerical and experimental study.

PubMed

Yan, Liang; Peng, Juanjuan; Jiao, Zongxia; Chen, Chin-Yin; Chen, I-Ming

2014-10-01

This paper proposes a novel permanent magnet linear motor possessing two movers and one stator. The two movers are isolated and can interact with the stator poles to generate independent forces and motions. Compared with conventional multiple motor driving system, it helps to increase the system compactness, and thus improve the power density and working efficiency. The magnetic field distribution is obtained by using equivalent magnetic circuit method. Following that, the formulation of force output considering armature reaction is carried out. Then inductances are analyzed with finite element method to investigate the relationships of the two movers. It is found that the mutual-inductances are nearly equal to zero, and thus the interaction between the two movers is negligible. A research prototype of the linear motor and a measurement apparatus on thrust force have been developed. Both numerical computation and experiment measurement are conducted to validate the analytical model of thrust force. Comparison shows that the analytical model matches the numerical and experimental results well.

Development and application of a three dimensional numerical model for predicting pollutant and sediment transport using an Eulerian-Lagrangian marker particle technique

NASA Technical Reports Server (NTRS)

Pavish, D. L.; Spaulding, M. L.

1977-01-01

A computer coded Lagrangian marker particle in Eulerian finite difference cell solution to the three dimensional incompressible mass transport equation, Water Advective Particle in Cell Technique, WAPIC, was developed, verified against analytic solutions, and subsequently applied in the prediction of long term transport of a suspended sediment cloud resulting from an instantaneous dredge spoil release. Numerical results from WAPIC were verified against analytic solutions to the three dimensional incompressible mass transport equation for turbulent diffusion and advection of Gaussian dye releases in unbounded uniform and uniformly sheared uni-directional flow, and for steady-uniform plug channel flow. WAPIC was utilized to simulate an analytic solution for non-equilibrium sediment dropout from an initially vertically uniform particle distribution in one dimensional turbulent channel flow.

Distribution of Steps with Finite-Range Interactions: Analytic Approximations and Numerical Results

NASA Astrophysics Data System (ADS)

GonzáLez, Diego Luis; Jaramillo, Diego Felipe; TéLlez, Gabriel; Einstein, T. L.

2013-03-01

While most Monte Carlo simulations assume only nearest-neighbor steps interact elastically, most analytic frameworks (especially the generalized Wigner distribution) posit that each step elastically repels all others. In addition to the elastic repulsions, we allow for possible surface-state-mediated interactions. We investigate analytically and numerically how next-nearest neighbor (NNN) interactions and, more generally, interactions out to q'th nearest neighbor alter the form of the terrace-width distribution and of pair correlation functions (i.e. the sum over n'th neighbor distribution functions, which we investigated recently.[2] For physically plausible interactions, we find modest changes when NNN interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

A Riemann-Hilbert formulation for the finite temperature Hubbard model

NASA Astrophysics Data System (ADS)

Cavaglià, Andrea; Cornagliotto, Martina; Mattelliano, Massimo; Tateo, Roberto

2015-06-01

Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are equivalent to a simple nonlinear Riemann-Hilbert problem for a finite number of unknown functions. The latter can be transformed into a set of three coupled nonlinear integral equations defined over a finite support, which can be easily solved numerically. We discuss the emergence of an exact Bethe Ansatz and the link between the TBA approach and the results by Jüttner, Klümper and Suzuki based on the Quantum Transfer Matrix method. We also comment on the analytic continuation mechanism leading to excited states and on the mirror equations describing the finite-size Hubbard model with twisted boundary conditions.

Slow Crack Growth Analysis of Brittle Materials with Finite Thickness Subjected to Constant Stress-Rate Flexural Loading

NASA Technical Reports Server (NTRS)

Chio, S. R.; Gyekenyesi, J. P.

1999-01-01

A two-dimensional, numerical analysis of slow crack growth (SCG) was performed for brittle materials with finite thickness subjected to constant stress-rate ("dynamic fatigue") loading in flexure. The numerical solution showed that the conventional, simple, one-dimensional analytical solution can be used with a maximum error of about 5% in determining the SCG parameters of a brittle material with the conditions of a normalized thickness (a ratio of specimen thickness to initial crack size) T > 3.3 and of a SCG parameter n > 10. The change in crack shape from semicircular to elliptical configurations was significant particularly at both low stress rate and low T, attributed to predominant difference in stress intensity factor along the crack front. The numerical solution of SCG parameters was supported within the experimental range by the data obtained from constant stress-rate flexural testing for soda-lime glass microslides at ambient temperature.

Comprehensive Numerical Analysis of Finite Difference Time Domain Methods for Improving Optical Waveguide Sensor Accuracy

PubMed Central

Samak, M. Mosleh E. Abu; Bakar, A. Ashrif A.; Kashif, Muhammad; Zan, Mohd Saiful Dzulkifly

2016-01-01

This paper discusses numerical analysis methods for different geometrical features that have limited interval values for typically used sensor wavelengths. Compared with existing Finite Difference Time Domain (FDTD) methods, the alternating direction implicit (ADI)-FDTD method reduces the number of sub-steps by a factor of two to three, which represents a 33% time savings in each single run. The local one-dimensional (LOD)-FDTD method has similar numerical equation properties, which should be calculated as in the previous method. Generally, a small number of arithmetic processes, which result in a shorter simulation time, are desired. The alternating direction implicit technique can be considered a significant step forward for improving the efficiency of unconditionally stable FDTD schemes. This comparative study shows that the local one-dimensional method had minimum relative error ranges of less than 40% for analytical frequencies above 42.85 GHz, and the same accuracy was generated by both methods.

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.

Analytical Solutions for the Surface States of Bi1-xSbx (0 ≤ x ≲ 0.1)

NASA Astrophysics Data System (ADS)

Fuseya, Yuki; Fukuyama, Hidetoshi

2018-04-01

Analytical solutions for the surface state (SS) of an extended Wolff Hamiltonian, which is a common Hamiltonian for strongly spin-orbit coupled systems, are obtained both for semi-infinite and finite-thickness boundary conditions. For the semi-infinite system, there are two types of SS solutions: (I-a) linearly crossing SSs in the direct bulk band gap, and (I-b) SSs with linear dispersions entering the bulk conduction or valence bands away from the band edge. For the finite-thickness system, a gap opens in the SS of solution I-a. Numerical solutions for the SS are also obtained based on the tight-binding model of Liu and Allen [Phys. Rev. B 52, 1566 (1995)] for Bi1-xSbx (0 ≤ x ≤ 0.1). A perfect correspondence between the analytic and numerical solutions is obtained around the \\bar{M} point including their thickness dependence. This is the first time that the character of the SS numerically obtained is identified with the help of analytical solutions. The size of the gap for I-a SS can be larger than that of bulk band gap even for a "thick" films ( ≲ 200 bilayers ≃ 80 nm) of pure bismuth. Consequently, in such a film of Bi1-xSbx, there is no apparent change in the SSs through the band inversion at x ≃ 0.04, even though the nature of the SS is changed from solution I-a to I-b. Based on our theoretical results, the experimental results on the SS of Bi1-xSbx (0 ≤ x ≲ 0.1) are discussed.

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; D'Costa, Joseph F.

1991-01-01

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

Modeling of Compressible Flow with Friction and Heat Transfer Using the Generalized Fluid System Simulation Program (GFSSP)

NASA Technical Reports Server (NTRS)

Bandyopadhyay, Alak; Majumdar, Alok

2007-01-01

The present paper describes the verification and validation of a quasi one-dimensional pressure based finite volume algorithm, implemented in Generalized Fluid System Simulation Program (GFSSP), for predicting compressible flow with friction, heat transfer and area change. The numerical predictions were compared with two classical solutions of compressible flow, i.e. Fanno and Rayleigh flow. Fanno flow provides an analytical solution of compressible flow in a long slender pipe where incoming subsonic flow can be choked due to friction. On the other hand, Raleigh flow provides analytical solution of frictionless compressible flow with heat transfer where incoming subsonic flow can be choked at the outlet boundary with heat addition to the control volume. Nonuniform grid distribution improves the accuracy of numerical prediction. A benchmark numerical solution of compressible flow in a converging-diverging nozzle with friction and heat transfer has been developed to verify GFSSP's numerical predictions. The numerical predictions compare favorably in all cases.

A new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

NASA Astrophysics Data System (ADS)

Yi, Dake; Wang, TzuChiang

2018-06-01

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J( z), the stress intensity factor K( z) and the tri-axial stress constraint level T z ( z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J( z) and T z ( z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.

A time-spectral approach to numerical weather prediction

NASA Astrophysics Data System (ADS)

Scheffel, Jan; Lindvall, Kristoffer; Yik, Hiu Fai

2018-05-01

Finite difference methods are traditionally used for modelling the time domain in numerical weather prediction (NWP). Time-spectral solution is an attractive alternative for reasons of accuracy and efficiency and because time step limitations associated with causal CFL-like criteria, typical for explicit finite difference methods, are avoided. In this work, the Lorenz 1984 chaotic equations are solved using the time-spectral algorithm GWRM (Generalized Weighted Residual Method). Comparisons of accuracy and efficiency are carried out for both explicit and implicit time-stepping algorithms. It is found that the efficiency of the GWRM compares well with these methods, in particular at high accuracy. For perturbative scenarios, the GWRM was found to be as much as four times faster than the finite difference methods. A primary reason is that the GWRM time intervals typically are two orders of magnitude larger than those of the finite difference methods. The GWRM has the additional advantage to produce analytical solutions in the form of Chebyshev series expansions. The results are encouraging for pursuing further studies, including spatial dependence, of the relevance of time-spectral methods for NWP modelling.

Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law

NASA Astrophysics Data System (ADS)

Želi, Velibor; Zorica, Dušan

2018-02-01

Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams-Bashforth and Grünwald-Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws.

Numerical evaluation of implantable hearing devices using a finite element model of human ear considering viscoelastic properties.

PubMed

Zhang, Jing; Tian, Jiabin; Ta, Na; Huang, Xinsheng; Rao, Zhushi

2016-08-01

Finite element method was employed in this study to analyze the change in performance of implantable hearing devices due to the consideration of soft tissues' viscoelasticity. An integrated finite element model of human ear including the external ear, middle ear and inner ear was first developed via reverse engineering and analyzed by acoustic-structure-fluid coupling. Viscoelastic properties of soft tissues in the middle ear were taken into consideration in this model. The model-derived dynamic responses including middle ear and cochlea functions showed a better agreement with experimental data at high frequencies above 3000 Hz than the Rayleigh-type damping. On this basis, a coupled finite element model consisting of the human ear and a piezoelectric actuator attached to the long process of incus was further constructed. Based on the electromechanical coupling analysis, equivalent sound pressure and power consumption of the actuator corresponding to viscoelasticity and Rayleigh damping were calculated using this model. The analytical results showed that the implant performance of the actuator evaluated using a finite element model considering viscoelastic properties gives a lower output above about 3 kHz than does Rayleigh damping model. Finite element model considering viscoelastic properties was more accurate to numerically evaluate implantable hearing devices. © IMechE 2016.

Solutions of the Bethe ansatz equations for XXX antiferromagnet of arbitrary spin in the case of a finite number of sites

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

Avdeev, L.V.; Doerfel, B.D.

1987-11-01

The exactly integrable isotropic Heisenberg chain of N spins s is studied, and numerical solutions to the Bethe ansatz equations corresponding to the antiferromagnetic vacuum (for sN less than or equal to 128) and the simplest excitations have been obtained. For s = 1, a complete set of states for N = 6 is given, and the vacuum solution for finite N is estimated analytically. The deviations from the string picture at large N are discussed.

Analytical, numerical, and experimental investigations on effective mechanical properties and performances of carbon nanotubes and nanotube based nanocomposites with novel three dimensional nanostructures

NASA Astrophysics Data System (ADS)

Askari, Davood

The theoretical objectives and accomplishment of this work are the analytical and numerical investigation of material properties and mechanical behavior of carbon nanotubes (CNTs) and nanotube nanocomposites when they are subjected to various loading conditions. First, the finite element method is employed to investigate numerically the effective Young's modulus and Poisson's ratio of a single-walled CNT. Next, the effects of chirality on the effective Young's modulus and Poisson's ratio are investigated and then variations of their effective coefficient of thermal expansions and effective thermal conductivities are studied for CNTs with different structural configurations. To study the influence of small vacancy defects on mechanical properties of CNTs, finite element analyses are performed and the behavior of CNTs with various structural configurations having different types of vacancy defects is studied. It is frequently reported that nano-materials are excellent candidates as reinforcements in nanocomposites to change or enhance material properties of polymers and their nanocomposites. Second, the inclusion of nano-materials can considerably improve electrical, thermal, and mechanical properties of the bonding agent, i.e., resin. Note that, materials atomic and molecular level do not usually show isotropic behaviour, rather they have orthotropic properties. Therefore, two-phase and three-phase cylindrically orthotropic composite models consisting of different constituents with orthotropic properties are developed and introduced in this work to analytically predict the effective mechanical properties and mechanical behavior of such structures when they are subjected to various external loading conditions. To verify the analytically obtained exact solutions, finite element analyses of identical cylindrical structures are also performed and then results are compared with those obtained analytically, and excellent agreement is achieved. The third part of this dissertation investigates the growth of vertically aligned, long, and high density arrays of CNTs and novel 3-D carbon nanotube nano-forests. A Chemical vapor deposition technique is used to grow radially aligned CNTs on various types of fibrous materials such as silicon carbide, carbon, Kevlar, and glass fibers and clothes that can be used for the fabrication of multifunctional high performing laminated nanocomposite structures. Using the CNTs nano-forest clothes, nanocomposite samples are prepared and tested giving promising results for the improvement of mechanical properties and performance of composites structures.

Verification of a magnetic island in gyro-kinetics by comparison with analytic theory

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

Zarzoso, D., E-mail: david.zarzoso-fernandez@polytechnique.org; Casson, F. J.; Poli, E.

A rotating magnetic island is imposed in the gyrokinetic code GKW, when finite differences are used for the radial direction, in order to develop the predictions of analytic tearing mode theory and understand its limitations. The implementation is verified against analytics in sheared slab geometry with three numerical tests that are suggested as benchmark cases for every code that imposes a magnetic island. The convergence requirements to properly resolve physics around the island separatrix are investigated. In the slab geometry, at low magnetic shear, binormal flows inside the island can drive Kelvin-Helmholtz instabilities which prevent the formation of the steadymore » state for which the analytic theory is formulated.« less

Push Force Analysis of Anchor Block of the Oil and Gas Pipeline in a Single-Slope Tunnel Based on the Energy Balance Method

PubMed Central

Yan, Yifei; Zhang, Lisong; Yan, Xiangzhen

2016-01-01

In this paper, a single-slope tunnel pipeline was analysed considering the effects of vertical earth pressure, horizontal soil pressure, inner pressure, thermal expansion force and pipeline—soil friction. The concept of stagnation point for the pipeline was proposed. Considering the deformation compatibility condition of the pipeline elbow, the push force of anchor blocks of a single-slope tunnel pipeline was derived based on an energy method. Then, the theoretical formula for this force is thus generated. Using the analytical equation, the push force of the anchor block of an X80 large-diameter pipeline from the West—East Gas Transmission Project was determined. Meanwhile, to verify the results of the analytical method, and the finite element method, four categories of finite element codes were introduced to calculate the push force, including CAESARII, ANSYS, AutoPIPE and ALGOR. The results show that the analytical results agree well with the numerical results, and the maximum relative error is only 4.1%. Therefore, the results obtained with the analytical method can satisfy engineering requirements. PMID:26963097

Mechanics of additively manufactured porous biomaterials based on the rhombicuboctahedron unit cell.

PubMed

Hedayati, R; Sadighi, M; Mohammadi-Aghdam, M; Zadpoor, A A

2016-01-01

Thanks to recent developments in additive manufacturing techniques, it is now possible to fabricate porous biomaterials with arbitrarily complex micro-architectures. Micro-architectures of such biomaterials determine their physical and biological properties, meaning that one could potentially improve the performance of such biomaterials through rational design of micro-architecture. The relationship between the micro-architecture of porous biomaterials and their physical and biological properties has therefore received increasing attention recently. In this paper, we studied the mechanical properties of porous biomaterials made from a relatively unexplored unit cell, namely rhombicuboctahedron. We derived analytical relationships that relate the micro-architecture of such porous biomaterials, i.e. the dimensions of the rhombicuboctahedron unit cell, to their elastic modulus, Poisson's ratio, and yield stress. Finite element models were also developed to validate the analytical solutions. Analytical and numerical results were compared with experimental data from one of our recent studies. It was found that analytical solutions and numerical results show a very good agreement particularly for smaller values of apparent density. The elastic moduli predicted by analytical and numerical models were in very good agreement with experimental observations too. While in excellent agreement with each other, analytical and numerical models somewhat over-predicted the yield stress of the porous structures as compared to experimental data. As the ratio of the vertical struts to the inclined struts, α, approaches zero and infinity, the rhombicuboctahedron unit cell respectively approaches the octahedron (or truncated cube) and cube unit cells. For those limits, the analytical solutions presented here were found to approach the analytic solutions obtained for the octahedron, truncated cube, and cube unit cells, meaning that the presented solutions are generalizations of the analytical solutions obtained for several other types of porous biomaterials. Copyright © 2015 Elsevier Ltd. All rights reserved.

Numerical analysis of the angular motion of a neutrally buoyant spheroid in shear flow at small Reynolds numbers.

PubMed

Rosén, T; Einarsson, J; Nordmark, A; Aidun, C K; Lundell, F; Mehlig, B

2015-12-01

We numerically analyze the rotation of a neutrally buoyant spheroid in a shear flow at small shear Reynolds number. Using direct numerical stability analysis of the coupled nonlinear particle-flow problem, we compute the linear stability of the log-rolling orbit at small shear Reynolds number Re(a). As Re(a)→0 and as the box size of the system tends to infinity, we find good agreement between the numerical results and earlier analytical predictions valid to linear order in Re(a) for the case of an unbounded shear. The numerical stability analysis indicates that there are substantial finite-size corrections to the analytical results obtained for the unbounded system. We also compare the analytical results to results of lattice Boltzmann simulations to analyze the stability of the tumbling orbit at shear Reynolds numbers of order unity. Theory for an unbounded system at infinitesimal shear Reynolds number predicts a bifurcation of the tumbling orbit at aspect ratio λ(c)≈0.137 below which tumbling is stable (as well as log rolling). The simulation results show a bifurcation line in the λ-Re(a) plane that reaches λ≈0.1275 at the smallest shear Reynolds number (Re(a)=1) at which we could simulate with the lattice Boltzmann code, in qualitative agreement with the analytical results.

Solidification of a binary alloy: Finite-element, single-domain simulation and new benchmark solutions

NASA Astrophysics Data System (ADS)

Le Bars, Michael; Worster, M. Grae

2006-07-01

A finite-element simulation of binary alloy solidification based on a single-domain formulation is presented and tested. Resolution of phase change is first checked by comparison with the analytical results of Worster [M.G. Worster, Solidification of an alloy from a cooled boundary, J. Fluid Mech. 167 (1986) 481-501] for purely diffusive solidification. Fluid dynamical processes without phase change are then tested by comparison with previous numerical studies of thermal convection in a pure fluid [G. de Vahl Davis, Natural convection of air in a square cavity: a bench mark numerical solution, Int. J. Numer. Meth. Fluids 3 (1983) 249-264; D.A. Mayne, A.S. Usmani, M. Crapper, h-adaptive finite element solution of high Rayleigh number thermally driven cavity problem, Int. J. Numer. Meth. Heat Fluid Flow 10 (2000) 598-615; D.C. Wan, B.S.V. Patnaik, G.W. Wei, A new benchmark quality solution for the buoyancy driven cavity by discrete singular convolution, Numer. Heat Transf. 40 (2001) 199-228], in a porous medium with a constant porosity [G. Lauriat, V. Prasad, Non-darcian effects on natural convection in a vertical porous enclosure, Int. J. Heat Mass Transf. 32 (1989) 2135-2148; P. Nithiarasu, K.N. Seetharamu, T. Sundararajan, Natural convective heat transfer in an enclosure filled with fluid saturated variable porosity medium, Int. J. Heat Mass Transf. 40 (1997) 3955-3967] and in a mixed liquid-porous medium with a spatially variable porosity [P. Nithiarasu, K.N. Seetharamu, T. Sundararajan, Natural convective heat transfer in an enclosure filled with fluid saturated variable porosity medium, Int. J. Heat Mass Transf. 40 (1997) 3955-3967; N. Zabaras, D. Samanta, A stabilized volume-averaging finite element method for flow in porous media and binary alloy solidification processes, Int. J. Numer. Meth. Eng. 60 (2004) 1103-1138]. Finally, new benchmark solutions for simultaneous flow through both fluid and porous domains and for convective solidification processes are presented, based on the similarity solutions in corner-flow geometries recently obtained by Le Bars and Worster [M. Le Bars, M.G. Worster, Interfacial conditions between a pure fluid and a porous medium: implications for binary alloy solidification, J. Fluid Mech. (in press)]. Good agreement is found for all tests, hence validating our physical and numerical methods. More generally, the computations presented here could now be considered as standard and reliable analytical benchmarks for numerical simulations, specifically and independently testing the different processes underlying binary alloy solidification.

Mathematical, Constitutive and Numerical Modelling of Catastrophic Landslides and Related Phenomena

NASA Astrophysics Data System (ADS)

Pastor, M.; Fernández Merodo, J. A.; Herreros, M. I.; Mira, P.; González, E.; Haddad, B.; Quecedo, M.; Tonni, L.; Drempetic, V.

2008-02-01

Mathematical and numerical models are a fundamental tool for predicting the behaviour of geostructures and their interaction with the environment. The term “mathematical model” refers to a mathematical description of the more relevant physical phenomena which take place in the problem being analyzed. It is indeed a wide area including models ranging from the very simple ones for which analytical solutions can be obtained to those more complicated requiring the use of numerical approximations such as the finite element method. During the last decades, mathematical, constitutive and numerical models have been very much improved and today their use is widespread both in industry and in research. One special case is that of fast catastrophic landslides, for which simplified methods are not able to provide accurate solutions in many occasions. Moreover, many finite element codes cannot be applied for propagation of the mobilized mass. The purpose of this work is to present an overview of the different alternative mathematical and numerical models which can be applied to both the initiation and propagation mechanisms of fast catastrophic landslides and other related problems such as waves caused by landslides.

Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: one-dimensional soil thaw with conduction and advection

USGS Publications Warehouse

Kurylyk, Barret L.; McKenzie, Jeffrey M; MacQuarrie, Kerry T. B.; Voss, Clifford I.

2014-01-01

Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.

Notch Sensitivity of Woven Ceramic Matrix Composites Under Tensile Loading: An Experimental, Analytical, and Finite Element Study

NASA Technical Reports Server (NTRS)

Haque, A.; Ahmed, L.; Ware, T.; Jeelani, S.; Verrilli, Michael J. (Technical Monitor)

2001-01-01

The stress concentrations associated with circular notches and subjected to uniform tensile loading in woven ceramic matrix composites (CMCs) have been investigated for high-efficient turbine engine applications. The CMC's were composed of Nicalon silicon carbide woven fabric in SiNC matrix manufactured through polymer impregnation process (PIP). Several combinations of hole diameter/plate width ratios and ply orientations were considered in this study. In the first part, the stress concentrations were calculated measuring strain distributions surrounding the hole using strain gages at different locations of the specimens during the initial portion of the stress-strain curve before any microdamage developed. The stress concentration was also calculated analytically using Lekhnitskii's solution for orthotropic plates. A finite-width correction factor for anisotropic and orthotropic composite plate was considered. The stress distributions surrounding the circular hole of a CMC's plate were further studied using finite element analysis. Both solid and shell elements were considered. The experimental results were compared with both the analytical and finite element solutions. Extensive optical and scanning electron microscopic examinations were carried out for identifying the fracture behavior and failure mechanisms of both the notched and notched specimens. The stress concentration factors (SCF) determined by analytical method overpredicted the experimental results. But the numerical solution underpredicted the experimental SCF. Stress concentration factors are shown to increase with enlarged hole size and the effects of ply orientations on stress concentration factors are observed to be negligible. In all the cases, the crack initiated at the notch edge and propagated along the width towards the edge of the specimens.

Implementation of Finite Volume based Navier Stokes Algorithm Within General Purpose Flow Network Code

NASA Technical Reports Server (NTRS)

Schallhorn, Paul; Majumdar, Alok

2012-01-01

This paper describes a finite volume based numerical algorithm that allows multi-dimensional computation of fluid flow within a system level network flow analysis. There are several thermo-fluid engineering problems where higher fidelity solutions are needed that are not within the capacity of system level codes. The proposed algorithm will allow NASA's Generalized Fluid System Simulation Program (GFSSP) to perform multi-dimensional flow calculation within the framework of GFSSP s typical system level flow network consisting of fluid nodes and branches. The paper presents several classical two-dimensional fluid dynamics problems that have been solved by GFSSP's multi-dimensional flow solver. The numerical solutions are compared with the analytical and benchmark solution of Poiseulle, Couette and flow in a driven cavity.

Blade loss transient dynamics analysis, volume 2. Task 2: Theoretical and analytical development. Task 3: Experimental verification

NASA Technical Reports Server (NTRS)

Gallardo, V. C.; Storace, A. S.; Gaffney, E. F.; Bach, L. J.; Stallone, M. J.

1981-01-01

The component element method was used to develop a transient dynamic analysis computer program which is essentially based on modal synthesis combined with a central, finite difference, numerical integration scheme. The methodology leads to a modular or building-block technique that is amenable to computer programming. To verify the analytical method, turbine engine transient response analysis (TETRA), was applied to two blade-out test vehicles that had been previously instrumented and tested. Comparison of the time dependent test data with those predicted by TETRA led to recommendations for refinement or extension of the analytical method to improve its accuracy and overcome its shortcomings. The development of working equations, their discretization, numerical solution scheme, the modular concept of engine modelling, the program logical structure and some illustrated results are discussed. The blade-loss test vehicles (rig full engine), the type of measured data, and the engine structural model are described.

Magnetic islands and singular currents at rational surfaces in three-dimensional magnetohydrodynamic equilibria

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

Loizu, J., E-mail: joaquim.loizu@ipp.mpg.de; Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton New Jersey 08543; Hudson, S.

2015-02-15

Using the recently developed multiregion, relaxed MHD (MRxMHD) theory, which bridges the gap between Taylor's relaxation theory and ideal MHD, we provide a thorough analytical and numerical proof of the formation of singular currents at rational surfaces in non-axisymmetric ideal MHD equilibria. These include the force-free singular current density represented by a Dirac δ-function, which presumably prevents the formation of islands, and the Pfirsch-Schlüter 1/x singular current, which arises as a result of finite pressure gradient. An analytical model based on linearized MRxMHD is derived that can accurately (1) describe the formation of magnetic islands at resonant rational surfaces, (2)more » retrieve the ideal MHD limit where magnetic islands are shielded, and (3) compute the subsequent formation of singular currents. The analytical results are benchmarked against numerical simulations carried out with a fully nonlinear implementation of MRxMHD.« less

Two-dimensional numerical simulation of a Stirling engine heat exchanger

NASA Technical Reports Server (NTRS)

Ibrahim, Mounir B.; Tew, Roy C.; Dudenhoefer, James E.

1989-01-01

The first phase of an effort to develop multidimensional models of Stirling engine components is described; the ultimate goal is to model an entire engine working space. More specifically, parallel plate and tubular heat exchanger models with emphasis on the central part of the channel (i.e., ignoring hydrodynamic and thermal end effects) are described. The model assumes: laminar, incompressible flow with constant thermophysical properties. In addition, a constant axial temperature gradient is imposed. The governing equations, describing the model, were solved using Crank-Nicloson finite-difference scheme. Model predictions were compared with analytical solutions for oscillating/reversing flow and heat transfer in order to check numerical accuracy. Excellent agreement was obtained for the model predictions with analytical solutions available for both flow in circular tubes and between parallel plates. Also the heat transfer computational results are in good agreement with the heat transfer analytical results for parallel plates.

Viscous damping and spring force in periodic perforated planar microstructures when the Reynolds’ equation cannot be applied

PubMed Central

Homentcovschi, Dorel; Miles, Ronald N.

2010-01-01

A model of squeeze-film behavior is developed based on Stokes’ equations for viscous, compressible isothermal flows. The flow domain is an axisymmetrical, unit cell approximation of a planar, periodic, perforated microstructure. The model is developed for cases when the lubrication approximation cannot be applied. The complex force generated by vibrations of the diaphragm driving the flow has two components: the damping force and the spring force. While for large frequencies the spring force dominates, at low (acoustical) frequencies the damping force is the most important part. The analytical approach developed here yields an explicit formula for both forces. In addition, using a finite element software package, the damping force is also obtained numerically. A comparison is made between the analytic result, numerical solution, and some experimental data found in the literature, which validates the analytic formula and provides compelling arguments about its value in designing microelectomechanical devices. PMID:20329828

Analytical study of nano-scale logical operations

NASA Astrophysics Data System (ADS)

Patra, Moumita; Maiti, Santanu K.

2018-07-01

A complete analytical prescription is given to perform three basic (OR, AND, NOT) and two universal (NAND, NOR) logic gates at nano-scale level using simple tailor made geometries. Two different geometries, ring-like and chain-like, are taken into account where in each case the bridging conductor is coupled to a local atomic site through a dangling bond whose site energy can be controlled by means of external gate electrode. The main idea is that when injecting electron energy matches with site energy of local atomic site transmission probability drops exactly to zero, whereas the junction exhibits finite transmission for other energies. Utilizing this prescription we perform logical operations, and, we strongly believe that the proposed results can be verified in laboratory. Finally, we numerically compute two-terminal transmission probability considering general models and the numerical results match exactly well with our analytical findings.

Interacting steps with finite-range interactions: Analytical approximation and numerical results

NASA Astrophysics Data System (ADS)

Jaramillo, Diego Felipe; Téllez, Gabriel; González, Diego Luis; Einstein, T. L.

2013-05-01

We calculate an analytical expression for the terrace-width distribution P(s) for an interacting step system with nearest- and next-nearest-neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent one-dimensional system of classical particles. The validity of the model is tested with several numerical simulations and experimental results. We explore the effect of the range of interactions q on the functional form of the terrace-width distribution and pair correlation functions. For physically plausible interactions, we find modest changes when next-nearest neighbor interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

A Combined FEM/MoM/GTD Technique To Analyze Elliptically Polarized Cavity-Backed Antennas With Finite Ground Plane

NASA Technical Reports Server (NTRS)

Reddy, C. J.; Deshpande, M. D.; Fralick, D. T.; Cockrell, C. R.; Beck, F. B.

1996-01-01

Radiation pattern prediction analysis of elliptically polarized cavity-backed aperture antennas in a finite ground plane is performed using a combined Finite Element Method/Method of Moments/Geometrical Theory of Diffraction (FEM/MoM/GTD) technique. The magnetic current on the cavity-backed aperture in an infinite ground plane is calculated using the combined FEM/MoM analysis. GTD, including the slope diffraction contribution, is used to calculate the diffracted fields caused by both soft and hard polarizations at the edges of the finite ground plane. Explicit expressions for regular diffraction coefficients and slope diffraction coefficients are presented. The slope of the incident magnetic field at the diffraction points is derived and analytical expressions are presented. Numerical results for the radiation patterns of a cavity-backed circular spiral microstrip patch antenna excited by a coaxial probe in a finite rectangular ground plane are computed and compared with experimental results.

Effect of finite particle number sampling on baryon number fluctuations

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

Steinheimer, Jan; Koch, Volker

The effects of finite particle number sampling on the net baryon number cumulants, extracted from fluid dynamical simulations, are studied. The commonly used finite particle number sampling procedure introduces an additional Poissonian (or multinomial if global baryon number conservation is enforced) contribution which increases the extracted moments of the baryon number distribution. If this procedure is applied to a fluctuating fluid dynamics framework, one severely overestimates the actual cumulants. We show that the sampling of so-called test particles suppresses the additional contribution to the moments by at least one power of the number of test particles. We demonstrate this methodmore » in a numerical fluid dynamics simulation that includes the effects of spinodal decomposition due to a first-order phase transition. Furthermore, in the limit where antibaryons can be ignored, we derive analytic formulas which capture exactly the effect of particle sampling on the baryon number cumulants. These formulas may be used to test the various numerical particle sampling algorithms.« less

Effect of finite particle number sampling on baryon number fluctuations

DOE PAGES

Steinheimer, Jan; Koch, Volker

2017-09-28

The effects of finite particle number sampling on the net baryon number cumulants, extracted from fluid dynamical simulations, are studied. The commonly used finite particle number sampling procedure introduces an additional Poissonian (or multinomial if global baryon number conservation is enforced) contribution which increases the extracted moments of the baryon number distribution. If this procedure is applied to a fluctuating fluid dynamics framework, one severely overestimates the actual cumulants. We show that the sampling of so-called test particles suppresses the additional contribution to the moments by at least one power of the number of test particles. We demonstrate this methodmore » in a numerical fluid dynamics simulation that includes the effects of spinodal decomposition due to a first-order phase transition. Furthermore, in the limit where antibaryons can be ignored, we derive analytic formulas which capture exactly the effect of particle sampling on the baryon number cumulants. These formulas may be used to test the various numerical particle sampling algorithms.« less

Nature of self-diffusion in two-dimensional fluids

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

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Nature of self-diffusion in two-dimensional fluids

DOE PAGES

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; ...

2017-12-18

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Finite Element modelling of deformation induced by interacting volcanic sources

NASA Astrophysics Data System (ADS)

Pascal, Karen; Neuberg, Jürgen; Rivalta, Eleonora

2010-05-01

The displacement field due to magma movements in the subsurface is commonly modelled using the solutions for a point source (Mogi, 1958), a finite spherical source (McTigue, 1987), or a dislocation source (Okada, 1992) embedded in a homogeneous elastic half-space. When the magmatic system comprises more than one source, the assumption of homogeneity in the half-space is violated and several sources are combined, their respective deformation field being summed. We have investigated the effects of neglecting the interaction between sources on the surface deformation field. To do so, we calculated the vertical and horizontal displacements for models with adjacent sources and we tested them against the solutions of corresponding numerical 3D finite element models. We implemented several models combining spherical pressure sources and dislocation sources, varying their relative position. Furthermore we considered the impact of topography, loading, and magma compressibility. To quantify the discrepancies and compare the various models, we calculated the difference between analytical and numerical maximum horizontal or vertical surface displacements.We will demonstrate that for certain conditions combining analytical sources can cause an error of up to 20%. References: McTigue, D. F. (1987), Elastic Stress and Deformation Near a Finite Spherical Magma Body: Resolution of the Point Source Paradox, J. Geophys. Res. 92, 12931-12940. Mogi, K. (1958), Relations between the eruptions of various volcanoes and the deformations of the ground surfaces around them, Bull Earthquake Res Inst, Univ Tokyo 36, 99-134. Okada, Y. (1992), Internal Deformation Due to Shear and Tensile Faults in a Half-Space, Bulletin of the Seismological Society of America 82(2), 1018-1040.

Analytical theory of coherent synchrotron radiation wakefield of short bunches shielded by conducting parallel plates

NASA Astrophysics Data System (ADS)

Stupakov, Gennady; Zhou, Demin

2016-04-01

We develop a general model of coherent synchrotron radiation (CSR) impedance with shielding provided by two parallel conducting plates. This model allows us to easily reproduce all previously known analytical CSR wakes and to expand the analysis to situations not explored before. It reduces calculations of the impedance to taking integrals along the trajectory of the beam. New analytical results are derived for the radiation impedance with shielding for the following orbits: a kink, a bending magnet, a wiggler of finite length, and an infinitely long wiggler. All our formulas are benchmarked against numerical simulations with the CSRZ computer code.

Analytical theory of coherent synchrotron radiation wakefield of short bunches shielded by conducting parallel plates

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

Stupakov, Gennady; Zhou, Demin

2016-04-21

We develop a general model of coherent synchrotron radiation (CSR) impedance with shielding provided by two parallel conducting plates. This model allows us to easily reproduce all previously known analytical CSR wakes and to expand the analysis to situations not explored before. It reduces calculations of the impedance to taking integrals along the trajectory of the beam. New analytical results are derived for the radiation impedance with shielding for the following orbits: a kink, a bending magnet, a wiggler of finite length, and an infinitely long wiggler. All our formulas are benchmarked against numerical simulations with the CSRZ computer code.

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.

Implications of long tails in the distribution of mutant effects

NASA Astrophysics Data System (ADS)

Waxman, D.; Feng, J.

2005-07-01

Long-tailed distributions possess an infinite variance, yet a finite sample that is drawn from such a distribution has a finite variance. In this work we consider a model of a population subject to mutation, selection and drift. We investigate the implications of a long-tailed distribution of mutant allelic effects on the distribution of genotypic effects in a model with a continuum of allelic effects. While the analysis is confined to asexual populations, it does also have implications for sexual populations. We obtain analytical results for a selectively neutral population as well as one subject to selection. We supplement these analytical results with numerical simulations, to take into account genetic drift. We find that a long-tailed distribution of mutant effects may affect both the equilibrium and the evolutionary adaptive behaviour of a population.

A Semi-Analytical Solution to Time Dependent Groundwater Flow Equation Incorporating Stream-Wetland-Aquifer Interactions

NASA Astrophysics Data System (ADS)

Boyraz, Uǧur; Melek Kazezyılmaz-Alhan, Cevza

2017-04-01

Groundwater is a vital element of hydrologic cycle and the analytical & numerical solutions of different forms of groundwater flow equations play an important role in understanding the hydrological behavior of subsurface water. The interaction between groundwater and surface water bodies can be determined using these solutions. In this study, new hypothetical approaches are implemented to groundwater flow system in order to contribute to the studies on surface water/groundwater interactions. A time dependent problem is considered in a 2-dimensional stream-wetland-aquifer system. The sloped stream boundary is used to represent the interaction between stream and aquifer. The rest of the aquifer boundaries are assumed as no-flux boundary. In addition, a wetland is considered as a surface water body which lies over the whole aquifer. The effect of the interaction between the wetland and the aquifer is taken into account with a source/sink term in the groundwater flow equation and the interaction flow is calculated by using Darcy's approach. A semi-analytical solution is developed for the 2-dimensional groundwater flow equation in 5 steps. First, Laplace and Fourier cosine transforms are employed to obtain the general solution in Fourier and Laplace domain. Then, the initial and boundary conditions are applied to obtain the particular solution. Finally, inverse Fourier transform is carried out analytically and inverse Laplace transform is carried out numerically to obtain the final solution in space and time domain, respectively. In order to verify the semi-analytical solution, an explicit finite difference algorithm is developed and analytical and numerical solutions are compared for synthetic examples. The comparison of the analytical and numerical solutions shows that the analytical solution gives accurate results.

Fractional Fourier transform of truncated elliptical Gaussian beams.

PubMed

Du, Xinyue; Zhao, Daomu

2006-12-20

Based on the fact that a hard-edged elliptical aperture can be expanded approximately as a finite sum of complex Gaussian functions in tensor form, an analytical expression for an elliptical Gaussian beam (EGB) truncated by an elliptical aperture and passing through a fractional Fourier transform system is derived by use of vector integration. The approximate analytical results provide more convenience for studying the propagation and transformation of truncated EGBs than the usual way by using the integral formula directly, and the efficiency of numerical calculation is significantly improved.

Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method.

PubMed

Reck, Kasper; Thomsen, Erik V; Hansen, Ole

2011-01-31

The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.

Description and application of capture zone delineation for a wellfield at Hilton Head Island, South Carolina

USGS Publications Warehouse

Landmeyer, J.E.

1994-01-01

Ground-water capture zone boundaries for individual pumped wells in a confined aquffer were delineated by using groundwater models. Both analytical and numerical (semi-analytical) models that more accurately represent the $round-water-flow system were used. All models delineated 2-dimensional boundaries (capture zones) that represent the areal extent of groundwater contribution to a pumped well. The resultant capture zones were evaluated on the basis of the ability of each model to realistically rapresent the part of the ground-water-flow system that contributed water to the pumped wells. Analytical models used were based on a fixed radius approach, and induded; an arbitrary radius model, a calculated fixed radius model based on the volumetric-flow equation with a time-of-travel criterion, and a calculated fixed radius model derived from modification of the Theis model with a drawdown criterion. Numerical models used induded the 2-dimensional, finite-difference models RESSQC and MWCAP. The arbitrary radius and Theis analytical models delineated capture zone boundaries that compared least favorably with capture zones delineated using the volumetric-flow analytical model and both numerical models. The numerical models produced more hydrologically reasonable capture zones (that were oriented parallel to the regional flow direction) than the volumetric-flow equation. The RESSQC numerical model computed more hydrologically realistic capture zones than the MWCAP numerical model by accounting for changes in the shape of capture zones caused by multiple-well interference. The capture zone boundaries generated by using both analytical and numerical models indicated that the curnmtly used 100-foot radius of protection around a wellhead in South Carolina is an underestimate of the extent of ground-water capture for pumped wetis in this particular wellfield in the Upper Floridan aquifer. The arbitrary fixed radius of 100 feet was shown to underestimate the upgradient contribution of ground-water flow to a pumped well.

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.

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.

Improving a complex finite-difference ground water flow model through the use of an analytic element screening model

USGS Publications Warehouse

Hunt, R.J.; Anderson, M.P.; Kelson, V.A.

1998-01-01

This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.

Analytical Computation of Effective Grid Parameters for the Finite-Difference Seismic Waveform Modeling With the PREM, IASP91, SP6, and AK135

NASA Astrophysics Data System (ADS)

Toyokuni, G.; Takenaka, H.

2007-12-01

We propose a method to obtain effective grid parameters for the finite-difference (FD) method with standard Earth models using analytical ways. In spite of the broad use of the heterogeneous FD formulation for seismic waveform modeling, accurate treatment of material discontinuities inside the grid cells has been a serious problem for many years. One possible way to solve this problem is to introduce effective grid elastic moduli and densities (effective parameters) calculated by the volume harmonic averaging of elastic moduli and volume arithmetic averaging of density in grid cells. This scheme enables us to put a material discontinuity into an arbitrary position in the spatial grids. Most of the methods used for synthetic seismogram calculation today receives the blessing of the standard Earth models, such as the PREM, IASP91, SP6, and AK135, represented as functions of normalized radius. For the FD computation of seismic waveform with such models, we first need accurate treatment of material discontinuities in radius. This study provides a numerical scheme for analytical calculations of the effective parameters for an arbitrary spatial grids in radial direction as to these major four standard Earth models making the best use of their functional features. This scheme can analytically obtain the integral volume averages through partial fraction decompositions (PFDs) and integral formulae. We have developed a FORTRAN subroutine to perform the computations, which is opened to utilization in a large variety of FD schemes ranging from 1-D to 3-D, with conventional- and staggered-grids. In the presentation, we show some numerical examples displaying the accuracy of the FD synthetics simulated with the analytical effective parameters.

