Computational aspects of sensitivity calculations in linear transient structural analysis. Ph.D. Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Greene, William H.

1990-01-01

A study was performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal of the study was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semi-analytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models. In several cases this fixed mode approach resulted in very poor approximations of the stress sensitivities. Almost all of the original modes were required for an accurate sensitivity and for small numbers of modes, the accuracy was extremely poor. To overcome this poor accuracy, two semi-analytical techniques were developed. The first technique accounts for the change in eigenvectors through approximate eigenvector derivatives. The second technique applies the mode acceleration method of transient analysis to the sensitivity calculations. Both result in accurate values of the stress sensitivities with a small number of modes and much lower computational costs than if the vibration modes were recalculated and then used in an overall finite difference method.

Perturbational blowup solutions to the compressible Euler equations with damping.

PubMed

Cheung, Ka Luen

2016-01-01

The N-dimensional isentropic compressible Euler system with a damping term is one of the most fundamental equations in fluid dynamics. Since it does not have a general solution in a closed form for arbitrary well-posed initial value problems. Constructing exact solutions to the system is a useful way to obtain important information on the properties of its solutions. In this article, we construct two families of exact solutions for the one-dimensional isentropic compressible Euler equations with damping by the perturbational method. The two families of exact solutions found include the cases [Formula: see text] and [Formula: see text], where [Formula: see text] is the adiabatic constant. With analysis of the key ordinary differential equation, we show that the classes of solutions include both blowup type and global existence type when the parameters are suitably chosen. Moreover, in the blowup cases, we show that the singularities are of essential type in the sense that they cannot be smoothed by redefining values at the odd points. The two families of exact solutions obtained in this paper can be useful to study of related numerical methods and algorithms such as the finite difference method, the finite element method and the finite volume method that are applied by scientists to simulate the fluids for applications.

Perturbational and nonperturbational inversion of Rayleigh-wave velocities

USGS Publications Warehouse

Haney, Matt; Tsai, Victor C.

2017-01-01

The inversion of Rayleigh-wave dispersion curves is a classic geophysical inverse problem. We have developed a set of MATLAB codes that performs forward modeling and inversion of Rayleigh-wave phase or group velocity measurements. We describe two different methods of inversion: a perturbational method based on finite elements and a nonperturbational method based on the recently developed Dix-type relation for Rayleigh waves. In practice, the nonperturbational method can be used to provide a good starting model that can be iteratively improved with the perturbational method. Although the perturbational method is well-known, we solve the forward problem using an eigenvalue/eigenvector solver instead of the conventional approach of root finding. Features of the codes include the ability to handle any mix of phase or group velocity measurements, combinations of modes of any order, the presence of a surface water layer, computation of partial derivatives due to changes in material properties and layer boundaries, and the implementation of an automatic grid of layers that is optimally suited for the depth sensitivity of Rayleigh waves.

Communication: Finite size correction in periodic coupled cluster theory calculations of solids.

PubMed

Liao, Ke; Grüneis, Andreas

2016-10-14

We present a method to correct for finite size errors in coupled cluster theory calculations of solids. The outlined technique shares similarities with electronic structure factor interpolation methods used in quantum Monte Carlo calculations. However, our approach does not require the calculation of density matrices. Furthermore we show that the proposed finite size corrections achieve chemical accuracy in the convergence of second-order Møller-Plesset perturbation and coupled cluster singles and doubles correlation energies per atom for insulating solids with two atomic unit cells using 2 × 2 × 2 and 3 × 3 × 3 k-point meshes only.

A Double Perturbation Method for Reducing Dynamical Degradation of the Digital Baker Map

NASA Astrophysics Data System (ADS)

Liu, Lingfeng; Lin, Jun; Miao, Suoxia; Liu, Bocheng

2017-06-01

The digital Baker map is widely used in different kinds of cryptosystems, especially for image encryption. However, any chaotic map which is realized on the finite precision device (e.g. computer) will suffer from dynamical degradation, which refers to short cycle lengths, low complexity and strong correlations. In this paper, a novel double perturbation method is proposed for reducing the dynamical degradation of the digital Baker map. Both state variables and system parameters are perturbed by the digital logistic map. Numerical experiments show that the perturbed Baker map can achieve good statistical and cryptographic properties. Furthermore, a new image encryption algorithm is provided as a simple application. With a rather simple algorithm, the encrypted image can achieve high security, which is competitive to the recently proposed image encryption algorithms.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Numerical solution of Euler's equation by perturbed functionals

NASA Technical Reports Server (NTRS)

Dey, S. K.

1985-01-01

A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

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

Mu, Lin; Wang, Junping; Ye, Xiu

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2017-08-17

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

Dynamical mean field theory equations on nearly real frequency axis

NASA Astrophysics Data System (ADS)

Fathi, M. B.; Jafari, S. A.

2010-03-01

The iterated perturbation theory (IPT) equations of the dynamical mean field theory (DMFT) for the half-filled Hubbard model are solved on nearly real frequencies at various values of the Hubbard parameters, U, to investigate the nature of metal-insulator transition (MIT) at finite temperatures. This method avoids the instabilities associated with the infamous Padé analytic continuation and reveals fine structures across the MIT at finite temperatures, which cannot be captured by conventional methods for solving DMFT-IPT equations on Matsubara frequencies. Our method suggests that at finite temperatures, there is a crossover from a bad metal to a bad insulator in which the height of the quasi-particle (Kondo) peak decreases to a non-zero small bump, which gradually suppresses as one moves deeper into the bad insulating regime.

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.

Celestial mechanics with geometric algebra

NASA Technical Reports Server (NTRS)

Hestenes, D.

1983-01-01

Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.

Application of the Finite Element Method in Atomic and Molecular Physics

NASA Technical Reports Server (NTRS)

Shertzer, Janine

2007-01-01

The finite element method (FEM) is a numerical algorithm for solving second order differential equations. It has been successfully used to solve many problems in atomic and molecular physics, including bound state and scattering calculations. To illustrate the diversity of the method, we present here details of two applications. First, we calculate the non-adiabatic dipole polarizability of Hi by directly solving the first and second order equations of perturbation theory with FEM. In the second application, we calculate the scattering amplitude for e-H scattering (without partial wave analysis) by reducing the Schrodinger equation to set of integro-differential equations, which are then solved with FEM.

Sensitivity of resistive and Hall measurements to local inhomogeneities: Finite-field, intensity, and area corrections

NASA Astrophysics Data System (ADS)

Koon, Daniel W.; Wang, Fei; Petersen, Dirch Hjorth; Hansen, Ole

2014-10-01

We derive exact, analytic expressions for the sensitivity of sheet resistance and Hall sheet resistance measurements to local inhomogeneities for the cases of nonzero magnetic fields, strong perturbations, and perturbations over a finite area, extending our earlier results on weak perturbations. We express these sensitivities for conductance tensor components and for other charge transport quantities. Both resistive and Hall sensitivities, for a van der Pauw specimen in a finite magnetic field, are a superposition of the zero-field sensitivities to both sheet resistance and Hall sheet resistance. Strong perturbations produce a nonlinear correction term that depends on the strength of the inhomogeneity. Solution of the specific case of a finite-sized circular inhomogeneity coaxial with a circular specimen suggests a first-order correction for the general case. Our results are confirmed by computer simulations on both a linear four-point probe array on a large circular disc and a van der Pauw square geometry. Furthermore, the results also agree well with Náhlík et al. published experimental results for physical holes in a circular copper foil disc.

Doi-Peliti path integral methods for stochastic systems with partial exclusion

NASA Astrophysics Data System (ADS)

Greenman, Chris D.

2018-09-01

Doi-Peliti methods are developed for stochastic models with finite maximum occupation numbers per site. We provide a generalized framework for the different Fock spaces reported in the literature. Paragrassmannian techniques are then utilized to construct path integral formulations of factorial moments. We show that for many models of interest, a Magnus expansion is required to construct a suitable action, meaning actions containing a finite number of terms are not always feasible. However, for such systems, perturbative techniques are still viable, and for some examples, including carrying capacity population dynamics, and diffusion with partial exclusion, the expansions are exactly summable.

Gaussian impurity moving through a Bose-Einstein superfluid

NASA Astrophysics Data System (ADS)

Pinsker, Florian

2017-09-01

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

Investigating a hybrid perturbation-Galerkin technique using computer algebra

NASA Technical Reports Server (NTRS)

Andersen, Carl M.; Geer, James F.