Effect of Carreau-Yasuda rheological parameters on subcritical Lapwood convection in horizontal porous cavity saturated by shear-thinning fluid

NASA Astrophysics Data System (ADS)

Khechiba, Khaled; Mamou, Mahmoud; Hachemi, Madjid; Delenda, Nassim; Rebhi, Redha

2017-06-01

The present study is focused on Lapwood convection in isotropic porous media saturated with non-Newtonian shear thinning fluid. The non-Newtonian rheological behavior of the fluid is modeled using the general viscosity model of Carreau-Yasuda. The convection configuration consists of a shallow porous cavity with a finite aspect ratio and subject to a vertical constant heat flux, whereas the vertical walls are maintained impermeable and adiabatic. An approximate analytical solution is developed on the basis of the parallel flow assumption, and numerical solutions are obtained by solving the full governing equations. The Darcy model with the Boussinesq approximation and energy transport equations are solved numerically using a finite difference method. The results are obtained in terms of the Nusselt number and the flow fields as functions of the governing parameters. A good agreement is obtained between the analytical approximation and the numerical solution of the full governing equations. The effects of the rheological parameters of the Carreau-Yasuda fluid and Rayleigh number on the onset of subcritical convection thresholds are demonstrated. Regardless of the aspect ratio of the enclosure and thermal boundary condition type, the subcritical convective flows are seen to occur below the onset of stationary convection. Correlations are proposed to estimate the subcritical Rayleigh number for the onset of finite amplitude convection as a function of the fluid rheological parameters. Linear stability of the convective motion, predicted by the parallel flow approximation, is studied, and the onset of Hopf bifurcation, from steady convective flow to oscillatory behavior, is found to depend strongly on the rheological parameters. In general, Hopf bifurcation is triggered earlier as the fluid becomes more and more shear-thinning.

An economical method of analyzing transient motion of gas-lubricated rotor-bearing systems.

NASA Technical Reports Server (NTRS)

Falkenhagen, G. L.; Ayers, A. L.; Barsalou, L. C.

1973-01-01

A method of economically evaluating the hydrodynamic forces generated in a gas-lubricated tilting-pad bearing is presented. The numerical method consists of solving the case of the infinite width bearing and then converting this solution to the case of the finite bearing by accounting for end leakage. The approximate method is compared to the finite-difference solution of Reynolds equation and yields acceptable accuracy while running about one-hundred times faster. A mathematical model of a gas-lubricated tilting-pad vertical rotor systems is developed. The model is capable of analyzing a two-bearing-rotor system in which the rotor center of mass is not at midspan by accounting for gyroscopic moments. The numerical results from the model are compared to actual test data as well as analytical results of other investigators.

Numerical analysis of a main crack interactions with micro-defects/inhomogeneities using two-scale generalized/extended finite element method

NASA Astrophysics Data System (ADS)

Malekan, Mohammad; Barros, Felício B.

2017-12-01

Generalized or extended finite element method (G/XFEM) models the crack by enriching functions of partition of unity type with discontinuous functions that represent well the physical behavior of the problem. However, this enrichment functions are not available for all problem types. Thus, one can use numerically-built (global-local) enrichment functions to have a better approximate procedure. This paper investigates the effects of micro-defects/inhomogeneities on a main crack behavior by modeling the micro-defects/inhomogeneities in the local problem using a two-scale G/XFEM. The global-local enrichment functions are influenced by the micro-defects/inhomogeneities from the local problem and thus change the approximate solution of the global problem with the main crack. This approach is presented in detail by solving three different linear elastic fracture mechanics problems for different cases: two plane stress and a Reissner-Mindlin plate problems. The numerical results obtained with the two-scale G/XFEM are compared with the reference solutions from the analytical, numerical solution using standard G/XFEM method and ABAQUS as well, and from the literature.

Energy Efficiency of Induction Motors Running Off Frequency Converters with Pulse-Width Voltage Modulation{sup 1}

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

Shvetsov, N. K., E-mail: elmash@em.ispu.ru

2016-11-15

The results of calculations of the increase in losses in an induction motor with frequency control and different forms of the supply voltage are presented. The calculations were performed by an analytic method based on harmonic analysis of the supply voltage as well as numerical calculation of the electromagnetic processes by the finite-element method.

Resolution of VTI anisotropy with elastic full-waveform inversion: theory and basic numerical examples

NASA Astrophysics Data System (ADS)

Podgornova, O.; Leaney, S.; Liang, L.

2018-07-01

Extracting medium properties from seismic data faces some limitations due to the finite frequency content of the data and restricted spatial positions of the sources and receivers. Some distributions of the medium properties make low impact on the data (including none). If these properties are used as the inversion parameters, then the inverse problem becomes overparametrized, leading to ambiguous results. We present an analysis of multiparameter resolution for the linearized inverse problem in the framework of elastic full-waveform inversion. We show that the spatial and multiparameter sensitivities are intertwined and non-sensitive properties are spatial distributions of some non-trivial combinations of the conventional elastic parameters. The analysis accounts for the Hessian information and frequency content of the data; it is semi-analytical (in some scenarios analytical), easy to interpret and enhances results of the widely used radiation pattern analysis. Single-type scattering is shown to have limited sensitivity, even for full-aperture data. Finite-frequency data lose multiparameter sensitivity at smooth and fine spatial scales. Also, we establish ways to quantify a spatial-multiparameter coupling and demonstrate that the theoretical predictions agree well with the numerical results.

Stope Stability Assessment and Effect of Horizontal to Vertical Stress Ratio on the Yielding and Relaxation Zones Around Underground Open Stopes Using Empirical and Finite Element Methods

NASA Astrophysics Data System (ADS)

Sepehri, Mohammadali; Apel, Derek; Liu, Wei

2017-09-01

Predicting the stability of open stopes can be a challenging task for underground mine engineers. For decades, the stability graph method has been used as the first step of open stope design around the world. However, there are some shortcomings with this method. For instance, the stability graph method does not account for the relaxation zones around the stopes. Another limitation of the stability graph is that this method cannot to be used to evaluate the stability of the stopes with high walls made of backfill materials. However, there are several analytical and numerical methods that can be used to overcome these limitations. In this study, both empirical and numerical methods have been used to assess the stability of an open stope located between mine levels N9225 and N9250 at Diavik diamond underground mine. It was shown that the numerical methods can be used as complementary methods along with other analytical and empirical methods to assess the stability of open stopes. A three dimensional elastoplastic finite element model was constructed using Abaqus software. In this paper a sensitivity analysis was performed to investigate the impact of the stress ratio "k" on the extent of the yielding and relaxation zones around the hangingwall and footwall of the understudy stope.

Neoclassical transport including collisional nonlinearity.

PubMed

Candy, J; Belli, E A

2011-06-10

In the standard δf theory of neoclassical transport, the zeroth-order (Maxwellian) solution is obtained analytically via the solution of a nonlinear equation. The first-order correction δf is subsequently computed as the solution of a linear, inhomogeneous equation that includes the linearized Fokker-Planck collision operator. This equation admits analytic solutions only in extreme asymptotic limits (banana, plateau, Pfirsch-Schlüter), and so must be solved numerically for realistic plasma parameters. Recently, numerical codes have appeared which attempt to compute the total distribution f more accurately than in the standard ordering by retaining some nonlinear terms related to finite-orbit width, while simultaneously reusing some form of the linearized collision operator. In this work we show that higher-order corrections to the distribution function may be unphysical if collisional nonlinearities are ignored.

Pressure data for four analytically defined arrow wings in supersonic flow. [Langley Unitary Plan Wind Tunnel tests

NASA Technical Reports Server (NTRS)

Townsend, J. C.

1980-01-01

In order to provide experimental data for comparison with newly developed finite difference methods for computing supersonic flows over aircraft configurations, wind tunnel tests were conducted on four arrow wing models. The models were machined under numeric control to precisely duplicate analytically defined shapes. They were heavily instrumented with pressure orifices at several cross sections ahead of and in the region where there is a gap between the body and the wing trailing edge. The test Mach numbers were 2.36, 2.96, and 4.63. Tabulated pressure data for the complete test series are presented along with selected oil flow photographs. Comparisons of some preliminary numerical results at zero angle of attack show good to excellent agreement with the experimental pressure distributions.

QED contributions to electron g-2

NASA Astrophysics Data System (ADS)

Laporta, Stefano

2018-05-01

In this paper I briefly describe the results of the numerical evaluation of the mass-independent 4-loop contribution to the electron g-2 in QED with 1100 digits of precision. In particular I also show the semi-analytical fit to the numerical value, which contains harmonic polylogarithms of eiπ/3, e2iπ/3 and eiπ/2 one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. I give also some information about the methods and the program used.

Study of transient behavior of finned coil heat exchangers

NASA Technical Reports Server (NTRS)

Rooke, S. P.; Elissa, M. G.

1993-01-01

The status of research on the transient behavior of finned coil cross-flow heat exchangers using single phase fluids is reviewed. Applications with available analytical or numerical solutions are discussed. Investigation of water-to-air type cross-flow finned tube heat exchangers is examined through the use of simplified governing equations and an up-wind finite difference scheme. The degenerate case of zero air-side capacitance rate is compared with available exact solution. Generalization of the numerical model is discussed for application to multi-row multi-circuit heat exchangers.

Semigroup theory and numerical approximation for equations in linear viscoelasticity

NASA Technical Reports Server (NTRS)

Fabiano, R. H.; Ito, K.

1990-01-01

A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

NASA Astrophysics Data System (ADS)

Dutykh, Denys; Hoefer, Mark; Mitsotakis, Dimitrios

2018-04-01

Some effects of surface tension on fully nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are presented. Analytical expressions for new peaked traveling wave solutions are presented in the dispersionless case of critical surface tension. Numerical experiments are performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge-Kutta method of order 4.

pySecDec: A toolbox for the numerical evaluation of multi-scale integrals

NASA Astrophysics Data System (ADS)

Borowka, S.; Heinrich, G.; Jahn, S.; Jones, S. P.; Kerner, M.; Schlenk, J.; Zirke, T.

2018-01-01

We present pySECDEC, a new version of the program SECDEC, which performs the factorization of dimensionally regulated poles in parametric integrals, and the subsequent numerical evaluation of the finite coefficients. The algebraic part of the program is now written in the form of python modules, which allow a very flexible usage. The optimization of the C++ code, generated using FORM, is improved, leading to a faster numerical convergence. The new version also creates a library of the integrand functions, such that it can be linked to user-specific codes for the evaluation of matrix elements in a way similar to analytic integral libraries.

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

NASA Astrophysics Data System (ADS)

Meyers, M. D.; Huang, C.-K.; Zeng, Y.; Yi, S. A.; Albright, B. J.

2015-09-01

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

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

Meyers, M.D., E-mail: mdmeyers@physics.ucla.edu; Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, CA 90095; Huang, C.-K., E-mail: huangck@lanl.gov

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTDmore » scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.« less

Saturated-unsaturated flow in a compressible leaky-unconfined aquifer

NASA Astrophysics Data System (ADS)

Mishra, Phoolendra K.; Vesselinov, Velimir V.; Kuhlman, Kristopher L.

2012-06-01

An analytical solution is developed for three-dimensional flow towards a partially penetrating large-diameter well in an unconfined aquifer bounded below by a leaky aquitard of finite or semi-infinite extent. The analytical solution is derived using Laplace and Hankel transforms, then inverted numerically. Existing solutions for flow in leaky unconfined aquifers neglect the unsaturated zone following an assumption of instantaneous drainage due to Neuman. We extend the theory of leakage in unconfined aquifers by (1) including water flow and storage in the unsaturated zone above the water table, and (2) allowing the finite-diameter pumping well to partially penetrate the aquifer. The investigation of model-predicted results shows that aquitard leakage leads to significant departure from the unconfined solution without leakage. The investigation of dimensionless time-drawdown relationships shows that the aquitard drawdown also depends on unsaturated zone properties and the pumping-well wellbore storage effects.

Radial flow towards well in leaky unconfined aquifer

NASA Astrophysics Data System (ADS)

Mishra, P. K.; Kuhlman, K. L.

2012-12-01

An analytical solution is developed for three-dimensional flow towards a partially penetrating large- diameter well in an unconfined aquifer bounded below by a leaky aquitard of finite or semi-infinite extent. The analytical solution is derived using Laplace and Hankel transforms, then inverted numerically. Existing solutions for flow in leaky unconfined aquifers neglect the unsaturated zone following an assumption of instantaneous drainage due to Neuman. We extend the theory of leakage in unconfined aquifers by (1) including water flow and storage in the unsaturated zone above the water table, and (2) allowing the finite-diameter pumping well to partially penetrate the aquifer. The investigation of model-predicted results shows that aquitard leakage leads to significant departure from the unconfined solution without leakage. The investigation of dimensionless time-drawdown relationships shows that the aquitard drawdown also depends on unsaturated zone properties and the pumping-well wellbore storage effects.

3D Tensorial Elastodynamics for Isotropic Media on Vertically Deformed Meshes

NASA Astrophysics Data System (ADS)

Shragge, J. C.

2017-12-01

Solutions of the 3D elastodynamic wave equation are sometimes required in industrial and academic applications of elastic reverse-time migration (E-RTM) and full waveform inversion (E-FWI) that involve vertically deformed meshes. Examples include incorporating irregular free-surface topography and handling internal boundaries (e.g., water bottom) directly into the computational meshes. In 3D E-RTM and E-FWI applications, the number of forward modeling simulations can number in the tens of thousands (per iteration), which necessitates the development of stable, accurate and efficient 3D elastodynamics solvers. For topographic scenarios, most finite-difference solution approaches use a change-of-variable strategy that has a number of associated computational challenges, including difficulties in handling of the free-surface boundary condition. In this study, I follow a tensorial approach and use a generalized family of analytic transforms to develop a set of analytic equations for 3D elastodynamics that directly incorporates vertical grid deformations. Importantly, this analytic approach allows for the specification of an analytic free-surface boundary condition appropriate for vertically deformed meshes. These equations are both straightforward and efficient to solve using a velocity-stress formulation with finite-difference (MFD) operators implemented on a fully staggered grid. Moreover, I demonstrate that the use of mimetic finite difference (MFD) methods allows stable, accurate, and efficient numerical solutions to be simulated for typical topographic scenarios. Examples demonstrate that high-quality elastic wavefields can be generated for topographic surfaces exhibiting significant topographic relief.

Analytical theory of coherent synchrotron radiation wakefield of short bunches shielded by conducting parallel plates

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

Stupakov, Gennady; Zhou, Demin

2016-04-21

We develop a general model of coherent synchrotron radiation (CSR) impedance with shielding provided by two parallel conducting plates. This model allows us to easily reproduce all previously known analytical CSR wakes and to expand the analysis to situations not explored before. It reduces calculations of the impedance to taking integrals along the trajectory of the beam. New analytical results are derived for the radiation impedance with shielding for the following orbits: a kink, a bending magnet, a wiggler of finite length, and an infinitely long wiggler. Furthermore, all our formulas are benchmarked against numerical simulations with the CSRZ computermore » code.« less

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

PubMed Central

Rocklin, Gabriel J.; Mobley, David L.; Dill, Ken A.; Hünenberger, Philippe H.

2013-01-01

The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges −5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol−1) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol−1). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning. PMID:24320250

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: an accurate correction scheme for electrostatic finite-size effects.

PubMed

Rocklin, Gabriel J; Mobley, David L; Dill, Ken A; Hünenberger, Philippe H

2013-11-14

The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol(-1)) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol(-1)). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning.

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

NASA Astrophysics Data System (ADS)

Rocklin, Gabriel J.; Mobley, David L.; Dill, Ken A.; Hünenberger, Philippe H.

2013-11-01

The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol-1) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol-1). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning.

Dynamical effects in Bragg coherent x-ray diffraction imaging of finite crystals

NASA Astrophysics Data System (ADS)

Shabalin, A. G.; Yefanov, O. M.; Nosik, V. L.; Bushuev, V. A.; Vartanyants, I. A.

2017-08-01

We present simulations of Bragg coherent x-ray diffractive imaging (CXDI) data from finite crystals in the frame of the dynamical theory of x-ray diffraction. The developed approach is based on a numerical solution of modified Takagi-Taupin equations and can be applied for modeling of a broad range of x-ray diffraction experiments with finite three-dimensional crystals of arbitrary shape also in the presence of strain. We performed simulations for nanocrystals of a cubic and hemispherical shape of different sizes and provided a detailed analysis of artifacts in the Bragg CXDI reconstructions introduced by the dynamical diffraction. Based on our theoretical analysis we developed an analytical procedure to treat effects of refraction and absorption in the reconstruction. Our results elucidate limitations for the kinematical approach in the Bragg CXDI and suggest a natural criterion to distinguish between kinematical and dynamical cases in coherent x-ray diffraction on a finite crystal.

The mechanical properties of human dentin for 3-D finite element modeling: Numerical and analytical evaluation.

PubMed

Grzebieluch, Wojciech; Będziński, Romuald; Czapliński, Tomasz; Kaczmarek, Urszula

2017-07-01

The FEM is often used in investigations of dentin loading conditions; however, its anisotropy is mostly neglected. The purpose of the study was to evaluate the anisotropy and the elastic properties of an equivalent homogenous material model of human dentin as well as to compare isotropic and anisotropic dentin FE-models. Analytical and numerical dentin homogenization according to Luciano and Barbero was performed and E-modulus (E), Poisson's ratios (v) G-modulus (G) were calculated. The E-modulus of the dentin matrix was 28.0 GPa, Poisson's ratio (v) was 0.3; finite element models of orthotropic and isotropic dentin were created, loaded and compared using Ansys® 14.5 and CodeAster® 11.2 software. Anisotropy of the dentin ranged from 6.9 to 35.2%. E-modulus and G-modulus were as follows: E1 = 22.0-26.0 GPa, E2/E3 = 15.7-23.0 GPa; G12/G13 = 6.96-9.35 GPa and G23 = 6.08-8.09 GPa (highest values in the superficial layer). In FEM analysis of the displacement values were higher in the isotropic than in the orthotropic model, reaching up to 16% by shear load, 37% by compression and 23% in the case of shear with bending. Strain values were higher in the isotropic model, up to 35% for the shear load, 31% for compression and 35% in the case of shear with bending. The decrease in the volumetric fraction and diameter of tubules increased the G and E values. Anisotropy of the dentin applied during FEM analysis decreased the displacements and strain values. The numerical and analytical homogenization of dentin showed similar results.

Subsurface Stress Fields in FCC Single Crystal Anisotropic Contacts

NASA Technical Reports Server (NTRS)

Arakere, Nagaraj K.; Knudsen, Erik; Swanson, Gregory R.; Duke, Gregory; Ham-Battista, Gilda

2004-01-01

Single crystal superalloy turbine blades used in high pressure turbomachinery are subject to conditions of high temperature, triaxial steady and alternating stresses, fretting stresses in the blade attachment and damper contact locations, and exposure to high-pressure hydrogen. The blades are also subjected to extreme variations in temperature during start-up and shutdown transients. The most prevalent high cycle fatigue (HCF) failure modes observed in these blades during operation include crystallographic crack initiation/propagation on octahedral planes, and non-crystallographic initiation with crystallographic growth. Numerous cases of crack initiation and crack propagation at the blade leading edge tip, blade attachment regions, and damper contact locations have been documented. Understanding crack initiation/propagation under mixed-mode loading conditions is critical for establishing a systematic procedure for evaluating HCF life of single crystal turbine blades. This paper presents analytical and numerical techniques for evaluating two and three dimensional subsurface stress fields in anisotropic contacts. The subsurface stress results are required for evaluating contact fatigue life at damper contacts and dovetail attachment regions in single crystal nickel-base superalloy turbine blades. An analytical procedure is presented for evaluating the subsurface stresses in the elastic half-space, based on the adaptation of a stress function method outlined by Lekhnitskii. Numerical results are presented for cylindrical and spherical anisotropic contacts, using finite element analysis (FEA). Effects of crystal orientation on stress response and fatigue life are examined. Obtaining accurate subsurface stress results for anisotropic single crystal contact problems require extremely refined three-dimensional (3-D) finite element grids, especially in the edge of contact region. Obtaining resolved shear stresses (RSS) on the principal slip planes also involves considerable post-processing work. For these reasons it is very advantageous to develop analytical solution schemes for subsurface stresses, whenever possible.

Analytical treatment of the deformation behavior of EUVL masks during electrostatic chucking

NASA Astrophysics Data System (ADS)

Brandstetter, Gerd; Govindjee, Sanjay

2012-03-01

A new analytical approach is presented to predict mask deformation during electro-static chucking in next generation extreme-ultraviolet-lithography (EUVL). Given an arbitrary profile measurement of the mask and chuck non-flatness, this method has been developed as an alternative to time-consuming finite element simulations for overlay error correction algorithms. We consider the feature transfer of each harmonic component in the profile shapes via linear elasticity theory and demonstrate analytically how high spatial frequencies are filtered. The method is compared to presumably more accurate finite element simulations and has been tested successfully in an overlay error compensation experiment, where the residual error y-component could be reduced by a factor 2. As a side outcome, the formulation provides a tool to estimate the critical pin-size and -pitch such that the distortion on the mask front-side remains within given tolerances. We find for a numerical example that pin-pitches of less than 5 mm will result in a mask pattern-distortion of less than 1 nm if the chucking pressure is below 30 kPa.

Analytical treatment of the deformation behavior of extreme-ultraviolet-lithography masks during electrostatic chucking

NASA Astrophysics Data System (ADS)

Brandstetter, Gerd; Govindjee, Sanjay

2012-10-01

A new analytical approach is presented to predict mask deformation during electrostatic chucking in next-generation extreme-ultraviolet-lithography. Given an arbitrary profile measurement of the mask and chuck nonflatness, this method has been developed as an alternative to time-consuming finite element simulations for overlay error correction algorithms. We consider the feature transfer of each harmonic component in the profile shapes via linear elasticity theory and demonstrate analytically how high spatial frequencies are filtered. The method is compared to presumably more accurate finite element simulations and has been tested successfully in an overlay error compensation experiment, where the residual error y-component could be reduced by a factor of 2. As a side outcome, the formulation provides a tool to estimate the critical pin-size and -pitch such that the distortion on the mask front-side remains within given tolerances. We find for a numerical example that pin-pitches of less than 5 mm will result in a mask pattern distortion of less than 1 nm if the chucking pressure is below 30 kPa.

Aeroelastic Stability of Rotor Blades Using Finite Element Analysis

NASA Technical Reports Server (NTRS)

Chopra, I.; Sivaneri, N.

1982-01-01

The flutter stability of flap bending, lead-lag bending, and torsion of helicopter rotor blades in hover is investigated using a finite element formulation based on Hamilton's principle. The blade is divided into a number of finite elements. Quasi-steady strip theory is used to evaluate the aerodynamic loads. The nonlinear equations of motion are solved for steady-state blade deflections through an iterative procedure. The equations of motion are linearized assuming blade motion to be a small perturbation about the steady deflected shape. The normal mode method based on the coupled rotating natural modes is used to reduce the number of equations in the flutter analysis. First the formulation is applied to single-load-path blades (articulated and hingeless blades). Numerical results show very good agreement with existing results obtained using the modal approach. The second part of the application concerns multiple-load-path blades, i.e. bearingless blades. Numerical results are presented for several analytical models of the bearingless blade. Results are also obtained using an equivalent beam approach wherein a bearingless blade is modelled as a single beam with equivalent properties. Results show the equivalent beam model.

Finite-element simulation of ceramic drying processes

NASA Astrophysics Data System (ADS)

Keum, Y. T.; Jeong, J. H.; Auh, K. H.

2000-07-01

A finite-element simulation for the drying process of ceramics is performed. The heat and moisture movements in green ceramics caused by the temperature gradient, moisture gradient, conduction, convection and evaporation are considered. The finite-element formulation for solving the temperature and moisture distributions, which not only change the volume but also induce the hygro-thermal stress, is carried out. Employing the internally discontinuous interface elements, the numerical divergence problem arising from sudden changes in heat capacity in the phase zone is solved. In order to verify the reliability of the formulation, the drying process of a coal and the wetting process of a graphite epoxy are simulated and the results are compared with the analytical solution and another investigator's result. Finally, the drying process of a ceramic electric insulator is simulated.

Time dependent wave envelope finite difference analysis of sound propagation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1984-01-01

A transient finite difference wave envelope formulation is presented for sound propagation, without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct. The numerical results are in good agreement with exact analytical results.

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

Giunta, G.; Belouettar, S.

In this paper, the static response of three-dimensional beams made of functionally graded materials is investigated through a family of hierarchical one-dimensional finite elements. A wide variety of elements is proposed differing by the kinematic formulation and the number of nodes per elements along the beam axis. Elements’ stiffness matrix and load vector are derived in a unified nuclear form that does not depend upon the a priori expansion order over the cross-section nor the finite element approximation along the beam axis. Results are validated towards three-dimensional finite element models as well as equivalent Navier-type analytical solutions. The numerical investigationsmore » show that accurate and efficient solutions (when compared with full three-dimensional FEM solutions) can be obtained by the proposed family of hierarchical one-dimensional elements’ family.« less

Bogoliubov theory of acoustic Hawking radiation in Bose-Einstein condensates

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

Recati, A.; Physik-Department, Technische Universitaet Muenchen, D-85748 Garching; Pavloff, N.

2009-10-15

We apply the microscopic Bogoliubov theory of dilute Bose-Einstein condensates to analyze quantum and thermal fluctuations in a flowing atomic condensate in the presence of a sonic horizon. For the simplest case of a step-like horizon, closed-form analytical expressions are found for the spectral distribution of the analog Hawking radiation and for the density correlation function. The peculiar long-distance density correlations that appear as a consequence of the Hawking emission features turns out to be reinforced by a finite initial temperature of the condensate. The analytical results are in good quantitative agreement with first principle numerical calculations.

Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

NASA Astrophysics Data System (ADS)

Chen, Shanzhen; Jiang, Xiaoyun

2012-08-01

In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.

A nonlinear delayed model for the immune response in the presence of viral mutation

NASA Astrophysics Data System (ADS)

Messias, D.; Gleria, Iram; Albuquerque, S. S.; Canabarro, Askery; Stanley, H. E.

2018-02-01

We consider a delayed nonlinear model of the dynamics of the immune system against a viral infection that contains a wild-type virus and a mutant. We consider the finite response time of the immune system and find sustained oscillatory behavior as well as chaotic behavior triggered by the presence of delays. We present a numeric analysis and some analytical results.

A computer program for cyclic plasticity and structural fatigue analysis

NASA Technical Reports Server (NTRS)

Kalev, I.

1980-01-01

A computerized tool for the analysis of time independent cyclic plasticity structural response, life to crack initiation prediction, and crack growth rate prediction for metallic materials is described. Three analytical items are combined: the finite element method with its associated numerical techniques for idealization of the structural component, cyclic plasticity models for idealization of the material behavior, and damage accumulation criteria for the fatigue failure.

Numerical computation of gravitational field for general axisymmetric objects

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2016-10-01

We developed a numerical method to compute the gravitational field of a general axisymmetric object. The method (I) numerically evaluates a double integral of the ring potential by the split quadrature method using the double exponential rules, and (II) derives the acceleration vector by numerically differentiating the numerically integrated potential by Ridder's algorithm. Numerical comparison with the analytical solutions for a finite uniform spheroid and an infinitely extended object of the Miyamoto-Nagai density distribution confirmed the 13- and 11-digit accuracy of the potential and the acceleration vector computed by the method, respectively. By using the method, we present the gravitational potential contour map and/or the rotation curve of various axisymmetric objects: (I) finite uniform objects covering rhombic spindles and circular toroids, (II) infinitely extended spheroids including Sérsic and Navarro-Frenk-White spheroids, and (III) other axisymmetric objects such as an X/peanut-shaped object like NGC 128, a power-law disc with a central hole like the protoplanetary disc of TW Hya, and a tear-drop-shaped toroid like an axisymmetric equilibrium solution of plasma charge distribution in an International Thermonuclear Experimental Reactor-like tokamak. The method is directly applicable to the electrostatic field and will be easily extended for the magnetostatic field. The FORTRAN 90 programs of the new method and some test results are electronically available.

Computing the optimal path in stochastic dynamical systems

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

Bauver, Martha; Forgoston, Eric, E-mail: eric.forgoston@montclair.edu; Billings, Lora

2016-08-15

In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensionalmore » system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.« less

Effect of risk perception on epidemic spreading in temporal networks

NASA Astrophysics Data System (ADS)

Moinet, Antoine; Pastor-Satorras, Romualdo; Barrat, Alain

2018-01-01

Many progresses in the understanding of epidemic spreading models have been obtained thanks to numerous modeling efforts and analytical and numerical studies, considering host populations with very different structures and properties, including complex and temporal interaction networks. Moreover, a number of recent studies have started to go beyond the assumption of an absence of coupling between the spread of a disease and the structure of the contacts on which it unfolds. Models including awareness of the spread have been proposed, to mimic possible precautionary measures taken by individuals that decrease their risk of infection, but have mostly considered static networks. Here, we adapt such a framework to the more realistic case of temporal networks of interactions between individuals. We study the resulting model by analytical and numerical means on both simple models of temporal networks and empirical time-resolved contact data. Analytical results show that the epidemic threshold is not affected by the awareness but that the prevalence can be significantly decreased. Numerical studies on synthetic temporal networks highlight, however, the presence of very strong finite-size effects, resulting in a significant shift of the effective epidemic threshold in the presence of risk awareness. For empirical contact networks, the awareness mechanism leads as well to a shift in the effective threshold and to a strong reduction of the epidemic prevalence.

Numerical analysis of one-dimensional temperature data for groundwater/surface-water exchange with 1DTempPro

NASA Astrophysics Data System (ADS)

Voytek, E. B.; Drenkelfuss, A.; Day-Lewis, F. D.; Healy, R. W.; Lane, J. W.; Werkema, D. D.

2012-12-01

Temperature is a naturally occurring tracer, which can be exploited to infer the movement of water through the vadose and saturated zones, as well as the exchange of water between aquifers and surface-water bodies, such as estuaries, lakes, and streams. One-dimensional (1D) vertical temperature profiles commonly show thermal amplitude attenuation and increasing phase lag of diurnal or seasonal temperature variations with propagation into the subsurface. This behavior is described by the heat-transport equation (i.e., the convection-conduction-dispersion equation), which can be solved analytically in 1D under certain simplifying assumptions (e.g., sinusoidal or steady-state boundary conditions and homogeneous hydraulic and thermal properties). Analysis of 1D temperature profiles using analytical models provides estimates of vertical groundwater/surface-water exchange. The utility of these estimates can be diminished when the model assumptions are violated, as is common in field applications. Alternatively, analysis of 1D temperature profiles using numerical models allows for consideration of more complex and realistic boundary conditions. However, such analyses commonly require model calibration and the development of input files for finite-difference or finite-element codes. To address the calibration and input file requirements, a new computer program, 1DTempPro, is presented that facilitates numerical analysis of vertical 1D temperature profiles. 1DTempPro is a graphical user interface (GUI) to the USGS code VS2DH, which numerically solves the flow- and heat-transport equations. Pre- and post-processor features within 1DTempPro allow the user to calibrate VS2DH models to estimate groundwater/surface-water exchange and hydraulic conductivity in cases where hydraulic head is known. This approach improves groundwater/ surface-water exchange-rate estimates for real-world data with complexities ill-suited for examination with analytical methods. Additionally, the code allows for time-varying temperature and hydraulic boundary conditions. Here, we present the approach and include examples for several datasets from stream/aquifer systems.

Effects of stochastic noise on dynamical decoupling procedures

NASA Astrophysics Data System (ADS)

Bernád, J. Z.; Frydrych, H.

2014-06-01

Dynamical decoupling is an important tool to counter decoherence and dissipation effects in quantum systems originating from environmental interactions. It has been used successfully in many experiments; however, there is still a gap between fidelity improvements achieved in practice compared to theoretical predictions. We propose a model for imperfect dynamical decoupling based on a stochastic Ito differential equation which could explain the observed gap. We discuss the impact of our model on the time evolution of various quantum systems in finite- and infinite-dimensional Hilbert spaces. Analytical results are given for the limit of continuous control, whereas we present numerical simulations and upper bounds for the case of finite control.

The fast kinematic magnetic dynamo and the dissipationless limit

NASA Technical Reports Server (NTRS)

Finn, John M.; Ott, Edward

1990-01-01

The evolution of the magnetic field in models that incorporate chaotic field line stretching, field cancellation, and finite magnetic Reynolds number is examined analytically and numerically. Although the models used here are highly idealized, it is claimed that they display and illustrate typical behavior relevant to fast magnetic dynamic behavior. It is shown, in particular, that consideration of magnetic flux through a finite fixed surface provides a simple and effective way of deducing fast dynamo behavior from the zero resistivity equation. Certain aspects of the fast dynamo problem can thus be reduced to a study of nonlinear dynamic properties of the underlying flow.

Finite Element Analysis of Magnetic Damping Effects on G-Jitter Induced Fluid Flow

NASA Technical Reports Server (NTRS)

Pan, Bo; Li, Ben Q.; deGroh, Henry C., III

1997-01-01

This paper reports some interim results on numerical modeling and analyses of magnetic damping of g-jitter driven fluid flow in microgravity. A finite element model is developed to represent the fluid flow, thermal and solute transport phenomena in a 2-D cavity under g-jitter conditions with and without an applied magnetic field. The numerical model is checked by comparing with analytical solutions obtained for a simple parallel plate channel flow driven by g-jitter in a transverse magnetic field. The model is then applied to study the effect of steady state g-jitter induced oscillation and on the solute redistribution in the liquid that bears direct relevance to the Bridgman-Stockbarger single crystal growth processes. A selection of computed results is presented and the results indicate that an applied magnetic field can effectively damp the velocity caused by g-jitter and help to reduce the time variation of solute redistribution.

A novel finite element analysis of three-dimensional circular crack

NASA Astrophysics Data System (ADS)

Ping, X. C.; Wang, C. G.; Cheng, L. P.

2018-06-01

A novel singular element containing a part of the circular crack front is established to solve the singular stress fields of circular cracks by using the numerical series eigensolutions of singular stress fields. The element is derived from the Hellinger-Reissner variational principle and can be directly incorporated into existing 3D brick elements. The singular stress fields are determined as the system unknowns appearing as displacement nodal values. The numerical studies are conducted to demonstrate the simplicity of the proposed technique in handling fracture problems of circular cracks. The usage of the novel singular element can avoid mesh refinement near the crack front domain without loss of calculation accuracy and velocity of convergence. Compared with the conventional finite element methods and existing analytical methods, the present method is more suitable for dealing with complicated structures with a large number of elements.

Crack Path Selection in Thermally Loaded Borosilicate/Steel Bibeam Specimen

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

Grutzik, Scott Joseph; Reedy, Jr., E. D.

Here, we have developed a novel specimen for studying crack paths in glass. Under certain conditions, the specimen reaches a state where the crack must select between multiple paths satisfying the K II = 0 condition. This path selection is a simple but challenging benchmark case for both analytical and numerical methods of predicting crack propagation. We document the development of the specimen, using an uncracked and instrumented test case to study the effect of adhesive choice and validate the accuracy of both a simple beam theory model and a finite element model. In addition, we present preliminary fracture testmore » results and provide a comparison to the path predicted by two numerical methods (mesh restructuring and XFEM). The directional stability of the crack path and differences in kink angle predicted by various crack kinking criteria is analyzed with a finite element model.« less

Crack Path Selection in Thermally Loaded Borosilicate/Steel Bibeam Specimen

DOE PAGES

Grutzik, Scott Joseph; Reedy, Jr., E. D.

2017-08-04

Here, we have developed a novel specimen for studying crack paths in glass. Under certain conditions, the specimen reaches a state where the crack must select between multiple paths satisfying the K II = 0 condition. This path selection is a simple but challenging benchmark case for both analytical and numerical methods of predicting crack propagation. We document the development of the specimen, using an uncracked and instrumented test case to study the effect of adhesive choice and validate the accuracy of both a simple beam theory model and a finite element model. In addition, we present preliminary fracture testmore » results and provide a comparison to the path predicted by two numerical methods (mesh restructuring and XFEM). The directional stability of the crack path and differences in kink angle predicted by various crack kinking criteria is analyzed with a finite element model.« less

New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics

NASA Astrophysics Data System (ADS)

Xie, Dexuan

2014-10-01

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model in the calculation of electrostatic potential energy for biomolecules in ionic solvent, but its numerical solution remains a challenge due to its strong singularity and nonlinearity caused by its singular distribution source terms and exponential nonlinear terms. To effectively deal with such a challenge, in this paper, new solution decomposition and minimization schemes are proposed, together with a new PBE analysis on solution existence and uniqueness. Moreover, a PBE finite element program package is developed in Python based on the FEniCS program library and GAMer, a molecular surface and volumetric mesh generation program package. Numerical tests on proteins and a nonlinear Born ball model with an analytical solution validate the new solution decomposition and minimization schemes, and demonstrate the effectiveness and efficiency of the new PBE finite element program package.

Science and society test VI: Energy economics

NASA Astrophysics Data System (ADS)

Hafemeister, David W.

1982-01-01

Simple numerical estimates are developed in order to quantify a variety of energy economics issues. The Verhulst equation, which considers the effect of finite resources on petroleum production, is modified to take into account supply and demand economics. Numerical and analytical solutions to these differential equations are presented in terms of supply and demand elasticity functions, various finite resources, and the rate of increase in fuel costs. The indirect cost per barrel of imported oil from OPEC is shown to be about the same as the direct cost. These effects, as well as those of discounted benefits and deregulation, are used in a calculation of payback periods for various energy conserving devices. A phenomenological model for market penetration is developed along with the factors for future energy growth rates. A brief analysis of the economic returns of the ''house doctor'' program to reprofit houses for energy conservation is presented.

Mechanical low-frequency filter via modes separation in 3D periodic structures

NASA Astrophysics Data System (ADS)

D'Alessandro, L.; Belloni, E.; Ardito, R.; Braghin, F.; Corigliano, A.

2017-12-01

This work presents a strategy to design three-dimensional elastic periodic structures endowed with complete bandgaps, the first of which is ultra-wide, where the top limits of the first two bandgaps are overstepped in terms of wave transmission in the finite structure. Thus, subsequent bandgaps are merged, approaching the behaviour of a three-dimensional low-pass mechanical filter. This result relies on a proper organization of the modal characteristics, and it is validated by performing numerical and analytical calculations over the unit cell. A prototype of the analysed layout, made of Nylon by means of additive manufacturing, is experimentally tested to assess the transmission spectrum of the finite structure, obtaining good agreement with numerical predictions. The presented strategy paves the way for the development of a class of periodic structures to be used in robust and reliable wave attenuation over a wide frequency band.

Adaptive eigenspace method for inverse scattering problems in the frequency domain

NASA Astrophysics Data System (ADS)

Grote, Marcus J.; Kray, Marie; Nahum, Uri

2017-02-01

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.

Numerical Study of the Effect of Presence of Geometric Singularities on the Mechanical Behavior of Laminated Plates

NASA Astrophysics Data System (ADS)

Khechai, Abdelhak; Tati, Abdelouahab; Guettala, Abdelhamid

2017-05-01

In this paper, an effort is made to understand the effects of geometric singularities on the load bearing capacity and stress distribution in thin laminated plates. Composite plates with variously shaped cutouts are frequently used in both modern and classical aerospace, mechanical and civil engineering structures. Finite element investigation is undertaken to show the effect of geometric singularities on stress distribution. In this study, the stress concentration factors (SCFs) in cross-and-angle-ply laminated as well as in isotropic plates subjected to uniaxial loading are studied using a quadrilateral finite element of four nodes with thirty-two degrees-of-freedom per element. The varying parameters such as the cutout shape and hole sizes (a/b) are considered. The numerical results obtained by the present element are compared favorably with those obtained using the finite element software Freefem++ and the analytic findings published in literature, which demonstrates the accuracy of the present element. Freefem++ is open source software based on the finite element method, which could be helpful to study and improving the analyses of the stress distribution in composite plates with cutouts. The Freefem++ and the quadrilateral finite element formulations will be given in the beginning of this paper. Finally, to show the effect of the fiber orientation angle and anisotropic modulus ratio on the (SCF), number of figures are given for various ratio (a/b).

Two-dimensional numerical simulation of a Stirling engine heat exchanger

NASA Technical Reports Server (NTRS)

Ibrahim, Mounir; Tew, Roy C.; Dudenhoefer, James E.

1989-01-01

The first phase of an effort to develop multidimensional models of Stirling engine components is described. The ultimate goal is to model an entire engine working space. Parallel plate and tubular heat exchanger models are described, with emphasis on the central part of the channel (i.e., ignoring hydrodynamic and thermal end effects). The model assumes laminar, incompressible flow with constant thermophysical properties. In addition, a constant axial temperature gradient is imposed. The governing equations describing the model have been solved using the Crack-Nicloson finite-difference scheme. Model predictions are compared with analytical solutions for oscillating/reversing flow and heat transfer in order to check numerical accuracy. Excellent agreement is obtained for flow both in circular tubes and between parallel plates. The computational heat transfer results are in good agreement with the analytical heat transfer results for parallel plates.

Nonlinear electroelastic deformations of dielectric elastomer composites: II - Non-Gaussian elastic dielectrics

NASA Astrophysics Data System (ADS)

Lefèvre, Victor; Lopez-Pamies, Oscar

2017-02-01

This paper presents an analytical framework to construct approximate homogenization solutions for the macroscopic elastic dielectric response - under finite deformations and finite electric fields - of dielectric elastomer composites with two-phase isotropic particulate microstructures. The central idea consists in employing the homogenization solution derived in Part I of this work for ideal elastic dielectric composites within the context of a nonlinear comparison medium method - this is derived as an extension of the comparison medium method of Lopez-Pamies et al. (2013) in nonlinear elastostatics to the coupled realm of nonlinear electroelastostatics - to generate in turn a corresponding solution for composite materials with non-ideal elastic dielectric constituents. Complementary to this analytical framework, a hybrid finite-element formulation to construct homogenization solutions numerically (in three dimensions) is also presented. The proposed analytical framework is utilized to work out a general approximate homogenization solution for non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. The solution applies to arbitrary (non-percolative) isotropic distributions of filler particles. By construction, it is exact in the limit of small deformations and moderate electric fields. For finite deformations and finite electric fields, its accuracy is demonstrated by means of direct comparisons with finite-element solutions. Aimed at gaining physical insight into the extreme enhancement in electrostriction properties displayed by emerging dielectric elastomer composites, various cases wherein the filler particles are of poly- and mono-disperse sizes and exhibit different types of elastic dielectric behavior are discussed in detail. Contrary to an initial conjecture in the literature, it is found (inter alia) that the isotropic addition of a small volume fraction of stiff (semi-)conducting/high-permittivity particles to dielectric elastomers does not lead to the extreme electrostriction enhancements observed in experiments. It is posited that such extreme enhancements are the manifestation of interphasial phenomena.

A generalized chemistry version of SPARK

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.

1988-01-01

An extension of the reacting H2-air computer code SPARK is presented, which enables the code to be used on any reacting flow problem. Routines are developed calculating in a general fashion, the reaction rates, and chemical Jacobians of any reacting system. In addition, an equilibrium routine is added so that the code will have frozen, finite rate, and equilibrium capabilities. The reaction rate for the species is determined from the law of mass action using Arrhenius expressions for the rate constants. The Jacobian routines are determined by numerically or analytically differentiating the law of mass action for each species. The equilibrium routine is based on a Gibbs free energy minimization routine. The routines are written in FORTRAN 77, with special consideration given to vectorization. Run times for the generalized routines are generally 20 percent slower than reaction specific routines. The numerical efficiency of the generalized analytical Jacobian, however, is nearly 300 percent better than the reaction specific numerical Jacobian used in SPARK.

Effects of viscosity on shock-induced damping of an initial sinusoidal disturbance

NASA Astrophysics Data System (ADS)

Ma, Xiaojuan; Liu, Fusheng; Jing, Fuqian

2010-05-01

A lack of reliable data treatment method has been for several decades the bottleneck of viscosity measurement by disturbance amplitude damping method of shock waves. In this work the finite difference method is firstly applied to obtain the numerical solutions for disturbance amplitude damping behavior of sinusoidal shock front in inviscid and viscous flow. When water shocked to 15 GPa is taken as an example, the main results are as follows: (1) For inviscid and lower viscous flows the numerical method gives results in good agreement with the analytic solutions under the condition of small disturbance ( a 0/ λ=0.02); (2) For the flow of viscosity beyond 200 Pa s ( η = κ) the analytic solution is found to overestimate obviously the effects of viscosity. It is attributed to the unreal pre-conditions of analytic solution by Miller and Ahrens; (3) The present numerical method provides an effective tool with more confidence to overcome the bottleneck of data treatment when the effects of higher viscosity in experiments of Sakharov and flyer impact are expected to be analyzed, because it can in principle simulate the development of shock waves in flows with larger disturbance amplitude, higher viscosity, and complicated initial flow.

Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

NASA Astrophysics Data System (ADS)

Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.

2017-11-01

When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.

Anderson metal-insulator transitions with classical magnetic impurities

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

Jung, Daniel; Kettemann, Stefan

We study the effects of classical magnetic impurities on the Anderson metal-insulator transition (AMIT) numerically. In particular we find that while a finite concentration of Ising impurities lowers the critical value of the site-diagonal disorder amplitude W{sub c}, in the presence of Heisenberg impurities, W{sub c} is first increased with increasing exchange coupling strength J due to time-reversal symmetry breaking. The resulting scaling with J is compared to analytical predictions by Wegner [1]. The results are obtained numerically, based on a finite-size scaling procedure for the typical density of states [2], which is the geometric average of the local densitymore » of states. The latter can efficiently be calculated using the kernel polynomial method [3]. Although still suffering from methodical shortcomings, our method proves to deliver results close to established results for the orthogonal symmetry class [4]. We extend previous approaches [5] by combining the KPM with a finite-size scaling analysis. We also discuss the relevance of our findings for systems like phosphor-doped silicon (Si:P), which are known to exhibit a quantum phase transition from metal to insulator driven by the interplay of both interaction and disorder, accompanied by the presence of a finite concentration of magnetic moments [6].« less

Propagation of Finite Amplitude Sound in Multiple Waveguide Modes.

NASA Astrophysics Data System (ADS)

van Doren, Thomas Walter

1993-01-01

This dissertation describes a theoretical and experimental investigation of the propagation of finite amplitude sound in multiple waveguide modes. Quasilinear analytical solutions of the full second order nonlinear wave equation, the Westervelt equation, and the KZK parabolic wave equation are obtained for the fundamental and second harmonic sound fields in a rectangular rigid-wall waveguide. It is shown that the Westervelt equation is an acceptable approximation of the full nonlinear wave equation for describing guided sound waves of finite amplitude. A system of first order equations based on both a modal and harmonic expansion of the Westervelt equation is developed for waveguides with locally reactive wall impedances. Fully nonlinear numerical solutions of the system of coupled equations are presented for waveguides formed by two parallel planes which are either both rigid, or one rigid and one pressure release. These numerical solutions are compared to finite -difference solutions of the KZK equation, and it is shown that solutions of the KZK equation are valid only at frequencies which are high compared to the cutoff frequencies of the most important modes of propagation (i.e., for which sound propagates at small grazing angles). Numerical solutions of both the Westervelt and KZK equations are compared to experiments performed in an air-filled, rigid-wall, rectangular waveguide. Solutions of the Westervelt equation are in good agreement with experiment for low source frequencies, at which sound propagates at large grazing angles, whereas solutions of the KZK equation are not valid for these cases. At higher frequencies, at which sound propagates at small grazing angles, agreement between numerical solutions of the Westervelt and KZK equations and experiment is only fair, because of problems in specifying the experimental source condition with sufficient accuracy.

Pulsed plane wave analytic solutions for generic shapes and the validation of Maxwell's equations solvers

NASA Technical Reports Server (NTRS)

Yarrow, Maurice; Vastano, John A.; Lomax, Harvard

1992-01-01

Generic shapes are subjected to pulsed plane waves of arbitrary shape. The resulting scattered electromagnetic fields are determined analytically. These fields are then computed efficiently at field locations for which numerically determined EM fields are required. Of particular interest are the pulsed waveform shapes typically utilized by radar systems. The results can be used to validate the accuracy of finite difference time domain Maxwell's equations solvers. A two-dimensional solver which is second- and fourth-order accurate in space and fourth-order accurate in time is examined. Dielectric media properties are modeled by a ramping technique which simplifies the associated gridding of body shapes. The attributes of the ramping technique are evaluated by comparison with the analytic solutions.

Dispersive models describing mosquitoes’ population dynamics

NASA Astrophysics Data System (ADS)

Yamashita, W. M. S.; Takahashi, L. T.; Chapiro, G.

2016-08-01

The global incidences of dengue and, more recently, zica virus have increased the interest in studying and understanding the mosquito population dynamics. Understanding this dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. This work is based on the study of nonlinear mathematical models dealing with the life cycle of the dengue mosquito using partial differential equations. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration. Obtained solutions are validated through numerical simulations using finite difference schemes.

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

Stershic, Andrew J.; Dolbow, John E.; Moës, Nicolas

The Thick Level-Set (TLS) model is implemented to simulate brittle media undergoing dynamic fragmentation. This non-local model is discretized by the finite element method with damage represented as a continuous field over the domain. A level-set function defines the extent and severity of damage, and a length scale is introduced to limit the damage gradient. Numerical studies in one dimension demonstrate that the proposed method reproduces the rate-dependent energy dissipation and fragment length observations from analytical, numerical, and experimental approaches. In conclusion, additional studies emphasize the importance of appropriate bulk constitutive models and sufficient spatial resolution of the length scale.

The three-dimensional compressible flow in a radial inflow turbine scroll

NASA Technical Reports Server (NTRS)

Hamed, A.; Tabakoff, W.; Malak, M.

1984-01-01

This work presents the results of an analytical study and an experimental investigation of the three-dimensional flow in a turbine scroll. The finite element method is used in the iterative numerical solution of the locally linearized governing equations for the three-dimensional velocity potential field. The results of the numerical computations are compared with the experimental measurements in the scroll cross sections, which were obtained using laser Doppler velocimetry and hot wire techniques. The results of the computations show a variation in the flow conditions around the rotor periphery which was found to depend on the scroll geometry.

Numerical Analysis of Prefabricated Steel-Concrete Composite Floor in Typical Lipsk Building

NASA Astrophysics Data System (ADS)

Lacki, Piotr; Kasza, Przemysław; Derlatka, Anna

2017-12-01

The aim of the work was to perform numerical analysis of a steel-concrete composite floor located in a LIPSK type building. A numerical model of the analytically designed floor was performed. The floor was in a six-storey, retail and service building. The thickness of a prefabricated slab was 100 mm. The two-row, crisscrossed reinforcement of the slab was made from φ16 mm rods with a spacing of 150 x 200 mm. The span of the beams made of steel IPE 160 profiles was 6.00 m and they were spaced every 1.20 m. The steelconcrete composite was obtained using 80×16 Nelson fasteners. The numerical analysis was carried out using the ADINA System based on the Finite Element Method. The stresses and strains in the steel and concrete elements, the distribution of the forces in the reinforcement bars and cracking in concrete were evaluated. The FEM model was made from 3D-solid finite elements (IPE profile and concrete slab) and truss elements (reinforcement bars). The adopted steel material model takes into consideration the plastic state, while the adopted concrete material model takes into account material cracks.

Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches.

PubMed

Xu, Zhenli; Ma, Manman; Liu, Pei

2014-07-01

We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-Hückel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, toward the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.

A comparative analysis of numerical approaches to the mechanics of elastic sheets

NASA Astrophysics Data System (ADS)

Taylor, Michael; Davidovitch, Benny; Qiu, Zhanlong; Bertoldi, Katia

2015-06-01

Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of wrinkles in these problems has important implications in design and is an area of increasing interest in the fields of physics and engineering. In this work, several numerical approaches previously proposed to model equilibrium deformations in thin elastic sheets are compared. These include standard finite element-based static post-buckling approaches as well as a recently proposed method based on dynamic relaxation, which are applied to the problem of an annular sheet with opposed tractions where wrinkling is a key feature. Numerical solutions are compared to analytic predictions of the ground state, enabling a quantitative evaluation of the predictive power of the various methods. Results indicate that static finite element approaches produce local minima that are highly sensitive to initial imperfections, relying on a priori knowledge of the equilibrium wrinkling pattern to generate optimal results. In contrast, dynamic relaxation is much less sensitive to initial imperfections and can generate low-energy solutions for a wide variety of loading conditions without requiring knowledge of the equilibrium solution beforehand.

FOLDER: A numerical tool to simulate the development of structures in layered media

NASA Astrophysics Data System (ADS)

Adamuszek, Marta; Dabrowski, Marcin; Schmid, Daniel W.

2015-04-01

FOLDER is a numerical toolbox for modelling deformation in layered media during layer parallel shortening or extension in two dimensions. FOLDER builds on MILAMIN [1], a finite element method based mechanical solver, with a range of utilities included from the MUTILS package [2]. Numerical mesh is generated using the Triangle software [3]. The toolbox includes features that allow for: 1) designing complex structures such as multi-layer stacks, 2) accurately simulating large-strain deformation of linear and non-linear viscous materials, 3) post-processing of various physical fields such as velocity (total and perturbing), rate of deformation, finite strain, stress, deviatoric stress, pressure, apparent viscosity. FOLDER is designed to ensure maximum flexibility to configure model geometry, define material parameters, specify range of numerical parameters in simulations and choose the plotting options. FOLDER is an open source MATLAB application and comes with a user friendly graphical interface. The toolbox additionally comprises an educational application that illustrates various analytical solutions of growth rates calculated for the cases of folding and necking of a single layer with interfaces perturbed with a single sinusoidal waveform. We further derive two novel analytical expressions for the growth rate in the cases of folding and necking of a linear viscous layer embedded in a linear viscous medium of a finite thickness. We use FOLDER to test the accuracy of single-layer folding simulations using various 1) spatial and temporal resolutions, 2) time integration schemes, and 3) iterative algorithms for non-linear materials. The accuracy of the numerical results is quantified by: 1) comparing them to analytical solution, if available, or 2) running convergence tests. As a result, we provide a map of the most optimal choice of grid size, time step, and number of iterations to keep the results of the numerical simulations below a given error for a given time integration scheme. We also demonstrate that Euler and Leapfrog time integration schemes are not recommended for any practical use. Finally, the capabilities of the toolbox are illustrated based on two examples: 1) shortening of a synthetic multi-layer sequence and 2) extension of a folded quartz vein embedded in phyllite from Sprague Upper Reservoir (example discussed by Sherwin and Chapple [4]). The latter example demonstrates that FOLDER can be successfully used for reverse modelling and mechanical restoration. [1] Dabrowski, M., Krotkiewski, M., and Schmid, D. W., 2008, MILAMIN: MATLAB-based finite element method solver for large problems. Geochemistry Geophysics Geosystems, vol. 9. [2] Krotkiewski, M. and Dabrowski M., 2010 Parallel symmetric sparse matrix-vector product on scalar multi-core cpus. Parallel Computing, 36(4):181-198 [3] Shewchuk, J. R., 1996, Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator, In: Applied Computational Geometry: Towards Geometric Engineering'' (Ming C. Lin and Dinesh Manocha, editors), Vol. 1148 of Lecture Notes in Computer Science, pp. 203-222, Springer-Verlag, Berlin [4] Sherwin, J.A., Chapple, W.M., 1968. Wavelengths of single layer folds - a Comparison between theory and Observation. American Journal of Science 266 (3), p. 167-179

Thermo-viscoelastic response of graphite/epoxy composites

NASA Technical Reports Server (NTRS)

Lin, Kuen; Hwang, I. H.

1988-01-01

The thermo-viscoelastic behavior of composite material is studied analytically using a special finite-element formulation. Numerical results on stress and deformation histories are obtained for both unnotched and notched graphite/epoxy composites subjected to mechanical and thermal spectrum loads. The results indicate that time-dependent effects are important in composites with matrix-dominated layup orientations. Such effects also strongly depend on the specific environment condition and load spectrum applied.

Brownian dynamics without Green's functions

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

Delong, Steven; Donev, Aleksandar, E-mail: donev@courant.nyu.edu; Usabiaga, Florencio Balboa

2014-04-07

We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions “on the fly.” Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. Thismore » is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.« less

Calculation of Sensitivity Derivatives in an MDAO Framework

NASA Technical Reports Server (NTRS)

Moore, Kenneth T.

2012-01-01

During gradient-based optimization of a system, it is necessary to generate the derivatives of each objective and constraint with respect to each design parameter. If the system is multidisciplinary, it may consist of a set of smaller "components" with some arbitrary data interconnection and process work ow. Analytical derivatives in these components can be used to improve the speed and accuracy of the derivative calculation over a purely numerical calculation; however, a multidisciplinary system may include both components for which derivatives are available and components for which they are not. Three methods to calculate the sensitivity of a mixed multidisciplinary system are presented: the finite difference method, where the derivatives are calculated numerically; the chain rule method, where the derivatives are successively cascaded along the system's network graph; and the analytic method, where the derivatives come from the solution of a linear system of equations. Some improvements to these methods, to accommodate mixed multidisciplinary systems, are also presented; in particular, a new method is introduced to allow existing derivatives to be used inside of finite difference. All three methods are implemented and demonstrated in the open-source MDAO framework OpenMDAO. It was found that there are advantages to each of them depending on the system being solved.

Poroelastic finite difference modeling of seismic attenuation and dispersion due to mesoscopic-scale heterogeneity

NASA Astrophysics Data System (ADS)

Masson, Y. J.; Pride, S. R.

2007-03-01

Seismic attenuation and dispersion are numerically determined for computer-generated porous materials that contain arbitrary amounts of mesoscopic-scale heterogeneity in the porous continuum properties. The local equations used to determine the poroelastic response within such materials are those of Biot (1962). Upon applying a step change in stress to samples containing mesoscopic-scale heterogeneity, the poroelastic response is determined using finite difference modeling, and the average strain throughout the sample computed, along with the effective complex and frequency-dependent elastic moduli of the sample. The ratio of the imaginary and real parts of these moduli determines the attenuation as a function of frequency associated with the modes of applied stress (pure compression and pure shear). By having a wide range of heterogeneity present, there exists a wide range of relaxation frequencies in the response with the result that the curves of attenuation as a function of frequency are broader than in existing analytical theories based on a single relaxation frequency. Analytical explanations are given for the various high-frequency and low-frequency asymptotic behavior observed in the numerical simulations. It is also shown that the overall level of attenuation of a given sample is proportional to the square of the incompressibility contrasts locally present.

A Finite Layer Formulation for Groundwater Flow to Horizontal Wells.

PubMed

Xu, Jin; Wang, Xudong

2016-09-01

A finite layer approach for the general problem of three-dimensional (3D) flow to horizontal wells in multilayered aquifer systems is presented, in which the unconfined flow can be taken into account. The flow is approximated by an integration of the standard finite element method in vertical direction and the analytical techniques in the other spatial directions. Because only the vertical discretization is involved, the horizontal wells can be completely contained in one specific nodal plane without discretization. Moreover, due to the analytical eigenfunctions introduced in the formulation, the weighted residual equations can be decoupled, and the formulas for the global matrices and flow vector corresponding to horizontal wells can be obtained explicitly. Consequently, the bandwidth of the global matrices and computational cost rising from 3D analysis can be significantly reduced. Two comparisons to the existing solutions are made to verify the validity of the formulation, including transient flow to horizontal wells in confined and unconfined aquifers. Furthermore, an additional numerical application to horizontal wells in three-layered systems is presented to demonstrate the applicability of the present method in modeling flow in more complex aquifer systems. © 2016, National Ground Water Association.

Time-domain simulation of constitutive relations for nonlinear acoustics including relaxation for frequency power law attenuation media modeling

NASA Astrophysics Data System (ADS)

Jiménez, Noé; Camarena, Francisco; Redondo, Javier; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.

2015-10-01

We report a numerical method for solving the constitutive relations of nonlinear acoustics, where multiple relaxation processes are included in a generalized formulation that allows the time-domain numerical solution by an explicit finite differences scheme. Thus, the proposed physical model overcomes the limitations of the one-way Khokhlov-Zabolotskaya-Kuznetsov (KZK) type models and, due to the Lagrangian density is implicitly included in the calculation, the proposed method also overcomes the limitations of Westervelt equation in complex configurations for medical ultrasound. In order to model frequency power law attenuation and dispersion, such as observed in biological media, the relaxation parameters are fitted to both exact frequency power law attenuation/dispersion media and also empirically measured attenuation of a variety of tissues that does not fit an exact power law. Finally, a computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the finite difference scheme, and, on the other hand, improve stability trough artificial attenuation when shock waves are present. This technique avoids the use of high-order finite-differences schemes leading to fast calculations. The present algorithm is especially suited for practical configuration where spatial discontinuities are present in the domain (e.g. axisymmetric domains or zero normal velocity boundary conditions in general). The accuracy of the method is discussed by comparing the proposed simulation solutions to one dimensional analytical and k-space numerical solutions.

Optimal implicit 2-D finite differences to model wave propagation in poroelastic media

NASA Astrophysics Data System (ADS)

Itzá, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.

2016-08-01

Numerical modeling of seismic waves in heterogeneous porous reservoir rocks is an important tool for the interpretation of seismic surveys in reservoir engineering. We apply globally optimal implicit staggered-grid finite differences (FD) to model 2-D wave propagation in heterogeneous poroelastic media at a low-frequency range (<10 kHz). We validate the numerical solution by comparing it to an analytical-transient solution obtaining clear seismic wavefields including fast P and slow P and S waves (for a porous media saturated with fluid). The numerical dispersion and stability conditions are derived using von Neumann analysis, showing that over a wide range of porous materials the Courant condition governs the stability and this optimal implicit scheme improves the stability of explicit schemes. High-order explicit FD can be replaced by some lower order optimal implicit FD so computational cost will not be as expensive while maintaining the accuracy. Here, we compute weights for the optimal implicit FD scheme to attain an accuracy of γ = 10-8. The implicit spatial differentiation involves solving tridiagonal linear systems of equations through Thomas' algorithm.

T-matrix method in plasmonics: An overview

NASA Astrophysics Data System (ADS)

Khlebtsov, Nikolai G.

2013-07-01

Optical properties of isolated and coupled plasmonic nanoparticles (NPs) are of great interest for many applications in nanophotonics, nanobiotechnology, and nanomedicine owing to rapid progress in fabrication, characterization, and surface functionalization technologies. To simulate optical responses from plasmonic nanostructures, various electromagnetic analytical and numerical methods have been adapted, tested, and used during the past two decades. Currently, the most popular numerical techniques are those that do not suffer from geometrical and composition limitations, e.g., the discrete dipole approximation (DDA), the boundary (finite) element method (BEM, FEM), the finite difference time domain method (FDTDM), and others. However, the T-matrix method still has its own niche in plasmonic science because of its great numerical efficiency, especially for systems with randomly oriented particles and clusters. In this review, I consider the application of the T-matrix method to various plasmonic problems, including dipolar, multipolar, and anisotropic properties of metal NPs; sensing applications; surface enhanced Raman scattering; optics of 1D-3D nanoparticle assemblies; plasmonic particles and clusters near and on substrates; and manipulation of plasmonic NPs with laser tweezers.

Solving the three-body Coulomb breakup problem using exterior complex scaling

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

McCurdy, C.W.; Baertschy, M.; Rescigno, T.N.

2004-05-17

Electron-impact ionization of the hydrogen atom is the prototypical three-body Coulomb breakup problem in quantum mechanics. The combination of subtle correlation effects and the difficult boundary conditions required to describe two electrons in the continuum have made this one of the outstanding challenges of atomic physics. A complete solution of this problem in the form of a ''reduction to computation'' of all aspects of the physics is given by the application of exterior complex scaling, a modern variant of the mathematical tool of analytic continuation of the electronic coordinates into the complex plane that was used historically to establish themore » formal analytic properties of the scattering matrix. This review first discusses the essential difficulties of the three-body Coulomb breakup problem in quantum mechanics. It then describes the formal basis of exterior complex scaling of electronic coordinates as well as the details of its numerical implementation using a variety of methods including finite difference, finite elements, discrete variable representations, and B-splines. Given these numerical implementations of exterior complex scaling, the scattering wave function can be generated with arbitrary accuracy on any finite volume in the space of electronic coordinates, but there remains the fundamental problem of extracting the breakup amplitudes from it. Methods are described for evaluating these amplitudes. The question of the volume-dependent overall phase that appears in the formal theory of ionization is resolved. A summary is presented of accurate results that have been obtained for the case of electron-impact ionization of hydrogen as well as a discussion of applications to the double photoionization of helium.« less

Elastic guided waves in a layered plate with rectangular cross section.

PubMed

Mukdadi, O M; Desai, Y M; Datta, S K; Shah, A H; Niklasson, A J

2002-11-01

Guided waves in a layered elastic plate of rectangular cross section (finite width and thickness) has been studied in this paper. A semianalytical finite element method in which the deformation of the cross section is modeled by two-dimensional finite elements and analytical representation of propagating waves along the length of the plate has been used. The method is applicable to arbitrary number of layers and general anisotropic material properties of each layer, and is similar to the stiffness method used earlier to study guided waves in a laminated composite plate of infinite width. Numerical results showing the effect of varying the width of the plate on the dispersion of guided waves are presented and are compared with those for an infinite plate. In addition, effect of thin anisotropic coating or interface layers on the guided waves is investigated.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

Analytical solution and numerical simulation of the liquid nitrogen freezing-temperature field of a single pipe

NASA Astrophysics Data System (ADS)

Cai, Haibing; Xu, Liuxun; Yang, Yugui; Li, Longqi

2018-05-01

Artificial liquid nitrogen freezing technology is widely used in urban underground engineering due to its technical advantages, such as simple freezing system, high freezing speed, low freezing temperature, high strength of frozen soil, and absence of pollution. However, technical difficulties such as undefined range of liquid nitrogen freezing and thickness of frozen wall gradually emerge during the application process. Thus, the analytical solution of the freezing-temperature field of a single pipe is established considering the freezing temperature of soil and the constant temperature of freezing pipe wall. This solution is then applied in a liquid nitrogen freezing project. Calculation results show that the radius of freezing front of liquid nitrogen is proportional to the square root of freezing time. The radius of the freezing front also decreases with decreased the freezing temperature, and the temperature gradient of soil decreases with increased distance from the freezing pipe. The radius of cooling zone in the unfrozen area is approximately four times the radius of the freezing front. Meanwhile, the numerical simulation of the liquid nitrogen freezing-temperature field of a single pipe is conducted using the Abaqus finite-element program. Results show that the numerical simulation of soil temperature distribution law well agrees with the analytical solution, further verifies the reliability of the established analytical solution of the liquid nitrogen freezing-temperature field of a single pipe.

An explicit closed-form analytical solution for European options under the CGMY model

NASA Astrophysics Data System (ADS)

Chen, Wenting; Du, Meiyu; Xu, Xiang

2017-01-01

In this paper, we consider the analytical pricing of European path-independent options under the CGMY model, which is a particular type of pure jump Le´vy process, and agrees well with many observed properties of the real market data by allowing the diffusions and jumps to have both finite and infinite activity and variation. It is shown that, under this model, the option price is governed by a fractional partial differential equation (FPDE) with both the left-side and right-side spatial-fractional derivatives. In comparison to derivatives of integer order, fractional derivatives at a point not only involve properties of the function at that particular point, but also the information of the function in a certain subset of the entire domain of definition. This ;globalness; of the fractional derivatives has added an additional degree of difficulty when either analytical methods or numerical solutions are attempted. Albeit difficult, we still have managed to derive an explicit closed-form analytical solution for European options under the CGMY model. Based on our solution, the asymptotic behaviors of the option price and the put-call parity under the CGMY model are further discussed. Practically, a reliable numerical evaluation technique for the current formula is proposed. With the numerical results, some analyses of impacts of four key parameters of the CGMY model on European option prices are also provided.

Numerical modelling and experimental analysis of acoustic emission

NASA Astrophysics Data System (ADS)

Gerasimov, S. I.; Sych, T. V.

2018-05-01

In the present paper, the authors report on the application of non-destructive acoustic waves technologies to determine the structural integrity of engineering components. In particular, a finite element (FE) system COSMOS/M is used to investigate propagation characteristics of ultrasonic waves in linear, plane and three-dimensional structures without and with geometric concentrators. In addition, the FE results obtained are compared to the analytical and experimental ones. The study illustrates the efficient use of the FE method to model guided wave propagation problems and demonstrates the FE method’s potential to solve problems when an analytical solution is not possible due to “complicated” geometry.

Matter-wave dark solitons: stochastic versus analytical results.

PubMed

Cockburn, S P; Nistazakis, H E; Horikis, T P; Kevrekidis, P G; Proukakis, N P; Frantzeskakis, D J

2010-04-30

The dynamics of dark matter-wave solitons in elongated atomic condensates are discussed at finite temperatures. Simulations with the stochastic Gross-Pitaevskii equation reveal a noticeable, experimentally observable spread in individual soliton trajectories, attributed to inherent fluctuations in both phase and density of the underlying medium. Averaging over a number of such trajectories (as done in experiments) washes out such background fluctuations, revealing a well-defined temperature-dependent temporal growth in the oscillation amplitude. The average soliton dynamics is well captured by the simpler dissipative Gross-Pitaevskii equation, both numerically and via an analytically derived equation for the soliton center based on perturbation theory for dark solitons.

The serpentine optical waveguide: engineering the dispersion relations and the stopped light points.

PubMed

Scheuer, Jacob; Weiss, Ori

2011-06-06

We present a study a new type of optical slow-light structure comprising a serpentine shaped waveguide were the loops are coupled. The dispersion relation, group velocity and GVD are studied analytically using a transfer matrix method and numerically using finite difference time domain simulations. The structure exhibits zero group velocity points at the ends of the Brillouin zone, but also within the zone. The position of mid-zone zero group velocity point can be tuned by modifying the coupling coefficient between adjacent loops. Closed-form analytic expressions for the dispersion relations, group velocity and the mid-zone zero v(g) points are found and presented.

An integral transform approach for a mixed boundary problem involving a flowing partially penetrating well with infinitesimal well skin

NASA Astrophysics Data System (ADS)

Chang, Chien-Chieh; Chen, Chia-Shyun

2002-06-01

A flowing partially penetrating well with infinitesimal well skin is a mixed boundary because a Cauchy condition is prescribed along the screen length and a Neumann condition of no flux is stipulated over the remaining unscreened part. An analytical approach based on the integral transform technique is developed to determine the Laplace domain solution for such a mixed boundary problem in a confined aquifer of finite thickness. First, the mixed boundary is changed into a homogeneous Neumann boundary by substituting the Cauchy condition with a Neumann condition in terms of well bore flux that varies along the screen length and is time dependent. Despite the well bore flux being unknown a priori, the modified model containing this homogeneous Neumann boundary can be solved with the Laplace and the finite Fourier cosine transforms. To determine well bore flux, screen length is discretized into a finite number of segments, to which the Cauchy condition is reinstated. This reinstatement also restores the relation between the original model and the solutions obtained. For a given time, the numerical inversion of the Laplace domain solution yields the drawdown distributions, well bore flux, and the well discharge. This analytical approach provides an alternative for dealing with the mixed boundary problems, especially when aquifer thickness is assumed to be finite.

On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach

NASA Astrophysics Data System (ADS)

Gerstmayr, Johannes; Irschik, Hans

2008-12-01

In finite element methods that are based on position and slope coordinates, a representation of axial and bending deformation by means of an elastic line approach has become popular. Such beam and plate formulations based on the so-called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories. Examining the existing planar absolute nodal coordinate element, which uses a curvature proportional bending strain expression, it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and, even more serious, the normal force is incorrect. A correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived. The strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the St. Venant-Kirchhoff material: therefore, the strain energy is derived for the latter case and compared to classical nonlinear rod theories. The error in the original absolute nodal coordinate formulation is documented by numerical examples. The numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach, while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications. The numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre-curved static and dynamic problems, including buckling and eigenvalue analysis. The resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy-momentum conservation.

Quasi-static finite element modeling of seismic attenuation and dispersion due to wave-induced fluid flow in poroelastic media

NASA Astrophysics Data System (ADS)

Quintal, Beatriz; Steeb, Holger; Frehner, Marcel; Schmalholz, Stefan M.

2011-01-01

The finite element method is used to solve Biot's equations of consolidation in the displacement-pressure (u - p) formulation. We compute one-dimensional (1-D) and two-dimensional (2-D) numerical quasi-static creep tests with poroelastic media exhibiting mesoscopic-scale heterogeneities to calculate the complex and frequency-dependent P wave moduli from the modeled stress-strain relations. The P wave modulus is used to calculate the frequency-dependent attenuation (i.e., inverse of quality factor) and phase velocity of the medium. Attenuation and velocity dispersion are due to fluid flow induced by pressure differences between regions of different compressibilities, e.g., regions (or patches) saturated with different fluids (i.e., so-called patchy saturation). Comparison of our numerical results with analytical solutions demonstrates the accuracy and stability of the algorithm for a wide range of frequencies (six orders of magnitude). The algorithm employs variable time stepping and an unstructured mesh which make it efficient and accurate for 2-D simulations in media with heterogeneities of arbitrary geometries (e.g., curved shapes). We further numerically calculate the quality factor and phase velocity for 1-D layered patchy saturated porous media exhibiting random distributions of patch sizes. We show that the numerical results for the random distributions can be approximated using a volume average of White's analytical solution and the proposed averaging method is, therefore, suitable for a fast and transparent prediction of both quality factor and phase velocity. Application of our results to frequency-dependent reflection coefficients of hydrocarbon reservoirs indicates that attenuation due to wave-induced flow can increase the reflection coefficient at low frequencies, as is observed at some reservoirs.

A numerical simulation of finite-length Taylor-Couette flow

NASA Technical Reports Server (NTRS)

Streett, C. L.; Hussaini, M. Y.

1987-01-01

The processes leading to laminar-turbulent transition in finite-channel-length Taylor-Couette flow are investigated analytically, solving the unsteady incompressible Navier-Stokes equations by spectral-collocation methods. A time-split algorithm, implementable in both axisymmetric and fully three-dimensional time-accurate versions, and an algorithm based on the staggered-mesh discretization of Bernardi and Maday (1986) are described in detail, and results obtained by applying the axisymmetric version of the first algorithm and a steady-state version of the second are presented graphically and compared with published experimental data. The feasibility of full three-dimensional simulations of the progression through chaotic states to turbulence under the constraints of Taylor-Couette flow is demonstrated.

Nonperturbative quark-gluon thermodynamics at finite density

NASA Astrophysics Data System (ADS)

Andreichikov, M. A.; Lukashov, M. S.; Simonov, Yu. A.

2018-03-01

Thermodynamics of the quark-gluon plasma at finite density is studied in the framework of the Field Correlator Method, where thermodynamical effects of Polyakov loops and color magnetic confinement are taken into account. Having found good agreement with numerical lattice data for zero density, we calculate pressure P(T,μ), for 0 < μ < 400 MeV and 150 < T < 1000 MeV. For the first time, the explicit integral form is found in this region, demonstrating analytic structure in the complex μ plane. The resulting multiple complex branch points are found at the Roberge-Weiss values of Imμ, with Reμ defined by the values of Polyakov lines and color magnetic confinement.

A MacCormack-TVD finite difference method to simulate the mass flow in mountainous terrain with variable computational domain

NASA Astrophysics Data System (ADS)

Ouyang, Chaojun; He, Siming; Xu, Qiang; Luo, Yu; Zhang, Wencheng

2013-03-01

A two-dimensional mountainous mass flow dynamic procedure solver (Massflow-2D) using the MacCormack-TVD finite difference scheme is proposed. The solver is implemented in Matlab on structured meshes with variable computational domain. To verify the model, a variety of numerical test scenarios, namely, the classical one-dimensional and two-dimensional dam break, the landslide in Hong Kong in 1993 and the Nora debris flow in the Italian Alps in 2000, are executed, and the model outputs are compared with published results. It is established that the model predictions agree well with both the analytical solution as well as the field observations.

Radiative nonrecoil nuclear finite size corrections of order α(Zα)5 to the Lamb shift in light muonic atoms

NASA Astrophysics Data System (ADS)

Faustov, R. N.; Martynenko, A. P.; Martynenko, F. A.; Sorokin, V. V.

2017-12-01

On the basis of quasipotential method in quantum electrodynamics we calculate nuclear finite size radiative corrections of order α(Zα) 5 to the Lamb shift in muonic hydrogen and helium. To construct the interaction potential of particles, which gives the necessary contributions to the energy spectrum, we use the method of projection operators to states with a definite spin. Separate analytic expressions for the contributions of the muon self-energy, the muon vertex operator and the amplitude with spanning photon are obtained. We present also numerical results for these contributions using modern experimental data on the electromagnetic form factors of light nuclei.

Nonlinear transient waves in coupled phase oscillators with inertia.

PubMed

Jörg, David J

2015-05-01

Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.

Experimental and numerical investigation of slabs on ground subjected to concentrated loads

NASA Astrophysics Data System (ADS)

Øverli, Jan

2014-09-01

An experimental program is presented where a slab on ground is subjected to concentrated loading at the centre, the edges and at the corners. Analytical solutions for the ultimate load capacity fit well with the results obtained in the tests. The non-linear behaviour of the slab is captured by performing nonlinear finite element analyses. The soil is modelled as a no-tension bedding and a smeared crack approach is employed for the concrete. Through a parametric study, the finite element model has been used to assess the influence of subgrade stiffness and shrinkage. The results indicate that drying shrinkage can cause severe cracking in slabs on grade.

Progressive Failure Studies of Stiffened Panels Subjected to Shear Loading

NASA Technical Reports Server (NTRS)

Ambur, Damodar R.; Jaunky, Navin; Hilburger, Mark W.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

Experimental and analytical results are presented for progressive failure of stiffened composite panels with and without a notch and subjected to in plane shear loading well into their postbuckling regime. Initial geometric imperfections are included in the finite element models. Ply damage modes such as matrix cracking, fiber-matrix shear, and fiber failure are modeled by degrading the material properties. Experimental results from the test include strain field data from video image correlation in three dimensions in addition to other strain and displacement measurements. Results from nonlinear finite element analyses are compared with experimental data. Good agreement between experimental data and numerical results are observed for the stitched stiffened composite panels studied.

Coherent beam combination of fiber lasers with a strongly confined waveguide: numerical model.

PubMed

Tao, Rumao; Si, Lei; Ma, Yanxing; Zhou, Pu; Liu, Zejin

2012-08-20

Self-imaging properties of fiber lasers in a strongly confined waveguide (SCW) and their application in coherent beam combination (CBC) are studied theoretically. Analytical formulas are derived for the positions, amplitudes, and phases of the N images at the end of an SCW, which is important for quantitative analysis of waveguide CBC. The formulas are verified with experimental results and numerical simulation of a finite difference beam propagation method (BPM). The error of our analytical formulas is less than 6%, which can be reduced to less than 1.5% with Goos-Hahnchen penetration depth considered. Based on the theoretical model and BPM, we studied the combination of two laser beams based on an SCW. The effects of the waveguide refractive index and Gaussian beam waist are studied. We also simulated the CBC of nine and 16 fiber lasers, and a single beam without side lobes was achieved.

Development of a computational testbed for numerical simulation of combustion instability

NASA Technical Reports Server (NTRS)

Grenda, Jeffrey; Venkateswaran, Sankaran; Merkle, Charles L.

1993-01-01

A synergistic hierarchy of analytical and computational fluid dynamic techniques is used to analyze three-dimensional combustion instabilities in liquid rocket engines. A mixed finite difference/spectral procedure is employed to study the effects of a distributed vaporization zone on standing and spinning instability modes within the chamber. Droplet atomization and vaporization are treated by a variety of classical models found in the literature. A multi-zone, linearized analytical solution is used to validate the accuracy of the numerical simulations at small amplitudes for a distributed vaporization region. This comparison indicates excellent amplitude and phase agreement under both stable and unstable operating conditions when amplitudes are small and proper grid resolution is used. As amplitudes get larger, expected nonlinearities are observed. The effect of liquid droplet temperature fluctuations was found to be of critical importance in driving the instabilities of the combustion chamber.

Fast Estimation of Strains for Cross-Beams Six-Axis Force/Torque Sensors by Mechanical Modeling

PubMed Central

Ma, Junqing; Song, Aiguo

2013-01-01

Strain distributions are crucial criteria of cross-beams six-axis force/torque sensors. The conventional method for calculating the criteria is to utilize Finite Element Analysis (FEA) to get numerical solutions. This paper aims to obtain analytical solutions of strains under the effect of external force/torque in each dimension. Genetic mechanical models for cross-beams six-axis force/torque sensors are proposed, in which deformable cross elastic beams and compliant beams are modeled as quasi-static Timoshenko beam. A detailed description of model assumptions, model idealizations, application scope and model establishment is presented. The results are validated by both numerical FEA simulations and calibration experiments, and test results are found to be compatible with each other for a wide range of geometric properties. The proposed analytical solutions are demonstrated to be an accurate estimation algorithm with higher efficiency. PMID:23686144

Radiation-stimulated explosive evaporation and burning of hydrogen droplets in hot aerosol mixtures

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

Osipov, V. V.; Marchenko, M. P.; Khasin, M.

2016-06-13

We present results of analytical and numerical investigation of explosive evaporation and burning scenarios of hydrogen droplets in hydrogen/oxygen aerosols. The following two scenarios have been elucidated. The first scenario, corresponding to sufficiently large droplets, is characterized by three stages: (i) an essentially homogeneous heating of a droplet to a near-critical temperature by IR radiation from the hot gas; (ii) explosive evaporation; and (iii) burning of hydrogen cloud formed by evaporation. The second scenario, corresponding to small droplets, differs in that a droplet is heated mainly by thermal conduction from the hot gas. The heating is accompanied by evaporation whichmore » can become explosive at the final stage of evaporation. The crossover droplet size separating the two scenarios is calculated. Conservative finite-difference numerical analysis is used to explore the predicted scenarios and verify analytical estimates.« less

Modeling the propagation of electromagnetic waves over the surface of the human body

NASA Astrophysics Data System (ADS)

Vendik, I. B.; Vendik, O. G.; Kirillov, V. V.; Pleskachev, V. V.; Tural'chuk, P. A.

2016-12-01

The results of modeling and an experimental study of electromagnetic (EM) waves in microwave range propagating along the surface of the human body have been presented. The parameters of wave propagation, such as the attenuation and phase velocity, have also been investigated. The calculation of the propagation of EM waves by the numerical method FDTD (finite difference time domain), as well as the use of the analytical model of the propagation of the EM wave along flat and curved surfaces has been fulfilled. An experimental study on a human body has been conducted. It has been shown that creeping waves are slow and exhibit a noticeable dispersion, while the surface waves are dispersionless and propagate at the speed of light in free space. A comparison of the results of numerical simulation, analytical calculation, and experimental investigations at a frequency of 2.55 GHz has been carried out.

Temperature distribution of a simplified rotor due to a uniform heat source

NASA Astrophysics Data System (ADS)

Welzenbach, Sarah; Fischer, Tim; Meier, Felix; Werner, Ewald; kyzy, Sonun Ulan; Munz, Oliver

2018-03-01

In gas turbines, high combustion efficiency as well as operational safety are required. Thus, labyrinth seal systems with honeycomb liners are commonly used. In the case of rubbing events in the seal system, the components can be damaged due to cyclic thermal and mechanical loads. Temperature differences occurring at labyrinth seal fins during rubbing events can be determined by considering a single heat source acting periodically on the surface of a rotating cylinder. Existing literature analysing the temperature distribution on rotating cylindrical bodies due to a stationary heat source is reviewed. The temperature distribution on the circumference of a simplified labyrinth seal fin is calculated using an available and easy to implement analytical approach. A finite element model of the simplified labyrinth seal fin is created and the numerical results are compared to the analytical results. The temperature distributions calculated by the analytical and the numerical approaches coincide for low sliding velocities, while there are discrepancies of the calculated maximum temperatures for higher sliding velocities. The use of the analytical approach allows the conservative estimation of the maximum temperatures arising in labyrinth seal fins during rubbing events. At the same time, high calculation costs can be avoided.