1988-01-01

A two-step hybrid perturbation-Galerkin method is presented for the solution of a variety of differential equations type problems which involve a scalar parameter. The resulting (approximate) solution has the form of a sum where each term consists of the product of two functions. The first function is a function of the independent field variable(s) x, and the second is a function of the parameter lambda. In step one the functions of x are determined by forming a perturbation expansion in lambda. In step two the functions of lambda are determined through the use of the classical Bubnov-Gelerkin method. The resulting hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Bubnov-Galerkin methods applied separately, while combining some of the good features of each. In particular, the results can be useful well beyond the radius of convergence associated with the perturbation expansion. The hybrid method is applied with the aid of computer algebra to a simple two-point boundary value problem where the radius of convergence is finite and to a quantum eigenvalue problem where the radius of convergence is zero. For both problems the hybrid method apparently converges for an infinite range of the parameter lambda. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Structural-change localization and monitoring through a perturbation-based inverse problem.

PubMed

Roux, Philippe; Guéguen, Philippe; Baillet, Laurent; Hamze, Alaa

2014-11-01

Structural-change detection and characterization, or structural-health monitoring, is generally based on modal analysis, for detection, localization, and quantification of changes in structure. Classical methods combine both variations in frequencies and mode shapes, which require accurate and spatially distributed measurements. In this study, the detection and localization of a local perturbation are assessed by analysis of frequency changes (in the fundamental mode and overtones) that are combined with a perturbation-based linear inverse method and a deconvolution process. This perturbation method is applied first to a bending beam with the change considered as a local perturbation of the Young's modulus, using a one-dimensional finite-element model for modal analysis. Localization is successful, even for extended and multiple changes. In a second step, the method is numerically tested under ambient-noise vibration from the beam support with local changes that are shifted step by step along the beam. The frequency values are revealed using the random decrement technique that is applied to the time-evolving vibrations recorded by one sensor at the free extremity of the beam. Finally, the inversion method is experimentally demonstrated at the laboratory scale with data recorded at the free end of a Plexiglas beam attached to a metallic support.

Probabilistic finite elements

NASA Technical Reports Server (NTRS)

Belytschko, Ted; Wing, Kam Liu

1987-01-01

In the Probabilistic Finite Element Method (PFEM), finite element methods have been efficiently combined with second-order perturbation techniques to provide an effective method for informing the designer of the range of response which is likely in a given problem. The designer must provide as input the statistical character of the input variables, such as yield strength, load magnitude, and Young's modulus, by specifying their mean values and their variances. The output then consists of the mean response and the variance in the response. Thus the designer is given a much broader picture of the predicted performance than with simply a single response curve. These methods are applicable to a wide class of problems, provided that the scale of randomness is not too large and the probabilistic density functions possess decaying tails. By incorporating the computational techniques we have developed in the past 3 years for efficiency, the probabilistic finite element methods are capable of handling large systems with many sources of uncertainties. Sample results for an elastic-plastic ten-bar structure and an elastic-plastic plane continuum with a circular hole subject to cyclic loadings with the yield stress on the random field are given.

Optimal guidance law development for an advanced launch system

NASA Technical Reports Server (NTRS)

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

1991-01-01

The proposed investigation on a Matched Asymptotic Expansion (MAE) method was carried out. It was concluded that the method of MAE is not applicable to launch vehicle ascent trajectory optimization due to a lack of a suitable stretched variable. More work was done on the earlier regular perturbation approach using a piecewise analytic zeroth order solution to generate a more accurate approximation. In the meantime, a singular perturbation approach using manifold theory is also under current investigation. Work on a general computational environment based on the use of MACSYMA and the weak Hamiltonian finite element method continued during this period. This methodology is capable of the solution of a large class of optimal control problems.

A hybrid Pade-Galerkin technique for differential equations

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1993-01-01

A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter epsilon associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade approximation in the form of a rational function in the parameter epsilon. In the third step, the various powers of epsilon which appear in the Pade approximation are replaced by new (unknown) parameters (delta(sub j)). These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade approximations fail to do so. The method is discussed and topics for future investigations are indicated.

The Chiral Separation Effect in quenched finite-density QCD

NASA Astrophysics Data System (ADS)

Puhr, Matthias; Buividovich, Pavel

2018-03-01

We present results of a study of the Chiral Separation Effect (CSE) in quenched finite-density QCD. Using a recently developed numerical method we calculate the conserved axial current for exactly chiral overlap fermions at finite density for the first time. We compute the anomalous transport coeffcient for the CSE in the confining and deconfining phase and investigate possible deviations from the universal value. In both phases we find that non-perturbative corrections to the CSE are absent and we reproduce the universal value for the transport coeffcient within small statistical errors. Our results suggest that the CSE can be used to determine the renormalisation factor of the axial current.

New results on finite-time parameter identification and synchronization of uncertain complex dynamical networks with perturbation

NASA Astrophysics Data System (ADS)

Zhao, Hui; Zheng, Mingwen; Li, Shudong; Wang, Weiping

2018-03-01

Some existing papers focused on finite-time parameter identification and synchronization, but provided incomplete theoretical analyses. Such works incorporated conflicting constraints for parameter identification, therefore, the practical significance could not be fully demonstrated. To overcome such limitations, the underlying paper presents new results of parameter identification and synchronization for uncertain complex dynamical networks with impulsive effect and stochastic perturbation based on finite-time stability theory. Novel results of parameter identification and synchronization control criteria are obtained in a finite time by utilizing Lyapunov function and linear matrix inequality respectively. Finally, numerical examples are presented to illustrate the effectiveness of our theoretical results.

Numerical calculation of thermo-mechanical problems at large strains based on complex step derivative approximation of tangent stiffness matrices

NASA Astrophysics Data System (ADS)

Balzani, Daniel; Gandhi, Ashutosh; Tanaka, Masato; Schröder, Jörg

2015-05-01

In this paper a robust approximation scheme for the numerical calculation of tangent stiffness matrices is presented in the context of nonlinear thermo-mechanical finite element problems and its performance is analyzed. The scheme extends the approach proposed in Kim et al. (Comput Methods Appl Mech Eng 200:403-413, 2011) and Tanaka et al. (Comput Methods Appl Mech Eng 269:454-470, 2014 and bases on applying the complex-step-derivative approximation to the linearizations of the weak forms of the balance of linear momentum and the balance of energy. By incorporating consistent perturbations along the imaginary axis to the displacement as well as thermal degrees of freedom, we demonstrate that numerical tangent stiffness matrices can be obtained with accuracy up to computer precision leading to quadratically converging schemes. The main advantage of this approach is that contrary to the classical forward difference scheme no round-off errors due to floating-point arithmetics exist within the calculation of the tangent stiffness. This enables arbitrarily small perturbation values and therefore leads to robust schemes even when choosing small values. An efficient algorithmic treatment is presented which enables a straightforward implementation of the method in any standard finite-element program. By means of thermo-elastic and thermo-elastoplastic boundary value problems at finite strains the performance of the proposed approach is analyzed.

Fuzzy interval Finite Element/Statistical Energy Analysis for mid-frequency analysis of built-up systems with mixed fuzzy and interval parameters

NASA Astrophysics Data System (ADS)

Yin, Hui; Yu, Dejie; Yin, Shengwen; Xia, Baizhan

2016-10-01

This paper introduces mixed fuzzy and interval parametric uncertainties into the FE components of the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) model for mid-frequency analysis of built-up systems, thus an uncertain ensemble combining non-parametric with mixed fuzzy and interval parametric uncertainties comes into being. A fuzzy interval Finite Element/Statistical Energy Analysis (FIFE/SEA) framework is proposed to obtain the uncertain responses of built-up systems, which are described as intervals with fuzzy bounds, termed as fuzzy-bounded intervals (FBIs) in this paper. Based on the level-cut technique, a first-order fuzzy interval perturbation FE/SEA (FFIPFE/SEA) and a second-order fuzzy interval perturbation FE/SEA method (SFIPFE/SEA) are developed to handle the mixed parametric uncertainties efficiently. FFIPFE/SEA approximates the response functions by the first-order Taylor series, while SFIPFE/SEA improves the accuracy by considering the second-order items of Taylor series, in which all the mixed second-order items are neglected. To further improve the accuracy, a Chebyshev fuzzy interval method (CFIM) is proposed, in which the Chebyshev polynomials is used to approximate the response functions. The FBIs are eventually reconstructed by assembling the extrema solutions at all cut levels. Numerical results on two built-up systems verify the effectiveness of the proposed methods.