On solving wave equations on fixed bounded intervals involving Robin boundary conditions with time-dependent coefficients

NASA Astrophysics Data System (ADS)

van Horssen, Wim T.; Wang, Yandong; Cao, Guohua

2018-06-01

In this paper, it is shown how characteristic coordinates, or equivalently how the well-known formula of d'Alembert, can be used to solve initial-boundary value problems for wave equations on fixed, bounded intervals involving Robin type of boundary conditions with time-dependent coefficients. A Robin boundary condition is a condition that specifies a linear combination of the dependent variable and its first order space-derivative on a boundary of the interval. Analytical methods, such as the method of separation of variables (SOV) or the Laplace transform method, are not applicable to those types of problems. The obtained analytical results by applying the proposed method, are in complete agreement with those obtained by using the numerical, finite difference method. For problems with time-independent coefficients in the Robin boundary condition(s), the results of the proposed method also completely agree with those as for instance obtained by the method of separation of variables, or by the finite difference method.

a Bounded Finite-Difference Discretization of a Two-Dimensional Diffusion Equation with Logistic Nonlinear Reaction

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

In the present manuscript, we introduce a finite-difference scheme to approximate solutions of the two-dimensional version of Fisher's equation from population dynamics, which is a model for which the existence of traveling-wave fronts bounded within (0,1) is a well-known fact. The method presented here is a nonstandard technique which, in the linear regime, approximates the solutions of the original model with a consistency of second order in space and first order in time. The theory of M-matrices is employed here in order to elucidate conditions under which the method is able to preserve the positivity and the boundedness of solutions. In fact, our main result establishes relatively flexible conditions under which the preservation of the positivity and the boundedness of new approximations is guaranteed. Some simulations of the propagation of a traveling-wave solution confirm the analytical results derived in this work; moreover, the experiments evince a good agreement between the numerical result and the analytical solutions.

Broadband impedance boundary conditions for the simulation of sound propagation in the time domain.

PubMed

Bin, Jonghoon; Yousuff Hussaini, M; Lee, Soogab

2009-02-01

An accurate and practical surface impedance boundary condition in the time domain has been developed for application to broadband-frequency simulation in aeroacoustic problems. To show the capability of this method, two kinds of numerical simulations are performed and compared with the analytical/experimental results: one is acoustic wave reflection by a monopole source over an impedance surface and the other is acoustic wave propagation in a duct with a finite impedance wall. Both single-frequency and broadband-frequency simulations are performed within the framework of linearized Euler equations. A high-order dispersion-relation-preserving finite-difference method and a low-dissipation, low-dispersion Runge-Kutta method are used for spatial discretization and time integration, respectively. The results show excellent agreement with the analytical/experimental results at various frequencies. The method accurately predicts both the amplitude and the phase of acoustic pressure and ensures the well-posedness of the broadband time-domain impedance boundary condition.

Extended Analytic Device Optimization Employing Asymptotic Expansion

NASA Technical Reports Server (NTRS)

Mackey, Jonathan; Sehirlioglu, Alp; Dynsys, Fred

2013-01-01

Analytic optimization of a thermoelectric junction often introduces several simplifying assumptionsincluding constant material properties, fixed known hot and cold shoe temperatures, and thermallyinsulated leg sides. In fact all of these simplifications will have an effect on device performance,ranging from negligible to significant depending on conditions. Numerical methods, such as FiniteElement Analysis or iterative techniques, are often used to perform more detailed analysis andaccount for these simplifications. While numerical methods may stand as a suitable solution scheme,they are weak in gaining physical understanding and only serve to optimize through iterativesearching techniques. Analytic and asymptotic expansion techniques can be used to solve thegoverning system of thermoelectric differential equations with fewer or less severe assumptionsthan the classic case. Analytic methods can provide meaningful closed form solutions and generatebetter physical understanding of the conditions for when simplifying assumptions may be valid.In obtaining the analytic solutions a set of dimensionless parameters, which characterize allthermoelectric couples, is formulated and provide the limiting cases for validating assumptions.Presentation includes optimization of both classic rectangular couples as well as practically andtheoretically interesting cylindrical couples using optimization parameters physically meaningful toa cylindrical couple. Solutions incorporate the physical behavior for i) thermal resistance of hot andcold shoes, ii) variable material properties with temperature, and iii) lateral heat transfer through legsides.

A multi-species reactive transport model to estimate biogeochemical rates based on single-well push-pull test data

NASA Astrophysics Data System (ADS)

Phanikumar, Mantha S.; McGuire, Jennifer T.

2010-08-01

Push-pull tests are a popular technique to investigate various aquifer properties and microbial reaction kinetics in situ. Most previous studies have interpreted push-pull test data using approximate analytical solutions to estimate (generally first-order) reaction rate coefficients. Though useful, these analytical solutions may not be able to describe important complexities in rate data. This paper reports the development of a multi-species, radial coordinate numerical model (PPTEST) that includes the effects of sorption, reaction lag time and arbitrary reaction order kinetics to estimate rates in the presence of mixing interfaces such as those created between injected "push" water and native aquifer water. The model has the ability to describe an arbitrary number of species and user-defined reaction rate expressions including Monod/Michelis-Menten kinetics. The FORTRAN code uses a finite-difference numerical model based on the advection-dispersion-reaction equation and was developed to describe the radial flow and transport during a push-pull test. The accuracy of the numerical solutions was assessed by comparing numerical results with analytical solutions and field data available in the literature. The model described the observed breakthrough data for tracers (chloride and iodide-131) and reactive components (sulfate and strontium-85) well and was found to be useful for testing hypotheses related to the complex set of processes operating near mixing interfaces.

Finite element method formulation in polar coordinates for transient heat conduction problems

NASA Astrophysics Data System (ADS)

Duda, Piotr

2016-04-01

The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method (FEM) in polar or cylindrical coordinates for the solution of heat transfer problems. This document shows how to apply the most often used boundary conditions. The global equation system is solved by the Crank-Nicolson method. The proposed algorithm is verified in three numerical tests. In the first example, the obtained transient temperature distribution is compared with the temperature obtained from the presented analytical solution. In the second numerical example, the variable boundary condition is assumed. In the last numerical example the component with the shape different than cylindrical is used. All examples show that the introduction of the polar coordinate system gives better results than in the Cartesian coordinate system. The finite element method formulation in polar coordinates is valuable since it provides a higher accuracy of the calculations without compacting the mesh in cylindrical or similar to tubular components. The proposed method can be applied for circular elements such as boiler drums, outlet headers, flux tubes. This algorithm can be useful during the solution of inverse problems, which do not allow for high density grid. This method can calculate the temperature distribution in the bodies of different properties in the circumferential and the radial direction. The presented algorithm can be developed for other coordinate systems. The examples demonstrate a good accuracy and stability of the proposed method.

An analytical/numerical correlation study of the multiple concentric cylinder model for the thermoplastic response of metal matrix composites

NASA Technical Reports Server (NTRS)

Pindera, Marek-Jerzy; Salzar, Robert S.; Williams, Todd O.

1993-01-01

The utility of a recently developed analytical micromechanics model for the response of metal matrix composites under thermal loading is illustrated by comparison with the results generated using the finite-element approach. The model is based on the concentric cylinder assemblage consisting of an arbitrary number of elastic or elastoplastic sublayers with isotropic or orthotropic, temperature-dependent properties. The elastoplastic boundary-value problem of an arbitrarily layered concentric cylinder is solved using the local/global stiffness matrix formulation (originally developed for elastic layered media) and Mendelson's iterative technique of successive elastic solutions. These features of the model facilitate efficient investigation of the effects of various microstructural details, such as functionally graded architectures of interfacial layers, on the evolution of residual stresses during cool down. The available closed-form expressions for the field variables can readily be incorporated into an optimization algorithm in order to efficiently identify optimal configurations of graded interfaces for given applications. Comparison of residual stress distributions after cool down generated using finite-element analysis and the present micromechanics model for four composite systems with substantially different temperature-dependent elastic, plastic, and thermal properties illustrates the efficacy of the developed analytical scheme.

Symmetry-breaking dynamics of the finite-size Lipkin-Meshkov-Glick model near ground state

NASA Astrophysics Data System (ADS)

Huang, Yi; Li, Tongcang; Yin, Zhang-qi

2018-01-01

We study the dynamics of the Lipkin-Meshkov-Glick (LMG) model with a finite number of spins. In the thermodynamic limit, the ground state of the LMG model with an isotropic Hamiltonian in the broken phase breaks to a mean-field ground state with a certain direction. However, when the spin number N is finite, the exact ground state is always unique and is not given by a classical mean-field ground state. Here, we prove that when N is large but finite, through a tiny external perturbation, a localized state which is close to a mean-field ground state can be prepared, which mimics spontaneous symmetry breaking. Also, we find the localized in-plane spin polarization oscillates with two different frequencies ˜O (1 /N ) , and the lifetime of the localized state is long enough to exhibit this oscillation. We numerically test the analytical results and find that they agree very well with each other. Finally, we link the phenomena to quantum time crystals and time quasicrystals.

The p-version of the finite element method in incremental elasto-plastic analysis

NASA Technical Reports Server (NTRS)

Holzer, Stefan M.; Yosibash, Zohar

1993-01-01

Whereas the higher-order versions of the finite elements method (the p- and hp-version) are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems, little has been done to exploit their benefits in elasto-plastic structural analysis. Aspects of incremental elasto-plastic finite element analysis which are particularly amenable to improvements by the p-version is discussed. These theoretical considerations are supported by several numerical experiments. First, an example for which an analytical solution is available is studied. It is demonstrated that the p-version performs very well even in cycles of elasto-plastic loading and unloading, not only as compared to the traditional h-version but also in respect to the exact solution. Finally, an example of considerable practical importance - the analysis of a cold-worked lug - is presented which demonstrates how the modeling tools offered by higher-order finite element techniques can contribute to an improved approximation of practical problems.

Mixed finite-difference scheme for analysis of simply supported thick plates.

NASA Technical Reports Server (NTRS)

Noor, A. K.

1973-01-01

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

Evaluation of the finite element software ABAQUS for biomechanical modelling of biphasic tissues.

PubMed

Wu, J Z; Herzog, W; Epstein, M

1998-02-01

The biphasic cartilage model proposed by Mow et al. (1980) has proven successful to capture the essential mechanical features of articular cartilage. In order to analyse the joint contact mechanics in real, anatomical joints, the cartilage model needs to be implemented into a suitable finite element code to approximate the irregular surface geometries of such joints. However, systematic and extensive evaluation of the capacity of commercial software for modelling the contact mechanics with biphasic cartilage layers has not been made. This research was aimed at evaluating the commercial finite element software ABAQUS for analysing biphasic soft tissues. The solutions obtained using ABAQUS were compared with those obtained using other finite element models and analytical solutions for three numerical tests: an unconfined indentation test, a test with the contact of a spherical cartilage surface with a rigid plate, and an axi-symmetric joint contact test. It was concluded that the biphasic cartilage model can be implemented into the commercial finite element software ABAQUS to analyse practical joint contact problems with biphasic articular cartilage layers.

Generations of orthogonal surface coordinates

NASA Technical Reports Server (NTRS)

Blottner, F. G.; Moreno, J. B.

1980-01-01

Two generation methods were developed for three dimensional flows where the computational domain normal to the surface is small. With this restriction the coordinate system requires orthogonality only at the body surface. The first method uses the orthogonal condition in finite-difference form to determine the surface coordinates with the metric coefficients and curvature of the coordinate lines calculated numerically. The second method obtains analytical expressions for the metric coefficients and for the curvature of the coordinate lines.

Kuramoto model with uniformly spaced frequencies: Finite-N asymptotics of the locking threshold.

PubMed

Ottino-Löffler, Bertrand; Strogatz, Steven H

2016-06-01

We study phase locking in the Kuramoto model of coupled oscillators in the special case where the number of oscillators, N, is large but finite, and the oscillators' natural frequencies are evenly spaced on a given interval. In this case, stable phase-locked solutions are known to exist if and only if the frequency interval is narrower than a certain critical width, called the locking threshold. For infinite N, the exact value of the locking threshold was calculated 30 years ago; however, the leading corrections to it for finite N have remained unsolved analytically. Here we derive an asymptotic formula for the locking threshold when N≫1. The leading correction to the infinite-N result scales like either N^{-3/2} or N^{-1}, depending on whether the frequencies are evenly spaced according to a midpoint rule or an end-point rule. These scaling laws agree with numerical results obtained by Pazó [D. Pazó, Phys. Rev. E 72, 046211 (2005)PLEEE81539-375510.1103/PhysRevE.72.046211]. Moreover, our analysis yields the exact prefactors in the scaling laws, which also match the numerics.

Finite element modeling of borehole heat exchanger systems. Part 1. Fundamentals

NASA Astrophysics Data System (ADS)

Diersch, H.-J. G.; Bauer, D.; Heidemann, W.; Rühaak, W.; Schätzl, P.

2011-08-01

Single borehole heat exchanger (BHE) and arrays of BHE are modeled by using the finite element method. The first part of the paper derives the fundamental equations for BHE systems and their finite element representations, where the thermal exchange between the borehole components is modeled via thermal transfer relations. For this purpose improved relationships for thermal resistances and capacities of BHE are introduced. Pipe-to-grout thermal transfer possesses multiple grout points for double U-shape and single U-shape BHE to attain a more accurate modeling. The numerical solution of the final 3D problems is performed via a widely non-sequential (essentially non-iterative) coupling strategy for the BHE and porous medium discretization. Four types of vertical BHE are supported: double U-shape (2U) pipe, single U-shape (1U) pipe, coaxial pipe with annular (CXA) and centred (CXC) inlet. Two computational strategies are used: (1) The analytical BHE method based on Eskilson and Claesson's (1988) solution, (2) numerical BHE method based on Al-Khoury et al.'s (2005) solution. The second part of the paper focusses on BHE meshing aspects, the validation of BHE solutions and practical applications for borehole thermal energy store systems.

A Fixed-point Scheme for the Numerical Construction of Magnetohydrostatic Atmospheres in Three Dimensions

NASA Astrophysics Data System (ADS)

Gilchrist, S. A.; Braun, D. C.; Barnes, G.

2016-12-01

Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have tended to focus on the two-dimensional problem. In this article we develop a numerical method for solving the nonlinear magnetohydrostatic equations in three dimensions. Our method is a fixed-point iteration scheme that extends the method of Grad and Rubin ( Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy 31, 190, 1958) to include a finite gravity force. We apply the method to a test case to demonstrate the method in general and our implementation in code in particular.

Two-dimensional atmospheric transport and chemistry model - Numerical experiments with a new advection algorithm

NASA Technical Reports Server (NTRS)

Shia, Run-Lie; Ha, Yuk Lung; Wen, Jun-Shan; Yung, Yuk L.

1990-01-01

Extensive testing of the advective scheme proposed by Prather (1986) has been carried out in support of the California Institute of Technology-Jet Propulsion Laboratory two-dimensional model of the middle atmosphere. The original scheme is generalized to include higher-order moments. In addition, it is shown how well the scheme works in the presence of chemistry as well as eddy diffusion. Six types of numerical experiments including simple clock motion and pure advection in two dimensions have been investigated in detail. By comparison with analytic solutions, it is shown that the new algorithm can faithfully preserve concentration profiles, has essentially no numerical diffusion, and is superior to a typical fourth-order finite difference scheme.

Heat Transfer Analysis of Thermal Protection Structures for Hypersonic Vehicles

NASA Astrophysics Data System (ADS)

Zhou, Chen; Wang, Zhijin; Hou, Tianjiao

2017-11-01

This research aims to develop an analytical approach to study the heat transfer problem of thermal protection systems (TPS) for hypersonic vehicles. Laplace transform and integral method are used to describe the temperature distribution through the TPS subject to aerodynamic heating during flight. Time-dependent incident heat flux is also taken into account. Two different cases with heat flux and radiation boundary conditions are studied and discussed. The results are compared with those obtained by finite element analyses and show a good agreement. Although temperature profiles of such problems can be readily accessed via numerical simulations, analytical solutions give a greater insight into the physical essence of the heat transfer problem. Furthermore, with the analytical approach, rapid thermal analyses and even thermal optimization can be achieved during the preliminary TPS design.

Double Wigner distribution function of a first-order optical system with a hard-edge aperture.

PubMed

Pan, Weiqing

2008-01-01

The effect of an apertured optical system on Wigner distribution can be expressed as a superposition integral of the input Wigner distribution function and the double Wigner distribution function of the apertured optical system. By introducing a hard aperture function into a finite sum of complex Gaussian functions, the double Wigner distribution functions of a first-order optical system with a hard aperture outside and inside it are derived. As an example of application, the analytical expressions of the Wigner distribution for a Gaussian beam passing through a spatial filtering optical system with an internal hard aperture are obtained. The analytical results are also compared with the numerical integral results, and they show that the analytical results are proper and ascendant.

Influence of the Numerical Scheme on the Solution Quality of the SWE for Tsunami Numerical Codes: The Tohoku-Oki, 2011Example.

NASA Astrophysics Data System (ADS)

Reis, C.; Clain, S.; Figueiredo, J.; Baptista, M. A.; Miranda, J. M. A.

2015-12-01

Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.

Experimental investigation and numerical simulation of 3He gas diffusion in simple geometries: implications for analytical models of 3He MR lung morphometry.

PubMed

Parra-Robles, J; Ajraoui, S; Deppe, M H; Parnell, S R; Wild, J M

2010-06-01

Models of lung acinar geometry have been proposed to analytically describe the diffusion of (3)He in the lung (as measured with pulsed gradient spin echo (PGSE) methods) as a possible means of characterizing lung microstructure from measurement of the (3)He ADC. In this work, major limitations in these analytical models are highlighted in simple diffusion weighted experiments with (3)He in cylindrical models of known geometry. The findings are substantiated with numerical simulations based on the same geometry using finite difference representation of the Bloch-Torrey equation. The validity of the existing "cylinder model" is discussed in terms of the physical diffusion regimes experienced and the basic reliance of the cylinder model and other ADC-based approaches on a Gaussian diffusion behaviour is highlighted. The results presented here demonstrate that physical assumptions of the cylinder model are not valid for large diffusion gradient strengths (above approximately 15 mT/m), which are commonly used for (3)He ADC measurements in human lungs. (c) 2010 Elsevier Inc. All rights reserved.

Adapting Surface Ground Motion Relations to Underground conditions: A case study for the Sudbury Neutrino Observatory in Sudbury, Ontario, Canada

NASA Astrophysics Data System (ADS)

Babaie Mahani, A.; Eaton, D. W.

2013-12-01

Ground Motion Prediction Equations (GMPEs) are widely used in Probabilistic Seismic Hazard Assessment (PSHA) to estimate ground-motion amplitudes at Earth's surface as a function of magnitude and distance. Certain applications, such as hazard assessment for caprock integrity in the case of underground storage of CO2, waste disposal sites, and underground pipelines, require subsurface estimates of ground motion; at present, such estimates depend upon theoretical modeling and simulations. The objective of this study is to derive correction factors for GMPEs to enable estimation of amplitudes in the subsurface. We use a semi-analytic approach along with finite-difference simulations of ground-motion amplitudes for surface and underground motions. Spectral ratios of underground to surface motions are used to calculate the correction factors. Two predictive methods are used. The first is a semi-analytic approach based on a quarter-wavelength method that is widely used for earthquake site-response investigations; the second is a numerical approach based on elastic finite-difference simulations of wave propagation. Both methods are evaluated using recordings of regional earthquakes by broadband seismometers installed at the surface and at depths of 1400 m and 2100 m in the Sudbury Neutrino Observatory, Canada. Overall, both methods provide a reasonable fit to the peaks and troughs observed in the ratios of real data. The finite-difference method, however, has the capability to simulate ground motion ratios more accurately than the semi-analytic approach.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi N. (Technical Monitor)

2002-01-01

This talk describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

NASA Technical Reports Server (NTRS)

Yee, H. C.

2005-01-01

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations. Chapter 2

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi N. (Technical Monitor)

2001-01-01

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

A new finite element and finite difference hybrid method for computing electrostatics of ionic solvated biomolecule

NASA Astrophysics Data System (ADS)

Ying, Jinyong; Xie, Dexuan

2015-10-01

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.

Switching synchronization in one-dimensional memristive networks

NASA Astrophysics Data System (ADS)

Slipko, Valeriy A.; Shumovskyi, Mykola; Pershin, Yuriy V.

2015-11-01

We report on a switching synchronization phenomenon in one-dimensional memristive networks, which occurs when several memristive systems with different switching constants are switched from the high- to low-resistance state. Our numerical simulations show that such a collective behavior is especially pronounced when the applied voltage slightly exceeds the combined threshold voltage of memristive systems. Moreover, a finite increase in the network switching time is found compared to the average switching time of individual systems. An analytical model is presented to explain our observations. Using this model, we have derived asymptotic expressions for memory resistances at short and long times, which are in excellent agreement with results of our numerical simulations.

Numerical simulation of water evaporation inside vertical circular tubes

NASA Astrophysics Data System (ADS)

Ocłoń, Paweł; Nowak, Marzena; Majewski, Karol

2013-10-01

In this paper the results of simplified numerical analysis of water evaporation in vertical circular tubes are presented. The heat transfer in fluid domain (water or wet steam) and solid domain (tube wall) is analyzed. For the fluid domain the temperature field is calculated solving energy equation using the Control Volume Method and for the solid domain using the Finite Element Method. The heat transfer between fluid and solid domains is conjugated using the value of heat transfer coefficient from evaporating liquid to the tube wall. It is determined using the analytical Steiner-Taborek correlation. The pressure changes in fluid are computed using Friedel model.

The Thick Level-Set model for dynamic fragmentation

DOE PAGES

Stershic, Andrew J.; Dolbow, John E.; Moës, Nicolas

2017-01-04

The Thick Level-Set (TLS) model is implemented to simulate brittle media undergoing dynamic fragmentation. This non-local model is discretized by the finite element method with damage represented as a continuous field over the domain. A level-set function defines the extent and severity of damage, and a length scale is introduced to limit the damage gradient. Numerical studies in one dimension demonstrate that the proposed method reproduces the rate-dependent energy dissipation and fragment length observations from analytical, numerical, and experimental approaches. In conclusion, additional studies emphasize the importance of appropriate bulk constitutive models and sufficient spatial resolution of the length scale.

On Multifunctional Collaborative Methods in Engineering Science

NASA Technical Reports Server (NTRS)

Ransom, Jonathan B.

2001-01-01

Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized.

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.

Finite temperature corrections to tachyon mass in intersecting D-branes

NASA Astrophysics Data System (ADS)

Sethi, Varun; Chowdhury, Sudipto Paul; Sarkar, Swarnendu

2017-04-01

We continue with the analysis of finite temperature corrections to the Tachyon mass in intersecting branes which was initiated in [1]. In this paper we extend the computation to the case of intersecting D3 branes by considering a setup of two intersecting branes in flat-space background. A holographic model dual to BCS superconductor consisting of intersecting D8 branes in D4 brane background was proposed in [2]. The background considered here is a simplified configuration of this dual model. We compute the one-loop Tachyon amplitude in the Yang-Mills approximation and show that the result is finite. Analyzing the amplitudes further we numerically compute the transition temperature at which the Tachyon becomes massless. The analytic expressions for the one-loop amplitudes obtained here reduce to those for intersecting D1 branes obtained in [1] as well as those for intersecting D2 branes.

Finite-volume method with lattice Boltzmann flux scheme for incompressible porous media flow at the representative-elementary-volume scale.

PubMed

Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

2016-02-01

Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions.

Sufficient condition for a finite-time singularity in a high-symmetry Euler flow: Analysis and statistics

NASA Astrophysics Data System (ADS)

Ng, C. S.; Bhattacharjee, A.

1996-08-01

A sufficient condition is obtained for the development of a finite-time singularity in a highly symmetric Euler flow, first proposed by Kida [J. Phys. Soc. Jpn. 54, 2132 (1995)] and recently simulated by Boratav and Pelz [Phys. Fluids 6, 2757 (1994)]. It is shown that if the second-order spatial derivative of the pressure (pxx) is positive following a Lagrangian element (on the x axis), then a finite-time singularity must occur. Under some assumptions, this Lagrangian sufficient condition can be reduced to an Eulerian sufficient condition which requires that the fourth-order spatial derivative of the pressure (pxxxx) at the origin be positive for all times leading up to the singularity. Analytical as well as direct numerical evaluation over a large ensemble of initial conditions demonstrate that for fixed total energy, pxxxx is predominantly positive with the average value growing with the numbers of modes.

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

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

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

Aeroelastic behavior of composite rotor blades with swept tips

NASA Technical Reports Server (NTRS)

Yuan, Kuo-An; Friedmann, Peretz P.; Venkatesan, Comandur

1992-01-01

This paper presents an analytical study of the aeroelastic behavior of composite rotor blades with straight and swept tips. The blade is modeled by beam type finite elements. A single finite element is used to model the swept tip. The nonlinear equations of motion for the finite element model are derived using Hamilton's principle and based on a moderate deflection theory and accounts for: arbitrary cross-sectional shape, pretwist, generally anisotropic material behavior, transverse shears and out-of-plane warping. Numerical results illustrating the effects of tip sweep, anhedral and composite ply orientation on blade aeroelastic behavior are presented. It is shown that composite ply orientation has a substantial effect on blade stability. At low thrust conditions, certain ply orientations can cause instability in the lag mode. The flap-torsion coupling associated with tip sweep can also induce aeroelastic instability in the blade. This instability can be removed by appropriate ply orientation in the composite construction.

A new aeroelastic model for composite rotor blades with straight and swept tips

NASA Technical Reports Server (NTRS)

Yuan, Kuo-An; Friedmann, Peretz P.; Venkatesan, Comandur

1992-01-01

An analytical model for predicting the aeroelastic behavior of composite rotor blades with straight and swept tips is presented. The blade is modeled by beam type finite elements along the elastic axis. A single finite element is used to model the swept tip. The nonlinear equations of motion for the finite element model are derived using Hamilton's principle and based on a moderate deflection theory and accounts for: arbitrary cross-sectional shape, pretwist, generally anisotropic material behavior, transverse shears and out-of-plane warping. Numerical results illustrating the effects of tip sweep, anhedral and composite ply orientation on blade aeroelastic behavior are presented. Tip sweep can induce aeroelastic instability by flap-twist coupling. Tip anhedral causes lag-torsion and flap-axial couplings, however, its effects on blade stability is less pronounced than the effect due to sweep. Composite ply orientation has a substantial effect on blade stability.

Analysis of composite ablators using massively parallel computation

NASA Technical Reports Server (NTRS)

Shia, David

1995-01-01

In this work, the feasibility of using massively parallel computation to study the response of ablative materials is investigated. Explicit and implicit finite difference methods are used on a massively parallel computer, the Thinking Machines CM-5. The governing equations are a set of nonlinear partial differential equations. The governing equations are developed for three sample problems: (1) transpiration cooling, (2) ablative composite plate, and (3) restrained thermal growth testing. The transpiration cooling problem is solved using a solution scheme based solely on the explicit finite difference method. The results are compared with available analytical steady-state through-thickness temperature and pressure distributions and good agreement between the numerical and analytical solutions is found. It is also found that a solution scheme based on the explicit finite difference method has the following advantages: incorporates complex physics easily, results in a simple algorithm, and is easily parallelizable. However, a solution scheme of this kind needs very small time steps to maintain stability. A solution scheme based on the implicit finite difference method has the advantage that it does not require very small times steps to maintain stability. However, this kind of solution scheme has the disadvantages that complex physics cannot be easily incorporated into the algorithm and that the solution scheme is difficult to parallelize. A hybrid solution scheme is then developed to combine the strengths of the explicit and implicit finite difference methods and minimize their weaknesses. This is achieved by identifying the critical time scale associated with the governing equations and applying the appropriate finite difference method according to this critical time scale. The hybrid solution scheme is then applied to the ablative composite plate and restrained thermal growth problems. The gas storage term is included in the explicit pressure calculation of both problems. Results from ablative composite plate problems are compared with previous numerical results which did not include the gas storage term. It is found that the through-thickness temperature distribution is not affected much by the gas storage term. However, the through-thickness pressure and stress distributions, and the extent of chemical reactions are different from the previous numerical results. Two types of chemical reaction models are used in the restrained thermal growth testing problem: (1) pressure-independent Arrhenius type rate equations and (2) pressure-dependent Arrhenius type rate equations. The numerical results are compared to experimental results and the pressure-dependent model is able to capture the trend better than the pressure-independent one. Finally, a performance study is done on the hybrid algorithm using the ablative composite plate problem. It is found that there is a good speedup of performance on the CM-5. For 32 CPU's, the speedup of performance is 20. The efficiency of the algorithm is found to be a function of the size and execution time of a given problem and the effective parallelization of the algorithm. It also seems that there is an optimum number of CPU's to use for a given problem.

Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.

2018-03-01

In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

Electromagnetic-field amplification in finite one-dimensional photonic crystals

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

Gorelik, V. S.; Kapaev, V. V., E-mail: kapaev@sci.lebedev.ru

2016-09-15

The electromagnetic-field distribution in a finite one-dimensional photonic crystal is studied using the numerical solution of Maxwell’s equations by the transfer-matrix method. The dependence of the transmission coefficient T on the period d (or the wavelength λ) has the characteristic form with M–1 (M is the number of periods in the structure) maxima with T = 1 in the allowed band of an infinite crystal and zero values in the forbidden band. The field-modulus distribution E(x) in the structure for parameters that correspond to the transmission maxima closest to the boundaries of forbidden bands has maxima at the center ofmore » the structure; the value at the maximum considerably exceeds the incident-field strength. For the number of periods M ~ 50, more than an order of magnitude increase in the field amplification is observed. The numerical results are interpreted with an analytic theory constructed by representing the solution in the form of a linear combination of counterpropagating Floquet modes in a periodic structure.« less

Approaches to the structural modelling of insect wings.

PubMed Central

Wootton, R J; Herbert, R C; Young, P G; Evans, K E

2003-01-01

Insect wings lack internal muscles, and the orderly, necessary deformations which they undergo in flight and folding are in part remotely controlled, in part encoded in their structure. This factor is crucial in understanding their complex, extremely varied morphology. Models have proved particularly useful in clarifying the facilitation and control of wing deformation. Their development has followed a logical sequence from conceptual models through physical and simple analytical to numerical models. All have value provided their limitations are realized and constant comparisons made with the properties and mechanical behaviour of real wings. Numerical modelling by the finite element method is by far the most time-consuming approach, but has real potential in analysing the adaptive significance of structural details and interpreting evolutionary trends. Published examples are used to review the strengths and weaknesses of each category of model, and a summary is given of new work using finite element modelling to investigate the vibration properties and response to impact of hawkmoth wings. PMID:14561349

A stabilized element-based finite volume method for poroelastic problems

NASA Astrophysics Data System (ADS)

Honório, Hermínio T.; Maliska, Clovis R.; Ferronato, Massimiliano; Janna, Carlo

2018-07-01

The coupled equations of Biot's poroelasticity, consisting of stress equilibrium and fluid mass balance in deforming porous media, are numerically solved. The governing partial differential equations are discretized by an Element-based Finite Volume Method (EbFVM), which can be used in three dimensional unstructured grids composed of elements of different types. One of the difficulties for solving these equations is the numerical pressure instability that can arise when undrained conditions take place. In this paper, a stabilization technique is developed to overcome this problem by employing an interpolation function for displacements that considers also the pressure gradient effect. The interpolation function is obtained by the so-called Physical Influence Scheme (PIS), typically employed for solving incompressible fluid flows governed by the Navier-Stokes equations. Classical problems with analytical solutions, as well as three-dimensional realistic cases are addressed. The results reveal that the proposed stabilization technique is able to eliminate the spurious pressure instabilities arising under undrained conditions at a low computational cost.

Numerical Simulation of a Solar Domestic Hot Water System

NASA Astrophysics Data System (ADS)

Mongibello, L.; Bianco, N.; Di Somma, M.; Graditi, G.; Naso, V.

2014-11-01

An innovative transient numerical model is presented for the simulation of a solar Domestic Hot Water (DHW) system. The solar collectors have been simulated by using a zerodimensional analytical model. The temperature distributions in the heat transfer fluid and in the water inside the tank have been evaluated by one-dimensional models. The reversion elimination algorithm has been used to include the effects of natural convection among the water layers at different heights in the tank on the thermal stratification. A finite difference implicit scheme has been implemented to solve the energy conservation equation in the coil heat exchanger, and the energy conservation equation in the tank has been solved by using the finite difference Euler implicit scheme. Energy conservation equations for the solar DHW components models have been coupled by means of a home-made implicit algorithm. Results of the simulation performed using as input data the experimental values of the ambient temperature and the solar irradiance in a summer day are presented and discussed.

EIT image reconstruction based on a hybrid FE-EFG forward method and the complete-electrode model.

PubMed

Hadinia, M; Jafari, R; Soleimani, M

2016-06-01

This paper presents the application of the hybrid finite element-element free Galerkin (FE-EFG) method for the forward and inverse problems of electrical impedance tomography (EIT). The proposed method is based on the complete electrode model. Finite element (FE) and element-free Galerkin (EFG) methods are accurate numerical techniques. However, the FE technique has meshing task problems and the EFG method is computationally expensive. In this paper, the hybrid FE-EFG method is applied to take both advantages of FE and EFG methods, the complete electrode model of the forward problem is solved, and an iterative regularized Gauss-Newton method is adopted to solve the inverse problem. The proposed method is applied to compute Jacobian in the inverse problem. Utilizing 2D circular homogenous models, the numerical results are validated with analytical and experimental results and the performance of the hybrid FE-EFG method compared with the FE method is illustrated. Results of image reconstruction are presented for a human chest experimental phantom.

Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method

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

Le Hardy, D.; Favennec, Y., E-mail: yann.favennec@univ-nantes.fr; Rousseau, B.

The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken intomore » account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.« less

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.

PubMed

Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2011-11-01

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

Numerical Analyses of Subsoil-structure Interaction in Original Non-commercial Software based on FEM

NASA Astrophysics Data System (ADS)

Cajka, R.; Vaskova, J.; Vasek, J.

2018-04-01

For decades attention has been paid to interaction of foundation structures and subsoil and development of interaction models. Given that analytical solutions of subsoil-structure interaction could be deduced only for some simple shapes of load, analytical solutions are increasingly being replaced by numerical solutions (eg. FEM – Finite element method). Numerical analyses provides greater possibilities for taking into account the real factors involved in the subsoil-structure interaction and was also used in this article. This makes it possible to design the foundation structures more efficiently and still reliably and securely. Currently there are several software that, can deal with the interaction of foundations and subsoil. It has been demonstrated that non-commercial software called MKPINTER (created by Cajka) provides appropriately results close to actual measured values. In MKPINTER software stress-strain analysis of elastic half-space by means of Gauss numerical integration and Jacobean of transformation is done. Input data for numerical analysis were observed by experimental loading test of concrete slab. The loading was performed using unique experimental equipment which was constructed in the area Faculty of Civil Engineering, VŠB-TU Ostrava. The purpose of this paper is to compare resulting deformation of the slab with values observed during experimental loading test.

A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

NASA Astrophysics Data System (ADS)

Gopalan, Giri; Hrafnkelsson, Birgir; Aðalgeirsdóttir, Guðfinna; Jarosch, Alexander H.; Pálsson, Finnur

2018-03-01

Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.

Semi-analytical and Numerical Studies on the Flattened Brazilian Splitting Test Used for Measuring the Indirect Tensile Strength of Rocks

NASA Astrophysics Data System (ADS)

Huang, Y. G.; Wang, L. G.; Lu, Y. L.; Chen, J. R.; Zhang, J. H.

2015-09-01

Based on the two-dimensional elasticity theory, this study established a mechanical model under chordally opposing distributed compressive loads, in order to perfect the theoretical foundation of the flattened Brazilian splitting test used for measuring the indirect tensile strength of rocks. The stress superposition method was used to obtain the approximate analytic solutions of stress components inside the flattened Brazilian disk. These analytic solutions were then verified through a comparison with the numerical results of the finite element method (FEM). Based on the theoretical derivation, this research carried out a contrastive study on the effect of the flattened loading angles on the stress value and stress concentration degree inside the disk. The results showed that the stress concentration degree near the loading point and the ratio of compressive/tensile stress inside the disk dramatically decreased as the flattened loading angle increased, avoiding the crushing failure near-loading point of Brazilian disk specimens. However, only the tensile stress value and the tensile region were slightly reduced with the increase of the flattened loading angle. Furthermore, this study found that the optimal flattened loading angle was 20°-30°; flattened load angles that were too large or too small made it difficult to guarantee the central tensile splitting failure principle of the Brazilian splitting test. According to the Griffith strength failure criterion, the calculative formula of the indirect tensile strength of rocks was derived theoretically. This study obtained a theoretical indirect tensile strength that closely coincided with existing and experimental results. Finally, this paper simulated the fracture evolution process of rocks under different loading angles through the use of the finite element numerical software ANSYS. The modeling results showed that the Flattened Brazilian Splitting Test using the optimal loading angle could guarantee the tensile splitting failure initiated by a central crack.

A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics.

PubMed

Aguayo-Ortiz, A; Mendoza, S; Olvera, D

2018-01-01

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and "Rankine-Hugoniot" jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges.

A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics

PubMed Central

Mendoza, S.; Olvera, D.

2018-01-01

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and “Rankine-Hugoniot” jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges. PMID:29659602

Numerical modeling of subsidence induced by hydrocarbon production in a reservoir in coastal Louisiana

NASA Astrophysics Data System (ADS)

Zhou, Y.; Voyiadjis, G.

2017-12-01

Subsidence has caused significant wetland losses in coastal Louisiana due to various anthropogenic and geologic processes. Releveling data from National Geodetic Survey show that one of the governing factors in the coastal Louisiana is hydrocarbon production, which has led to the acceleration of spatial- and temporal-dependent subsidence. This work investigates the influence of hydrocarbon production on subsidence for a typical reservoir, the Valentine field in coastal Louisiana, based on finite element modeling in the framework of poroelasticity and poroplasticity. Geertsma's analytical model is first used in this work to interpret the observed subsidence, for a disc-shaped reservoir embedded in a semi-infinite homogeneous elastic medium. Based on the calibrated elastic material properties, the authors set up a 3D finite element model and validate the numerical results with Geertsma's analytical model. As the plastic deformation of a reservoir in an inhomogeneous medium plays an important role in the compaction of the reservoir and the land subsidence, the authors further adopt a modified Cam-Clay model to take account of the plastic compaction of the reservoir. The material properties in the Cam-Clay model are calibrated based on the subsidence observed in the field and that in the homogeneous elastic case. The observed trend and magnitude of subsidence in the Valentine field can be approximately reproduced through finite element modeling in both the homogeneous elastic case and the inhomogeneous plastic case, by using the calibrated material properties. The maximum compaction in the inhomogeneous plastic case is around half of that in the homogeneous elastic case, and thus the ratio of subsidence over compaction is larger in the inhomogeneous plastic case for a softer reservoir embedded in a stiffer medium.

Radiation Heat Transfer Between Diffuse-Gray Surfaces Using Higher Order Finite Elements

NASA Technical Reports Server (NTRS)

Gould, Dana C.

2000-01-01

This paper presents recent work on developing methods for analyzing radiation heat transfer between diffuse-gray surfaces using p-version finite elements. The work was motivated by a thermal analysis of a High Speed Civil Transport (HSCT) wing structure which showed the importance of radiation heat transfer throughout the structure. The analysis also showed that refining the finite element mesh to accurately capture the temperature distribution on the internal structure led to very large meshes with unacceptably long execution times. Traditional methods for calculating surface-to-surface radiation are based on assumptions that are not appropriate for p-version finite elements. Two methods for determining internal radiation heat transfer are developed for one and two-dimensional p-version finite elements. In the first method, higher-order elements are divided into a number of sub-elements. Traditional methods are used to determine radiation heat flux along each sub-element and then mapped back to the parent element. In the second method, the radiation heat transfer equations are numerically integrated over the higher-order element. Comparisons with analytical solutions show that the integration scheme is generally more accurate than the sub-element method. Comparison to results from traditional finite elements shows that significant reduction in the number of elements in the mesh is possible using higher-order (p-version) finite elements.

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

Rycroft, Chris H.; Bazant, Martin Z.

An advection-diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow is presented. By taking advantage of the conformal invariance of the model, a numerical method is introduced that tracks the evolution of the object boundary in terms of a time-dependent Laurent series. Simulations of a variety of dissolving objects are shown, which shrink and collapse to a single point in finite time. The simulations reveal a surprising exact relationship, whereby the collapse point is the root of a non-Analytic function given in terms of the flow velocity and the Laurent series coefficients describing the initial shape.more » This result is subsequently derived using residue calculus. The structure of the non-Analytic function is examined for three different test cases, and a practical approach to determine the collapse point using a generalized Newton-Raphson root-finding algorithm is outlined. These examples also illustrate the possibility that the model breaks down in finite time prior to complete collapse, due to a topological singularity, as the dissolving boundary overlaps itself rather than breaking up into multiple domains (analogous to droplet pinch-off in fluid mechanics). In conclusion, the model raises fundamental mathematical questions about broken symmetries in finite-Time singularities of both continuous and stochastic dynamical systems.« less

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.

Asymmetric collapse by dissolution or melting in a uniform flow

PubMed Central

Bazant, Martin Z.

2016-01-01

An advection–diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow is presented. By taking advantage of the conformal invariance of the model, a numerical method is introduced that tracks the evolution of the object boundary in terms of a time-dependent Laurent series. Simulations of a variety of dissolving objects are shown, which shrink and collapse to a single point in finite time. The simulations reveal a surprising exact relationship, whereby the collapse point is the root of a non-analytic function given in terms of the flow velocity and the Laurent series coefficients describing the initial shape. This result is subsequently derived using residue calculus. The structure of the non-analytic function is examined for three different test cases, and a practical approach to determine the collapse point using a generalized Newton–Raphson root-finding algorithm is outlined. These examples also illustrate the possibility that the model breaks down in finite time prior to complete collapse, due to a topological singularity, as the dissolving boundary overlaps itself rather than breaking up into multiple domains (analogous to droplet pinch-off in fluid mechanics). The model raises fundamental mathematical questions about broken symmetries in finite-time singularities of both continuous and stochastic dynamical systems. PMID:26997890

Asymmetric collapse by dissolution or melting in a uniform flow

DOE PAGES

Rycroft, Chris H.; Bazant, Martin Z.

2016-01-06

An advection-diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow is presented. By taking advantage of the conformal invariance of the model, a numerical method is introduced that tracks the evolution of the object boundary in terms of a time-dependent Laurent series. Simulations of a variety of dissolving objects are shown, which shrink and collapse to a single point in finite time. The simulations reveal a surprising exact relationship, whereby the collapse point is the root of a non-Analytic function given in terms of the flow velocity and the Laurent series coefficients describing the initial shape.more » This result is subsequently derived using residue calculus. The structure of the non-Analytic function is examined for three different test cases, and a practical approach to determine the collapse point using a generalized Newton-Raphson root-finding algorithm is outlined. These examples also illustrate the possibility that the model breaks down in finite time prior to complete collapse, due to a topological singularity, as the dissolving boundary overlaps itself rather than breaking up into multiple domains (analogous to droplet pinch-off in fluid mechanics). In conclusion, the model raises fundamental mathematical questions about broken symmetries in finite-Time singularities of both continuous and stochastic dynamical systems.« less

Generation of dark hollow beams by using a fractional radial Hilbert transform system

NASA Astrophysics Data System (ADS)

Xie, Qiansen; Zhao, Daomu

2007-07-01

The radial Hilbert transform has been extend to the fractional field, which could be called the fractional radial Hilbert transform (FRHT). Using edge-enhancement characteristics of this transform, we convert a Gaussian light beam into a variety of dark hollow beams (DHBs). Based on the fact that a hard-edged aperture can be expanded approximately as a finite sum of complex Gaussian functions, the analytical expression of a Gaussian beam passing through a FRHT system has been derived. As a numerical example, the properties of the DHBs with different fractional orders are illustrated graphically. The calculation results obtained by use of the analytical method and the integral method are also compared.

Analytical and numerical study of electroosmotic slip flows of fractional second grade fluids

NASA Astrophysics Data System (ADS)

Wang, Xiaoping; Qi, Haitao; Yu, Bo; Xiong, Zhen; Xu, Huanying

2017-09-01

This work investigates the unsteady electroosmotic slip flow of viscoelastic fluid through a parallel plate micro-channel under combined influence of electroosmotic and pressure gradient forcings with asymmetric zeta potentials at the walls. The generalized second grade fluid with fractional derivative was used for the constitutive equation. The Navier slip model with different slip coefficients at both walls was also considered. By employing the Debye-Hückel linearization and the Laplace and sin-cos-Fourier transforms, the analytical solutions for the velocity distribution are derived. And the finite difference method for this problem was also given. Finally, the influence of pertinent parameters on the generation of flow is presented graphically.

Propagation of Bessel-Gaussian beams through a double-apertured fractional Fourier transform optical system.

PubMed

Tang, Bin; Jiang, Chun; Zhu, Haibin

2012-08-01

Based on the scalar diffraction theory and the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical solution for Bessel-Gaussian (BG) beams propagating through a double-apertured fractional Fourier transform (FrFT) system is derived in the cylindrical coordinate. By using the approximate analytical formulas, the propagation properties of BG beams passing through a double-apertured FrFT optical system have been studied in detail by some typical numerical examples. The results indicate that the double-apertured FrFT optical system provides a convenient way for controlling the properties of the BG beams by properly choosing the optical parameters.

NOTE: Solving the ECG forward problem by means of a meshless finite element method

NASA Astrophysics Data System (ADS)

Li, Z. S.; Zhu, S. A.; He, Bin

2007-07-01

The conventional numerical computational techniques such as the finite element method (FEM) and the boundary element method (BEM) require laborious and time-consuming model meshing. The new meshless FEM only uses the boundary description and the node distribution and no meshing of the model is required. This paper presents the fundamentals and implementation of meshless FEM and the meshless FEM method is adapted to solve the electrocardiography (ECG) forward problem. The method is evaluated on a single-layer torso model, in which the analytical solution exists, and tested in a realistic geometry homogeneous torso model, with satisfactory results being obtained. The present results suggest that the meshless FEM may provide an alternative for ECG forward solutions.

Solution of the 2-D steady-state radiative transfer equation in participating media with specular reflections using SUPG and DG finite elements

NASA Astrophysics Data System (ADS)

Le Hardy, D.; Favennec, Y.; Rousseau, B.

2016-08-01

The 2D radiative transfer equation coupled with specular reflection boundary conditions is solved using finite element schemes. Both Discontinuous Galerkin and Streamline-Upwind Petrov-Galerkin variational formulations are fully developed. These two schemes are validated step-by-step for all involved operators (transport, scattering, reflection) using analytical formulations. Numerical comparisons of the two schemes, in terms of convergence rate, reveal that the quadratic SUPG scheme proves efficient for solving such problems. This comparison constitutes the main issue of the paper. Moreover, the solution process is accelerated using block SOR-type iterative methods, for which the determination of the optimal parameter is found in a very cheap way.

Periodic and quasiperiodic revivals in periodically driven interacting quantum systems

NASA Astrophysics Data System (ADS)

Luitz, David J.; Lazarides, Achilleas; Bar Lev, Yevgeny

2018-01-01

Recently it has been shown that interparticle interactions generically destroy dynamical localization in periodically driven systems, resulting in diffusive transport and heating. In this Rapid Communication we rigorously construct a family of interacting driven systems which are dynamically localized and effectively decoupled from the external driving potential. We show that these systems exhibit tunable periodic or quasiperiodic revivals of the many-body wave function and thus of all physical observables. By numerically examining spinless fermions on a one-dimensional lattice we show that the analytically obtained revivals of such systems remain stable for finite systems with open boundary conditions while having a finite lifetime in the presence of static spatial disorder. We find this lifetime to be inversely proportional to the disorder strength.

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

Mechanical behavior of regular open-cell porous biomaterials made of diamond lattice unit cells.

PubMed

Ahmadi, S M; Campoli, G; Amin Yavari, S; Sajadi, B; Wauthle, R; Schrooten, J; Weinans, H; Zadpoor, A A

2014-06-01

Cellular structures with highly controlled micro-architectures are promising materials for orthopedic applications that require bone-substituting biomaterials or implants. The availability of additive manufacturing techniques has enabled manufacturing of biomaterials made of one or multiple types of unit cells. The diamond lattice unit cell is one of the relatively new types of unit cells that are used in manufacturing of regular porous biomaterials. As opposed to many other types of unit cells, there is currently no analytical solution that could be used for prediction of the mechanical properties of cellular structures made of the diamond lattice unit cells. In this paper, we present new analytical solutions and closed-form relationships for predicting the elastic modulus, Poisson׳s ratio, critical buckling load, and yield (plateau) stress of cellular structures made of the diamond lattice unit cell. The mechanical properties predicted using the analytical solutions are compared with those obtained using finite element models. A number of solid and porous titanium (Ti6Al4V) specimens were manufactured using selective laser melting. A series of experiments were then performed to determine the mechanical properties of the matrix material and cellular structures. The experimentally measured mechanical properties were compared with those obtained using analytical solutions and finite element (FE) models. It has been shown that, for small apparent density values, the mechanical properties obtained using analytical and numerical solutions are in agreement with each other and with experimental observations. The properties estimated using an analytical solution based on the Euler-Bernoulli theory markedly deviated from experimental results for large apparent density values. The mechanical properties estimated using FE models and another analytical solution based on the Timoshenko beam theory better matched the experimental observations. Copyright © 2014 Elsevier Ltd. All rights reserved.

A conservative numerical scheme for modeling nonlinear acoustic propagation in thermoviscous homogeneous media

NASA Astrophysics Data System (ADS)

Diaz, Manuel A.; Solovchuk, Maxim A.; Sheu, Tony W. H.

2018-06-01

A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax-Wendroff theorem, and the scheme can match the solutions of the Westervelt and Burgers equations numerically. Here, high-order numerical descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) schemes associated with explicit strong stability preserving Runge-Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.

Transition to Turbulence in curved pipe

NASA Astrophysics Data System (ADS)

Hashemi, Amirreza; Loth, Francis

2014-11-01

Studies have shown that transitional turbulence in a curved pipe is delayed significantly compared with straight pipes. These analytical, numerical and experimental studies employed a helical geometry that is infinitely long such that the effect of the inlet and outlet can be neglected. The present study examined transition to turbulence in a finite curved pipe with a straight inlet/outlet and a 180 degrees curved pipe with a constant radius of curvature and diameter (D). We have employed the large scale direct numerical simulation (DNS) by using the spectral element method, nek5000, to simulate the flow field within curved pipe geometry with different curvature radii and Reynolds numbers to determine the point of the transition to turbulence. Long extensions for the inlet (5D) and outlet (20D) were used to diminish the effect of the boundary conditions. Our numerical results for radius of curvatures of 1.5D and 5D show transition turbulence is near Re = 3000. This is delayed compared with a straight pipe (Re = 2200) but still less that observed for helical geometries (Reynolds number less than 5000). Our research aims to describe the critical Reynolds number for transition to turbulence for a finite curved pipe at various curvature radii.

Numerical modeling of the exterior-to-interior transmission of impulsive sound through three-dimensional, thin-walled elastic structures

NASA Astrophysics Data System (ADS)

Remillieux, Marcel C.; Pasareanu, Stephanie M.; Svensson, U. Peter

2013-12-01

Exterior propagation of impulsive sound and its transmission through three-dimensional, thin-walled elastic structures, into enclosed cavities, are investigated numerically in the framework of linear dynamics. A model was developed in the time domain by combining two numerical tools: (i) exterior sound propagation and induced structural loading are computed using the image-source method for the reflected field (specular reflections) combined with an extension of the Biot-Tolstoy-Medwin method for the diffracted field, (ii) the fully coupled vibro-acoustic response of the interior fluid-structure system is computed using a truncated modal-decomposition approach. In the model for exterior sound propagation, it is assumed that all surfaces are acoustically rigid. Since coupling between the structure and the exterior fluid is not enforced, the model is applicable to the case of a light exterior fluid and arbitrary interior fluid(s). The structural modes are computed with the finite-element method using shell elements. Acoustic modes are computed analytically assuming acoustically rigid boundaries and rectangular geometries of the enclosed cavities. This model is verified against finite-element solutions for the cases of rectangular structures containing one and two cavities, respectively.

A Second Law Based Unstructured Finite Volume Procedure for Generalized Flow Simulation

NASA Technical Reports Server (NTRS)

Majumdar, Alok

1998-01-01

An unstructured finite volume procedure has been developed for steady and transient thermo-fluid dynamic analysis of fluid systems and components. The procedure is applicable for a flow network consisting of pipes and various fittings where flow is assumed to be one dimensional. It can also be used to simulate flow in a component by modeling a multi-dimensional flow using the same numerical scheme. The flow domain is discretized into a number of interconnected control volumes located arbitrarily in space. The conservation equations for each control volume account for the transport of mass, momentum and entropy from the neighboring control volumes. In addition, they also include the sources of each conserved variable and time dependent terms. The source term of entropy equation contains entropy generation due to heat transfer and fluid friction. Thermodynamic properties are computed from the equation of state of a real fluid. The system of equations is solved by a hybrid numerical method which is a combination of simultaneous Newton-Raphson and successive substitution schemes. The paper also describes the application and verification of the procedure by comparing its predictions with the analytical and numerical solution of several benchmark problems.

High Sensitivity Refractive Index Sensor Based on Dual-Core Photonic Crystal Fiber with Hexagonal Lattice.

PubMed

Wang, Haiyang; Yan, Xin; Li, Shuguang; An, Guowen; Zhang, Xuenan

2016-10-08

A refractive index sensor based on dual-core photonic crystal fiber (PCF) with hexagonal lattice is proposed. The effects of geometrical parameters of the PCF on performances of the sensor are investigated by using the finite element method (FEM). Two fiber cores are separated by two air holes filled with the analyte whose refractive index is in the range of 1.33-1.41. Numerical simulation results show that the highest sensitivity can be up to 22,983 nm/RIU(refractive index unit) when the analyte refractive index is 1.41. The lowest sensitivity can reach to 21,679 nm/RIU when the analyte refractive index is 1.33. The sensor we proposed has significant advantages in the field of biomolecule detection as it provides a wide-range of detection with high sensitivity.

High Sensitivity Refractive Index Sensor Based on Dual-Core Photonic Crystal Fiber with Hexagonal Lattice

PubMed Central

Wang, Haiyang; Yan, Xin; Li, Shuguang; An, Guowen; Zhang, Xuenan

2016-01-01

A refractive index sensor based on dual-core photonic crystal fiber (PCF) with hexagonal lattice is proposed. The effects of geometrical parameters of the PCF on performances of the sensor are investigated by using the finite element method (FEM). Two fiber cores are separated by two air holes filled with the analyte whose refractive index is in the range of 1.33–1.41. Numerical simulation results show that the highest sensitivity can be up to 22,983 nm/RIU(refractive index unit) when the analyte refractive index is 1.41. The lowest sensitivity can reach to 21,679 nm/RIU when the analyte refractive index is 1.33. The sensor we proposed has significant advantages in the field of biomolecule detection as it provides a wide-range of detection with high sensitivity. PMID:27740607

Numerical prediction of the energy efficiency of the three-dimensional fish school using the discretized Adomian decomposition method

NASA Astrophysics Data System (ADS)

Lin, Yinwei

2018-06-01

A three-dimensional modeling of fish school performed by a modified Adomian decomposition method (ADM) discretized by the finite difference method is proposed. To our knowledge, few studies of the fish school are documented due to expensive cost of numerical computing and tedious three-dimensional data analysis. Here, we propose a simple model replied on the Adomian decomposition method to estimate the efficiency of energy saving of the flow motion of the fish school. First, the analytic solutions of Navier-Stokes equations are used for numerical validation. The influences of the distance between the side-by-side two fishes are studied on the energy efficiency of the fish school. In addition, the complete error analysis for this method is presented.

Corrected Four-Sphere Head Model for EEG Signals.

PubMed

Næss, Solveig; Chintaluri, Chaitanya; Ness, Torbjørn V; Dale, Anders M; Einevoll, Gaute T; Wójcik, Daniel K

2017-01-01

The EEG signal is generated by electrical brain cell activity, often described in terms of current dipoles. By applying EEG forward models we can compute the contribution from such dipoles to the electrical potential recorded by EEG electrodes. Forward models are key both for generating understanding and intuition about the neural origin of EEG signals as well as inverse modeling, i.e., the estimation of the underlying dipole sources from recorded EEG signals. Different models of varying complexity and biological detail are used in the field. One such analytical model is the four-sphere model which assumes a four-layered spherical head where the layers represent brain tissue, cerebrospinal fluid (CSF), skull, and scalp, respectively. While conceptually clear, the mathematical expression for the electric potentials in the four-sphere model is cumbersome, and we observed that the formulas presented in the literature contain errors. Here, we derive and present the correct analytical formulas with a detailed derivation. A useful application of the analytical four-sphere model is that it can serve as ground truth to test the accuracy of numerical schemes such as the Finite Element Method (FEM). We performed FEM simulations of the four-sphere head model and showed that they were consistent with the corrected analytical formulas. For future reference we provide scripts for computing EEG potentials with the four-sphere model, both by means of the correct analytical formulas and numerical FEM simulations.

Corrected Four-Sphere Head Model for EEG Signals

PubMed Central

Næss, Solveig; Chintaluri, Chaitanya; Ness, Torbjørn V.; Dale, Anders M.; Einevoll, Gaute T.; Wójcik, Daniel K.

2017-01-01

The EEG signal is generated by electrical brain cell activity, often described in terms of current dipoles. By applying EEG forward models we can compute the contribution from such dipoles to the electrical potential recorded by EEG electrodes. Forward models are key both for generating understanding and intuition about the neural origin of EEG signals as well as inverse modeling, i.e., the estimation of the underlying dipole sources from recorded EEG signals. Different models of varying complexity and biological detail are used in the field. One such analytical model is the four-sphere model which assumes a four-layered spherical head where the layers represent brain tissue, cerebrospinal fluid (CSF), skull, and scalp, respectively. While conceptually clear, the mathematical expression for the electric potentials in the four-sphere model is cumbersome, and we observed that the formulas presented in the literature contain errors. Here, we derive and present the correct analytical formulas with a detailed derivation. A useful application of the analytical four-sphere model is that it can serve as ground truth to test the accuracy of numerical schemes such as the Finite Element Method (FEM). We performed FEM simulations of the four-sphere head model and showed that they were consistent with the corrected analytical formulas. For future reference we provide scripts for computing EEG potentials with the four-sphere model, both by means of the correct analytical formulas and numerical FEM simulations. PMID:29093671

Electron-cyclotron absorption in high-temperature plasmas: quasi-exact analytical evaluation and comparative numerical analysis

NASA Astrophysics Data System (ADS)

Albajar, F.; Bertelli, N.; Bornatici, M.; Engelmann, F.

2007-01-01

On the basis of the electromagnetic energy balance equation, a quasi-exact analytical evaluation of the electron-cyclotron (EC) absorption coefficient is performed for arbitrary propagation (with respect to the magnetic field) in a (Maxwellian) magneto-plasma for the temperature range of interest for fusion reactors (in which EC radiation losses tend to be important in the plasma power balance). The calculation makes use of Bateman's expansion for the product of two Bessel functions, retaining the lowest-order contribution. The integration over electron momentum can then be carried out analytically, fully accounting for finite Larmor radius effects in this approximation. On the basis of the analytical expressions for the EC absorption coefficients of both the extraordinary and ordinary modes thus obtained, (i) for the case of perpendicular propagation simple formulae are derived for both modes and (ii) a numerical analysis of the angular distribution of EC absorption is carried out. An assessment of the accuracy of asymptotic expressions that have been given earlier is also performed, showing that these approximations can be usefully applied for calculating EC power losses from reactor-grade plasmas. Presented in part at the 14th Joint Workshop on Electron Cyclotron Emission and Electron Cyclotron Resonance Heating, Santorini, Greece, 9-12 May 2006.

Scattering of In-Plane Waves by Elastic Wedges

NASA Astrophysics Data System (ADS)

Mohammadi, K.; Asimaki, D.; Fradkin, L.

2014-12-01

The scattering of seismic waves by elastic wedges has been a topic of interest in seismology and geophysics for many decades. Analytical, semi-analytical, experimental and numerical studies on idealized wedges have provided insight into the seismic behavior of continental margins, mountain roots and crustal discontinuities. Published results, however, have almost exclusively focused on incident Rayleigh waves and out-of-plane body (SH) waves. Complementing the existing body of work, we here present results from our study on the res­ponse of elastic wedges to incident P or SV waves, an idealized pro­blem that can provide valuable insight to the understanding and parameterization of topographic ampli­fication of seismic ground mo­tion. We first show our earlier work on explicit finite difference simulations of SV-wave scattering by elastic wedges over a wide range of internal angles. We next present a semi-analytical solution that we developed using the approach proposed by Gautesen, to describe the scattered wavefield in the immediate vicinity of the wedge's tip (near-field). We use the semi-analytical solution to validate the numerical analyses, and improve resolution of the amplification factor at the wedge vertex that spikes when the internal wedge angle approaches the critical angle of incidence.

Numerical investigation of band gaps in 3D printed cantilever-in-mass metamaterials

NASA Astrophysics Data System (ADS)

Qureshi, Awais; Li, Bing; Tan, K. T.

2016-06-01

In this research, the negative effective mass behavior of elastic/mechanical metamaterials is exhibited by a cantilever-in-mass structure as a proposed design for creating frequency stopping band gaps, based on local resonance of the internal structure. The mass-in-mass unit cell model is transformed into a cantilever-in-mass model using the Bernoulli-Euler beam theory. An analytical model of the cantilever-in-mass structure is derived and the effects of geometrical dimensions and material parameters to create frequency band gaps are examined. A two-dimensional finite element model is created to validate the analytical results, and excellent agreement is achieved. The analytical model establishes an easily tunable metamaterial design to realize wave attenuation based on locally resonant frequency. To demonstrate feasibility for 3D printing, the analytical model is employed to design and fabricate 3D printable mechanical metamaterial. A three-dimensional numerical experiment is performed using COMSOL Multiphysics to validate the wave attenuation performance. Results show that the cantilever-in-mass metamaterial is capable of mitigating stress waves at the desired resonance frequency. Our study successfully presents the use of one constituent material to create a 3D printed cantilever-in-mass metamaterial with negative effective mass density for stress wave mitigation purposes.

Analysis and algorithms for a regularized Cauchy problem arising from a non-linear elliptic PDE for seismic velocity estimation

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

Cameron, M.K.; Fomel, S.B.; Sethian, J.A.

2009-01-01

In the present work we derive and study a nonlinear elliptic PDE coming from the problem of estimation of sound speed inside the Earth. The physical setting of the PDE allows us to pose only a Cauchy problem, and hence is ill-posed. However we are still able to solve it numerically on a long enough time interval to be of practical use. We used two approaches. The first approach is a finite difference time-marching numerical scheme inspired by the Lax-Friedrichs method. The key features of this scheme is the Lax-Friedrichs averaging and the wide stencil in space. The second approachmore » is a spectral Chebyshev method with truncated series. We show that our schemes work because of (1) the special input corresponding to a positive finite seismic velocity, (2) special initial conditions corresponding to the image rays, (3) the fact that our finite-difference scheme contains small error terms which damp the high harmonics; truncation of the Chebyshev series, and (4) the need to compute the solution only for a short interval of time. We test our numerical scheme on a collection of analytic examples and demonstrate a dramatic improvement in accuracy in the estimation of the sound speed inside the Earth in comparison with the conventional Dix inversion. Our test on the Marmousi example confirms the effectiveness of the proposed approach.« less

An Analytical Finite-Strain Parameterization for Texture Evolution in Deformed Olivine Polycrystals

NASA Astrophysics Data System (ADS)

Ribe, N. M.; Castelnau, O.

2017-12-01

Current methods for calculating the evolution of flow-induced seismic anisotropy in the upper mantle describe crystal preferred orientation (CPO) using ensembles of 103-104 individual grains, and are too computationally expensive to be used in three-dimensional time-dependent convection models. We propose a much faster method based on the hypothesis that CPO of olivine polycrystals is a unique function of the finite strain. Our goal is then to determine how the CPO depends on the ratios r12 and r23 of the axes of the finite strain ellipsoid and on the two independent ratios p12 and p23 of the strengths (critical resolved shear stresses) of the three independent slip systems of olivine. To do this, we introduce a new analytical representation of olivine CPO in terms of three `structured basis functions' (SBFs) Fs(g, r12, r23) (s = 1, 2, 3), where g is the set of three Eulerian angles that describe the orientation of a crystal lattice relative to an external reference frame. Each SBF represents the virtual CPO that would be produced by the action of only one of the slip systems of olivine, and can be determined analytically to within an unknown time-dependent amplitude. The amplitudes are then determined by fitting the SBFs to the predictions of the second-order self-consistent (SOSC) model of Ponte-Castaneda (2002). To implement the SBF representation, we express the orientation distribution function (ODF) f(g) of the polycrystal approximately as a linear superposition of SBFs with weighting coefficients Cs. Substituting the superposition into the general evolution equation for the ODF and minimizing the residual error, we find that the weighting coefficients Cs(t) satisfy coupled evolution equations of the form αisCs + βisCs + γs = 0 where the coefficients αis, βis and γs can be calculated in advance from the expressions for the SBFs. These equations are solved numerically for different values of p12 and p23, yielding numerical values of Cs(r12, r23, p12, p23) that can be fit using simple analytical functions. Our new parameterization allows CPO to be calculated some 107 times faster than full self-consistent methods such as SOSC.

Propagation of various dark hollow beams through an apertured paraxial ABCD optical system

NASA Astrophysics Data System (ADS)

Cai, Yangjian; Ge, Di

2006-08-01

Propagation of a dark hollow beam (DHB) of circular, elliptical or rectangular symmetry through an apertured paraxial ABCD optical system is investigated. Approximate analytical formulas for various DHBs propagating through an apertured paraxial optical system are derived by expanding the hard-aperture function into a finite sum of complex Gaussian functions in terms of a tensor method. Some numerical results are given. Our formulas provide a convenient way for studying the propagation of various DHBs through an apertured paraxial optical system.

Lateral trapping of DNA inside a voltage gated nanopore

NASA Astrophysics Data System (ADS)

Töws, Thomas; Reimann, Peter

2017-06-01

The translocation of a short DNA fragment through a nanopore is addressed when the perforated membrane contains an embedded electrode. Accurate numerical solutions of the coupled Poisson, Nernst-Planck, and Stokes equations for a realistic, fully three-dimensional setup as well as analytical approximations for a simplified model are worked out. By applying a suitable voltage to the membrane electrode, the DNA can be forced to preferably traverse the pore either along the pore axis or at a small but finite distance from the pore wall.

An efficient solution procedure for the thermoelastic analysis of truss space structures

NASA Technical Reports Server (NTRS)

Givoli, D.; Rand, O.

1992-01-01

A solution procedure is proposed for the thermal and thermoelastic analysis of truss space structures in periodic motion. In this method, the spatial domain is first descretized using a consistent finite element formulation. Then the resulting semi-discrete equations in time are solved analytically by using Fourier decomposition. Geometrical symmetry is taken advantage of completely. An algorithm is presented for the calculation of heat flux distribution. The method is demonstrated via a numerical example of a cylindrically shaped space structure.

Reconfigurable silicon thermo-optical device based on spectral tuning of ring resonators.

PubMed

Fegadolli, William S; Almeida, Vilson R; Oliveira, José Edimar Barbosa

2011-06-20

A novel tunable and reconfigurable thermo-optical device is theoretically proposed and analyzed in this paper. The device is designed to be entirely compatible with CMOS process and to work as a thermo-optical filter or modulator. Numerical results, made by means of analytical and Finite-Difference Time-Domain (FDTD) methods, show that a compact device enables a broad bandwidth operation, of up to 830 GHz, which allows the device to work under a large temperature variation, of up to 96 K.

Finite Element and Analytical Analysis of Cracks in Thick Stiffened Plates Repaired with a Single Sided Composite Patch

DTIC Science & Technology

2014-06-01

DC,Tech. Rep. CG-D-05–00, 2000. [16] S. Kou, Welding Metallurgy , 2nd edition, Hoboken: Wiley Interscience, 2003. [17] C. Poe, “Stress intensity...continuous aluminum superstructure welded to the deck. The shape of the superstructure created numerous stress concentration areas. Of the greatest concern...study as it will help provide a conservative estimate. In marine applications almost all stiffening members are attached by welding . Unlike a

Nonlinear whistler waves

NASA Astrophysics Data System (ADS)

Vasko, I.; Agapitov, O. V.; Mozer, F.; Bonnell, J. W.; Krasnoselskikh, V.; Artemyev, A.; Drake, J. F.

2017-12-01

Chorus waves observed in the Earth inner magnetosphere sometimes exhibit significantly distorted (nonharmonic) parallel electric field waveform. In spectrograms these waveform features show up as overtones of chorus wave. In this work we show that the chorus wave parallel electric field is distorted due to finite temperature of electrons. The distortion of the parallel electric field is described analytically and reproduced in the numerical fluid simulations. Due to this effect the chorus energy is transferred to higher frequencies making possible efficient scattering of low ( a few keV) energy electrons.

A performability solution method for degradable nonrepairable systems

NASA Technical Reports Server (NTRS)

Furchtgott, D. G.; Meyer, J. F.

1984-01-01

The present performability model-solving algorithm identifies performance with 'reward', representing the state behavior of a system S by a finite-state stochastic process and determining reward by means of reward rates that are associated with the states of the base model. A general method is obtained for determining the probability distribution function of the performance (reward) variable, and therefore the performability, of the corresponding system. This is done for bounded utilization periods, and the result is an integral expression which is either analytically or numerically solvable.

Numerical Solution of the Extended Nernst-Planck Model.

PubMed

Samson; Marchand

1999-07-01

The main features of a numerical model aiming at predicting the drift of ions in an electrolytic solution upon a chemical potential gradient are presented. The mechanisms of ionic diffusion are described by solving the extended Nernst-Planck system of equations. The electrical coupling between the various ionic fluxes is accounted for by the Poisson equation. Furthermore, chemical activity effects are considered in the model. The whole system of nonlinear equations is solved using the finite-element method. Results yielded by the model for simple test cases are compared to those obtained using an analytical solution. Applications of the model to more complex problems are also presented and discussed. Copyright 1999 Academic Press.

Kinetic theory analysis of rarefied gas flow through finite length slots

NASA Technical Reports Server (NTRS)

Raghuraman, P.

1972-01-01

An analytic study is made of the flow a rarefied monatomic gas through a two dimensional slot. The parameters of the problem are the ratios of downstream to upstream pressures, the Knudsen number at the high pressure end (based on slot half width) and the length to slot half width ratio. A moment method of solution is used by assuming a discontinuous distribution function consisting of four Maxwellians split equally in angular space. Numerical solutions are obtained for the resulting equations. The characteristics of the transition regime are portrayed. The solutions in the free molecule limit are systematically lower than the results obtained in that limit by more accurate numerical methods.

Comment on "Modified quantum-speed-limit bounds for open quantum dynamics in quantum channels"

NASA Astrophysics Data System (ADS)

Mirkin, Nicolás; Toscano, Fabricio; Wisniacki, Diego A.

2018-04-01

In a recent paper [Phys. Rev. A 95, 052118 (2017), 10.1103/PhysRevA.95.052118], the authors claim that our criticism, in Phys. Rev. A 94, 052125 (2016), 10.1103/PhysRevA.94.052125, to some quantum speed limit bounds for open quantum dynamics that appeared recently in literature are invalid. According to the authors, the problem with our analysis would be generated by an artifact of the finite-precision numerical calculations. We analytically show here that it is not possible to have any inconsistency associated with the numerical precision of calculations. Therefore, our criticism of the quantum speed limit bounds continues to be valid.

A novel finite volume discretization method for advection-diffusion systems on stretched meshes

NASA Astrophysics Data System (ADS)

Merrick, D. G.; Malan, A. G.; van Rooyen, J. A.

2018-06-01

This work is concerned with spatial advection and diffusion discretization technology within the field of Computational Fluid Dynamics (CFD). In this context, a novel method is proposed, which is dubbed the Enhanced Taylor Advection-Diffusion (ETAD) scheme. The model equation employed for design of the scheme is the scalar advection-diffusion equation, the industrial application being incompressible laminar and turbulent flow. Developed to be implementable into finite volume codes, ETAD places specific emphasis on improving accuracy on stretched structured and unstructured meshes while considering both advection and diffusion aspects in a holistic manner. A vertex-centered structured and unstructured finite volume scheme is used, and only data available on either side of the volume face is employed. This includes the addition of a so-called mesh stretching metric. Additionally, non-linear blending with the existing NVSF scheme was performed in the interest of robustness and stability, particularly on equispaced meshes. The developed scheme is assessed in terms of accuracy - this is done analytically and numerically, via comparison to upwind methods which include the popular QUICK and CUI techniques. Numerical tests involved the 1D scalar advection-diffusion equation, a 2D lid driven cavity and turbulent flow case. Significant improvements in accuracy were achieved, with L2 error reductions of up to 75%.

Parallelized modelling and solution scheme for hierarchically scaled simulations

NASA Technical Reports Server (NTRS)

Padovan, Joe

1995-01-01

This two-part paper presents the results of a benchmarked analytical-numerical investigation into the operational characteristics of a unified parallel processing strategy for implicit fluid mechanics formulations. This hierarchical poly tree (HPT) strategy is based on multilevel substructural decomposition. The Tree morphology is chosen to minimize memory, communications and computational effort. The methodology is general enough to apply to existing finite difference (FD), finite element (FEM), finite volume (FV) or spectral element (SE) based computer programs without an extensive rewrite of code. In addition to finding large reductions in memory, communications, and computational effort associated with a parallel computing environment, substantial reductions are generated in the sequential mode of application. Such improvements grow with increasing problem size. Along with a theoretical development of general 2-D and 3-D HPT, several techniques for expanding the problem size that the current generation of computers are capable of solving, are presented and discussed. Among these techniques are several interpolative reduction methods. It was found that by combining several of these techniques that a relatively small interpolative reduction resulted in substantial performance gains. Several other unique features/benefits are discussed in this paper. Along with Part 1's theoretical development, Part 2 presents a numerical approach to the HPT along with four prototype CFD applications. These demonstrate the potential of the HPT strategy.

Thermodynamic Modelling of Phase Transformation in a Multi-Component System

NASA Astrophysics Data System (ADS)

Vala, J.

2007-09-01

Diffusion in multi-component alloys can be characterized by the vacancy mechanism for substitutional components, by the existence of sources and sinks for vacancies and by the motion of atoms of interstitial components. The description of diffusive and massive phase transformation of a multi-component system is based on the thermodynamic extremal principle by Onsager; the finite thickness of the interface between both phases is respected. The resulting system of partial differential equations of evolution with integral terms for unknown mole fractions (and additional variables in case of non-ideal sources and sinks for vacancies), can be analyzed using the method of lines and the finite difference technique (or, alternatively, the finite element one) together with the semi-analytic and numerical integration formulae and with certain iteration procedure, making use of the spectral properties of linear operators. The original software code for the numerical evaluation of solutions of such systems, written in MATLAB, offers a chance to simulate various real processes of diffusional phase transformation. Some results for the (nearly) steady-state real processes in substitutional alloys have been published yet. The aim of this paper is to demonstrate that the same approach can handle both substitutional and interstitial components even in case of a general system of evolution.

A study of unsteady physiological magneto-fluid flow and heat transfer through a finite length channel by peristaltic pumping.

PubMed

Tripathi, Dharmendra; Bég, O Anwar

2012-08-01

Magnetohydrodynamic peristaltic flows arise in controlled magnetic drug targeting, hybrid haemodynamic pumps and biomagnetic phenomena interacting with the human digestive system. Motivated by the objective of improving an understanding of the complex fluid dynamics in such flows, we consider in the present article the transient magneto-fluid flow and heat transfer through a finite length channel by peristaltic pumping. Reynolds number is small enough and the wavelength to diameter ratio is large enough to negate inertial effects. Analytical solutions for temperature field, axial velocity, transverse velocity, pressure gradient, local wall shear stress, volume flowrate and averaged volume flowrate are obtained. The effects of the transverse magnetic field, Grashof number and thermal conductivity on the flow patterns induced by peristaltic waves (sinusoidal propagation along the length of channel) are studied using graphical plots. The present study identifies that greater pressure is required to propel the magneto-fluid by peristaltic pumping in comparison to a non-conducting Newtonian fluid, whereas, a lower pressure is required if heat transfer is effective. The analytical solutions further provide an important benchmark for future numerical simulations.

Finite Element Analysis of Active and Sensory Thermopiezoelectric Composite Materials. Degree awarded by Northwestern Univ., Dec. 2000

NASA Technical Reports Server (NTRS)

Lee, Ho-Jun

2001-01-01

Analytical formulations are developed to account for the coupled mechanical, electrical, and thermal response of piezoelectric composite materials. The coupled response is captured at the material level through the thermopiezoelectric constitutive equations and leads to the inherent capability to model both the sensory and active responses of piezoelectric materials. A layerwise laminate theory is incorporated to provide more accurate analysis of the displacements, strains, stresses, electric fields, and thermal fields through-the-thickness. Thermal effects which arise from coefficient of thermal expansion mismatch, pyroelectric effects, and temperature dependent material properties are explicitly accounted for in the formulation. Corresponding finite element formulations are developed for piezoelectric beam, plate, and shell elements to provide a more generalized capability for the analysis of arbitrary piezoelectric composite structures. The accuracy of the current formulation is verified with comparisons from published experimental data and other analytical models. Additional numerical studies are also conducted to demonstrate additional capabilities of the formulation to represent the sensory and active behaviors. A future plan of experimental studies is provided to characterize the high temperature dynamic response of piezoelectric composite materials.

Computation of turbulent boundary layers employing the defect wall-function method. M.S. Thesis

NASA Technical Reports Server (NTRS)

Brown, Douglas L.

1994-01-01

In order to decrease overall computational time requirements of spatially-marching parabolized Navier-Stokes finite-difference computer code when applied to turbulent fluid flow, a wall-function methodology, originally proposed by R. Barnwell, was implemented. This numerical effort increases computational speed and calculates reasonably accurate wall shear stress spatial distributions and boundary-layer profiles. Since the wall shear stress is analytically determined from the wall-function model, the computational grid near the wall is not required to spatially resolve the laminar-viscous sublayer. Consequently, a substantially increased computational integration step size is achieved resulting in a considerable decrease in net computational time. This wall-function technique is demonstrated for adiabatic flat plate test cases from Mach 2 to Mach 8. These test cases are analytically verified employing: (1) Eckert reference method solutions, (2) experimental turbulent boundary-layer data of Mabey, and (3) finite-difference computational code solutions with fully resolved laminar-viscous sublayers. Additionally, results have been obtained for two pressure-gradient cases: (1) an adiabatic expansion corner and (2) an adiabatic compression corner.

Continuum calculations of continental deformation in transcurrent environments

NASA Technical Reports Server (NTRS)

Sonder, L. J.; England, P. C.; Houseman, G. A.

1986-01-01

A thin viscous sheet approximation is used to investigate continental deformation near a strike-slip boundary. The vertically averaged velocity field is calculated for a medium characterized by a power law rheology with stress exponent n. Driving stresses include those applied along boundaries of the sheet and those arising from buoyancy forces related to lateral differences in crustal thickness. Exact and approximate analytic solutions for a region with a sinusoidal strike-slip boundary condition are compared with solutions for more geologically relevant boundary conditions obtained using a finite element technique. The across-strike length scale of the deformation is approximately 1/4pi x sq rt n times the dominant wavelength of the imposed strike-slip boundary condition for both the analytic and the numerical solutions; this result is consistent with length scales observed in continental regions of large-scale transcurrent faulting. An approximate, linear relationship between displacement and rotation is found that depends only on the deformation length scale and the rheology. Calculated displacements, finite rotations, and distribution of crustal thicknesses are consistent with those observed in the region of the Pacific-North America plate boundary in California.

Two-particle problem in comblike structures

NASA Astrophysics Data System (ADS)

Agliari, Elena; Cassi, Davide; Cattivelli, Luca; Sartori, Fabio

2016-05-01

Encounters between walkers performing a random motion on an appropriate structure can describe a wide variety of natural phenomena ranging from pharmacokinetics to foraging. On homogeneous structures the asymptotic encounter probability between two walkers is (qualitatively) independent of whether both walkers are moving or one is kept fixed. On infinite comblike structures this is no longer the case and here we deepen the mechanisms underlying the emergence of a finite probability that two random walkers will never meet, while one single random walker is certain to visit any site. In particular, we introduce an analytical approach to address this problem and even more general problems such as the case of two walkers with different diffusivity, particles walking on a finite comb and on arbitrary bundled structures, possibly in the presence of loops. Our investigations are both analytical and numerical and highlight that, in general, the outcome of a reaction involving two reactants on a comblike architecture can strongly differ according to whether both reactants are moving (no matter their relative diffusivities) or only one is moving and according to the density of shortcuts among the branches.

An Unstructured Finite Volume Approach for Structural Dynamics in Response to Fluid Motions.

PubMed

Xia, Guohua; Lin, Ching-Long

2008-04-01

A new cell-vortex unstructured finite volume method for structural dynamics is assessed for simulations of structural dynamics in response to fluid motions. A robust implicit dual-time stepping method is employed to obtain time accurate solutions. The resulting system of algebraic equations is matrix-free and allows solid elements to include structure thickness, inertia, and structural stresses for accurate predictions of structural responses and stress distributions. The method is coupled with a fluid dynamics solver for fluid-structure interaction, providing a viable alternative to the finite element method for structural dynamics calculations. A mesh sensitivity test indicates that the finite volume method is at least of second-order accuracy. The method is validated by the problem of vortex-induced vibration of an elastic plate with different initial conditions and material properties. The results are in good agreement with existing numerical data and analytical solutions. The method is then applied to simulate a channel flow with an elastic wall. The effects of wall inertia and structural stresses on the fluid flow are investigated.

Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows

DOE PAGES

Xia, Yidong; Wang, Chuanjin; Luo, Hong; ...

2015-12-15

Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in themore » simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, we have attempted some form of solution verification to identify sensitivities in the solution methods, and to suggest best practices when using the Hydra-TH code.« less

Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows

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

Xia, Yidong; Wang, Chuanjin; Luo, Hong

Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in themore » simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, we have attempted some form of solution verification to identify sensitivities in the solution methods, and to suggest best practices when using the Hydra-TH code.« less

Non-idealities in the 3ω method for thermal characterization in the low- and high-frequency regimes

NASA Astrophysics Data System (ADS)

Jaber, Wassim; Chapuis, Pierre-Olivier

2018-04-01

This work is devoted to analytical and numerical studies of diffusive heat conduction in configurations considered in 3ω experiments, which aim at measuring thermal conductivity of materials. The widespread 2D analytical model considers infinite media and translational invariance, a situation which cannot be met in practice in numerous cases due to the constraints in low-dimensional materials and systems. We investigate how thermal boundary resistance between heating wire and sample, native oxide and heating wire shape affect the temperature fields. 3D finite element modelling is also performed to account for the effect of the bonding pads and the 3D heat spreading down to a typical package. Emphasis is given on the low-frequency regime, which is less known than the so-called slope regime. These results will serve as guides for the design of ideal experiments where the 2D model can be applied and for the analyses of non-ideal ones.

High frequency fishbone driven by passing energetic ions in tokamak plasmas

NASA Astrophysics Data System (ADS)

Wang, Feng; Yu, L. M.; Fu, G. Y.; Shen, Wei

2017-05-01

High frequency fishbone instability driven by passing energetic ions was first reported in the Princeton beta experiment with tangential neutral-beam-injection (Heidbrink et al 1986 Phys. Rev. Lett. 57 835-8). It could play an important role for ITER-like burning plasmas, where α particles are mostly passing particles. In this work, a generalized energetic ion distribution function and finite drift orbit width effect are considered to improve the theoretical model for passing particle driving fishbone instability. For purely passing energetic ions with zero drift orbit width, the kinetic energy δ {{W}k} is derived analytically. The derived analytic expression is more accurate as compared to the result of previous work (Wang 2001 Phys. Rev. Lett. 86 5286-8). For a generalized energetic ion distribution function, the fishbone dispersion relation is derived and is solved numerically. Numerical results show that broad and off-axis beam density profiles can significantly increase the beam ion beta threshold {βc} for instability and decrease mode frequency.

High frequency fishbone driven by passing energetic ions in tokamak plasmas

DOE PAGES

Wang, Feng; Yu, L. M.; Fu, G. Y.; ...