A finite element method to compute three-dimensional equilibrium configurations of fluid membranes: Optimal parameterization, variational formulation and applications

NASA Astrophysics Data System (ADS)

Rangarajan, Ramsharan; Gao, Huajian

2015-09-01

We introduce a finite element method to compute equilibrium configurations of fluid membranes, identified as stationary points of a curvature-dependent bending energy functional under certain geometric constraints. The reparameterization symmetries in the problem pose a challenge in designing parametric finite element methods, and existing methods commonly resort to Lagrange multipliers or penalty parameters. In contrast, we exploit these symmetries by representing solution surfaces as normal offsets of given reference surfaces and entirely bypass the need for artificial constraints. We then resort to a Galerkin finite element method to compute discrete C1 approximations of the normal offset coordinate. The variational framework presented is suitable for computing deformations of three-dimensional membranes subject to a broad range of external interactions. We provide a systematic algorithm for computing large deformations, wherein solutions at subsequent load steps are identified as perturbations of previously computed ones. We discuss the numerical implementation of the method in detail and demonstrate its optimal convergence properties using examples. We discuss applications of the method to studying adhesive interactions of fluid membranes with rigid substrates and to investigate the influence of membrane tension in tether formation.

Tensor renormalization group methods for spin and gauge models

NASA Astrophysics Data System (ADS)

Zou, Haiyuan

The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Test problems for inviscid transonic flow

NASA Technical Reports Server (NTRS)

Carlson, L. A.

1979-01-01

Solving of test problems with the TRANDES program is discussed. This method utilizes the full, inviscid, perturbation potential flow equation in a Cartesian grid system that is stretched to infinity. This equation is represented by a nonconservative system of finite difference equations that includes at supersonic points a rotated difference scheme and is solved by column relaxation. The solution usually starts from a zero perturbation potential on a very coarse grid (typically 13 by 7) followed by several grid halvings until a final solution is obtained on a fine grid (97 by 49).

Methods for the calculation of axial wave numbers in lined ducts with mean flow

NASA Technical Reports Server (NTRS)

Eversman, W.

1981-01-01

A survey is made of the methods available for the calculation of axial wave numbers in lined ducts. Rectangular and circular ducts with both uniform and non-uniform flow are considered as are ducts with peripherally varying liners. A historical perspective is provided by a discussion of the classical methods for computing attenuation when no mean flow is present. When flow is present these techniques become either impractical or impossible. A number of direct eigenvalue determination schemes which have been used when flow is present are discussed. Methods described are extensions of the classical no-flow technique, perturbation methods based on the no-flow technique, direct integration methods for solution of the eigenvalue equation, an integration-iteration method based on the governing differential equation for acoustic transmission, Galerkin methods, finite difference methods, and finite element methods.

Adjoint sensitivity analysis of plasmonic structures using the FDTD method.

PubMed

Zhang, Yu; Ahmed, Osman S; Bakr, Mohamed H

2014-05-15

We present an adjoint variable method for estimating the sensitivities of arbitrary responses with respect to the parameters of dispersive discontinuities in nanoplasmonic devices. Our theory is formulated in terms of the electric field components at the vicinity of perturbed discontinuities. The adjoint sensitivities are computed using at most one extra finite-difference time-domain (FDTD) simulation regardless of the number of parameters. Our approach is illustrated through the sensitivity analysis of an add-drop coupler consisting of a square ring resonator between two parallel waveguides. The computed adjoint sensitivities of the scattering parameters are compared with those obtained using the accurate but computationally expensive central finite difference approach.

Effects of the finite size of the ion (dd{mu}){sup +} on the energy levels of the molecules (dd{mu})e and (dd{mu})dee

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

Harston, M.R.; Hara, S.; Kino, Y.

1997-10-01

The energy shift due to the finite size of the pseudonucleus (dd{mu}){sub 11}{sup +} in the molecules (dd{mu}){sub 11}e and (dd{mu}){sub 11}dee, the subscripts indicating the first excited state with total angular momentum of one unit, is of importance in the theoretical estimation of the rate of d-d fusion catalyzed by negative muons. The energy shift in the molecule (dd{mu}){sub 11}e is calculated using perturbation theory up to second order. The finite-size shift is found to be 1.46 meV. This is significantly larger than the value of 0.7 meV for this energy shift calculated by Bakalov [Muon Catalyzed Fusion {boldmore » 3}, 321 (1988)] by a method similar to the present method; recently found excellent agreement of theory with experimental results for the formation rate of the molecule (dd{mu}){sub 11}dee was based on Bakalov{close_quote}s value with some modifications. The results of a direct calculation of the finite-size energy shifts in (dd{mu}){sub 11}dee using first-order perturbation theory are presented. The contribution from the quadrupole component of the (dd{mu}){sub 11} charge distribution, which is not taken into account in the conventional scaling procedure based on the finite-size energy shifts of (dd{mu}){sub 11}e, is found to be of the order of 1 meV and to depend on the angular-momentum states of (dd{mu}){sub 11}dee. Sources of uncertainty in the current theoretical estimates are also discussed. {copyright} {ital 1997} {ital The American Physical Society}« less

Internal wave energy flux from density perturbations in nonlinear stratifications

NASA Astrophysics Data System (ADS)

Lee, Frank M.; Allshouse, Michael R.; Swinney, Harry L.; Morrison, P. J.

2017-11-01

Tidal flow over the topography at the bottom of the ocean, whose density varies with depth, generates internal gravity waves that have a significant impact on the energy budget of the ocean. Thus, understanding the energy flux (J = p v) is important, but it is difficult to measure simultaneously the pressure and velocity perturbation fields, p and v . In a previous work, a Green's-function-based method was developed to calculate the instantaneous p, v , and thus J , given a density perturbation field for a constant buoyancy frequency N. Here we extend the previous analytic Green's function work to include nonuniform N profiles, namely the tanh-shaped and linear cases, because background density stratifications that occur in the ocean and some experiments are nonlinear. In addition, we present a finite-difference method for the general case where N has an arbitrary profile. Each method is validated against numerical simulations. The methods we present can be applied to measured density perturbation data by using our MATLAB graphical user interface EnergyFlux. PJM was supported by the U.S. Department of Energy Contract DE-FG05-80ET-53088. HLS and MRA were supported by ONR Grant No. N000141110701.

Reduction of parameters in Finite Unified Theories and the MSSM

NASA Astrophysics Data System (ADS)

Heinemeyer, Sven; Mondragón, Myriam; Tracas, Nicholas; Zoupanos, George

2018-02-01

The method of reduction of couplings developed by W. Zimmermann, combined with supersymmetry, can lead to realistic quantum field theories, where the gauge and Yukawa sectors are related. It is the basis to find all-loop Finite Unified Theories, where the β-function vanishes to all-loops in perturbation theory. It can also be applied to the Minimal Supersymmetric Standard Model, leading to a drastic reduction in the number of parameters. Both Finite Unified Theories and the reduced MSSM lead to successful predictions for the masses of the third generation of quarks and the Higgs boson, and also predict a heavy supersymmetric spectrum, consistent with the non-observation of supersymmetry so far.

Electromagnetic beam diffraction by a finite lamellar structure: an aperiodic coupled-wave method.

PubMed

Guizal, Brahim; Barchiesi, Dominique; Felbacq, Didier

2003-12-01

We have developed a new formulation of the coupled-wave method (CWM) to handle aperiodic lamellar structures, and it will be referred to as the aperiodic coupled-wave method (ACWM). The space is still divided into three regions, but the fields are written by use of their Fourier integrals instead of the Fourier series. In the modulated region the relative permittivity is represented by its Fourier transform, and then a set of integro-differential equations is derived. Discretizing the last system leads to a set of ordinary differential equations that is reduced to an eigenvalue problem, as is usually done in the CWM. To assess the method, we compare our results with three independent formalisms: the Rayleigh perturbation method for small samples, the volume integral method, and the finite-element method.

Finite volume for three-flavour Partially Quenched Chiral Perturbation Theory through NNLO in the meson sector

NASA Astrophysics Data System (ADS)

Bijnens, Johan; Rössler, Thomas

2015-11-01

We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark flow technique.

Computation of the transonic perturbation flow fields around two- and three-dimensional oscillating wings

NASA Technical Reports Server (NTRS)

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

1975-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about an harmonically oscillating wing are presented along with a discussion of the development of a pilot program for three-dimensional flow. In addition, some two- and three-dimensional examples are presented.

Evaluating the role of higher order nonlinearity in water of finite and shallow depth with a direct numerical simulation method of Euler equations

NASA Astrophysics Data System (ADS)

Fernandez, L.; Toffoli, A.; Monbaliu, J.