2017-03-22

High frequency fishbone instability driven by passing energetic ions was first reported in the Princeton beta experiment with tangential neutral-beam-injection (Heidbrink et al 1986 Phys. Rev. Lett. 57 835–8). It could play an important role for ITER-like burning plasmas, where α particles are mostly passing particles. In this work, a generalized energetic ion distribution function and finite drift orbit width effect are considered to improve the theoretical model for passing particle driving fishbone instability. For purely passing energetic ions with zero drift orbit width, the kinetic energymore » $$\\delta {{W}_{k}}$$ is derived analytically. The derived analytic expression is more accurate as compared to the result of previous work. For a generalized energetic ion distribution function, the fishbone dispersion relation is derived and is solved numerically. As a result, numerical results show that broad and off-axis beam density profiles can significantly increase the beam ion beta threshold $${{\\beta}_{c}}$$ for instability and decrease mode frequency.« less

Resonant tunneling assisted propagation and amplification of plasmons in high electron mobility transistors

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

Bhardwaj, Shubhendu; Sensale-Rodriguez, Berardi; Xing, Huili Grace

A rigorous theoretical and computational model is developed for the plasma-wave propagation in high electron mobility transistor structures with electron injection from a resonant tunneling diode at the gate. We discuss the conditions in which low-loss and sustainable plasmon modes can be supported in such structures. The developed analytical model is used to derive the dispersion relation for these plasmon-modes. A non-linear full-wave-hydrodynamic numerical solver is also developed using a finite difference time domain algorithm. The developed analytical solutions are validated via the numerical solution. We also verify previous observations that were based on a simplified transmission line model. Itmore » is shown that at high levels of negative differential conductance, plasmon amplification is indeed possible. The proposed rigorous models can enable accurate design and optimization of practical resonant tunnel diode-based plasma-wave devices for terahertz sources, mixers, and detectors, by allowing a precise representation of their coupling when integrated with other electromagnetic structures.« less

Many-body localization transition: Schmidt gap, entanglement length, and scaling

NASA Astrophysics Data System (ADS)

Gray, Johnnie; Bose, Sougato; Bayat, Abolfazl

2018-05-01

Many-body localization has become an important phenomenon for illuminating a potential rift between nonequilibrium quantum systems and statistical mechanics. However, the nature of the transition between ergodic and localized phases in models displaying many-body localization is not yet well understood. Assuming that this is a continuous transition, analytic results show that the length scale should diverge with a critical exponent ν ≥2 in one-dimensional systems. Interestingly, this is in stark contrast with all exact numerical studies which find ν ˜1 . We introduce the Schmidt gap, new in this context, which scales near the transition with an exponent ν >2 compatible with the analytical bound. We attribute this to an insensitivity to certain finite-size fluctuations, which remain significant in other quantities at the sizes accessible to exact numerical methods. Additionally, we find that a physical manifestation of the diverging length scale is apparent in the entanglement length computed using the logarithmic negativity between disjoint blocks.

Analytical and numerical solutions for mass diffusion in a composite cylindrical body

NASA Astrophysics Data System (ADS)

Kumar, A.

1980-12-01

The analytical and numerical solution techniques were investigated to study moisture diffusion problems in cylindrical bodies that are assumed to be composed of a finite number of layers of different materials. A generalized diffusion model for an n-layer cylindrical body with discontinuous moisture content at the interfaces was developed and the formal solutions were obtained. The model is to be used for describing mass transfer rates of any composite body, such as an ear of corn which could be assumed of consisting two different layers: the inner core represents the woody cob and the outer cylinder represents the kernel layer. Data describing the fully exposed drying characteristics of ear corn at high air velocity were obtained under different drying conditions. Ear corns were modeled as homogeneous bodies since composite model did not improve the fit substantially. A computer program using multidimensional optimization technique showed that diffusivity was an exponential function of moisture content and an arrhenius function of temperature of drying air.

Critical Nucleation Length for Accelerating Frictional Slip

NASA Astrophysics Data System (ADS)

Aldam, Michael; Weikamp, Marc; Spatschek, Robert; Brener, Efim A.; Bouchbinder, Eran

2017-11-01

The spontaneous nucleation of accelerating slip along slowly driven frictional interfaces is central to a broad range of geophysical, physical, and engineering systems, with particularly far-reaching implications for earthquake physics. A common approach to this problem associates nucleation with an instability of an expanding creep patch upon surpassing a critical length Lc. The critical nucleation length Lc is conventionally obtained from a spring-block linear stability analysis extended to interfaces separating elastically deformable bodies using model-dependent fracture mechanics estimates. We propose an alternative approach in which the critical nucleation length is obtained from a related linear stability analysis of homogeneous sliding along interfaces separating elastically deformable bodies. For elastically identical half-spaces and rate-and-state friction, the two approaches are shown to yield Lc that features the same scaling structure, but with substantially different numerical prefactors, resulting in a significantly larger Lc in our approach. The proposed approach is also shown to be naturally applicable to finite-size systems and bimaterial interfaces, for which various analytic results are derived. To quantitatively test the proposed approach, we performed inertial Finite-Element-Method calculations for a finite-size two-dimensional elastically deformable body in rate-and-state frictional contact with a rigid body under sideway loading. We show that the theoretically predicted Lc and its finite-size dependence are in reasonably good quantitative agreement with the full numerical solutions, lending support to the proposed approach. These results offer a theoretical framework for predicting rapid slip nucleation along frictional interfaces.

The possible equilibrium shapes of static pendant drops

NASA Astrophysics Data System (ADS)

Sumesh, P. T.; Govindarajan, Rama

2010-10-01

Analytical and numerical studies are carried out on the shapes of two-dimensional and axisymmetric pendant drops hanging under gravity from a solid surface. Drop shapes with both pinned and equilibrium contact angles are obtained naturally from a single boundary condition in the analytical energy optimization procedure. The numerical procedure also yields optimum energy shapes, satisfying Young's equation without the explicit imposition of a boundary condition at the plate. It is shown analytically that a static pendant two-dimensional drop can never be longer than 3.42 times the capillary length. A related finding is that a range of existing solutions for long two-dimensional drops correspond to unphysical drop shapes. Therefore, two-dimensional drops of small volume display only one static solution. In contrast, it is known that axisymmetric drops can display multiple solutions for a given volume. We demonstrate numerically that there is no limit to the height of multiple-lobed Kelvin drops, but the total volume is finite, with the volume of successive lobes forming a convergent series. The stability of such drops is in question, though. Drops of small volume can attain large heights. A bifurcation is found within the one-parameter space of Laplacian shapes, with a range of longer drops displaying a minimum in energy in the investigated space. Axisymmetric Kelvin drops exhibit an infinite number of bifurcations.

Evaluation of Resuspension from Propeller Wash in DoD Harbors

DTIC Science & Technology

2016-09-01

Environmental Research and Development Center FANS FOV ICP-MS Finite Analytical Navier-Stoker Solver Field of View Inductively Coupled Plasma with...Model (1984) and the Finite Analytical Navier- Stoker Solver (FANS) model (Chen et al., 2003) were set up to simulate and evaluate flow velocities and...model for evaluating the resuspension potential of propeller wash by a tugboat and the FANS model for a DDG. The Finite -Analytic Navier-Stokes (FANS

Application of variational principles and adjoint integrating factors for constructing numerical GFD models

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey

2015-04-01

The proposed method is considered on an example of hydrothermodynamics and atmospheric chemistry models [1,2]. In the development of the existing methods for constructing numerical schemes possessing the properties of total approximation for operators of multiscale process models, we have developed a new variational technique, which uses the concept of adjoint integrating factors. The technique is as follows. First, a basic functional of the variational principle (the integral identity that unites the model equations, initial and boundary conditions) is transformed using Lagrange's identity and the second Green's formula. As a result, the action of the operators of main problem in the space of state functions is transferred to the adjoint operators defined in the space of sufficiently smooth adjoint functions. By the choice of adjoint functions the order of the derivatives becomes lower by one than those in the original equations. We obtain a set of new balance relationships that take into account the sources and boundary conditions. Next, we introduce the decomposition of the model domain into a set of finite volumes. For multi-dimensional non-stationary problems, this technique is applied in the framework of the variational principle and schemes of decomposition and splitting on the set of physical processes for each coordinate directions successively at each time step. For each direction within the finite volume, the analytical solutions of one-dimensional homogeneous adjoint equations are constructed. In this case, the solutions of adjoint equations serve as integrating factors. The results are the hybrid discrete-analytical schemes. They have the properties of stability, approximation and unconditional monotony for convection-diffusion operators. These schemes are discrete in time and analytic in the spatial variables. They are exact in case of piecewise-constant coefficients within the finite volume and along the coordinate lines of the grid area in each direction on a time step. In each direction, they have tridiagonal structure. They are solved by the sweep method. An important advantage of the discrete-analytical schemes is that the values of derivatives at the boundaries of finite volume are calculated together with the values of the unknown functions. This technique is particularly attractive for problems with dominant convection, as it does not require artificial monotonization and limiters. The same idea of integrating factors is applied in temporal dimension to the stiff systems of equations describing chemical transformation models [2]. The proposed method is applicable for the problems involving convection-diffusion-reaction operators. The work has been partially supported by the Presidium of RAS under Program 43, and by the RFBR grants 14-01-00125 and 14-01-31482. References: 1. V.V. Penenko, E.A. Tsvetova, A.V. Penenko. Variational approach and Euler's integrating factors for environmental studies// Computers and Mathematics with Applications, (2014) V.67, Issue 12, P. 2240-2256. 2. V.V.Penenko, E.A.Tsvetova. Variational methods of constructing monotone approximations for atmospheric chemistry models // Numerical analysis and applications, 2013, V. 6, Issue 3, pp 210-220.

Efficient finite element modeling of radiation forces on elastic particles of arbitrary size and geometry.

PubMed

Glynne-Jones, Peter; Mishra, Puja P; Boltryk, Rosemary J; Hill, Martyn

2013-04-01

A finite element based method is presented for calculating the acoustic radiation force on arbitrarily shaped elastic and fluid particles. Importantly for future applications, this development will permit the modeling of acoustic forces on complex structures such as biological cells, and the interactions between them and other bodies. The model is based on a non-viscous approximation, allowing the results from an efficient, numerical, linear scattering model to provide the basis for the second-order forces. Simulation times are of the order of a few seconds for an axi-symmetric structure. The model is verified against a range of existing analytical solutions (typical accuracy better than 0.1%), including those for cylinders, elastic spheres that are of significant size compared to the acoustic wavelength, and spheroidal particles.

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.

Investigation of non-linear contact for a clearance-fit bolt in a graphite/epoxy laminate

NASA Technical Reports Server (NTRS)

Prabhakaran, R.; Naik, R. A.

1986-01-01

Numerous analytical studies have been published for the nonlinear load-contact variations in clearance-fit bolted joints. In these studies, stress distributions have been obtained and failure predictions have been made. However, very little experimental work has been reported regarding the contact or the stresses. This paper describes a fiber-optic technique for measuring the angle of contact in a clearance-fit bolt-loaded hole. Measurements of the contact angle have been made in a quasi-isotropic graphite-epoxy laminate by the optical as well as an electrical technique, and the results have been compared with those obtained from a finite-element analysis. The results from the two experimental techniques show excellent agreement; the finite-element results show some discrepancy, probably due to the interfacial frictions.

Efficiency of encounter-controlled reaction between diffusing reactants in a finite lattice: Non-nearest-neighbor effects

NASA Astrophysics Data System (ADS)

Bentz, Jonathan L.; Kozak, John J.; Nicolis, Gregoire

2005-08-01

The influence of non-nearest-neighbor displacements on the efficiency of diffusion-reaction processes involving one and two mobile diffusing reactants is studied. An exact analytic result is given for dimension d=1 from which, for large lattices, one can recover the asymptotic estimate reported 30 years ago by Lakatos-Lindenberg and Shuler. For dimensions d=2,3 we present numerically exact values for the mean time to reaction, as gauged by the mean walklength before reactive encounter, obtained via the theory of finite Markov processes and supported by Monte Carlo simulations. Qualitatively different results are found between processes occurring on d=1 versus d>1 lattices, and between results obtained assuming nearest-neighbor (only) versus non-nearest-neighbor displacements.

Cotton-Mouton effect and shielding polarizabilities of ethylene: An MCSCF study

NASA Astrophysics Data System (ADS)

Coriani, Sonia; Rizzo, Antonio; Ruud, Kenneth; Helgaker, Trygve

1997-03-01

The static hypermagnetizabilities and nuclear shielding polarizabilities of the carbon and hydrogen atoms of ethylene have been computed using multiconfigurational linear-response theory and a finite-field method, in a mixed analytical-numerical approach. Extended sets of magnetic-field-dependent basis functions have been employed in large MCSCF calculations, involving active spaces giving rise to a few million configurations in the finite-field perturbed symmetry. The convergence of the observables with respect to the extension of the basis set as well as the effect of electron correlation have been investigated. Whereas for the shielding polarizabilities we can compare with other published SCF results, the ab initio estimates for the static hypermagnetizabilities and the observable to which they are related - the Cotton-Mouton constant, - are presented for the first time.

A probabilistic model of a porous heat exchanger

NASA Technical Reports Server (NTRS)

Agrawal, O. P.; Lin, X. A.

1995-01-01

This paper presents a probabilistic one-dimensional finite element model for heat transfer processes in porous heat exchangers. The Galerkin approach is used to develop the finite element matrices. Some of the submatrices are asymmetric due to the presence of the flow term. The Neumann expansion is used to write the temperature distribution as a series of random variables, and the expectation operator is applied to obtain the mean and deviation statistics. To demonstrate the feasibility of the formulation, a one-dimensional model of heat transfer phenomenon in superfluid flow through a porous media is considered. Results of this formulation agree well with the Monte-Carlo simulations and the analytical solutions. Although the numerical experiments are confined to parametric random variables, a formulation is presented to account for the random spatial variations.

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.

Displacement potential solution of a guided deep beam of composite materials under symmetric three-point bending

NASA Astrophysics Data System (ADS)

Rahman, M. Muzibur; Ahmad, S. Reaz

2017-12-01

An analytical investigation of elastic fields for a guided deep beam of orthotropic composite material having three point symmetric bending is carried out using displacement potential boundary modeling approach. Here, the formulation is developed as a single function of space variables defined in terms of displacement components, which has to satisfy the mixed type of boundary conditions. The relevant displacement and stress components are derived into infinite series using Fourier integral along with suitable polynomials coincided with boundary conditions. The results are presented mainly in the form of graphs and verified with finite element solutions using ANSYS. This study shows that the analytical and numerical solutions are in good agreement and thus enhances reliability of the displacement potential approach.

Modeling walker synchronization on the Millennium Bridge.

PubMed

Eckhardt, Bruno; Ott, Edward; Strogatz, Steven H; Abrams, Daniel M; McRobie, Allan

2007-02-01

On its opening day the London Millennium footbridge experienced unexpected large amplitude wobbling subsequent to the migration of pedestrians onto the bridge. Modeling the stepping of the pedestrians on the bridge as phase oscillators, we obtain a model for the combined dynamics of people and the bridge that is analytically tractable. It provides predictions for the phase dynamics of individual walkers and for the critical number of people for the onset of oscillations. Numerical simulations and analytical estimates reproduce the linear relation between pedestrian force and bridge velocity as observed in experiments. They allow prediction of the amplitude of bridge motion, the rate of relaxation to the synchronized state and the magnitude of the fluctuations due to a finite number of people.

Chain-reaction crash in traffic flow controlled by taillights

NASA Astrophysics Data System (ADS)

Nagatani, Takashi

2015-02-01

We study the chain-reaction crash (multiple-vehicle collision) in low-visibility condition on a road. In the traffic situation, drivers brake according to taillights of the forward vehicle. The first crash may induce more collisions. We investigate whether or not the first collision induces the chain-reaction crash, numerically and analytically. The dynamic transitions occur from no collisions through a single collision, double collisions and triple collisions, to multiple collisions with decreasing the headway. Also, we find that the dynamic transition occurs from the finite chain reaction to the infinite chain reaction when the headway is less than the critical value. We derive, analytically, the transition points and the region maps for the chain-reaction crash in traffic flow controlled by taillights.

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...

The Behaviour of Naturally Debonded Composites Due to Bending Using a Meso-Level Model

NASA Astrophysics Data System (ADS)

Lord, C. E.; Rongong, J. A.; Hodzic, A.

2012-06-01

Numerical simulations and analytical models are increasingly being sought for the design and behaviour prediction of composite materials. The use of high-performance composite materials is growing in both civilian and defence related applications. With this growth comes the necessity to understand and predict how these new materials will behave under their exposed environments. In this study, the displacement behaviour of naturally debonded composites under out-of-plane bending conditions has been investigated. An analytical approach has been developed to predict the displacement response behaviour. The analytical model supports multi-layered composites with full and partial delaminations. The model can be used to extract bulk effective material properties in which can be represented, later, as an ESL (Equivalent Single Layer). The friction between each of the layers is included in the analytical model and is shown to have distinct behaviour for these types of composites. Acceptable agreement was observed between the model predictions, the ANSYS finite element model, and the experiments.

Analytical Model for Thermal Elastoplastic Stresses of Functionally Graded Materials

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

Zhai, P. C.; Chen, G.; Liu, L. S.

2008-02-15

A modification analytical model is presented for the thermal elastoplastic stresses of functionally graded materials subjected to thermal loading. The presented model follows the analytical scheme presented by Y. L. Shen and S. Suresh [6]. In the present model, the functionally graded materials are considered as multilayered materials. Each layer consists of metal and ceramic with different volume fraction. The ceramic layer and the FGM interlayers are considered as elastic brittle materials. The metal layer is considered as elastic-perfectly plastic ductile materials. Closed-form solutions for different characteristic temperature for thermal loading are presented as a function of the structure geometriesmore » and the thermomechanical properties of the materials. A main advance of the present model is that the possibility of the initial and spread of plasticity from the two sides of the ductile layers taken into account. Comparing the analytical results with the results from the finite element analysis, the thermal stresses and deformation from the present model are in good agreement with the numerical ones.« less

Buckling of a stiff thin film on an elastic graded compliant substrate.

PubMed

Chen, Zhou; Chen, Weiqiu; Song, Jizhou

2017-12-01

The buckling of a stiff film on a compliant substrate has attracted much attention due to its wide applications such as thin-film metrology, surface patterning and stretchable electronics. An analytical model is established for the buckling of a stiff thin film on a semi-infinite elastic graded compliant substrate subjected to in-plane compression. The critical compressive strain and buckling wavelength for the sinusoidal mode are obtained analytically for the case with the substrate modulus decaying exponentially. The rigorous finite element analysis (FEA) is performed to validate the analytical model and investigate the postbuckling behaviour of the system. The critical buckling strain for the period-doubling mode is obtained numerically. The influences of various material parameters on the results are investigated. These results are helpful to provide physical insights on the buckling of elastic graded substrate-supported thin film.

Three-Dimensional Dynamic Deformation Measurements Using Stereoscopic Imaging and Digital Speckle Photography

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

Prentice, H. J.; Proud, W. G.

2006-07-28

A technique has been developed to determine experimentally the three-dimensional displacement field on the rear surface of a dynamically deforming plate. The technique combines speckle analysis with stereoscopy, using a modified angular-lens method: this incorporates split-frame photography and a simple method by which the effective lens separation can be adjusted and calibrated in situ. Whilst several analytical models exist to predict deformation in extended or semi-infinite targets, the non-trivial nature of the wave interactions complicates the generation and development of analytical models for targets of finite depth. By interrogating specimens experimentally to acquire three-dimensional strain data points, both analytical andmore » numerical model predictions can be verified more rigorously. The technique is applied to the quasi-static deformation of a rubber sheet and dynamically to Mild Steel sheets of various thicknesses.« less

Roy-Steiner equations for pion-nucleon scattering

NASA Astrophysics Data System (ADS)

Ditsche, C.; Hoferichter, M.; Kubis, B.; Meißner, U.-G.

2012-06-01

Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations for pion-nucleon scattering that respects analyticity, unitarity, and crossing symmetry. We work out analytically all kernel functions and unitarity relations required for the lowest partial waves. In order to suppress the dependence on the high energy regime we also consider once- and twice-subtracted versions of the equations, where we identify the subtraction constants with subthreshold parameters. Assuming Mandelstam analyticity we determine the maximal range of validity of these equations. As a first step towards the solution of the full system we cast the equations for the π π to overline N N partial waves into the form of a Muskhelishvili-Omnès problem with finite matching point, which we solve numerically in the single-channel approximation. We investigate in detail the role of individual contributions to our solutions and discuss some consequences for the spectral functions of the nucleon electromagnetic form factors.

Analytical expressions for the evolution of many-body quantum systems quenched far from equilibrium

NASA Astrophysics Data System (ADS)

Santos, Lea F.; Torres-Herrera, E. Jonathan

2017-12-01

Possible strategies to describe analytically the dynamics of many-body quantum systems out of equilibrium include the use of solvable models and of full random matrices. None of the two approaches represent actual realistic systems, but they serve as references for the studies of these ones. We take the second path and obtain analytical expressions for the survival probability, density imbalance, and out-of-time-ordered correlator. Using these findings, we then propose an approximate expression that matches very well numerical results for the evolution of realistic finite quantum systems that are strongly chaotic and quenched far from equilibrium. In the case of the survival probability, the expression proposed covers all different time scales, from the moment the system is taken out of equilibrium to the moment it reaches a new equilibrium. The realistic systems considered are described by one-dimensional spin-1/2 models.

Buckling of a stiff thin film on an elastic graded compliant substrate

NASA Astrophysics Data System (ADS)

Chen, Zhou; Chen, Weiqiu; Song, Jizhou

2017-12-01

The buckling of a stiff film on a compliant substrate has attracted much attention due to its wide applications such as thin-film metrology, surface patterning and stretchable electronics. An analytical model is established for the buckling of a stiff thin film on a semi-infinite elastic graded compliant substrate subjected to in-plane compression. The critical compressive strain and buckling wavelength for the sinusoidal mode are obtained analytically for the case with the substrate modulus decaying exponentially. The rigorous finite element analysis (FEA) is performed to validate the analytical model and investigate the postbuckling behaviour of the system. The critical buckling strain for the period-doubling mode is obtained numerically. The influences of various material parameters on the results are investigated. These results are helpful to provide physical insights on the buckling of elastic graded substrate-supported thin film.

Analytical and Numerical Solutions of Generalized Fokker-Planck Equations - Final Report

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

Prinja, Anil K.

The overall goal of this project was to develop advanced theoretical and numerical techniques to quantitatively describe the spreading of a collimated beam of charged particles in space, in angle, and in energy, as a result of small deflection, small energy transfer Coulomb collisions with the target nuclei and electrons. Such beams arise in several applications of great interest in nuclear engineering, and include electron and ion radiotherapy, ion beam modification of materials, accelerator transmutation of waste, and accelerator production of tritium, to name some important candidates. These applications present unique and difficult modeling challenges, but from the outset aremore » amenable to the language of ''transport theory'', which is very familiar to nuclear engineers and considerably less-so to physicists and material scientists. Thus, our approach has been to adopt a fundamental description based on transport equations, but the forward peakedness associated with charged particle interactions precludes a direct application of solution methods developed for neutral particle transport. Unique problem formulations and solution techniques are necessary to describe the transport and interaction of charged particles. In particular, we have developed the Generalized Fokker-Planck (GFP) approach to describe the angular and radial spreading of a collimated beam and a renormalized transport model to describe the energy-loss straggling of an initially monoenergetic distribution. Both analytic and numerical solutions have been investigated and in particular novel finite element numerical methods have been developed. In the first phase of the project, asymptotic methods were used to develop closed form solutions to the GFP equation for different orders of expansion, and was described in a previous progress report. In this final report we present a detailed description of (i) a novel energy straggling model based on a Fokker-Planck approximation but which is adapted for a multigroup transport setting, and (ii) two unique families of discontinuous finite element schemes, one linear and the other nonlinear.« less

Analyte preconcentration in nanofluidic channels with nonuniform zeta potential

NASA Astrophysics Data System (ADS)

Eden, A.; McCallum, C.; Storey, B. D.; Pennathur, S.; Meinhart, C. D.

2017-12-01

It is well known that charged analytes in the presence of nonuniform electric fields concentrate at locations where the relevant driving forces balance, and a wide range of ionic stacking and focusing methods are commonly employed to leverage these physical mechanisms in order to improve signal levels in biosensing applications. In particular, nanofluidic channels with spatially varying conductivity distributions have been shown to provide increased preconcentration of charged analytes due to the existence of a finite electric double layer (EDL), in which electrostatic attraction and repulsion from charged surfaces produce nonuniform transverse ion distributions. In this work, we use numerical simulations to show that one can achieve greater levels of sample accumulation by using field-effect control via wall-embedded electrodes to tailor the surface potential heterogeneity in a nanochannel with overlapped EDLs. In addition to previously demonstrated stacking and focusing mechanisms, we find that the coupling between two-dimensional ion distributions and the axial electric field under overlapped EDL conditions can generate an ion concentration polarization interface in the middle of the channel. Under an applied electric field, this interface can be used to concentrate sample ions between two stationary regions of different surface potential and charge density. Our numerical model uses the Poisson-Nernst-Planck system of equations coupled with the Stokes equation to demonstrate the phenomenon, and we discuss in detail the driving forces behind the predicted sample enhancement. The numerical velocity and salt concentration profiles exhibit good agreement with analytical results from a simplified one-dimensional area-averaged model for several limiting cases, and we show predicted amplification ratios of up to 105.

Viscoelastic modeling of deformation and gravity changes induced by pressurized magmatic sources

NASA Astrophysics Data System (ADS)

Currenti, Gilda

2018-05-01

Gravity and height changes, which reflect magma accumulation in subsurface chambers, are evaluated using analytical and numerical models in order to investigate their relationships and temporal evolutions. The analysis focuses mainly on the exploration of the time-dependent response of gravity and height changes to the pressurization of ellipsoidal magmatic chambers in viscoelastic media. Firstly, the validation of the numerical Finite Element results is performed by comparison with analytical solutions, which are devised for a simple spherical source embedded in a homogeneous viscoelastic half-space medium. Then, the effect of several model parameters on time-dependent height and gravity changes is investigated thanks to the flexibility of the numerical method in handling complex configurations. Both homogeneous and viscoelastic shell models reveal significantly different amplitudes in the ratio between gravity and height changes depending on geometry factors and medium rheology. The results show that these factors also influence the relaxation characteristic times of the investigated geophysical changes. Overall, these temporal patterns are compatible with time-dependent height and gravity changes observed on Etna volcano during the 1994-1997 inflation period. By modeling the viscoelastic response of a pressurized prolate magmatic source, a general agreement between computed and observed geophysical variations is achieved.

Distribution of diameters for Erdős-Rényi random graphs.

PubMed

Hartmann, A K; Mézard, M

2018-03-01

We study the distribution of diameters d of Erdős-Rényi random graphs with average connectivity c. The diameter d is the maximum among all the shortest distances between pairs of nodes in a graph and an important quantity for all dynamic processes taking place on graphs. Here we study the distribution P(d) numerically for various values of c, in the nonpercolating and percolating regimes. Using large-deviation techniques, we are able to reach small probabilities like 10^{-100} which allow us to obtain the distribution over basically the full range of the support, for graphs up to N=1000 nodes. For values c<1, our results are in good agreement with analytical results, proving the reliability of our numerical approach. For c>1 the distribution is more complex and no complete analytical results are available. For this parameter range, P(d) exhibits an inflection point, which we found to be related to a structural change of the graphs. For all values of c, we determined the finite-size rate function Φ(d/N) and were able to extrapolate numerically to N→∞, indicating that the large-deviation principle holds.

Distribution of diameters for Erdős-Rényi random graphs

NASA Astrophysics Data System (ADS)

Hartmann, A. K.; Mézard, M.

2018-03-01

We study the distribution of diameters d of Erdős-Rényi random graphs with average connectivity c . The diameter d is the maximum among all the shortest distances between pairs of nodes in a graph and an important quantity for all dynamic processes taking place on graphs. Here we study the distribution P (d ) numerically for various values of c , in the nonpercolating and percolating regimes. Using large-deviation techniques, we are able to reach small probabilities like 10-100 which allow us to obtain the distribution over basically the full range of the support, for graphs up to N =1000 nodes. For values c <1 , our results are in good agreement with analytical results, proving the reliability of our numerical approach. For c >1 the distribution is more complex and no complete analytical results are available. For this parameter range, P (d ) exhibits an inflection point, which we found to be related to a structural change of the graphs. For all values of c , we determined the finite-size rate function Φ (d /N ) and were able to extrapolate numerically to N →∞ , indicating that the large-deviation principle holds.

Stiffness of frictional contact of dissimilar elastic solids

DOE PAGES

Lee, Jin Haeng; Gao, Yanfei; Bower, Allan F.; ...

2017-12-22

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This study gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the frictionmore » coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations – adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. Finally, the correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.« less

Stiffness of frictional contact of dissimilar elastic solids

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

Lee, Jin Haeng; Gao, Yanfei; Bower, Allan F.

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This study gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the frictionmore » coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations – adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. Finally, the correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.« less

Stiffness of frictional contact of dissimilar elastic solids

NASA Astrophysics Data System (ADS)

Lee, Jin Haeng; Gao, Yanfei; Bower, Allan F.; Xu, Haitao; Pharr, George M.

2018-03-01

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This paper gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the friction coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations - adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. The correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.

Evaluation of Transverse Thermal Stresses in Composite Plates Based on First-Order Shear Deformation Theory

NASA Technical Reports Server (NTRS)

Rolfes, R.; Noor, A. K.; Sparr, H.

1998-01-01

A postprocessing procedure is presented for the evaluation of the transverse thermal stresses in laminated plates. The analytical formulation is based on the first-order shear deformation theory and the plate is discretized by using a single-field displacement finite element model. The procedure is based on neglecting the derivatives of the in-plane forces and the twisting moments, as well as the mixed derivatives of the bending moments, with respect to the in-plane coordinates. The calculated transverse shear stiffnesses reflect the actual stacking sequence of the composite plate. The distributions of the transverse stresses through-the-thickness are evaluated by using only the transverse shear forces and the thermal effects resulting from the finite element analysis. The procedure is implemented into a postprocessing routine which can be easily incorporated into existing commercial finite element codes. Numerical results are presented for four- and ten-layer cross-ply laminates subjected to mechanical and thermal loads.

Bananas, Doughnuts and Seismic Traveltimes

NASA Astrophysics Data System (ADS)

Dahlen, F. A.

2002-12-01

Most of what we know about the 3-D seismic heterogeneity of the mantle is based upon ray-theoretical traveltime tomography. In this infinite-frequency approximation, a measured traveltime anomaly depends only upon the wavespeed along an infinitesimally thin geometrical ray between a seismic source and a seismographic station. In this lecture I shall describe a new formulation of the seismic traveltime inverse problem which accounts for the ability of a finite-frequency wave to ``feel'' 3-D structure off of the source-receiver ray. Finite-frequency diffraction effects associated with this off-ray sensitivity act to ``heal'' the corrugations that develop in a wavefront propagating through a heterogeneous medium. Ray-theoretical tomography is based upon the premise that a seismic wave ``remembers'' all of the traveltime advances or delays that it accrues along its path, whereas actual finite-frequency waves ``forget''. I shall describe a number of recent analytical and numerical investigations, which have led to an improved theoretical understanding of this phenomenon.

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.

A Mixed Multi-Field Finite Element Formulation for Thermopiezoelectric Composite Shells

NASA Technical Reports Server (NTRS)

Lee, Ho-Jun; Saravanos, Dimitris A.

1999-01-01

Analytical formulations are presented which account for the coupled mechanical, electrical, and thermal response of piezoelectric composite shell structures. A new mixed multi-field laminate theory is developed which combines "single layer" assumptions for the displacements along with layerwise fields for the electric potential and temperature. This laminate theory is formulated using curvilinear coordinates and is based on the principles of linear thermopiezoelectricity. The mechanics have the inherent capability to explicitly model both the active and sensory responses of piezoelectric composite shells in thermal environment. Finite element equations are derived and implemented for an eight-noded shell element. Numerical studies are conducted to investigate both the sensory and active responses of piezoelectric composite shell structures subjected to thermal loads. Results for a cantilevered plate with an attached piezoelectric layer are com- pared with corresponding results from a commercial finite element code and a previously developed program. Additional studies are conducted on a cylindrical shell with an attached piezoelectric layer to demonstrate capabilities to achieve thermal shape control on curved piezoelectric structures.

Quasispecies theory for finite populations

PubMed Central

Park, Jeong-Man; Muñoz, Enrique; Deem, Michael W.

2015-01-01

We present stochastic, finite-population formulations of the Crow-Kimura and Eigen models of quasispecies theory, for fitness functions that depend in an arbitrary way on the number of mutations from the wild type. We include back mutations in our description. We show that the fluctuation of the population numbers about the average values are exceedingly large in these physical models of evolution. We further show that horizontal gene transfer reduces by orders of magnitude the fluctuations in the population numbers and reduces the accumulation of deleterious mutations in the finite population due to Muller’s ratchet. Indeed the population sizes needed to converge to the infinite population limit are often larger than those found in nature for smooth fitness functions in the absence of horizontal gene transfer. These analytical results are derived for the steady-state by means of a field-theoretic representation. Numerical results are presented that indicate horizontal gene transfer speeds up the dynamics of evolution as well. PMID:20365394

The forced sound transmission of finite single leaf walls using a variational technique.

PubMed

Brunskog, Jonas

2012-09-01

The single wall is the simplest element of concern in building acoustics, but there still remain some open questions regarding the sound insulation of this simple case. The two main reasons for this are the effects on the excitation and sound radiation of the wall when it has a finite size, and the fact that the wave field in the wall is consisting of two types of waves, namely forced waves due to the exciting acoustic field, and free bending waves due to reflections in the boundary. The aim of the present paper is to derive simple analytical formulas for the forced part of the airborne sound insulation of a single homogeneous wall of finite size, using a variational technique based on the integral-differential equation of the fluid loaded wall. The so derived formulas are valid in the entire audible frequency range. The results are compared with full numerical calculations, measurements and alternative theory, with reasonable agreement.

Casimir interaction of rodlike particles in a two-dimensional critical system.

PubMed

Eisenriegler, E; Burkhardt, T W

2016-09-01

We consider the fluctuation-induced interaction of two thin, rodlike particles, or "needles," immersed in a two-dimensional critical fluid of Ising symmetry right at the critical point. Conformally mapping the plane containing the needles onto a simpler geometry in which the stress tensor is known, we analyze the force and torque between needles of arbitrary length, separation, and orientation. For infinite and semi-infinite needles we utilize the mapping of the plane bounded by the needles onto the half plane, and for two needles of finite length we use the mapping onto an annulus. For semi-infinite and infinite needles the force is expressed in terms of elementary functions, and we also obtain analytical results for the force and torque between needles of finite length with separation much greater than their length. Evaluating formulas in our approach numerically for several needle geometries and surface universality classes, we study the full crossover from small to large values of the separation to length ratio. In these two limits the numerical results agree with results for infinitely long needles and with predictions of the small-particle operator expansion, respectively.

Simulation of one-sided heating of boiler unit membrane-type water walls

NASA Astrophysics Data System (ADS)

Kurepin, M. P.; Serbinovskiy, M. Yu.

2017-03-01

This study describes the results of simulation of the temperature field and the stress-strain state of membrane-type gastight water walls of boiler units using the finite element method. The methods of analytical and standard calculation of one-sided heating of fin-tube water walls by a radiative heat flux are analyzed. The methods and software for input data calculation in the finite-element simulation, including thermoelastic moments in welded panels that result from their one-sided heating, are proposed. The method and software modules are used for water wall simulation using ANSYS. The results of simulation of the temperature field, stress field, deformations and displacement of the membrane-type panel for the boiler furnace water wall using the finite-element method, as well as the results of calculation of the panel tube temperature, stresses and deformations using the known methods, are presented. The comparison of the known experimental results on heating and bending by given moments of membrane-type water walls and numerical simulations is performed. It is demonstrated that numerical results agree with high accuracy with the experimental data. The relative temperature difference does not exceed 1%. The relative difference of the experimental fin mutual turning angle caused by one-sided heating by radiative heat flux and the results obtained in the finite element simulation does not exceed 8.5% for nondisplaced fins and 7% for fins with displacement. The same difference for the theoretical results and the simulation using the finite-element method does not exceed 3% and 7.1%, respectively. The proposed method and software modules for simulation of the temperature field and stress-strain state of the water walls are verified and the feasibility of their application in practical design is proven.

A novel Lagrangian approach for the stable numerical simulation of fault and fracture mechanics

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

Franceschini, Andrea; Ferronato, Massimiliano, E-mail: massimiliano.ferronato@unipd.it; Janna, Carlo

The simulation of the mechanics of geological faults and fractures is of paramount importance in several applications, such as ensuring the safety of the underground storage of wastes and hydrocarbons or predicting the possible seismicity triggered by the production and injection of subsurface fluids. However, the stable numerical modeling of ground ruptures is still an open issue. The present work introduces a novel formulation based on the use of the Lagrange multipliers to prescribe the constraints on the contact surfaces. The variational formulation is modified in order to take into account the frictional work along the activated fault portion accordingmore » to the principle of maximum plastic dissipation. The numerical model, developed in the framework of the Finite Element method, provides stable solutions with a fast convergence of the non-linear problem. The stabilizing properties of the proposed model are emphasized with the aid of a realistic numerical example dealing with the generation of ground fractures due to groundwater withdrawal in arid regions. - Highlights: • A numerical model is developed for the simulation of fault and fracture mechanics. • The model is implemented in the framework of the Finite Element method and with the aid of Lagrange multipliers. • The proposed formulation introduces a new contribution due to the frictional work on the portion of activated fault. • The resulting algorithm is highly non-linear as the portion of activated fault is itself unknown. • The numerical solution is validated against analytical results and proves to be stable also in realistic applications.« less

Numerical and Experimental Investigations on Mechanical Behavior of Composite Corrugated Core

NASA Astrophysics Data System (ADS)

Dayyani, Iman; Ziaei-Rad, Saeed; Salehi, Hamid

2012-06-01

Tensile and flexural characteristics of corrugated laminate panels were studied using numerical and analytical methods and compared with experimental data. Prepreg laminates of glass fiber plain woven cloth were hand-laid by use of a heat gun to ease the creation of the panel. The corrugated panels were then manufactured by using a trapezoidal machined aluminium mould. First, a series of simple tension tests were performed on standard samples to evaluate the material characteristics. Next, the corrugated panels were subjected to tensile and three-point bending tests. The force-displacement graphs were recorded. Numerical and analytical solutions were proposed to simulate the mechanical behavior of the panels. In order to model the energy dissipation due to delamination phenomenon observed in tensile tests in all members of corrugated core, plastic behavior was assigned to the whole geometry, not only to the corner regions. Contrary to the literature, it is shown that the three-stage mechanical behavior of composite corrugated core is not confined to aramid reinforced corrugated laminates and can be observed in other types such as fiber glass. The results reveal that the mechanical behavior of the core in tension is sensitive to the variation of core height. In addition, for the first time, the behavior of composite corrugated core was studied and verified in bending. Finally, the analytical and numerical results were validated by comparing them with experimental data. A good degree of correlation was observed which showed the suitability of the finite element model for predicting the mechanical behavior of corrugated laminate panels.

The inverse Numerical Computer Program FLUX-BOT for estimating Vertical Water Fluxes from Temperature Time-Series.

NASA Astrophysics Data System (ADS)

Trauth, N.; Schmidt, C.; Munz, M.

2016-12-01

Heat as a natural tracer to quantify water fluxes between groundwater and surface water has evolved to a standard hydrological method. Typically, time series of temperatures in the surface water and in the sediment are observed and are subsequently evaluated by a vertical 1D representation of heat transport by advection and dispersion. Several analytical solutions as well as their implementation into user-friendly software exist in order to estimate water fluxes from the observed temperatures. Analytical solutions can be easily implemented but assumptions on the boundary conditions have to be made a priori, e.g. sinusoidal upper temperature boundary. Numerical models offer more flexibility and can handle temperature data which is characterized by irregular variations such as storm-event induced temperature changes and thus cannot readily be incorporated in analytical solutions. This also reduced the effort of data preprocessing such as the extraction of the diurnal temperature variation. We developed a software to estimate water FLUXes Based On Temperatures- FLUX-BOT. FLUX-BOT is a numerical code written in MATLAB which is intended to calculate vertical water fluxes in saturated sediments, based on the inversion of measured temperature time series observed at multiple depths. It applies a cell-centered Crank-Nicolson implicit finite difference scheme to solve the one-dimensional heat advection-conduction equation. Besides its core inverse numerical routines, FLUX-BOT includes functions visualizing the results and functions for performing uncertainty analysis. We provide applications of FLUX-BOT to generic as well as to measured temperature data to demonstrate its performance.

Occurrence of dead core in catalytic particles containing immobilized enzymes: analysis for the Michaelis-Menten kinetics and assessment of numerical methods.

PubMed

Pereira, Félix Monteiro; Oliveira, Samuel Conceição

2016-11-01

In this article, the occurrence of dead core in catalytic particles containing immobilized enzymes is analyzed for the Michaelis-Menten kinetics. An assessment of numerical methods is performed to solve the boundary value problem generated by the mathematical modeling of diffusion and reaction processes under steady state and isothermal conditions. Two classes of numerical methods were employed: shooting and collocation. The shooting method used the ode function from Scilab software. The collocation methods included: that implemented by the bvode function of Scilab, the orthogonal collocation, and the orthogonal collocation on finite elements. The methods were validated for simplified forms of the Michaelis-Menten equation (zero-order and first-order kinetics), for which analytical solutions are available. Among the methods covered in this article, the orthogonal collocation on finite elements proved to be the most robust and efficient method to solve the boundary value problem concerning Michaelis-Menten kinetics. For this enzyme kinetics, it was found that the dead core can occur when verified certain conditions of diffusion-reaction within the catalytic particle. The application of the concepts and methods presented in this study will allow for a more generalized analysis and more accurate designs of heterogeneous enzymatic reactors.

A mathematical model for describing the mechanical behaviour of root canal instruments.

PubMed

Zhang, E W; Cheung, G S P; Zheng, Y F

2011-01-01

The purpose of this study was to establish a general mathematical model for describing the mechanical behaviour of root canal instruments by combining a theoretical analytical approach with a numerical finite-element method. Mathematical formulas representing the longitudinal (taper, helical angle and pitch) and cross-sectional configurations and area, the bending and torsional inertia, the curvature of the boundary point and the (geometry of) loading condition were derived. Torsional and bending stresses and the resultant deformation were expressed mathematically as a function of these geometric parameters, modulus of elasticity of the material and the applied load. As illustrations, three brands of NiTi endodontic files of different cross-sectional configurations (ProTaper, Hero 642, and Mani NRT) were analysed under pure torsion and pure bending situation by entering the model into a finite-element analysis package (ANSYS). Numerical results confirmed that mathematical models were a feasible method to analyse the mechanical properties and predict the stress and deformation for root canal instruments during root canal preparation. Mathematical and numerical model can be a suitable way to examine mechanical behaviours as a criterion of the instrument design and to predict the stress and strain experienced by the endodontic instruments during root canal preparation. © 2010 International Endodontic Journal.

Probabilistic homogenization of random composite with ellipsoidal particle reinforcement by the iterative stochastic finite element method

NASA Astrophysics Data System (ADS)

Sokołowski, Damian; Kamiński, Marcin

2018-01-01

This study proposes a framework for determination of basic probabilistic characteristics of the orthotropic homogenized elastic properties of the periodic composite reinforced with ellipsoidal particles and a high stiffness contrast between the reinforcement and the matrix. Homogenization problem, solved by the Iterative Stochastic Finite Element Method (ISFEM) is implemented according to the stochastic perturbation, Monte Carlo simulation and semi-analytical techniques with the use of cubic Representative Volume Element (RVE) of this composite containing single particle. The given input Gaussian random variable is Young modulus of the matrix, while 3D homogenization scheme is based on numerical determination of the strain energy of the RVE under uniform unit stretches carried out in the FEM system ABAQUS. The entire series of several deterministic solutions with varying Young modulus of the matrix serves for the Weighted Least Squares Method (WLSM) recovery of polynomial response functions finally used in stochastic Taylor expansions inherent for the ISFEM. A numerical example consists of the High Density Polyurethane (HDPU) reinforced with the Carbon Black particle. It is numerically investigated (1) if the resulting homogenized characteristics are also Gaussian and (2) how the uncertainty in matrix Young modulus affects the effective stiffness tensor components and their PDF (Probability Density Function).

Numerical simulation of the nonlinear response of composite plates under combined thermal and acoustic loading

NASA Technical Reports Server (NTRS)

Mei, Chuh; Moorthy, Jayashree

1995-01-01

A time-domain study of the random response of a laminated plate subjected to combined acoustic and thermal loads is carried out. The features of this problem also include given uniform static inplane forces. The formulation takes into consideration a possible initial imperfection in the flatness of the plate. High decibel sound pressure levels along with high thermal gradients across thickness drive the plate response into nonlinear regimes. This calls for the analysis to use von Karman large deflection strain-displacement relationships. A finite element model that combines the von Karman strains with the first-order shear deformation plate theory is developed. The development of the analytical model can accommodate an anisotropic composite laminate built up of uniformly thick layers of orthotropic, linearly elastic laminae. The global system of finite element equations is then reduced to a modal system of equations. Numerical simulation using a single-step algorithm in the time-domain is then carried out to solve for the modal coordinates. Nonlinear algebraic equations within each time-step are solved by the Newton-Raphson method. The random gaussian filtered white noise load is generated using Monte Carlo simulation. The acoustic pressure distribution over the plate is capable of accounting for a grazing incidence wavefront. Numerical results are presented to study a variety of cases.

Analytic representations of mK , FK, mη, and Fη in two loop S U (3 ) chiral perturbation theory

NASA Astrophysics Data System (ADS)

Ananthanarayan, B.; Bijnens, Johan; Friot, Samuel; Ghosh, Shayan

2018-06-01

In this work, we consider expressions for the masses and decay constants of the pseudoscalar mesons in S U (3 ) chiral perturbation theory. These involve sunset diagrams and their derivatives evaluated at p2=mP2 (P =π , K , η ). Recalling that there are three mass scales in this theory, mπ, mK and mη, there are instances when the finite part of the sunset diagrams do not admit an expression in terms of elementary functions, and have therefore been evaluated numerically in the past. In a recent publication, an expansion in the external momentum was performed to obtain approximate analytic expressions for mπ and Fπ, the pion mass and decay constant. We provide fully analytic exact expressions for mK and mη, the kaon and eta masses, and FK and Fη, the kaon and eta decay constants. These expressions, calculated using Mellin-Barnes methods, are in the form of double series in terms of two mass ratios. A numerical analysis of the results to evaluate the relative size of contributions coming from loops, chiral logarithms as well as phenomenological low-energy constants is presented. We also present a set of approximate analytic expressions for mK, FK, mη and Fη that facilitate comparisons with lattice results. Finally, we show how exact analytic expressions for mπ and Fπ may be obtained, the latter having been used in conjunction with the results for FK to produce a recently published analytic representation of FK/Fπ.

Analytical Modeling of Groundwater Seepages to St. Lucie Estuary

NASA Astrophysics Data System (ADS)

Lee, J.; Yeh, G.; Hu, G.

2008-12-01

In this paper, six analytical models describing hydraulic interaction of stream-aquifer systems were applied to St Lucie Estuary (SLE) River Estuaries. These are analytical solutions for: (1) flow from a finite aquifer to a canal, (2) flow from an infinite aquifer to a canal, (3) the linearized Laplace system in a seepage surface, (4) wave propagation in the aquifer, (5) potential flow through stratified unconfined aquifers, and (6) flow through stratified confined aquifers. Input data for analytical solutions were obtained from monitoring wells and river stages at seepage-meter sites. Four transects in the study area are available: Club Med, Harbour Ridge, Lutz/MacMillan, and Pendarvis Cove located in the St. Lucie River. The analytical models were first calibrated with seepage meter measurements and then used to estimate of groundwater discharges into St. Lucie River. From this process, analytical relationships between the seepage rate and river stages and/or groundwater tables were established to predict the seasonal and monthly variation in groundwater seepage into SLE. It was found the seepage rate estimations by analytical models agreed well with measured data for some cases but only fair for some other cases. This is not unexpected because analytical solutions have some inherently simplified assumptions, which may be more valid for some cases than the others. From analytical calculations, it is possible to predict approximate seepage rates in the study domain when the assumptions underlying these analytical models are valid. The finite and infinite aquifer models and the linearized Laplace method are good for sites Pendarvis Cove and Lutz/MacMillian, but fair for the other two sites. The wave propagation model gave very good agreement in phase but only fairly agreement in magnitude for all four sites. The stratified unconfined and confined aquifer models gave similarly good agreements with measurements at three sites but poorly at the Club Med site. None of the analytical models presented here can fit the data at this site. To give better estimates at all sites numerical modeling that couple river hydraulics and groundwater flow involving less simplifications of and assumptions for the system may have to be adapted.

A Gas-Actuated Projectile Launcher for High-Energy Impact Testing of Structures

NASA Technical Reports Server (NTRS)

Ambur, Damodar R.; Jaunky, Navin; Lawson, Robin E.; Knight, Norman F., Jr.; Lyle, Karen H.

1999-01-01

A gas-act,uated penetration device has been developed for high-energy impact testing of structures. The high-energy impact. t,estiiig is for experimental simulation of uncontained engine failures. The non-linear transient finite element, code LS-DYNA3D has been used in the numerical simula.tions of a titanium rectangular blade with a.n aluminum target, plate. Threshold velocities for different combinations of pitch and yaw angles of the impactor were obtained for the impactor-target, t8est configuration in the numerica.1 simulations. Complet,e penet,ration of the target plate was also simulat,ed numerically. Finally, limited comparison of analytical and experimental results is presented for complete penetration of the target by the impactor.

TH-AB-BRA-09: Stability Analysis of a Novel Dose Calculation Algorithm for MRI Guided Radiotherapy

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

Zelyak, O; Fallone, B; Cross Cancer Institute, Edmonton, AB

2016-06-15

Purpose: To determine the iterative deterministic solution stability of the Linear Boltzmann Transport Equation (LBTE) in the presence of magnetic fields. Methods: The LBTE with magnetic fields under investigation is derived using a discrete ordinates approach. The stability analysis is performed using analytical and numerical methods. Analytically, the spectral Fourier analysis is used to obtain the convergence rate of the source iteration procedures based on finding the largest eigenvalue of the iterative operator. This eigenvalue is a function of relevant physical parameters, such as magnetic field strength and material properties, and provides essential information about the domain of applicability requiredmore » for clinically optimal parameter selection and maximum speed of convergence. The analytical results are reinforced by numerical simulations performed using the same discrete ordinates method in angle, and a discontinuous finite element spatial approach. Results: The spectral radius for the source iteration technique of the time independent transport equation with isotropic and anisotropic scattering centers inside infinite 3D medium is equal to the ratio of differential and total cross sections. The result is confirmed numerically by solving LBTE and is in full agreement with previously published results. The addition of magnetic field reveals that the convergence becomes dependent on the strength of magnetic field, the energy group discretization, and the order of anisotropic expansion. Conclusion: The source iteration technique for solving the LBTE with magnetic fields with the discrete ordinates method leads to divergent solutions in the limiting cases of small energy discretizations and high magnetic field strengths. Future investigations into non-stationary Krylov subspace techniques as an iterative solver will be performed as this has been shown to produce greater stability than source iteration. Furthermore, a stability analysis of a discontinuous finite element space-angle approach (which has been shown to provide the greatest stability) will also be investigated. Dr. B Gino Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization)« less

Analysis of thin-walled cylindrical composite shell structures subject to axial and bending loads: Concept development, analytical modeling and experimental verification

NASA Astrophysics Data System (ADS)

Mahadev, Sthanu

Continued research and development efforts devoted in recent years have generated novel avenues towards the advancement of efficient and effective, slender laminated fiber-reinforced composite members. Numerous studies have focused on the modeling and response characterization of composite structures with particular relevance to thin-walled cylindrical composite shells. This class of shell configurations is being actively explored to fully determine their mechanical efficacy as primary aerospace structural members. The proposed research is targeted towards formulating a composite shell theory based prognosis methodology that entails an elaborate analysis and investigation of thin-walled cylindrical shell type laminated composite configurations that are highly desirable in increasing number of mechanical and aerospace applications. The prime motivation to adopt this theory arises from its superior ability to generate simple yet viable closed-form analytical solution procedure to numerous geometrically intense, inherent curvature possessing composite structures. This analytical evaluative routine offers to acquire a first-hand insight on the primary mechanical characteristics that essentially govern the behavior of slender composite shells under typical static loading conditions. Current work exposes the robustness of this mathematical framework via demonstrating its potential towards the prediction of structural properties such as axial stiffness and bending stiffness respectively. Longitudinal ply-stress computations are investigated upon deriving the global stiffness matrix model for composite cylindrical tubes with circular cross-sections. Additionally, this work employs a finite element based numerical technique to substantiate the analytical results reported for cylindrically shaped circular composite tubes. Furthermore, this concept development is extended to the study of thin-walled, open cross-sectioned, curved laminated shells that are geometrically distinguished with respect to the circumferential arc angle, thickness-to-mean radius ratio and total laminate thickness. The potential of this methodology is challenged to analytically determine the location of the centroid. This precise location dictates the decoupling of extension-bending type deformational response in tension loaded composite structures. Upon the cross-validation of the centroidal point through the implementation of an ANSYS based finite element routine, influence of centroid is analytically examined under the application of a concentrated longitudinal tension and bending type loadings on a series of cylindrical shells characterized by three different symmetric-balanced stacking sequences. In-plane ply-stresses are computed and analyzed across the circumferential contour. An experimental investigation has been incorporated via designing an ad-hoc apparatus and test-up that accommodates the quantification of in-plane strains, computation of ply-stresses and addresses the physical characteristics for a set of auto-clave fabricated cylindrical shell articles. Consequently, this work is shown to essentially capture the mechanical aspects of cylindrical shells, thus facilitating structural engineers to design and manufacture viable structures.

Origin of the Norton-type wave scattered by a subwavelength metallic slit

NASA Astrophysics Data System (ADS)

Le Perchec, Jérôme

2015-10-01

We clarify analytically and numerically the physical origin and the behavior of the Norton field scattered by a narrow slit, at optical frequencies. This apparent surface field, which comes in addition to the surface plasmon-polariton and classic cylindrical light waves, features its own radiation lobe associated with oscillating induced currents that spread over both horizontal metallic parts forming the slit. Theory is given taking into account the finite size of the aperture and is illustrated with materials such as gold and amorphous silicon in different spectral regions.

Generalized eigenstate typicality in translation-invariant quasifree fermionic models

NASA Astrophysics Data System (ADS)

Riddell, Jonathon; Müller, Markus P.

2018-01-01

We demonstrate a generalized notion of eigenstate thermalization for translation-invariant quasifree fermionic models: the vast majority of eigenstates satisfying a finite number of suitable constraints (e.g., fixed energy and particle number) have the property that their reduced density matrix on small subsystems approximates the corresponding generalized Gibbs ensemble. To this end, we generalize analytic results by H. Lai and K. Yang [Phys. Rev. B 91, 081110(R) (2015), 10.1103/PhysRevB.91.081110] and illustrate the claim numerically by example of the Jordan-Wigner transform of the XX spin chain.

Hamiltonian chaos acts like a finite energy reservoir: accuracy of the Fokker-Planck approximation.

PubMed

Riegert, Anja; Baba, Nilüfer; Gelfert, Katrin; Just, Wolfram; Kantz, Holger

2005-02-11

The Hamiltonian dynamics of slow variables coupled to fast degrees of freedom is modeled by an effective stochastic differential equation. Formal perturbation expansions, involving a Markov approximation, yield a Fokker-Planck equation in the slow subspace which respects conservation of energy. A detailed numerical and analytical analysis of suitable model systems demonstrates the feasibility of obtaining the system specific drift and diffusion terms and the accuracy of the stochastic approximation on all time scales. Non-Markovian and non-Gaussian features of the fast variables are negligible.

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

Dulat, Falko; Lionetti, Simone; Mistlberger, Bernhard

We present an analytic computation of the Higgs production cross section in the gluon fusion channel, which is differential in the components of the Higgs momentum and inclusive in the associated partonic radiation through NNLO in perturbative QCD. Our computation includes the necessary higher order terms in the dimensional regulator beyond the finite part that are required for renormalisation and collinear factorisation at N 3LO. We outline in detail the computational methods which we employ. We present numerical predictions for realistic final state observables, specifically distributions for the decay products of the Higgs boson in the γγ decay channel.

FEMFLOW3D; a finite-element program for the simulation of three-dimensional aquifers; version 1.0

USGS Publications Warehouse

Durbin, Timothy J.; Bond, Linda D.

1998-01-01

This document also includes model validation, source code, and example input and output files. Model validation was performed using four test problems. For each test problem, the results of a model simulation with FEMFLOW3D were compared with either an analytic solution or the results of an independent numerical approach. The source code, written in the ANSI x3.9-1978 FORTRAN standard, and the complete input and output of an example problem are listed in the appendixes.

An exact analysis of a rectangular plate piezoelectric generator.

PubMed

Yang, Jiashi; Chen, Ziguang; Hu, Yuantai

2007-01-01

We study thickness-twist vibration of a finite, piezoelectric plate of polarized ceramics or 6-mm crystals driven by surface mechanical loads. An exact solution from the three-dimensional equations of piezoelectricity is obtained. The plate is properly electroded and connected to a circuit such that an electric output is generated. The structure analyzed represents a piezoelectric generator for converting mechanical energy to electrical energy. Analytical expressions for the output voltage, current, power, efficiency, and power density are given. The basic behaviors of the generator are shown by numerical results.

Bernstein-Greene-Kruskal Modes in a Three-Dimensional Plasma

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

Ng, C.S.; Bhattacharjee, A.

2005-12-09

Bernstein-Greene-Kruskal modes in a three-dimensional (3D) unmagnetized plasma are constructed. It is shown that 3D solutions that depend only on energy do not exist. However, 3D solutions that depend on energy and additional constants of motion (such as angular momentum) do exist. Exact analytical as well as numerical solutions are constructed assuming spherical symmetry, and their properties are contrasted with those of 1D solutions. Possible extensions to solutions with cylindrical symmetry with or without a finite magnetic guide field are discussed.

Numerical analysis of some problems related to the mechanics of pneumatic tires: Finite deformation/rolling contact of a viscoelastic cylinder and finite deformation of cord-reinforced rubber composites

NASA Technical Reports Server (NTRS)

Oden, J. T.; Becker, E. B.; Lin, T. L.; Hsieh, K. T.

1984-01-01

The formulation and numerical analysis of several problems related to the behavior of pneumatic tires are considered. These problems include the general rolling contact problem of a rubber-like viscoelastic cylinder undergoing finite deformations and the finite deformation of cord-reinforced rubber composites. New finite element models are developed for these problems. Numerical results obtained for several representative cases are presented.

A mixed-penalty biphasic finite element formulation incorporating viscous fluids and material interfaces.

PubMed

Chan, B; Donzelli, P S; Spilker, R L

2000-06-01

The fluid viscosity term of the fluid phase constitutive equation and the interface boundary conditions between biphasic, solid and fluid domains have been incorporated into a mixed-penalty finite element formulation of the linear biphasic theory for hydrated soft tissue. The finite element code can now model a single-phase viscous incompressible fluid, or a single-phase elastic solid, as limiting cases of a biphasic material. Interface boundary conditions allow the solution of problems involving combinations of biphasic, fluid and solid regions. To incorporate these conditions, the volume-weighted mixture velocity is introduced as a degree of freedom at interface nodes so that the kinematic continuity conditions are satisfied by conventional finite element assembly techniques. Results comparing our numerical method with an independent, analytic solution for the problem of Couette flow over rigid and deformable porous biphasic layers show that the finite element code accurately predicts the viscous fluid flows and deformation in the porous biphasic region. Thus, the analysis can be used to model the interface between synovial fluid and articular cartilage in diarthrodial joints. This is an important step toward modeling and understanding the mechanisms of joint lubrication and another step toward fully modeling the in vivo behavior of a diarthrodial joint.

Finite element code FENIA verification and application for 3D modelling of thermal state of radioactive waste deep geological repository

NASA Astrophysics Data System (ADS)

Butov, R. A.; Drobyshevsky, N. I.; Moiseenko, E. V.; Tokarev, U. N.

2017-11-01

The verification of the FENIA finite element code on some problems and an example of its application are presented in the paper. The code is being developing for 3D modelling of thermal, mechanical and hydrodynamical (THM) problems related to the functioning of deep geological repositories. Verification of the code for two analytical problems has been performed. The first one is point heat source with exponential heat decrease, the second one - linear heat source with similar behavior. Analytical solutions have been obtained by the authors. The problems have been chosen because they reflect the processes influencing the thermal state of deep geological repository of radioactive waste. Verification was performed for several meshes with different resolution. Good convergence between analytical and numerical solutions was achieved. The application of the FENIA code is illustrated by 3D modelling of thermal state of a prototypic deep geological repository of radioactive waste. The repository is designed for disposal of radioactive waste in a rock at depth of several hundred meters with no intention of later retrieval. Vitrified radioactive waste is placed in the containers, which are placed in vertical boreholes. The residual decay heat of radioactive waste leads to containers, engineered safety barriers and host rock heating. Maximum temperatures and corresponding times of their establishment have been determined.

Dynamic Response of Layered TiB/Ti Functionally Graded Material Specimens

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

Byrd, Larry; Beberniss, Tim; Chapman, Ben

2008-02-15

This paper covers the dynamic response of rectangular (25.4x101.6x3.175 mm) specimens manufactured from layers of TiB/Ti. The layers contained volume fractions of TiB that varied from 0 to 85% and thus formed a functionally graded material. Witness samples of the 85% TiB material were also tested to provide a baseline for the statistical variability of the test techniques. Static and dynamic tests were performed to determine the in situ material properties and fundamental frequencies. Damping in the material/ fixture was also found from the dynamic response. These tests were simulated using composite beam theory which gave an analytical solution, andmore » using finite element analysis. The response of the 85% TiB specimens was found to be much more uniform than the functionally graded material and the dynamic response more uniform than the static response. A least squares analysis of the data using the analytical solutions were used to determine the elastic modulus and Poisson's ratio of each layer. These results were used to model the response in the finite element analysis. The results indicate that current analytical and numerical methods for modeling the material give similar and adequate predictions for natural frequencies if the measured property values were used. The models did not agree as well if the properties from the manufacturer or those of Hill and Linn were used.« less

Bending and stretching finite element analysis of anisotropic viscoelastic composite plates

NASA Technical Reports Server (NTRS)

Hilton, Harry H.; Yi, Sung

1990-01-01

Finite element algorithms have been developed to analyze linear anisotropic viscoelastic plates, with or without holes, subjected to mechanical (bending, tension), temperature, and hygrothermal loadings. The analysis is based on Laplace transforms rather than direct time integrations in order to improve the accuracy of the results and save on extensive computational time and storage. The time dependent displacement fields in the transverse direction for the cross ply and angle ply laminates are calculated and the stacking sequence effects of the laminates are discussed in detail. Creep responses for the plates with or without a circular hole are also studied. The numerical results compare favorably with analytical solutions, i.e. within 1.8 percent for bending and 10(exp -3) 3 percent for tension. The tension results of the present method are compared with those using the direct time integration scheme.

Hydrodynamic ion sound instability in systems of a finite length

NASA Astrophysics Data System (ADS)

Koshkarov, O.; Chapurin, O.; Smolyakov, A.; Kaganovich, I.; Ilgisonis, V.

2016-09-01

Plasmas permeated by an energetic ion beam is prone to the kinetic ion-sound instability that occurs as a result of the inverse Landau damping for ion velocity. It is shown here that in a finite length system there exists another type of the ion sound instability which occurs for v02

Effect of spatial bias on the nonequilibrium phase transition in a system of coagulating and fragmenting particles.

PubMed

Rajesh, R; Krishnamurthy, Supriya

2002-10-01

We examine the effect of spatial bias on a nonequilibrium system in which masses on a lattice evolve through the elementary moves of diffusion, coagulation, and fragmentation. When there is no preferred directionality in the motion of the masses, the model is known to exhibit a nonequilibrium phase transition between two different types of steady state, in all dimensions. We show analytically that introducing a preferred direction in the motion of the masses inhibits the occurrence of the phase transition in one dimension, in the thermodynamic limit. A finite-size system, however, continues to show a signature of the original transition, and we characterize the finite-size scaling implications of this. Our analysis is supported by numerical simulations. In two dimensions, bias is shown to be irrelevant.

Lateral conduction effects on heat-transfer data obtained with the phase-change paint technique

NASA Technical Reports Server (NTRS)

Maise, G.; Rossi, M. J.

1974-01-01

A computerized tool, CAPE, (Conduction Analysis Program using Eigenvalues) has been developed to account for lateral heat conduction in wind tunnel models in the data reduction of the phase-change paint technique. The tool also accounts for the effects of finite thickness (thin wings) and surface curvature. A special reduction procedure using just one time of melt is also possible on leading edges. A novel iterative numerical scheme was used, with discretized spatial coordinates but analytic integration in time, to solve the inverse conduction problem involved in the data reduction. A yes-no chart is provided which tells the test engineer when various corrections are large enough so that CAPE should be used. The accuracy of the phase-change paint technique in the presence of finite thickness and lateral conduction is also investigated.

Laser generated guided waves and finite element modeling for the thickness gauging of thin layers.

PubMed

Lefevre, F; Jenot, F; Ouaftouh, M; Duquennoy, M; Ourak, M

2010-03-01

In this paper, nondestructive testing has been performed on a thin gold layer deposited on a 2 in. silicon wafer. Guided waves were generated and studied using a laser ultrasonic setup and a two-dimensional fast Fourier transform technique was employed to obtain the dispersion curves. A gold layer thickness of 1.33 microm has been determined with a +/-5% margin of error using the shape of the two first propagating modes, assuming for the substrate and the layer an uncertainty on the elastic parameters of +/-2.5%. A finite element model has been implemented to validate the data post-treatment and the experimental results. A good agreement between the numerical simulation, the analytical modeling and the experimentations has been observed. This method was considered suitable for thickness layer higher than 0.7 microm.

A two-dimensional analytical model for groundwater flow in a leaky aquifer extending finite distance under the estuary

NASA Astrophysics Data System (ADS)

Chuang, Mo-Hsiung; Hung, Chi-Tung; -Yen Lin, Wen; Ma, Kuo-chen

2017-04-01

In recent years, cities and industries in the vicinity of the estuarine region have developed rapidly, resulting in a sharp increase in the population concerned. The increasing demand for human activities, agriculture irrigation, and aquaculture relies on massive pumping of water in estuarine area. Since the 1950s, numerous studies have focused on the effects of tidal fluctuations on groundwater flow in the estuarine area. Tide-induced head fluctuation in a two-dimensional estuarine aquifer system is complicated and rather important in dealing with many groundwater management or remediation problems. The conceptual model of the aquifer system considered is multi-layered with estuarine bank and the leaky aquifer extend finite distance under the estuary. The solution of the model describing the groundwater head distribution in such an estuarine aquifer system and subject to the tidal fluctuation effects from estuarine river is developed based on the method of separation of variables along with river boundary. The solutions by Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour. Res. 1997; 33:1429-35) as well as Tang and Jiao (Tang Z. and J. J. Jiao, A two-dimensional analytical solution for groundwater flow in a leaky confined aquifer system near open tidal water, Hydrological Processes, 2001; 15: 573-585) can be shown to be special cases of the present solution. On the basis of the analytical solution, the groundwater head distribution in response to estuarine boundary is examined and the influences of leakage, hydraulic parameters, and loading effect on the groundwater head fluctuation due to tide are investigated and discussed. KEYWORDS: analytical model, estuarine river, groundwater fluctuation, leaky aquifer.

Analytical analysis and implementation of a low-speed high-torque permanent magnet vernier in-wheel motor for electric vehicle

NASA Astrophysics Data System (ADS)

Li, Jiangui; Wang, Junhua; Zhigang, Zhao; Yan, Weili

2012-04-01

In this paper, analytical analysis of the permanent magnet vernier (PMV) is presented. The key is to analytically solve the governing Laplacian/quasi-Poissonian field equations in the motor regions. By using the time-stepping finite element method, the analytical method is verified. Hence, the performances of the PMV machine are quantitatively compared with that of the analytical results. The analytical results agree well with the finite element method results. Finally, the experimental results are given to further show the validity of the analysis.

Modeling for Ultrasonic Health Monitoring of Foams with Embedded Sensors

NASA Technical Reports Server (NTRS)

Wang, L.; Rokhlin, S. I.; Rokhlin, Stanislav, I.

2005-01-01

In this report analytical and numerical methods are proposed to estimate the effective elastic properties of regular and random open-cell foams. The methods are based on the principle of minimum energy and on structural beam models. The analytical solutions are obtained using symbolic processing software. The microstructure of the random foam is simulated using Voronoi tessellation together with a rate-dependent random close-packing algorithm. The statistics of the geometrical properties of random foams corresponding to different packing fractions have been studied. The effects of the packing fraction on elastic properties of the foams have been investigated by decomposing the compliance into bending and axial compliance components. It is shown that the bending compliance increases and the axial compliance decreases when the packing fraction increases. Keywords: Foam; Elastic properties; Finite element; Randomness

Fermi gases with imaginary mass imbalance and the sign problem in Monte-Carlo calculations

NASA Astrophysics Data System (ADS)

Roscher, Dietrich; Braun, Jens; Chen, Jiunn-Wei; Drut, Joaquín E.

2014-05-01

Fermi gases in strongly coupled regimes are inherently challenging for many-body methods. Although progress has been made analytically, quantitative results require ab initio numerical approaches, such as Monte-Carlo (MC) calculations. However, mass-imbalanced and spin-imbalanced gases are not accessible to MC calculations due to the infamous sign problem. For finite spin imbalance, the problem can be circumvented using imaginary polarizations and analytic continuation, and large parts of the phase diagram then become accessible. We propose to apply this strategy to the mass-imbalanced case, which opens up the possibility to study the associated phase diagram with MC calculations. We perform a first mean-field analysis which suggests that zero-temperature studies, as well as detecting a potential (tri)critical point, are feasible.

Experimental and Simulative Investigation of Laser Transmission Welding under Consideration of Scattering

NASA Astrophysics Data System (ADS)

Devrient, M.; Da, X.; Frick, T.; Schmidt, M.

Laser transmission welding is a well known joining technology for thermoplastics. Because of the needs of lightweight, cost effective and green production thermoplastics are usually filled with glass fibers. These lead to higher absorption and more scattering within the upper joining partner with a negative influence on the welding process. Here an experimental method for the characterization of the scattering behavior of semi crystalline thermoplastics filled with short glass fibers and a finite element model of the welding process capable to consider scattering as well as an analytical model are introduced. The experimental data is used for the numerical and analytical investigation of laser transmission welding under consideration of scattering. The scattering effects of several thermoplastics onto the calculated temperature fields as well as weld seam geometries are quantified.

Finite element analysis of the effect of a non-planar solid-liquid interface on the lateral solute segregation during unidirectional solidification

NASA Technical Reports Server (NTRS)

Carlson, F. M.; Chin, L.-Y.; Fripp, A. L.; Crouch, R. K.

1982-01-01

The effect of solid-liquid interface shape on lateral solute segregation during steady-state unidirectional solidification of a binary mixture is calculated under the assumption of no convection in the liquid. A finite element technique is employed to compute the concentration field in the liquid and the lateral segregation in the solid with a curved boundary between the liquid and solid phases. The computational model is constructed assuming knowledge of the solid-liquid interface shape; no attempt is made to relate this shape to the thermal field. The influence of interface curvature on the lateral compositional variation is investigated over a range of system parameters including diffusivity, growth speed, distribution coefficient, and geometric factors of the system. In the limiting case of a slightly nonplanar interface, numerical results from the finite element technique are in good agreement with the analytical solutions of Coriell and Sekerka obtained by using linear theory. For the general case of highly non-planar interface shapes, the linear theory fails and the concentration field in the liquid as well as the lateral solute segregation in the solid can be calculated by using the finite element method.

Universal scaling for the quantum Ising chain with a classical impurity

NASA Astrophysics Data System (ADS)

Apollaro, Tony J. G.; Francica, Gianluca; Giuliano, Domenico; Falcone, Giovanni; Palma, G. Massimo; Plastina, Francesco

2017-10-01

We study finite-size scaling for the magnetic observables of an impurity residing at the end point of an open quantum Ising chain with transverse magnetic field, realized by locally rescaling the field by a factor μ ≠1 . In the homogeneous chain limit at μ =1 , we find the expected finite-size scaling for the longitudinal impurity magnetization, with no specific scaling for the transverse magnetization. At variance, in the classical impurity limit μ =0 , we recover finite scaling for the longitudinal magnetization, while the transverse one basically does not scale. We provide both analytic approximate expressions for the magnetization and the susceptibility as well as numerical evidences for the scaling behavior. At intermediate values of μ , finite-size scaling is violated, and we provide a possible explanation of this result in terms of the appearance of a second, impurity-related length scale. Finally, by going along the standard quantum-to-classical mapping between statistical models, we derive the classical counterpart of the quantum Ising chain with an end-point impurity as a classical Ising model on a square lattice wrapped on a half-infinite cylinder, with the links along the first circle modified as a function of μ .

Numerical determination of lateral loss coefficients for subchannel analysis in nuclear fuel bundles

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

Sin Kim; Goon-Cherl Park

1995-09-01

An accurate prediction of cross-flow based on detailed knowledge of the velocity field in subchannels of a nuclear fuel assembly is of importance in nuclear fuel performance analysis. In this study, the low-Reynolds number {kappa}-{epsilon} turbulence model has been adopted in two adjacent subchannels with cross-flow. The secondary flow is estimated accurately by the anisotropic algebraic Reynolds stress model. This model was numerically calculated by the finite element method and has been verified successfully through comparison with existing experimental data. Finally, with the numerical analysis of the velocity field in such subchannel domain, an analytical correlation of the lateral lossmore » coefficient is obtained to predict the cross-flow rate in subchannel analysis codes. The correlation is expressed as a function of the ratio of the lateral flow velocity to the donor subchannel axial velocity, recipient channel Reynolds number and pitch-to-diameter.« less

Investigating anomalous transport of electrolytes in charged porous media

NASA Astrophysics Data System (ADS)

Skjøde Bolet, Asger Johannes; Mathiesen, Joachim

2017-04-01

Surface charge is know to play an important role in microfluidics devices when dealing with electrolytes and their transport properties. Similarly, surface charge could play a role for transport in porous rock with submicron pore sizes. Estimates of the streaming potentials and electro osmotic are mostly considered in simple geometries both using analytic and numerical tools, however it is unclear at present how realistic complex geometries will modify the dynamics. Our work have focused on doing numerical studies of the full three-dimensional Stokes-Poisson-Nernst-Planck problem for electrolyte transport in porous rock. As the numerical implementation, we have used a finite element solver made using the FEniCS project code base, which can both solve for a steady state configuration and the full transient. In the presentation, we will show our results on anomalous transport due to electro kinetic effects such as the streaming potential or the electro osmotic effect.

Review of FD-TD numerical modeling of electromagnetic wave scattering and radar cross section

NASA Technical Reports Server (NTRS)

Taflove, Allen; Umashankar, Korada R.

1989-01-01

Applications of the finite-difference time-domain (FD-TD) method for numerical modeling of electromagnetic wave interactions with structures are reviewed, concentrating on scattering and radar cross section (RCS). A number of two- and three-dimensional examples of FD-TD modeling of scattering and penetration are provided. The objects modeled range in nature from simple geometric shapes to extremely complex aerospace and biological systems. Rigorous analytical or experimental validatons are provided for the canonical shapes, and it is shown that FD-TD predictive data for near fields and RCS are in excellent agreement with the benchmark data. It is concluded that with continuing advances in FD-TD modeling theory for target features relevant to the RCS problems and in vector and concurrent supercomputer technology, it is likely that FD-TD numerical modeling will occupy an important place in RCS technology in the 1990s and beyond.

Engine dynamic analysis with general nonlinear finite element codes. Part 2: Bearing element implementation overall numerical characteristics and benchmaking

NASA Technical Reports Server (NTRS)

Padovan, J.; Adams, M.; Fertis, J.; Zeid, I.; Lam, P.

1982-01-01

Finite element codes are used in modelling rotor-bearing-stator structure common to the turbine industry. Engine dynamic simulation is used by developing strategies which enable the use of available finite element codes. benchmarking the elements developed are benchmarked by incorporation into a general purpose code (ADINA); the numerical characteristics of finite element type rotor-bearing-stator simulations are evaluated through the use of various types of explicit/implicit numerical integration operators. Improving the overall numerical efficiency of the procedure is improved.

Turbine engine rotor health monitoring evaluation by means of finite element analyses and spin tests data

NASA Astrophysics Data System (ADS)

Abdul-Aziz, Ali; Woike, Mark R.; Clem, Michelle; Baaklini, George Y.

2014-04-01

Generally, rotating engine components undergo high centrifugal loading environment which subject them to various types of failure initiation mechanisms. Health monitoring of these components is a necessity and is often challenging to implement. This is primarily due to numerous factors including the presence of scattered loading conditions, flaw sizes, component geometry and materials properties, all which hinder the simplicity of applying health monitoring applications. This paper represents a summary work of combined experimental and analytical modeling that included data collection from a spin test experiment of a rotor disk addressing the aforementioned durability issues. It further covers presentation of results obtained from a finite element modeling study to characterize the structural durability of a cracked rotor as it relates to the experimental findings. The experimental data include blade tip clearance, blade tip timing and shaft displacement measurements. The tests were conducted at the NASA Glenn Research Center's Rotordynamics Laboratory, a high precision spin rig. The results are evaluated and examined to determine their significance on the development of a health monitoring system to pre-predict cracks and other anomalies and to assist in initiating a supplemental physics based fault prediction analytical model.

Evolutionary dynamics of public goods games with diverse contributions in finite populations

NASA Astrophysics Data System (ADS)

Wang, Jing; Wu, Bin; Chen, Xiaojie; Wang, Long

2010-05-01

The public goods game is a powerful metaphor for exploring the maintenance of social cooperative behavior in a group of interactional selfish players. Here we study the emergence of cooperation in the public goods games with diverse contributions in finite populations. The theory of stochastic process is innovatively adopted to investigate the evolutionary dynamics of the public goods games involving a diversity of contributions. In the limit of rare mutations, the general stationary distribution of this stochastic process can be analytically approximated by means of diffusion theory. Moreover, we demonstrate that increasing the diversity of contributions greatly reduces the probability of finding the population in a homogeneous state full of defectors. This increase also raises the expectation of the total contribution in the entire population and thus promotes social cooperation. Furthermore, by investigating the evolutionary dynamics of optional public goods games with diverse contributions, we find that nonparticipation can assist players who contribute more in resisting invasion and taking over individuals who contribute less. In addition, numerical simulations are performed to confirm our analytical results. Our results may provide insight into the effect of diverse contributions on cooperative behaviors in the real world.

An efficient numerical method for the solution of the problem of elasticity for 3D-homogeneous elastic medium with cracks and inclusions

NASA Astrophysics Data System (ADS)

Kanaun, S.; Markov, A.

2017-06-01

An efficient numerical method for solution of static problems of elasticity for an infinite homogeneous medium containing inhomogeneities (cracks and inclusions) is developed. Finite number of heterogeneous inclusions and planar parallel cracks of arbitrary shapes is considered. The problem is reduced to a system of surface integral equations for crack opening vectors and volume integral equations for stress tensors inside the inclusions. For the numerical solution of these equations, a class of Gaussian approximating functions is used. The method based on these functions is mesh free. For such functions, the elements of the matrix of the discretized system are combinations of explicit analytical functions and five standard 1D-integrals that can be tabulated. Thus, the numerical integration is excluded from the construction of the matrix of the discretized problem. For regular node grids, the matrix of the discretized system has Toeplitz's properties, and Fast Fourier Transform technique can be used for calculation matrix-vector products of such matrices.

Design study of beam position monitors for measuring second-order moments of charged particle beams

NASA Astrophysics Data System (ADS)

Yanagida, Kenichi; Suzuki, Shinsuke; Hanaki, Hirofumi

2012-01-01

This paper presents a theoretical investigation on the multipole moments of charged particle beams in two-dimensional polar coordinates. The theoretical description of multipole moments is based on a single-particle system that is expanded to a multiparticle system by superposition, i.e., summing over all single-particle results. This paper also presents an analysis and design method for a beam position monitor (BPM) that detects higher-order (multipole) moments of a charged particle beam. To calculate the electric fields, a numerical analysis based on the finite difference method was created and carried out. Validity of the numerical analysis was proven by comparing the numerical with the analytical results for a BPM with circular cross section. Six-electrode BPMs with circular and elliptical cross sections were designed for the SPring-8 linac. The results of the numerical calculations show that the second-order moment can be detected for beam sizes ≧420μm (circular) and ≧550μm (elliptical).

Analytical modeling of large amplitude free vibration of non-uniform beams carrying a both transversely and axially eccentric tip mass

NASA Astrophysics Data System (ADS)

Malaeke, Hasan; Moeenfard, Hamid

2016-03-01

The objective of this paper is to study large amplitude flexural-extensional free vibration of non-uniform cantilever beams carrying a both transversely and axially eccentric tip mass. The effects of variable axial force is also taken into account. Hamilton's principle is utilized to obtain the partial differential equations governing the nonlinear vibration of the system as well as the corresponding boundary conditions. A numerical finite difference scheme is proposed to find the natural frequencies and mode shapes of the system which is validated specifically for a beam with linearly varying cross section. Using a single mode approximation in conjunction with the Lagrange method, the governing equations are reduced to a set of two nonlinear ordinary differential equations in terms of end displacement components of the beam which are coupled due to the presence of the transverse eccentricity. These temporal coupled equations are then solved analytically using the multiple time scales perturbation technique. The obtained analytical results are compared with the numerical ones and excellent agreement is observed. The qualitative and quantitative knowledge resulting from this research is expected to enable the study of the effects of eccentric tip mass and non-uniformity on the large amplitude flexural-extensional vibration of beams for improved dynamic performance.

Thermal gravitational separation of ternary mixture n-dodecane/isobutylbenzene/tetralin components in a porous medium

NASA Astrophysics Data System (ADS)

Larabi, Mohamed Aziz; Mutschler, Dimitri; Mojtabi, Abdelkader

2016-06-01

Our present work focuses on the coupling between thermal diffusion and convection in order to improve the thermal gravitational separation of mixture components. The separation phenomenon was studied in a porous medium contained in vertical columns. We performed analytical and numerical simulations to corroborate the experimental measurements of the thermal diffusion coefficients of ternary mixture n-dodecane, isobutylbenzene, and tetralin obtained in microgravity in the international space station. Our approach corroborates the existing data published in the literature. The authors show that it is possible to quantify and to optimize the species separation for ternary mixtures. The authors checked, for ternary mixtures, the validity of the "forgotten effect hypothesis" established for binary mixtures by Furry, Jones, and Onsager. Two complete and different analytical resolution methods were used in order to describe the separation in terms of Lewis numbers, the separation ratios, the cross-diffusion coefficients, and the Rayleigh number. The analytical model is based on the parallel flow approximation. In order to validate this model, a numerical simulation was performed using the finite element method. From our new approach to vertical separation columns, new relations for mass fraction gradients and the optimal Rayleigh number for each component of the ternary mixture were obtained.

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Godfrey, Andrew G.

1993-01-01

The extension of Van Leer's preconditioning procedure to generalized finite-rate chemistry is discussed. Application to viscous flow is begun with the proper preconditioning matrix for the one-dimensional Navier-Stokes equations. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from nearly stagnant flow to hypersonic. Specific benefits are realized at the low and transonic flow speeds typical of complete propulsion-system simulations. The extended preconditioning matrix necessarily accounts for both thermal and chemical nonequilibrium. Numerical analysis reveals the possible theoretical improvements from using a preconditioner for all Mach number regimes. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number areas. Van Leer, Lee, and Roe recently developed an optimal, analytic preconditioning technique to reduce eigenvalue stiffness over the full Mach-number range. By multiplying the flux-balance residual with the preconditioning matrix, the acoustic wave speeds are scaled so that all waves propagate at the same rate, an essential property to eliminate inherent eigenvalue stiffness. This session discusses a synthesis of the thermochemical nonequilibrium flux-splitting developed by Grossman and Cinnella and the characteristic wave preconditioning of Van Leer into a powerful tool for implicitly solving two and three-dimensional flows with generalized finite-rate chemistry. For finite-rate chemistry, the state vector of unknowns is variable in length. Therefore, the preconditioning matrix extended to generalized finite-rate chemistry must accommodate a flexible system of moving waves. Fortunately, no new kind of wave appears in the system. The only existing waves are entropy and vorticity waves, which move with the fluid, and acoustic waves, which propagate in Mach number dependent directions. The nonequilibrium vibrational energies and species densities in the unknown state vector act strictly as convective waves. The essential concept for extending the preconditioning to generalized chemistry models is determining the differential variables which symmetrize the flux Jacobians. The extension is then straight-forward. This algorithm research effort will be released in a future version of the production level computational code coined the General Aerodynamic Simulation Program (GASP), developed by Walters, Slack, and McGrory.