2012-04-01

In deep water, the dynamics of surface gravity waves is dominated by the instability of wave packets to side band perturbations. This mechanism, which is a nonlinear third order in wave steepness effect, can lead to a particularly strong focusing of wave energy, which in turn results in the formation of waves of very large amplitude also known as freak or rogue waves [1]. In finite water depth, however, the interaction between waves and the ocean floor induces a mean current. This subtracts energy from wave instability and causes it to cease for relative water depth , where k is the wavenumber and h the water depth [2]. Yet, this contradicts field observations of extreme waves such as the infamous 26-m "New Year" wave that have mainly been recorded in regions of relatively shallow water . In this respect, recent studies [3] seem to suggest that higher order nonlinearity in water of finite depth may sustain instability. In order to assess the role of higher order nonlinearity in water of finite and shallow depth, here we use a Higher Order Spectral Method [4] to simulate the evolution of surface gravity waves according to the Euler equations of motion. This method is based on an expansion of the vertical velocity about the surface elevation under the assumption of weak nonlinearity and has a great advantage of allowing the activation or deactivation of different orders of nonlinearity. The model is constructed to deal with an arbitrary order of nonlinearity and water depths so that finite and shallow water regimes can be analyzed. Several wave configurations are considered with oblique and collinear with the primary waves disturbances and different water depths. The analysis confirms that nonlinearity higher than third order play a substantial role in the destabilization of a primary wave train and subsequent growth of side band perturbations.

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.

Vector two-point functions in finite volume using partially quenched chiral perturbation theory at two loops

NASA Astrophysics Data System (ADS)

Bijnens, Johan; Relefors, Johan

2017-12-01

We calculate vector-vector correlation functions at two loops using partially quenched chiral perturbation theory including finite volume effects and twisted boundary conditions. We present expressions for the flavor neutral cases and the flavor charged case with equal masses. Using these expressions we give an estimate for the ratio of disconnected to connected contributions for the strange part of the electromagnetic current. We give numerical examples for the effects of partial quenching, finite volume and twisting and suggest the use of different twists to check the size of finite volume effects. The main use of this work is expected to be for lattice QCD calculations of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.

A Simple Method for Deriving the Confidence Regions for the Penalized Cox's Model via the Minimand Perturbation.

PubMed

Lin, Chen-Yen; Halabi, Susan

2017-01-01

We propose a minimand perturbation method to derive the confidence regions for the regularized estimators for the Cox's proportional hazards model. Although the regularized estimation procedure produces a more stable point estimate, it remains challenging to provide an interval estimator or an analytic variance estimator for the associated point estimate. Based on the sandwich formula, the current variance estimator provides a simple approximation, but its finite sample performance is not entirely satisfactory. Besides, the sandwich formula can only provide variance estimates for the non-zero coefficients. In this article, we present a generic description for the perturbation method and then introduce a computation algorithm using the adaptive least absolute shrinkage and selection operator (LASSO) penalty. Through simulation studies, we demonstrate that our method can better approximate the limiting distribution of the adaptive LASSO estimator and produces more accurate inference compared with the sandwich formula. The simulation results also indicate the possibility of extending the applications to the adaptive elastic-net penalty. We further demonstrate our method using data from a phase III clinical trial in prostate cancer.

Turbulence and mixing from optimal perturbations to a stratified shear layer

NASA Astrophysics Data System (ADS)

Kaminski, Alexis; Caulfield, C. P.; Taylor, John

2014-11-01

The stability and mixing of stratified shear layers is a canonical problem in fluid dynamics with relevance to flows in the ocean and atmosphere. The Miles-Howard theorem states that a necessary condition for normal-mode instability in parallel, inviscid, steady stratified shear flows is that the gradient Richardson number, Rig is less than 1/4 somewhere in the flow. However, substantial transient growth of non-normal modes may be possible at finite times even when Rig > 1 / 4 everywhere in the flow. We have calculated the ``optimal perturbations'' associated with maximum perturbation energy gain for a stably-stratified shear layer. These optimal perturbations are then used to initialize direct numerical simulations. For small but finite perturbation amplitudes, the optimal perturbations grow at the predicted linear rate initially, but then experience sufficient transient growth to become nonlinear and susceptible to secondary instabilities, which then break down into turbulence. Remarkably, this occurs even in flows for which Rig > 1 / 4 everywhere. We will describe the nonlinear evolution of the optimal perturbations and characterize the resulting turbulence and mixing.

Interlaminar stresses in composite laminates: A perturbation analysis

NASA Technical Reports Server (NTRS)

Hsu, P. W.; Herakovich, C. T.

1976-01-01

A general method of solution for an elastic balanced symmetric composite laminate subject to a uniaxial extension was developed based upon a perturbation analysis of a limiting free body containing an interfacial plane. The solution satisfies more physical requirements and boundary conditions than previous investigations, and predicts smooth continuous interlaminar stresses with no instabilities. It determines the finite maximum intensity for the interlaminar normal stress in all laminates, provides mathematical evidences for the singular stresses in angle-ply laminates, suggests the need for the experimental determination of an important problem parameter, and introduces a viable means for solving related problems of practical interest.

Non-perturbative theory of dispersion interactions

NASA Astrophysics Data System (ADS)

Boström, M.; Thiyam, P.; Persson, C.; Parsons, D. F.; Buhmann, S. Y.; Brevik, I.; Sernelius, Bo E.

2015-03-01

Some open questions exist with fluctuation-induced forces between extended dipoles. Conventional intuition derives from large-separation perturbative approximations to dispersion force theory. Here, we present a full non-perturbative theory. In addition, we discuss how one can take into account finite dipole size corrections. It is of fundamental value to investigate the limits of validity of the perturbative dispersion force theory.

Non-perturbative background field calculations

NASA Astrophysics Data System (ADS)

Stephens, C. R.

1988-01-01

New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation—perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation.

Fast calculation of the sensitivity matrix in magnetic induction tomography by tetrahedral edge finite elements and the reciprocity theorem.

PubMed

Hollaus, K; Magele, C; Merwa, R; Scharfetter, H

2004-02-01

Magnetic induction tomography of biological tissue is used to reconstruct the changes in the complex conductivity distribution by measuring the perturbation of an alternating primary magnetic field. To facilitate the sensitivity analysis and the solution of the inverse problem a fast calculation of the sensitivity matrix, i.e. the Jacobian matrix, which maps the changes of the conductivity distribution onto the changes of the voltage induced in a receiver coil, is needed. The use of finite differences to determine the entries of the sensitivity matrix does not represent a feasible solution because of the high computational costs of the basic eddy current problem. Therefore, the reciprocity theorem was exploited. The basic eddy current problem was simulated by the finite element method using symmetric tetrahedral edge elements of second order. To test the method various simulations were carried out and discussed.

Rotordynamic coefficients for labyrinth seals calculated by means of a finite difference technique

NASA Technical Reports Server (NTRS)

Nordmann, R.; Weiser, P.

1989-01-01

The compressible, turbulent, time dependent and three dimensional flow in a labyrinth seal can be described by the Navier-Stokes equations in conjunction with a turbulence model. Additionally, equations for mass and energy conservation and an equation of state are required. To solve these equations, a perturbation analysis is performed yielding zeroth order equations for centric shaft position and first order equations describing the flow field for small motions around the seal center. For numerical solution a finite difference method is applied to the zeroth and first order equations resulting in leakage and dynamic seal coefficients respectively.

Optimal perturbations for nonlinear systems using graph-based optimal transport

NASA Astrophysics Data System (ADS)

Grover, Piyush; Elamvazhuthi, Karthik

2018-06-01

We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on the phase space to a final measure in finite time. The measure is propagated under system dynamics in between the perturbations via the associated transfer operator. Each perturbation is described by a deterministic map in the measure space that implements a version of Monge-Kantorovich optimal transport with quadratic cost. Hence, the optimal solution minimizes a sum of quadratic costs on phase space transport due to the perturbations applied at specified times. The action of the transport map is approximated by a continuous pseudo-time flow on a graph, resulting in a tractable convex optimization problem. This problem is solved via state-of-the-art solvers to global optimality. We apply this algorithm to a problem of transport between measures supported on two disjoint almost-invariant sets in a chaotic fluid system, and to a finite-time optimal mixing problem by choosing the final measure to be uniform. In both cases, the optimal perturbations are found to exploit the phase space structures, such as lobe dynamics, leading to efficient global transport. As the time-horizon of the problem is increased, the optimal perturbations become increasingly localized. Hence, by combining the transfer operator approach with ideas from the theory of optimal mass transportation, we obtain a discrete-time graph-based algorithm for optimal transport and mixing in nonlinear systems.

Effects of Gas Rarefaction on Dynamic Characteristics of Micro Spiral-Grooved Thrust Bearing.

PubMed

Liu, Ren; Wang, Xiao-Li; Zhang, Xiao-Qing

2012-04-01

The effects of gas-rarefaction on dynamic characteristics of micro spiral-grooved-thrust-bearing are studied. The Reynolds equation is modified by the first order slip model, and the corresponding perturbation equations are then obtained on the basis of the linear small perturbation method. In the converted spiral-curve-coordinates system, the finite-volume-method (FVM) is employed to discrete the surface domain of micro bearing. The results show, compared with the continuum-flow model, that under the slip-flow regime, the decrease in the pressure and stiffness become obvious with the increasing of the compressibility number. Moreover, with the decrease of the relative gas-film-thickness, the deviations of dynamic coefficients between slip-flow-model and continuum-flow-model are increasing.

Superiorization with level control

NASA Astrophysics Data System (ADS)

Cegielski, Andrzej; Al-Musallam, Fadhel

2017-04-01

The convex feasibility problem is to find a common point of a finite family of closed convex subsets. In many applications one requires something more, namely finding a common point of closed convex subsets which minimizes a continuous convex function. The latter requirement leads to an application of the superiorization methodology which is actually settled between methods for convex feasibility problem and the convex constrained minimization. Inspired by the superiorization idea we introduce a method which sequentially applies a long-step algorithm for a sequence of convex feasibility problems; the method employs quasi-nonexpansive operators as well as subgradient projections with level control and does not require evaluation of the metric projection. We replace a perturbation of the iterations (applied in the superiorization methodology) by a perturbation of the current level in minimizing the objective function. We consider the method in the Euclidean space in order to guarantee the strong convergence, although the method is well defined in a Hilbert space.

Three-loop hard-thermal-loop perturbation theory thermodynamics at finite temperature and finite baryonic and isospin chemical potential

NASA Astrophysics Data System (ADS)

Andersen, Jens O.; Haque, Najmul; Mustafa, Munshi G.; Strickland, Michael

2016-03-01

In a previous paper [N. Haque et al., J. High Energy Phys. 05 (2014) 27], we calculated the three-loop thermodynamic potential of QCD at finite temperature T and quark chemical potentials μq using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The result allows us to study the thermodynamics of QCD at finite temperature and finite baryon, strangeness, and isospin chemical potentials μB, μS, and μI. We calculate the pressure at nonzero μB and μI with μS=0 , and the energy density, the entropy density, the trace anomaly, and the speed of sound at nonzero μI with μB=μS=0 . The second- and fourth-order isospin susceptibilities are calculated at μB=μS=μI=0 . Our results can be directly compared to lattice QCD without Taylor expansions around μq=0 since QCD has no sign problem at μB=μS=0 and finite isospin chemical potential μI.

Robustness of controllability and observability of linear time-varying systems with application to the emergency control of power systems

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

Sastry, S. S.; Desoer, C. A.

1980-01-01

Fixed point methods from nonlinear anaysis are used to establish conditions under which the uniform complete controllability of linear time-varying systems is preserved under non-linear perturbations in the state dynamics and the zero-input uniform complete observability of linear time-varying systems is preserved under non-linear perturbation in the state dynamics and output read out map. Algorithms for computing the specific input to steer the perturbed systems from a given initial state to a given final state are also presented. As an application, a very specific emergency control of an interconnected power system is formulated as a steering problem and it ismore » shown that this emergency control is indeed possible in finite time.« less

A finite-element-based perturbation model for the rotordynamic analysis of shrouded pump impellers: Part 2: User's guide

NASA Technical Reports Server (NTRS)

Baskharone, Erian A.

1993-01-01

This report describes the computational steps involved in executing a finite-element-based perturbation model for computing the rotor dynamic coefficients of a shrouded pump impeller or a simple seal. These arise from the fluid/rotor interaction in the clearance gap. In addition to the sample cases, the computational procedure also applies to a separate category of problems referred to as the 'seal-like' category. The problem, in this case, concerns a shrouded impeller, with the exception that the secondary, or leakage, passage is totally isolated from the primary-flow passage. The difference between this and the pump problem is that the former is analytically of the simple 'seal-like' configuration, with two (inlet and exit) flow-permeable stations, while the latter constitutes a double-entry / double-discharge flow problem. In all cases, the problem is that of a rotor clearance gap. The problem here is that of a rotor excitation in the form of a cylindrical whirl around the housing centerline for a smooth annular seal. In its centered operation mode, the rotor is assumed to give rise to an axisymmetric flow field in the clearance gap. As a result, problems involving longitudinal or helical grooves, in the rotor or housing surfaces, go beyond the code capabilities. Discarding, for the moment, the pre- and post-processing phases, the bulk of the computational procedure consists of two main steps. The first is aimed at producing the axisymmetric 'zeroth-order' flow solution in the given flow domain. Detailed description of this problem, including the flow-governing equations, turbulence closure, boundary conditions, and the finite-element formulation, was covered by Baskharone and Hensel. The second main step is where the perturbation model is implemented, with the input being the centered-rotor 'zeroth-order' flow solution and a prescribed whirl frequency ratio (whirl frequency divided by the impeller speed). The computational domain, in the latter case, is treated as three dimensional, with the number of computational planes in the circumferential direction being specified a priori. The reader is reminded that the deformations in the finite elements are all infinitesimally small because the rotor eccentricity itself is a virtual displacement. This explains why we have generically termed the perturbation model the 'virtually' deformable finite-element category. The primary outcome of implementing the perturbation model is the tangential and radial components, F(sub theta)(sup *) and F(sub r)(sup *) of the fluid-exerted force on the rotor surface due to the whirling motion. Repetitive execution of the perturbation model subprogram over a sufficient range of whirl frequency ratios, and subsequent interpolation of these fluid forces, using the least-square method, finally enable the user to compute the impeller rotor dynamic coefficients of the fluid/rotor interaction. These are the direct and cross-coupled stiffness, damping, and inertia effects of the fluid/rotor interaction.

A Non-Intrusive Algorithm for Sensitivity Analysis of Chaotic Flow Simulations

NASA Technical Reports Server (NTRS)

Blonigan, Patrick J.; Wang, Qiqi; Nielsen, Eric J.; Diskin, Boris

2017-01-01

We demonstrate a novel algorithm for computing the sensitivity of statistics in chaotic flow simulations to parameter perturbations. The algorithm is non-intrusive but requires exposing an interface. Based on the principle of shadowing in dynamical systems, this algorithm is designed to reduce the effect of the sampling error in computing sensitivity of statistics in chaotic simulations. We compare the effectiveness of this method to that of the conventional finite difference method.

Optimal Transient Growth of Submesoscale Baroclinic Instabilities

NASA Astrophysics Data System (ADS)

White, Brian; Zemskova, Varvara; Passaggia, Pierre-Yves

2016-11-01

Submesoscale instabilities are analyzed using a transient growth approach to determine the optimal perturbation for a rotating Boussinesq fluid subject to baroclinic instabilities. We consider a base flow with uniform shear and stratification and consider the non-normal evolution over finite-time horizons of linear perturbations in an ageostrophic, non-hydrostatic regime. Stone (1966, 1971) showed that the stability of the base flow to normal modes depends on the Rossby and Richardson numbers, with instabilities ranging from geostrophic (Ro -> 0) and ageostrophic (finite Ro) baroclinic modes to symmetric (Ri < 1 , Ro > 1) and Kelvin-Helmholtz (Ri < 1 / 4) modes. Non-normal transient growth, initiated by localized optimal wave packets, represents a faster mechanism for the growth of perturbations and may provide an energetic link between large-scale flows in geostrophic balance and dissipation scales via submesoscale instabilities. Here we consider two- and three-dimensional optimal perturbations by means of direct-adjoint iterations of the linearized Boussinesq Navier-Stokes equations to determine the form of the optimal perturbation, the optimal energy gain, and the characteristics of the most unstable perturbation.

Optimization of block-floating-point realizations for digital controllers with finite-word-length considerations.

PubMed

Wu, Jun; Hu, Xie-he; Chen, Sheng; Chu, Jian

2003-01-01

The closed-loop stability issue of finite-precision realizations was investigated for digital controllers implemented in block-floating-point format. The controller coefficient perturbation was analyzed resulting from using finite word length (FWL) block-floating-point representation scheme. A block-floating-point FWL closed-loop stability measure was derived which considers both the dynamic range and precision. To facilitate the design of optimal finite-precision controller realizations, a computationally tractable block-floating-point FWL closed-loop stability measure was then introduced and the method of computing the value of this measure for a given controller realization was developed. The optimal controller realization is defined as the solution that maximizes the corresponding measure, and a numerical optimization approach was adopted to solve the resulting optimal realization problem. A numerical example was used to illustrate the design procedure and to compare the optimal controller realization with the initial realization.