Singularities in the classical Rayleigh-Taylor flow - Formation and subsequent motion

NASA Technical Reports Server (NTRS)

Tanveer, S.

1993-01-01

The creation and subsequent motion of singularities of solution to classical Rayleigh-Taylor flow (two dimensional inviscid, incompressible fluid over a vacuum) are discussed. For a specific set of initial conditions, we give analytical evidence to suggest the instantaneous formation of one or more singularities at specific points in the unphysical plane, whose locations depend sensitively on small changes in initial conditions in the physical domain. One-half power singularities are created in accordance with an earlier conjecture; however, depending on initial conditions, other forms of singularities are also possible. For a specific initial condition, we follow a numerical procedure in the unphysical plane to compute the motion of a one-half singularity. This computation confirms our previous conjecture that the approach of a one-half singularity towards the physical domain corresponds to the development of a spike at the physical interface. Under some assumptions that appear to be consistent with numerical calculations, we present analytical evidence to suggest that a singularity of the one-half type cannot impinge the physical domain in finite time.

Singularities in the classical Rayleigh-Taylor flow: Formation and subsequent motion

NASA Technical Reports Server (NTRS)

Tanveer, S.

1992-01-01

The creation and subsequent motion of singularities of solution to classical Rayleigh-Taylor flow (two dimensional inviscid, incompressible fluid over a vacuum) are discussed. For a specific set of initial conditions, we give analytical evidence to suggest the instantaneous formation of one or more singularities at specific points in the unphysical plane, whose locations depend sensitively on small changes in initial conditions in the physical domain. One-half power singularities are created in accordance with an earlier conjecture; however, depending on initial conditions, other forms of singularities are also possible. For a specific initial condition, we follow a numerical procedure in the unphysical plane to compute the motion of a one-half singularity. This computation confirms our previous conjecture that the approach of a one-half singularity towards the physical domain corresponds to the development of a spike at the physical interface. Under some assumptions that appear to be consistent with numerical calculations, we present analytical evidence to suggest that a singularity of the one-half type cannot impinge the physical domain in finite time.

Investigation of the three-dimensional flow field within a transonic fan rotor: Experiment and analysis

NASA Technical Reports Server (NTRS)

Pierzga, M. J.; Wood, J. R.

1984-01-01

An experimental investigation of the three dimensional flow field through a low aspect ratio, transonic, axial flow fan rotor has been conducted using an advanced laser anemometer (LA) system. Laser velocimeter measurements of the rotor flow field at the design operating speed and over a range of through flow conditions are compared to analytical solutions. The numerical technique used herein yields the solution to the full, three dimensional, unsteady Euler equations using an explicit time marching, finite volume approach. The numerical analysis, when coupled with a simplified boundary layer calculation, generally yields good agreement with the experimental data. The test rotor has an aspect ratio of 1.56, a design total pressure ratio of 1.629 and a tip relative Mach number of 1.38. The high spatial resolution of the LA data matrix (9 radial by 30 axial by 50 blade to blade) permits details of the transonic flow field such as shock location, turning distribution and blade loading levels to be investigated and compared to analytical results.

On the emergence of an ‘intention field’ for socially cohesive agents

NASA Astrophysics Data System (ADS)

Bouchaud, Jean-Philippe; Borghesi, Christian; Jensen, Pablo

2014-03-01

We argue that when a social convergence mechanism exists and is strong enough, one should expect the emergence of a well-defined ‘field’, i.e. a slowly evolving, local quantity around which individual attributes fluctuate in a finite range. This condensation phenomenon is well illustrated by the Deffuant-Weisbuch opinion model for which we provide a natural extension to allow for spatial heterogeneities. We show analytically and numerically that the resulting dynamics of the emergent field is a noisy diffusion equation that has a slow dynamics. This random diffusion equation reproduces the long-ranged, logarithmic decrease of the correlation of spatial voting patterns empirically found in Borghesi and Bouchaud (2010 Eur. Phys. J. B 75 395) and Borghesi et al (2012 PLoS One 7 e36289). Interestingly enough, we find that when the social cohesion mechanism becomes too weak, cultural cohesion breaks down completely, in the sense that the distribution of intentions/opinions becomes infinitely broad. No emerging field exists in this case. All these analytical findings are confirmed by numerical simulations of an agent-based model.

Accurate modelling of unsteady flows in collapsible tubes.

PubMed

Marchandise, Emilie; Flaud, Patrice

2010-01-01

The context of this paper is the development of a general and efficient numerical haemodynamic tool to help clinicians and researchers in understanding of physiological flow phenomena. We propose an accurate one-dimensional Runge-Kutta discontinuous Galerkin (RK-DG) method coupled with lumped parameter models for the boundary conditions. The suggested model has already been successfully applied to haemodynamics in arteries and is now extended for the flow in collapsible tubes such as veins. The main difference with cardiovascular simulations is that the flow may become supercritical and elastic jumps may appear with the numerical consequence that scheme may not remain monotone if no limiting procedure is introduced. We show that our second-order RK-DG method equipped with an approximate Roe's Riemann solver and a slope-limiting procedure allows us to capture elastic jumps accurately. Moreover, this paper demonstrates that the complex physics associated with such flows is more accurately modelled than with traditional methods such as finite difference methods or finite volumes. We present various benchmark problems that show the flexibility and applicability of the numerical method. Our solutions are compared with analytical solutions when they are available and with solutions obtained using other numerical methods. Finally, to illustrate the clinical interest, we study the emptying process in a calf vein squeezed by contracting skeletal muscle in a normal and pathological subject. We compare our results with experimental simulations and discuss the sensitivity to parameters of our model.

Assessment of Efficiency and Performance in Tsunami Numerical Modeling with GPU

NASA Astrophysics Data System (ADS)

Yalciner, Bora; Zaytsev, Andrey

2017-04-01

Non-linear shallow water equations (NSWE) are used to solve the propagation and coastal amplification of long waves and tsunamis. Leap Frog scheme of finite difference technique is one of the satisfactory numerical methods which is widely used in these problems. Tsunami numerical models are necessary for not only academic but also operational purposes which need faster and accurate solutions. Recent developments in information technology provide considerably faster numerical solutions in this respect and are becoming one of the crucial requirements. Tsunami numerical code NAMI DANCE uses finite difference numerical method to solve linear and non-linear forms of shallow water equations for long wave problems, specifically for tsunamis. In this study, the new code is structured for Graphical Processing Unit (GPU) using CUDA API. The new code is applied to different (analytical, experimental and field) benchmark problems of tsunamis for tests. One of those applications is 2011 Great East Japan tsunami which was instrumentally recorded on various types of gauges including tide and wave gauges and offshore GPS buoys cabled Ocean Bottom Pressure (OBP) gauges and DART buoys. The accuracy of the results are compared with the measurements and fairly well agreements are obtained. The efficiency and performance of the code is also compared with the version using multi-core Central Processing Unit (CPU). Dependence of simulation speed with GPU on linear or non-linear solutions is also investigated. One of the results is that the simulation speed is increased up to 75 times comparing to the process time in the computer using single 4/8 thread multi-core CPU. The results are presented with comparisons and discussions. Furthermore how multi-dimensional finite difference problems fits towards GPU architecture is also discussed. The research leading to this study has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement No: 603839 (Project ASTARTE-Assessment, Strategy and Risk Reduction for Tsunamis in Europe). PARI, Japan and NOAA, USA are acknowledged for the data of the measurements. Prof. Ahmet C. Yalciner is also acknowledged for his long term and sustained support to the authors.

Bend-Twist Coupled Carbon-Fiber Laminate Beams: Fundamental Behavior and Applications

NASA Astrophysics Data System (ADS)

Babuska, Pavel

Material-induced bend-twist coupling in laminated composite beams has seen applications in engineered structures for decades, ranging from airplane wings to turbine blades. Symmetric, unbalanced, carbon fiber laminates which exhibit bend-twist coupling can be difficult to characterize and exhibit unintuitive deformation states which may pose challenges to the engineer. In this thesis, bend-twist coupled beams are investigated comprehensively, by experimentation, numerical modeling, and analytical methods. Beams of varying fiber angle and amount of coupling were manufactured and physically tested in both linear and nonlinear static and dynamic settings. Analytical mass and stiffness matrices were derived for the development of a beam element to use in the stiffness matrix analysis method. Additionally, an ABAQUS finite element model was used in conjunction with the analytical methods to predict and further characterize the behavior of the beams. The three regimes, experimental, analytical, and numerical, represent a full-field characterization of bend-twist coupling in composite beams. A notable application of bend-twist coupled composites is for passively adaptive turbine blades whereby the deformation coupling can be built into the blade structure to simultaneously bend and twist, thus pitching the blade into or away from the fluid flow, changing the blade angle of attack. Passive pitch adaptation has been implemented successfully in wind turbine blades, however, for marine turbine blades, the technology is still in the development phase. Bend-twist coupling has been shown numerically to be beneficial to the tidal turbine performance, however little validation has been conducted in the experimental regime. In this thesis, passively adaptive experiment scale tidal turbine blades were designed, analyzed, manufactured, and physically tested, validating the foundational numerical work. It was shown that blade forces and root moments as well as turbine thrust and power coefficients can be manipulated by inclusion of passive pitch adaption by bend-twist coupling.

SENR /NRPy + : Numerical relativity in singular curvilinear coordinate systems

NASA Astrophysics Data System (ADS)

Ruchlin, Ian; Etienne, Zachariah B.; Baumgarte, Thomas W.

2018-03-01

We report on a new open-source, user-friendly numerical relativity code package called SENR /NRPy + . Our code extends previous implementations of the BSSN reference-metric formulation to a much broader class of curvilinear coordinate systems, making it ideally suited to modeling physical configurations with approximate or exact symmetries. In the context of modeling black hole dynamics, it is orders of magnitude more efficient than other widely used open-source numerical relativity codes. NRPy + provides a Python-based interface in which equations are written in natural tensorial form and output at arbitrary finite difference order as highly efficient C code, putting complex tensorial equations at the scientist's fingertips without the need for an expensive software license. SENR provides the algorithmic framework that combines the C codes generated by NRPy + into a functioning numerical relativity code. We validate against two other established, state-of-the-art codes, and achieve excellent agreement. For the first time—in the context of moving puncture black hole evolutions—we demonstrate nearly exponential convergence of constraint violation and gravitational waveform errors to zero as the order of spatial finite difference derivatives is increased, while fixing the numerical grids at moderate resolution in a singular coordinate system. Such behavior outside the horizons is remarkable, as numerical errors do not converge to zero near punctures, and all points along the polar axis are coordinate singularities. The formulation addresses such coordinate singularities via cell-centered grids and a simple change of basis that analytically regularizes tensor components with respect to the coordinates. Future plans include extending this formulation to allow dynamical coordinate grids and bispherical-like distribution of points to efficiently capture orbiting compact binary dynamics.

Elastic modelling in tilted transversely isotropic media with convolutional perfectly matched layer boundary conditions

NASA Astrophysics Data System (ADS)

Han, Byeongho; Seol, Soon Jee; Byun, Joongmoo

2012-04-01

To simulate wave propagation in a tilted transversely isotropic (TTI) medium with a tilting symmetry-axis of anisotropy, we develop a 2D elastic forward modelling algorithm. In this algorithm, we use the staggered-grid finite-difference method which has fourth-order accuracy in space and second-order accuracy in time. Since velocity-stress formulations are defined for staggered grids, we include auxiliary grid points in the z-direction to meet the free surface boundary conditions for shear stress. Through comparisons of displacements obtained from our algorithm, not only with analytical solutions but also with finite element solutions, we are able to validate that the free surface conditions operate appropriately and elastic waves propagate correctly. In order to handle the artificial boundary reflections efficiently, we also implement convolutional perfectly matched layer (CPML) absorbing boundaries in our algorithm. The CPML sufficiently attenuates energy at the grazing incidence by modifying the damping profile of the PML boundary. Numerical experiments indicate that the algorithm accurately expresses elastic wave propagation in the TTI medium. At the free surface, the numerical results show good agreement with analytical solutions not only for body waves but also for the Rayleigh wave which has strong amplitude along the surface. In addition, we demonstrate the efficiency of CPML for a homogeneous TI medium and a dipping layered model. Only using 10 grid points to the CPML regions, the artificial reflections are successfully suppressed and the energy of the boundary reflection back into the effective modelling area is significantly decayed.

Nonequilibrium self-energies, Ng approach, and heat current of a nanodevice for small bias voltage and temperature

NASA Astrophysics Data System (ADS)

Aligia, A. A.

2014-03-01

Using nonequilibrium renormalized perturbation theory to second order in the renormalized Coulomb repulsion, we calculate the lesser Σ< and and greater Σ> self-energies of the impurity Anderson model, which describes the current through a quantum dot, in the general asymmetric case. While in general a numerical integration is required to evaluate the perturbative result, we derive an analytical approximation for small frequency ω, bias voltage V, and temperature T, which is exact to total second order in these quantities. The approximation is valid when the corresponding energies ℏω, eV, and kBT are small compared to kBTK, where TK is the Kondo temperature. The result of the numerical integration is compared with the analytical one and with Ng approximation, in which Σ< and Σ> are assumed proportional to the retarded self-energy Σr times an average Fermi function. While it fails at T =0 for ℏ |ω|≲eV, we find that the Ng approximation is excellent for kBT>eV/2 and improves for asymmetric coupling to the leads. Even at T =0, the effect of the Ng approximation on the total occupation at the dot is very small. The dependence on ω and V are discussed in comparison with a Ward identity that is fulfilled by the three approaches. We also calculate the heat currents between the dot and any of the leads at finite bias voltage. One of the heat currents changes sign with the applied bias voltage at finite temperature.

Spheroidal and conical shapes of ferrofluid-filled capsules in magnetic fields

NASA Astrophysics Data System (ADS)

Wischnewski, Christian; Kierfeld, Jan

2018-04-01

We investigate the deformation of soft spherical elastic capsules filled with a ferrofluid in external uniform magnetic fields at fixed volume by a combination of numerical and analytical approaches. We develop a numerical iterative solution strategy based on nonlinear elastic shape equations to calculate the stretched capsule shape numerically and a coupled finite element and boundary element method to solve the corresponding magnetostatic problem and employ analytical linear response theory, approximative energy minimization, and slender-body theory. The observed deformation behavior is qualitatively similar to the deformation of ferrofluid droplets in uniform magnetic fields. Homogeneous magnetic fields elongate the capsule and a discontinuous shape transition from a spheroidal shape to a conical shape takes place at a critical field strength. We investigate how capsule elasticity modifies this hysteretic shape transition. We show that conical capsule shapes are possible but involve diverging stretch factors at the tips, which gives rise to rupture for real capsule materials. In a slender-body approximation we find that the critical susceptibility above which conical shapes occur for ferrofluid capsules is the same as for droplets. At small fields capsules remain spheroidal and we characterize the deformation of spheroidal capsules both analytically and numerically. Finally, we determine whether wrinkling of a spheroidal capsule occurs during elongation in a magnetic field and how it modifies the stretching behavior. We find the nontrivial dependence between the extent of the wrinkled region and capsule elongation. Our results can be helpful in quantitatively determining capsule or ferrofluid material properties from magnetic deformation experiments. All results also apply to elastic capsules filled with a dielectric liquid in an external uniform electric field.

Untangling Slab Dynamics Using 3-D Numerical and Analytical Models

NASA Astrophysics Data System (ADS)

Holt, A. F.; Royden, L.; Becker, T. W.

2016-12-01

Increasingly sophisticated numerical models have enabled us to make significant strides in identifying the key controls on how subducting slabs deform. For example, 3-D models have demonstrated that subducting plate width, and the related strength of toroidal flow around the plate edge, exerts a strong control on both the curvature and the rate of migration of the trench. However, the results of numerical subduction models can be difficult to interpret, and many first order dynamics issues remain at least partially unresolved. Such issues include the dominant controls on trench migration, the interdependence of asthenospheric pressure and slab dynamics, and how nearby slabs influence each other's dynamics. We augment 3-D, dynamically evolving finite element models with simple, analytical force-balance models to distill the physics associated with subduction into more manageable parts. We demonstrate that for single, isolated subducting slabs much of the complexity of our fully numerical models can be encapsulated by simple analytical expressions. Rates of subduction and slab dip correlate strongly with the asthenospheric pressure difference across the subducting slab. For double subduction, an additional slab gives rise to more complex mantle pressure and flow fields, and significantly extends the range of plate kinematics (e.g., convergence rate, trench migration rate) beyond those present in single slab models. Despite these additional complexities, we show that much of the dynamics of such multi-slab systems can be understood using the physics illuminated by our single slab study, and that a force-balance method can be used to relate intra-plate stress to viscous pressure in the asthenosphere and coupling forces at plate boundaries. This method has promise for rapid modeling of large systems of subduction zones on a global scale.

Experimental analysis and modeling of ultrasound assisted freezing of potato spheres.

PubMed

Kiani, Hossein; Zhang, Zhihang; Sun, Da-Wen

2015-09-01

In recent years, innovative methods such as ultrasound assisted freezing have been developed in order to improve the freezing process. During freezing of foods, accurate prediction of the temperature distribution, phase ratios, and process time is very important. In the present study, ultrasound assisted immersion freezing process (in 1:1 ethylene glycol-water solution at 253.15K) of potato spheres (0.02 m diameter) was evaluated using experimental, numerical and analytical approaches. Ultrasound (25 kHz, 890 W m(-2)) was irradiated for different duty cycles (DCs=0-100%). A finite volume based enthalpy method was used in the numerical model, based on which temperature and liquid fraction profiles were simulated by a program developed using OpenFOAM® CFD software. An analytical technique was also employed to calculate freezing times. The results showed that ultrasound irradiation could decrease the characteristic freezing time of potatoes. Since ultrasound irradiation increased the heat transfer coefficient but simultaneously generated heat at the surface of the samples, an optimum DC was needed for the shortest freezing time which occurred in the range of 30-70% DC. DCs higher than 70% increased the freezing time. DCs lower than 30% did not provide significant effects on the freezing time compared to the control sample. The numerical model predicted the characteristic freezing time in accordance with the experimental results. In addition, analytical calculation of characteristic freezing time exhibited qualitative agreement with the experimental results. As the numerical simulations provided profiles of temperature and water fraction within potatoes frozen with or without ultrasound, the models can be used to study and control different operation situations, and to improve the understanding of the freezing process. Copyright © 2015 Elsevier B.V. All rights reserved.

Characteristics of steady vibration in a rotating hub-beam system

NASA Astrophysics Data System (ADS)

Zhao, Zhen; Liu, Caishan; Ma, Wei

2016-02-01

A rotating beam features a puzzling character in which its frequencies and modal shapes may vary with the hub's inertia and its rotating speed. To highlight the essential nature behind the vibration phenomena, we analyze the steady vibration of a rotating Euler-Bernoulli beam with a quasi-steady-state stretch. Newton's law is used to derive the equations governing the beam's elastic motion and the hub's rotation. A combination of these equations results in a nonlinear partial differential equation (PDE) that fully reflects the mutual interaction between the two kinds of motion. Via the Fourier series expansion within a finite interval of time, we reduce the PDE into an infinite system of a nonlinear ordinary differential equation (ODE) in spatial domain. We further nondimensionalize the ODE and discretize it via a difference method. The frequencies and modal shapes of a general rotating beam are then determined numerically. For a low-speed beam where the ignorance of geometric stiffening is feasible, the beam's vibration characteristics are solved analytically. We validate our numerical method and the analytical solutions by comparing with either the past experiments or the past numerical findings reported in existing literature. Finally, systematic simulations are performed to demonstrate how the beam's eigenfrequencies vary with the hub's inertia and rotating speed.

Combined structures-controls optimization of lattice trusses

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1991-01-01

The role that distributed parameter model can play in CSI is demonstrated, in particular in combined structures controls optimization problems of importance in preliminary design. Closed form solutions can be obtained for performance criteria such as rms attitude error, making possible analytical solutions of the optimization problem. This is in contrast to the need for numerical computer solution involving the inversion of large matrices in traditional finite element model (FEM) use. Another advantage of the analytic solution is that it can provide much needed insight into phenomena that can otherwise be obscured or difficult to discern from numerical computer results. As a compromise in level of complexity between a toy lab model and a real space structure, the lattice truss used in the EPS (Earth Pointing Satellite) was chosen. The optimization problem chosen is a generic one: of minimizing the structure mass subject to a specified stability margin and to a specified upper bond on the rms attitude error, using a co-located controller and sensors. Standard FEM treating each bar as a truss element is used, while the continuum model is anisotropic Timoshenko beam model. Performance criteria are derived for each model, except that for the distributed parameter model, explicit closed form solutions was obtained. Numerical results obtained by the two model show complete agreement.

Analytical and numerical analyses for a penny-shaped crack embedded in an infinite transversely isotropic multi-ferroic composite medium: semi-permeable electro-magnetic boundary condition

NASA Astrophysics Data System (ADS)

Zheng, R.-F.; Wu, T.-H.; Li, X.-Y.; Chen, W.-Q.

2018-06-01

The problem of a penny-shaped crack embedded in an infinite space of transversely isotropic multi-ferroic composite medium is investigated. The crack is assumed to be subjected to uniformly distributed mechanical, electric and magnetic loads applied symmetrically on the upper and lower crack surfaces. The semi-permeable (limited-permeable) electro-magnetic boundary condition is adopted. By virtue of the generalized method of potential theory and the general solutions, the boundary integro-differential equations governing the mode I crack problem, which are of nonlinear nature, are established and solved analytically. Exact and complete coupling magneto-electro-elastic field is obtained in terms of elementary functions. Important parameters in fracture mechanics on the crack plane, e.g., the generalized crack surface displacements, the distributions of generalized stresses at the crack tip, the generalized stress intensity factors and the energy release rate, are explicitly presented. To validate the present solutions, a numerical code by virtue of finite element method is established for 3D crack problems in the framework of magneto-electro-elasticity. To evaluate conveniently the effect of the medium inside the crack, several empirical formulae are developed, based on the numerical results.

A semi-analytical study of positive corona discharge in wire-plane electrode configuration

NASA Astrophysics Data System (ADS)

Yanallah, K.; Pontiga, F.; Chen, J. H.

2013-08-01

Wire-to-plane positive corona discharge in air has been studied using an analytical model of two species (electrons and positive ions). The spatial distributions of electric field and charged species are obtained by integrating Gauss's law and the continuity equations of species along the Laplacian field lines. The experimental values of corona current intensity and applied voltage, together with Warburg's law, have been used to formulate the boundary condition for the electron density on the corona wire. To test the accuracy of the model, the approximate electric field distribution has been compared with the exact numerical solution obtained from a finite element analysis. A parametrical study of wire-to-plane corona discharge has then been undertaken using the approximate semi-analytical solutions. Thus, the spatial distributions of electric field and charged particles have been computed for different values of the gas pressure, wire radius and electrode separation. Also, the two dimensional distribution of ozone density has been obtained using a simplified plasma chemistry model. The approximate semi-analytical solutions can be evaluated in a negligible computational time, yet provide precise estimates of corona discharge variables.

Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem

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

Jeong, Yongjin; Park, Jinsu; Lee, Hyun Chul

2015-12-01

In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also notedmore » that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.« less

Cylindrical optical resonators: fundamental properties and bio-sensing characteristics

NASA Astrophysics Data System (ADS)

Khozeymeh, Foroogh; Razaghi, Mohammad

2018-04-01

In this paper, detailed theoretical analysis of cylindrical resonators is demonstrated. As illustrated, these kinds of resonators can be used as optical bio-sensing devices. The proposed structure is analyzed using an analytical method based on Lam's approximation. This method is systematic and has simplified the tedious process of whispering-gallery mode (WGM) wavelength analysis in optical cylindrical biosensors. By this method, analysis of higher radial orders of high angular momentum WGMs has been possible. Using closed-form analytical equations, resonance wavelengths of higher radial and angular order WGMs of TE and TM polarization waves are calculated. It is shown that high angular momentum WGMs are more appropriate for bio-sensing applications. Some of the calculations are done using a numerical non-linear Newton method. A perfect match of 99.84% between the analytical and the numerical methods has been achieved. In order to verify the validity of the calculations, Meep simulations based on the finite difference time domain (FDTD) method are performed. In this case, a match of 96.70% between the analytical and FDTD results has been obtained. The analytical predictions are in good agreement with other experimental work (99.99% match). These results validate the proposed analytical modelling for the fast design of optical cylindrical biosensors. It is shown that by extending the proposed two-layer resonator structure analyzing scheme, it is possible to study a three-layer cylindrical resonator structure as well. Moreover, by this method, fast sensitivity optimization in cylindrical resonator-based biosensors has been possible. Sensitivity of the WGM resonances is analyzed as a function of the structural parameters of the cylindrical resonators. Based on the results, fourth radial order WGMs, with a resonator radius of 50 μm, display the most bulk refractive index sensitivity of 41.50 (nm/RIU).

FINIFLUX: An implicit finite element model for quantification of groundwater fluxes and hyporheic exchange in streams and rivers using radon

NASA Astrophysics Data System (ADS)

Frei, S.; Gilfedder, B. S.

2015-08-01

A quantitative understanding of groundwater-surface water interactions is vital for sustainable management of water quantity and quality. The noble gas radon-222 (Rn) is becoming increasingly used as a sensitive tracer to quantify groundwater discharge to wetlands, lakes, and rivers: a development driven by technical and methodological advances in Rn measurement. However, quantitative interpretation of these data is not trivial, and the methods used to date are based on the simplest solutions to the mass balance equation (e.g., first-order finite difference and inversion). Here we present a new implicit numerical model (FINIFLUX) based on finite elements for quantifying groundwater discharge to streams and rivers using Rn surveys at the reach scale (1-50 km). The model is coupled to a state-of-the-art parameter optimization code Parallel-PEST to iteratively solve the mass balance equation for groundwater discharge and hyporheic exchange. The major benefit of this model is that it is programed to be very simple to use, reduces nonuniqueness, and provides numerically stable estimates of groundwater fluxes and hyporheic residence times from field data. FINIFLUX was tested against an analytical solution and then implemented on two German rivers of differing magnitude, the Salzach (˜112 m3 s-1) and the Rote Main (˜4 m3 s-1). We show that using previous inversion techniques numerical instability can lead to physically impossible negative values, whereas the new model provides stable positive values for all scenarios. We hope that by making FINIFLUX freely available to the community that Rn might find wider application in quantifying groundwater discharge to streams and rivers and thus assist in a combined management of surface and groundwater systems.

Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

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

Messaris, Gerasimos A. T., E-mail: messaris@upatras.gr; School of Science and Technology, Hellenic Open University, 11 Sahtouri Street, GR 262 22 Patras; Hadjinicolaou, Maria

The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient inmore » a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions, a factor that may contribute jointly with other pathological factors to the faster aging of the arterial system and the possible malfunction of the aorta.« less

Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

NASA Astrophysics Data System (ADS)

Messaris, Gerasimos A. T.; Hadjinicolaou, Maria; Karahalios, George T.

2016-08-01

The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions, a factor that may contribute jointly with other pathological factors to the faster aging of the arterial system and the possible malfunction of the aorta.

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

Modal element method for scattering of sound by absorbing bodies

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1992-01-01

The modal element method for acoustic scattering from 2-D body is presented. The body may be acoustically soft (absorbing) or hard (reflecting). The infinite computational region is divided into two subdomains - the bounded finite element domain, which is characterized by complicated geometry and/or variable material properties, and the surrounding unbounded homogeneous domain. The acoustic pressure field is represented approximately in the finite element domain by a finite element solution, and is represented analytically by an eigenfunction expansion in the homogeneous domain. The two solutions are coupled by the continuity of pressure and velocity across the interface between the two subdomains. Also, for hard bodies, a compact modal ring grid system is introduced for which computing requirements are drastically reduced. Analysis for 2-D scattering from solid and coated (acoustically treated) bodies is presented, and several simple numerical examples are discussed. In addition, criteria are presented for determining the number of modes to accurately resolve the scattered pressure field from a solid cylinder as a function of the frequency of the incoming wave and the radius of the cylinder.

Experimental and analytical analysis of stress-strain behavior in a (90/0 deg)2s, SiC/Ti-15-3 laminate

NASA Technical Reports Server (NTRS)

Lerch, Bradley A.; Melis, Matthew E.; Tong, Mike

1991-01-01

The nonlinear stress strain behavior of 90 degree/0 degree sub 2s, SiC/Ti-15-3 composite laminate was numerically investigated with a finite element, unit cell approach. Tensile stress-strain curves from room temperature experiments depicted three distinct regions of deformation, and these regions were predicted by finite element analysis. The first region of behavior, which was linear elastic, occurred at low applied stresses. As applied stresses increased, fiber/matrix debonding in the 90 degree plies caused a break in the stress-strain curve and initiated a second linear region. In this second region, matrix plasticity in the 90 degree plies developed. The third region, which was typified by nonlinear, stress-strain behavior occr red at high stresses. In this region, the onset of matrix plasticity in the 0 degree plies stiffened the laminate in the direction transverse to the applied load. Metallographic sections confirmed the existence of matrix plasticity in specific areas of the structure. Finite element analysis also predicted these locations of matrix slip.

Peakompactons: Peaked compact nonlinear waves

DOE PAGES

Christov, Ivan C.; Kress, Tyler; Saxena, Avadh

2017-04-20

This paper is meant as an accessible introduction to/tutorial on the analytical construction and numerical simulation of a class of nonstandard solitary waves termed peakompactons. We present that these peaked compactly supported waves arise as solutions to nonlinear evolution equations from a hierarchy of nonlinearly dispersive Korteweg–de Vries-type models. Peakompactons, like the now-well-known compactons and unlike the soliton solutions of the Korteweg–de Vries equation, have finite support, i.e., they are of finite wavelength. However, unlike compactons, peakompactons are also peaked, i.e., a higher spatial derivative suffers a jump discontinuity at the wave’s crest. Here, we construct such solutions exactly bymore » reducing the governing partial differential equation to a nonlinear ordinary differential equation and employing a phase-plane analysis. Lastly, a simple, but reliable, finite-difference scheme is also designed and tested for the simulation of collisions of peakompactons. In addition to the peakompacton class of solutions, the general physical features of the so-called K #(n,m) hierarchy of nonlinearly dispersive Korteweg–de Vries-type models are discussed as well.« less

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

Heat Transfer to Surfaces of Finite Catalytic Activity in Frozen Dissociated Hypersonic Flow

NASA Technical Reports Server (NTRS)

Chung, Paul M.; Anderson, Aemer D.

1961-01-01

The heat transfer due to catalytic recombination of a partially dissociated diatomic gas along the surfaces of two-dimensional and axisymmetric bodies with finite catalytic efficiencies is studied analytically. An integral method is employed resulting in simple yet relatively complete solutions for the particular configurations considered. A closed form solution is derived which enables one to calculate atom mass-fraction distribution, therefore catalytic heat transfer distribution, along the surface of a flat plate in frozen compressible flow with and without transpiration. Numerical calculations are made to determine the atom mass-fraction distribution along an axisymmetric conical body with spherical nose in frozen hypersonic compressible flow. A simple solution based on a local similarity concept is found to be in good agreement with these numerical calculations. The conditions are given for which the local similarity solution is expected to be satisfactory. The limitations on the practical application of the analysis to the flight of the blunt bodies in the atmosphere are discussed. The use of boundary-layer theory and the assumption of frozen flow restrict application of the analysis to altitudes between about 150,000 and 250,000 feet.

Behavior of Industrial Steel Rack Connections

NASA Astrophysics Data System (ADS)

Shah, S. N. R.; Ramli Sulong, N. H.; Khan, R.; Jumaat, M. Z.; Shariati, M.

2016-03-01

Beam-to-column connections (BCCs) used in steel pallet racks (SPRs) play a significant role to maintain the stability of rack structures in the down-aisle direction. The variety in the geometry of commercially available beam end connectors hampers the development of a generalized analytic design approach for SPR BCCs. The experimental prediction of flexibility in SPR BCCs is prohibitively expensive and difficult for all types of commercially available beam end connectors. A suitable solution to derive a particular uniform M-θ relationship for each connection type in terms of geometric parameters may be achieved through finite element (FE) modeling. This study first presents a comprehensive description of the experimental investigations that were performed and used as the calibration bases for the numerical study that constituted its main contribution. A three dimensioned (3D) non-linear finite element (FE) model was developed and calibrated against the experimental results. The FE model took into account material nonlinearities, geometrical properties and large displacements. Comparisons between numerical and experimental data for observed failure modes and M-θ relationship showed close agreement. The validated FE model was further extended to perform parametric analysis to identify the effects of various parameters which may affect the overall performance of the connection.

Toward patient-specific articular contact mechanics

PubMed Central

Ateshian, Gerard A.; Henak, Corinne R.; Weiss, Jeffrey A.

2015-01-01

The mechanics of contacting cartilage layers is fundamentally important to understanding the development, homeostasis and pathology of diarthrodial joints. Because of the highly nonlinear nature of both the materials and the contact problem itself, numerical methods such as the finite element method are typically incorporated to obtain solutions. Over the course of five decades, we have moved from an initial qualitative understanding of articular cartilage material behavior to the ability to perform complex, three-dimensional contact analysis, including multiphasic material representations. This history includes the development of analytical and computational contact analysis methods that now provide the ability to perform highly nonlinear analyses. Numerical implementations of contact analysis based on the finite element method are rapidly advancing and will soon enable patient-specific analysis of joint contact mechanics using models based on medical image data. In addition to contact stress on the articular surfaces, these techniques can predict variations in strain and strain through the cartilage layers, providing the basis to predict damage and failure. This opens up exciting areas for future research and application to patient-specific diagnosis and treatment planning applied to a variety of pathologies that affect joint function and cartilage homeostasis. PMID:25698236

Frequency-domain Green's functions for radar waves in heterogeneous 2.5D media

USGS Publications Warehouse

Ellefsen, K.J.; Croize, D.; Mazzella, A.T.; McKenna, J.R.

2009-01-01

Green's functions for radar waves propagating in heterogeneous 2.5D media might be calculated in the frequency domain using a hybrid method. The model is defined in the Cartesian coordinate system, and its electromagnetic properties might vary in the x- and z-directions, but not in the y-direction. Wave propagation in the x- and z-directions is simulated with the finite-difference method, and wave propagation in the y-direction is simulated with an analytic function. The absorbing boundaries on the finite-difference grid are perfectly matched layers that have been modified to make them compatible with the hybrid method. The accuracy of these numerical Greens functions is assessed by comparing them with independently calculated Green's functions. For a homogeneous model, the magnitude errors range from -4.16% through 0.44%, and the phase errors range from -0.06% through 4.86%. For a layered model, the magnitude errors range from -2.60% through 2.06%, and the phase errors range from -0.49% through 2.73%. These numerical Green's functions might be used for forward modeling and full waveform inversion. ?? 2009 Society of Exploration Geophysicists. All rights reserved.

Control/structure interaction conceptual design tool

NASA Technical Reports Server (NTRS)

Briggs, Hugh C.

1990-01-01

The JPL Control/Structure Interaction Program is developing new analytical methods for designing micro-precision spacecraft with controlled structures. One of these, the Conceptual Design Tool, will illustrate innovative new approaches to the integration of multi-disciplinary analysis and design methods. The tool will be used to demonstrate homogeneity of presentation, uniform data representation across analytical methods, and integrated systems modeling. The tool differs from current 'integrated systems' that support design teams most notably in its support for the new CSI multi-disciplinary engineer. The design tool will utilize a three dimensional solid model of the spacecraft under design as the central data organization metaphor. Various analytical methods, such as finite element structural analysis, control system analysis, and mechanical configuration layout, will store and retrieve data from a hierarchical, object oriented data structure that supports assemblies of components with associated data and algorithms. In addition to managing numerical model data, the tool will assist the designer in organizing, stating, and tracking system requirements.

Exact mode volume and Purcell factor of open optical systems

NASA Astrophysics Data System (ADS)

Muljarov, E. A.; Langbein, W.

2016-12-01

The Purcell factor quantifies the change of the radiative decay of a dipole in an electromagnetic environment relative to free space. Designing this factor is at the heart of photonics technology, striving to develop ever smaller or less lossy optical resonators. The Purcell factor can be expressed using the electromagnetic eigenmodes of the resonators, introducing the notion of a mode volume for each mode. This approach allows an analytic treatment, reducing the Purcell factor and other observables to sums over eigenmode resonances. Calculating the mode volumes requires a correct normalization of the modes. We introduce an exact normalization of modes, not relying on perfectly matched layers. We present an analytic theory of the Purcell effect based on this exact mode normalization and the resulting effective mode volume. We use a homogeneous dielectric sphere in vacuum, which is analytically solvable, to exemplify these findings. We furthermore verify the applicability of the normalization to numerically determined modes of a finite dielectric cylinder.

Indentation of a stretched elastomer

NASA Astrophysics Data System (ADS)

Zheng, Yue; Crosby, Alfred J.; Cai, Shengqiang

2017-10-01

Indentation has been intensively used to characterize mechanical properties of soft materials such as elastomers, gels, and soft biological tissues. In most indentation measurements, residual stress or stretch which can be commonly found in soft materials is ignored. In this article, we aim to quantitatively understand the effects of prestretches of an elastomer on its indentation measurement. Based on surface Green's function, we analytically derive the relationship between indentation force and indentation depth for a prestretched Neo-Hookean solid with a flat-ended cylindrical indenter as well as a spherical indenter. In addition, for a non-equal biaxially stretched elastomer, we obtain the equation determining the eccentricity of the elliptical contacting area between a spherical indenter and the elastomer. Our results clearly demonstrate that the effects of prestretches of an elastomer on its indentation measurement can be significant. To validate our analytical results, we further conduct correspondent finite element simulations of indentation of prestretched elastomers. The numerical results agree well with our analytical predictions.

Mathematical and field analysis of longitudinal reservoir infill

NASA Astrophysics Data System (ADS)

Ke, W. T.; Capart, H.

2016-12-01

In reservoirs, severe problems are caused by infilled sediment deposits. In long term, the sediment accumulation reduces the capacity of reservoir storage and flood control benefits. In the short term, the sediment deposits influence the intakes of water-supply and hydroelectricity generation. For the management of reservoir, it is important to understand the deposition process and then to predict the sedimentation in reservoir. To investigate the behaviors of sediment deposits, we propose a one-dimensional simplified theory derived by the Exner equation to predict the longitudinal sedimentation distribution in idealized reservoirs. The theory models the reservoir infill geomorphic actions for three scenarios: delta progradation, near-dam bottom deposition, and final infill. These yield three kinds of self-similar analytical solutions for the reservoir bed profiles, under different boundary conditions. Three analytical solutions are composed by error function, complementary error function, and imaginary error function, respectively. The theory is also computed by finite volume method to test the analytical solutions. The theoretical and numerical predictions are in good agreement with one-dimensional small-scale laboratory experiment. As the theory is simple to apply with analytical solutions and numerical computation, we propose some applications to simulate the long-profile evolution of field reservoirs and focus on the infill sediment deposit volume resulting the uplift of near-dam bottom elevation. These field reservoirs introduced here are Wushe Reservoir, Tsengwen Reservoir, Mudan Reservoir in Taiwan, Lago Dos Bocas in Puerto Rico, and Sakuma Dam in Japan.

Fretting Fatigue Analysis of Additively Manufactured Blade Root Made of Intermetallic Ti-48Al-2Cr-2Nb Alloy at High Temperature.

PubMed

Lavella, Mario; Botto, Daniele

2018-06-21

Slots in the disk of aircraft turbines restrain the centrifugal load of blades. Contact surfaces between the blade root and the disk slot undergo high contact pressure and relative displacement that is the typical condition in which fretting occurs. The load level ranges from zero to the maximum during take-off. This cycle is repeated for each mission. In this paper, a fretting fatigue analysis of additively manufactured blades is presented. Blades are made of an intermetallic alloy γTiAl. Fretting fatigue experiments were performed at a frequency of 0.5 Hz and at a temperature of 640 °C to match the operating condition of real blades. The minimum load was fixed at 0.5 KN and three maximum loads were applied, namely 16, 18 and 20 kN. Both an analytical and a two-dimensional finite element model were used to evaluate the state of stress at the contact interfaces. The results of the analytical model showed good agreement with the numerical model. Experiments showed that cracks nucleate where the analytical model predicts the maximum contact pressure and the numerical model predicts the maximum equivalent stress. A parametric analysis performed with the analytical model indicates that there exists an optimum geometry to minimize the contact pressure. Tests showed that the component life changed dramatically with the maximum load variation. Optical topography and scanning electron microscopy (SEM) analysis reveals information about the damage mechanism.

ICASE Semiannual Report, October 1, 1992 through March 31, 1993

DTIC Science & Technology

1993-06-01

NUMERICAL MATHEMATICS Saul Abarbanel Further results have been obtained regarding long time integration of high order compact finite difference schemes...overall accuracy. These problems are common to all numerical methods: finite differences , finite elements and spectral methods. It should be noted that...fourth order finite difference scheme. * In the same case, the D6 wavelets provide a sixth order finite difference , noncompact formula. * The wavelets

Numerical evaluation of moiré pattern in touch sensor module with electrode mesh structure in oblique view

NASA Astrophysics Data System (ADS)

Pournoury, M.; Zamiri, A.; Kim, T. Y.; Yurlov, V.; Oh, K.

2016-03-01

Capacitive touch sensor screen with the metal materials has recently become qualified for substitution of ITO; however several obstacles still have to be solved. One of the most important issues is moiré phenomenon. The visibility problem of the metal-mesh, in touch sensor module (TSM) is numerically considered in this paper. Based on human eye contract sensitivity function (CSF), moiré pattern of TSM electrode mesh structure is simulated with MATLAB software for 8 inch screen display in oblique view. Standard deviation of the generated moiré by the superposition of electrode mesh and screen image is calculated to find the optimal parameters which provide the minimum moiré visibility. To create the screen pixel array and mesh electrode, rectangular function is used. The filtered image, in frequency domain, is obtained by multiplication of Fourier transform of the finite mesh pattern (product of screen pixel and mesh electrode) with the calculated CSF function for three different observer distances (L=200, 300 and 400 mm). It is observed that the discrepancy between analytical and numerical results is less than 0.6% for 400 mm viewer distance. Moreover, in the case of oblique view due to considering the thickness of the finite film between mesh electrodes and screen, different points of minimum standard deviation of moiré pattern are predicted compared to normal view.