On the divergences of inflationary superhorizon perturbations

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

Enqvist, K; Nurmi, S; Podolsky, D

2008-04-15

We discuss the infrared divergences that appear to plague cosmological perturbation theory. We show that, within the stochastic framework, they are regulated by eternal inflation so that the theory predicts finite fluctuations. Using the {Delta}N formalism to one loop, we demonstrate that the infrared modes can be absorbed into additive constants and the coefficients of the diagrammatic expansion for the connected parts of two-and three-point functions of the curvature perturbation. As a result, the use of any infrared cutoff below the scale of eternal inflation is permitted, provided that the background fields are appropriately redefined. The natural choice for themore » infrared cutoff would, of course, be the present horizon; other choices manifest themselves in the running of the correlators. We also demonstrate that it is possible to define observables that are renormalization-group-invariant. As an example, we derive a non-perturbative, infrared finite and renormalization point-independent relation between the two-point correlators of the curvature perturbation for the case of the free single field.« less

Perturbative expansions from Monte Carlo simulations at weak coupling: Wilson loops and the static-quark self-energy

NASA Astrophysics Data System (ADS)

Trottier, H. D.; Shakespeare, N. H.; Lepage, G. P.; MacKenzie, P. B.

2002-05-01

Perturbative coefficients for Wilson loops and the static-quark self-energy are extracted from Monte Carlo simulations at weak coupling. The lattice volumes and couplings are chosen to ensure that the lattice momenta are all perturbative. Twisted boundary conditions are used to eliminate the effects of lattice zero modes and to suppress nonperturbative finite-volume effects due to Z(3) phases. Simulations of the Wilson gluon action are done with both periodic and twisted boundary conditions, and over a wide range of lattice volumes (from 34 to 164) and couplings (from β~9 to β~60). A high precision comparison is made between the simulation data and results from finite-volume lattice perturbation theory. The Monte Carlo results are shown to be in excellent agreement with perturbation theory through second order. New results for third-order coefficients for a number of Wilson loops and the static-quark self-energy are reported.

Non-perturbative determination of improvement b-coefficients in Nf = 3

NASA Astrophysics Data System (ADS)

Giulia Maria de Divitiis1, 2**, Maurizio Firrotta1, 2, Jochen Heitger3, Carl Christian Köster3; Anastassios Vladikas2

2018-03-01

We present our preliminary results of the non-perturbative determination of the valence mass dependent coefficients bA - bP and bm as well as the ratio ZPZm=ZA entering the flavour non-singlet PCAC relation in lattice QCD with Nf = 3 dynamical flavours. We apply the method proposed in the past for quenched approximation and Nf = 2 cases, employing a set of finite-volume ALPHA configurations with Schrödinger functional boundary conditions, generated with O(a) improved Wilson fermions and the tree-level Symanzik-improved gauge action for a range of couplings relevant for simulations at lattice spacings of about 0.09 fm and below.

Creation of a magnetic barrier at a noble q close to physical midpoint between two resonant surfaces in the ASDEX UG tokamak

NASA Astrophysics Data System (ADS)

Vazquez, Justin; Ali, Halima; Punjabi, Alkesh

2009-11-01

Ciraolo, Vittot and Chandre method of building invariant manifolds inside chaos in Hamiltonian systems [Ali H. and Punjabi A, Plasma Phys. Control. Fusion, 49, 1565--1582 (2007)] is used in the ASDEX UG tokamak. In this method, a second order perturbation is added to the perturbed Hamiltonian [op cit]. It creates an invariant torus inside the chaos, and reduces the plasma transport. The perturbation that is added to the equilibrium Hamiltonian is at least an order of magnitude smaller than the perturbation that causes chaos. This additional term has a finite, limited number of Fourier modes. Resonant magnetic perturbations (m,n) = (3,2)+(4,3) are added to the field line Hamiltonian for the ASDEX UG. An area-preserving map for the field line trajectories in the ASDEX UG is used. The common amplitude δ of these modes that gives complete chaos between the resonant surfaces ψ43 and ψ32 is determined. A magnetic barrier is built at a surface with noble q that is very nearly equals to the q at the physical midpoint between the two resonant surfaces. The maximum amplitude of magnetic perturbation for which this barrier can be sustained is determined. This work is supported by US Department of Energy grants DE-FG02-07ER54937, DE-FG02-01ER54624 and DE-FG02-04ER54793.

Cellular interface morphologies in directional solidification. III - The effects of heat transfer and solid diffusivity

NASA Technical Reports Server (NTRS)

Ungar, Lyle H.; Bennett, Mark J.; Brown, Robert A.

1985-01-01

The shape and stability of two-dimensional finite-amplitude cellular interfaces arising during directional solidification are compared for several solidification models that account differently for latent heat released at the interface, unequal thermal conductivities of melt and solid, and solute diffusivity in the solid. Finite-element analysis and computer-implemented perturbation methods are used to analyze the families of steadily growing cellular forms that evolve from the planar state. In all models a secondary bifurcation between different families of finite-amplitude cells exists that halves the spatial wavelength of the stable interface. The quantitative location of this transition is very dependent on the details of the model. Large amounts of solute diffusion in the solid retard the growth of large-amplitude cells.

Exploring the spectrum of planar AdS4 /CFT3 at finite coupling

NASA Astrophysics Data System (ADS)

Bombardelli, Diego; Cavaglià, Andrea; Conti, Riccardo; Tateo, Roberto

2018-04-01

The Quantum Spectral Curve (QSC) equations for planar N=6 super-conformal Chern-Simons (SCS) are solved numerically at finite values of the coupling constant for states in the sl(2\\Big|1) sector. New weak coupling results for conformal dimensions of operators outside the sl(2) -like sector are obtained by adapting a recently proposed algorithm for the QSC perturbative solution. Besides being interesting in their own right, these perturbative results are necessary initial inputs for the numerical algorithm to converge on the correct solution. The non-perturbative numerical outcomes nicely interpolate between the weak coupling and the known semiclassical expansions, and novel strong coupling exact results are deduced from the numerics. Finally, the existence of contour crossing singularities in the TBA equations for the operator 20 is ruled out by our analysis. The results of this paper are an important test of the QSC formalism for this model, open the way to new quantitative studies and provide further evidence in favour of the conjectured weak/strong coupling duality between N=6 SCS and type IIA superstring theory on AdS4 × CP 3. Attached to the arXiv submission, a Mathematica implementation of the numerical method and ancillary files containing the numerical results are provided.

Approximate non-linear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-03-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-waves scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform (GRT). After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic non-linear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P-wave and S-wave information.

Approximate nonlinear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-07-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-wave scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform. After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic nonlinear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P- and S-wave information.

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

NASA Astrophysics Data System (ADS)

Yu, Di; Ji, Xiang Yang

2018-01-01

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

Finite-frequency sensitivity kernels for global seismic wave propagation based upon adjoint methods

NASA Astrophysics Data System (ADS)

Liu, Qinya; Tromp, Jeroen

2008-07-01

We determine adjoint equations and Fréchet kernels for global seismic wave propagation based upon a Lagrange multiplier method. We start from the equations of motion for a rotating, self-gravitating earth model initially in hydrostatic equilibrium, and derive the corresponding adjoint equations that involve motions on an earth model that rotates in the opposite direction. Variations in the misfit function χ then may be expressed as , where δlnm = δm/m denotes relative model perturbations in the volume V, δlnd denotes relative topographic variations on solid-solid or fluid-solid boundaries Σ, and ∇Σδlnd denotes surface gradients in relative topographic variations on fluid-solid boundaries ΣFS. The 3-D Fréchet kernel Km determines the sensitivity to model perturbations δlnm, and the 2-D kernels Kd and Kd determine the sensitivity to topographic variations δlnd. We demonstrate also how anelasticity may be incorporated within the framework of adjoint methods. Finite-frequency sensitivity kernels are calculated by simultaneously computing the adjoint wavefield forward in time and reconstructing the regular wavefield backward in time. Both the forward and adjoint simulations are based upon a spectral-element method. We apply the adjoint technique to generate finite-frequency traveltime kernels for global seismic phases (P, Pdiff, PKP, S, SKS, depth phases, surface-reflected phases, surface waves, etc.) in both 1-D and 3-D earth models. For 1-D models these adjoint-generated kernels generally agree well with results obtained from ray-based methods. However, adjoint methods do not have the same theoretical limitations as ray-based methods, and can produce sensitivity kernels for any given phase in any 3-D earth model. The Fréchet kernels presented in this paper illustrate the sensitivity of seismic observations to structural parameters and topography on internal discontinuities. These kernels form the basis of future 3-D tomographic inversions.

Extended pseudo-screen migration with multiple reference velocities

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

Huang, Lian-Jie; Fehler, M.C.

1997-11-01

The pseudo-screen propagator is a kind of one way wave propagation based on the local Born approximation. The problem of the propagator is that it is difficult to calculate the scattered fields when the velocity perturbation is large; not to mention the accuracy of the propagator. We develop an extended pseudo-screen propagator by introducing different reference velocities in different regions of a medium to ensure the condition of small perturbation. The exploding reflector data for a 2D slice of the SEG/EAEG 3D salt model is generated by a finite difference scheme to test the feasibility of the method. The migrationmore » result demonstrates that the method can handle severe lateral velocity variations and provides high quality images for complex structures.« less

Confinement with Perturbation Theory, After All?

NASA Astrophysics Data System (ADS)

Hoyer, Paul

2015-09-01

I call attention to the possibility that QCD bound states (hadrons) could be derived using rigorous Hamiltonian, perturbative methods. Solving Gauss' law for A 0 with a non-vanishing boundary condition at spatial infinity gives an linear potential for color singlet and qqq states. These states are Poincaré and gauge covariant and thus can serve as initial states of a perturbative expansion, replacing the conventional free in and out states. The coupling freezes at , allowing reasonable convergence. The bound states have a sea of pairs, while transverse gluons contribute only at . Pair creation in the linear A 0 potential leads to string breaking and hadron loop corrections. These corrections give finite widths to excited states, as required by unitarity. Several of these features have been verified analytically in D = 1 + 1 dimensions, and some in D = 3 + 1.

Pinning by rare defects and effective mobility for elastic interfaces in high dimensions

NASA Astrophysics Data System (ADS)

Cao, Xiangyu; Démery, Vincent; Rosso, Alberto

2018-06-01

The existence of a depinning transition for a high dimensional interface in a weakly disordered medium is controversial. Following Larkin arguments and a perturbative expansion, one expects a linear response with a renormalized mobility . In this paper, we compare these predictions with the exact solution of a fully connected model, which displays a finite critical force . At small disorder, we unveil an intermediary linear regime for characterized by the renormalized mobility . Our results suggest that in high dimension the critical force is always finite and determined by the effect of rare impurities that is missed by the perturbative expansion. However, the perturbative expansion correctly describes an intermediate regime that should be visible at small disorder.

New Methods in Non-Perturbative QCD

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

Unsal, Mithat

2017-01-31

In this work, we investigate the properties of quantum chromodynamics (QCD), by using newly developing mathematics and physics formalisms. Almost all of the mass in the visible universe emerges from a quantum chromodynamics (QCD), which has a completely negligible microscopic mass content. An intimately related issue in QCD is the quark confinement problem. Answers to non-perturbative questions in QCD remained largely elusive despite much effort over the years. It is also believed that the usual perturbation theory is inadequate to address these kinds of problems. Perturbation theory gives a divergent asymptotic series (even when the theory is properly renormalized), andmore » there are non-perturbative phenomena which never appear at any order in perturbation theory. Recently, a fascinating bridge between perturbation theory and non-perturbative effects has been found: a formalism called resurgence theory in mathematics tells us that perturbative data and non-perturbative data are intimately related. Translating this to the language of quantum field theory, it turns out that non-perturbative information is present in a coded form in perturbation theory and it can be decoded. We take advantage of this feature, which is particularly useful to understand some unresolved mysteries of QCD from first principles. In particular, we use: a) Circle compactifications which provide a semi-classical window to study confinement and mass gap problems, and calculable prototypes of the deconfinement phase transition; b) Resurgence theory and transseries which provide a unified framework for perturbative and non-perturbative expansion; c) Analytic continuation of path integrals and Lefschetz thimbles which may be useful to address sign problem in QCD at finite density.« less

Ground state energies from converging and diverging power series expansions

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

Lisowski, C.; Norris, S.; Pelphrey, R.

2016-10-15

It is often assumed that bound states of quantum mechanical systems are intrinsically non-perturbative in nature and therefore any power series expansion methods should be inapplicable to predict the energies for attractive potentials. However, if the spatial domain of the Schrödinger Hamiltonian for attractive one-dimensional potentials is confined to a finite length L, the usual Rayleigh–Schrödinger perturbation theory can converge rapidly and is perfectly accurate in the weak-binding region where the ground state’s spatial extension is comparable to L. Once the binding strength is so strong that the ground state’s extension is less than L, the power expansion becomes divergent,more » consistent with the expectation that bound states are non-perturbative. However, we propose a new truncated Borel-like summation technique that can recover the bound state energy from the diverging sum. We also show that perturbation theory becomes divergent in the vicinity of an avoided-level crossing. Here the same numerical summation technique can be applied to reproduce the energies from the diverging perturbative sums.« less

The nuclear size and mass effects on muonic hydrogen-like atoms embedded in Debye plasma

NASA Astrophysics Data System (ADS)

Poszwa, A.; Bahar, M. K.; Soylu, A.

2016-10-01

Effects of finite nuclear size and finite nuclear mass are investigated for muonic atoms and muonic ions embedded in the Debye plasma. Both nuclear charge radii and nuclear masses are taken into account with experimentally determined values. In particular, isotope shifts of bound state energies, radial probability densities, transition energies, and binding energies for several atoms are studied as functions of Debye length. The theoretical model based on semianalytical calculations, the Sturmian expansion method, and the perturbative approach has been constructed, in the nonrelativistic frame. For some limiting cases, the comparison with previous most accurate literature results has been made.

A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory

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

Lindesay, James V

2001-05-11

We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require ''renormalization'' ormore » ''dressing'' of these parameters to connect them to the boundary states.« less

Shape design sensitivity analysis and optimization of three dimensional elastic solids using geometric modeling and automatic regridding. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Yao, Tse-Min; Choi, Kyung K.

1987-01-01

An automatic regridding method and a three dimensional shape design parameterization technique were constructed and integrated into a unified theory of shape design sensitivity analysis. An algorithm was developed for general shape design sensitivity analysis of three dimensional eleastic solids. Numerical implementation of this shape design sensitivity analysis method was carried out using the finite element code ANSYS. The unified theory of shape design sensitivity analysis uses the material derivative of continuum mechanics with a design velocity field that represents shape change effects over the structural design. Automatic regridding methods were developed by generating a domain velocity field with boundary displacement method. Shape design parameterization for three dimensional surface design problems was illustrated using a Bezier surface with boundary perturbations that depend linearly on the perturbation of design parameters. A linearization method of optimization, LINRM, was used to obtain optimum shapes. Three examples from different engineering disciplines were investigated to demonstrate the accuracy and versatility of this shape design sensitivity analysis method.

Domain Derivatives in Dielectric Rough Surface Scattering

DTIC Science & Technology

2015-01-01

and require the gradient of the objective function in the unknown model parameter vector at each stage of iteration. For large N, finite...differencing becomes numerically intensive, and an efficient alternative is domain differentiation in which the full gradient is obtained by solving a single...derivative calculation of the gradient for a locally perturbed dielectric interface. The method is non-variational, and algebraic in nature in that it

Unsteady transonic flows - Introduction, current trends, applications

NASA Technical Reports Server (NTRS)

Yates, E. C., Jr.

1985-01-01

The computational treatment of unsteady transonic flows is discussed, reviewing the historical development and current techniques. The fundamental physical principles are outlined; the governing equations are introduced; three-dimensional linearized and two-dimensional linear-perturbation theories in frequency domain are described in detail; and consideration is given to frequency-domain FEMs and time-domain finite-difference and integral-equation methods. Extensive graphs and diagrams are included.

Numerical algorithms for computations of feedback laws arising in control of flexible systems

NASA Technical Reports Server (NTRS)

Lasiecka, Irena

1989-01-01

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

Implementation of Hybrid V-Cycle Multilevel Methods for Mixed Finite Element Systems with Penalty

NASA Technical Reports Server (NTRS)

Lai, Chen-Yao G.

1996-01-01

The goal of this paper is the implementation of hybrid V-cycle hierarchical multilevel methods for the indefinite discrete systems which arise when a mixed finite element approximation is used to solve elliptic boundary value problems. By introducing a penalty parameter, the perturbed indefinite system can be reduced to a symmetric positive definite system containing the small penalty parameter for the velocity unknown alone. We stabilize the hierarchical spatial decomposition approach proposed by Cai, Goldstein, and Pasciak for the reduced system. We demonstrate that the relative condition number of the preconditioner is bounded uniformly with respect to the penalty parameter, the number of levels and possible jumps of the coefficients as long as they occur only across the edges of the coarsest elements.

On the application of transonic similarity rules to wings of finite span

NASA Technical Reports Server (NTRS)

Spreiter, John R

1953-01-01

The transonic aerodynamic characteristics of wings of finite span are discussed from the point of view of a unified small perturbation theory for subsonic, transonic, and supersonic flows about thin wings. This approach avoids certain ambiguities which appear if one studies transonic flows by means of equations derived under the more restrictive assumption that the local velocities are everywhere close to sonic velocity. The relation between the two methods of analysis of transonic flow is examined, the similarity rules and known solutions of transonic flow theory are reviewed, and the asymptotic behavior of the lift, drag, and pitching-moment characteristics of wings of large and small aspect ratio is discussed. It is shown that certain methods of data presentation are advantageous for the effective display of these characteristics.

Cosmological perturbation theory using the FFTLog: formalism and connection to QFT loop integrals

NASA Astrophysics Data System (ADS)

Simonović, Marko; Baldauf, Tobias; Zaldarriaga, Matias; Carrasco, John Joseph; Kollmeier, Juna A.

2018-04-01

We present a new method for calculating loops in cosmological perturbation theory. This method is based on approximating a ΛCDM-like cosmology as a finite sum of complex power-law universes. The decomposition is naturally achieved using an FFTLog algorithm. For power-law cosmologies, all loop integrals are formally equivalent to loop integrals of massless quantum field theory. These integrals have analytic solutions in terms of generalized hypergeometric functions. We provide explicit formulae for the one-loop and the two-loop power spectrum and the one-loop bispectrum. A chief advantage of our approach is that the difficult part of the calculation is cosmology independent, need be done only once, and can be recycled for any relevant predictions. Evaluation of standard loop diagrams then boils down to a simple matrix multiplication. We demonstrate the promise of this method for applications to higher multiplicity/loop correlation functions.

A high-order perturbation of surfaces method for scattering of linear waves by periodic multiply layered gratings in two and three dimensions

NASA Astrophysics Data System (ADS)

Hong, Youngjoon; Nicholls, David P.

2017-09-01

The capability to rapidly and robustly simulate the scattering of linear waves by periodic, multiply layered media in two and three dimensions is crucial in many engineering applications. In this regard, we present a High-Order Perturbation of Surfaces method for linear wave scattering in a multiply layered periodic medium to find an accurate numerical solution of the governing Helmholtz equations. For this we truncate the bi-infinite computational domain to a finite one with artificial boundaries, above and below the structure, and enforce transparent boundary conditions there via Dirichlet-Neumann Operators. This is followed by a Transformed Field Expansion resulting in a Fourier collocation, Legendre-Galerkin, Taylor series method for solving the problem in a transformed set of coordinates. Assorted numerical simulations display the spectral convergence of the proposed algorithm.

Finite-frequency sensitivity kernels for head waves

NASA Astrophysics Data System (ADS)

Zhang, Zhigang; Shen, Yang; Zhao, Li

2007-11-01

Head waves are extremely important in determining the structure of the predominantly layered Earth. While several recent studies have shown the diffractive nature and the 3-D Fréchet kernels of finite-frequency turning waves, analogues of head waves in a continuous velocity structure, the finite-frequency effects and sensitivity kernels of head waves are yet to be carefully examined. We present the results of a numerical study focusing on the finite-frequency effects of head waves. Our model has a low-velocity layer over a high-velocity half-space and a cylindrical-shaped velocity perturbation placed beneath the interface at different locations. A 3-D finite-difference method is used to calculate synthetic waveforms. Traveltime and amplitude anomalies are measured by the cross-correlation of synthetic seismograms from models with and without the velocity perturbation and are compared to the 3-D sensitivity kernels constructed from full waveform simulations. The results show that the head wave arrival-time and amplitude are influenced by the velocity structure surrounding the ray path in a pattern that is consistent with the Fresnel zones. Unlike the `banana-doughnut' traveltime sensitivity kernels of turning waves, the traveltime sensitivity of the head wave along the ray path below the interface is weak, but non-zero. Below the ray path, the traveltime sensitivity reaches the maximum (absolute value) at a depth that depends on the wavelength and propagation distance. The sensitivity kernels vary with the vertical velocity gradient in the lower layer, but the variation is relatively small at short propagation distances when the vertical velocity gradient is within the range of the commonly accepted values. Finally, the depression or shoaling of the interface results in increased or decreased sensitivities, respectively, beneath the interface topography.

Solution of transonic flows by an integro-differential equation method

NASA Technical Reports Server (NTRS)

Ogana, W.

1978-01-01

Solutions of steady transonic flow past a two-dimensional airfoil are obtained from a singular integro-differential equation which involves a tangential derivative of the perturbation velocity potential. Subcritical flows are solved by taking central differences everywhere. For supercritical flows with shocks, central differences are taken in subsonic flow regions and backward differences in supersonic flow regions. The method is applied to a nonlifting parabolic-arc airfoil and to a lifting NACA 0012 airfoil. Results compare favorably with those of finite-difference schemes.

SU-F-T-192: Study of Robustness Analysis Method of Multiple Field Optimized IMPT Plans for Head & Neck Patients

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

Li, Y; Wang, X; Li, H

Purpose: Proton therapy is more sensitive to uncertainties than photon treatments due to protons’ finite range depending on the tissue density. Worst case scenario (WCS) method originally proposed by Lomax has been adopted in our institute for robustness analysis of IMPT plans. This work demonstrates that WCS method is sufficient enough to take into account of the uncertainties which could be encountered during daily clinical treatment. Methods: A fast and approximate dose calculation method is developed to calculate the dose for the IMPT plan under different setup and range uncertainties. Effects of two factors, inversed square factor and range uncertainty,more » are explored. WCS robustness analysis method was evaluated using this fast dose calculation method. The worst-case dose distribution was generated by shifting isocenter by 3 mm along x,y and z directions and modifying stopping power ratios by ±3.5%. 1000 randomly perturbed cases in proton range and x, yz directions were created and the corresponding dose distributions were calculated using this approximated method. DVH and dosimetric indexes of all 1000 perturbed cases were calculated and compared with the result using worst case scenario method. Results: The distributions of dosimetric indexes of 1000 perturbed cases were generated and compared with the results using worst case scenario. For D95 of CTVs, at least 97% of 1000 perturbed cases show higher values than the one of worst case scenario. For D5 of CTVs, at least 98% of perturbed cases have lower values than worst case scenario. Conclusion: By extensively calculating the dose distributions under random uncertainties, WCS method was verified to be reliable in evaluating the robustness level of MFO IMPT plans of H&N patients. The extensively sampling approach using fast approximated method could be used in evaluating the effects of different factors on the robustness level of IMPT plans in the future.« less

A finite difference method for the solution of the transonic flow around harmonically oscillating wings

NASA Technical Reports Server (NTRS)

Ehlers, E. F.

1974-01-01

A finite difference method for the solution of the transonic flow about a harmonically oscillating wing is presented. The partial differential equation for the unsteady transonic flow was linearized by dividing the flow into separate steady and unsteady perturbation velocity potentials and by assuming small amplitudes of harmonic oscillation. The resulting linear differential equation is of mixed type, being elliptic or hyperbolic whereever the steady flow equation is elliptic or hyperbolic. Central differences were used for all derivatives except at supersonic points where backward differencing was used for the streamwise direction. Detailed formulas and procedures are described in sufficient detail for programming on high speed computers. To test the method, the problem of the oscillating flap on a NACA 64A006 airfoil was programmed. The numerical procedure was found to be stable and convergent even in regions of local supersonic flow with shocks.

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

Ghosh, Debojyoti; Constantinescu, Emil M.

The numerical simulation of meso-, convective-, and microscale atmospheric flows requires the solution of the Euler or the Navier-Stokes equations. Nonhydrostatic weather prediction algorithms often solve the equations in terms of derived quantities such as Exner pressure and potential temperature (and are thus not conservative) and/or as perturbations to the hydrostatically balanced equilibrium state. This paper presents a well-balanced, conservative finite difference formulation for the Euler equations with a gravitational source term, where the governing equations are solved as conservation laws for mass, momentum, and energy. Preservation of the hydrostatic balance to machine precision by the discretized equations is essentialmore » because atmospheric phenomena are often small perturbations to this balance. The proposed algorithm uses the weighted essentially nonoscillatory and compact-reconstruction weighted essentially nonoscillatory schemes for spatial discretization that yields high-order accurate solutions for smooth flows and is essentially nonoscillatory across strong gradients; however, the well-balanced formulation may be used with other conservative finite difference methods. The performance of the algorithm is demonstrated on test problems as well as benchmark atmospheric flow problems, and the results are verified with those in the literature.« less

Subleading soft graviton theorem for loop amplitudes

NASA Astrophysics Data System (ADS)

Sen, Ashoke

2017-11-01

Superstring field theory gives expressions for heterotic and type II string loop amplitudes that are free from ultraviolet and infrared divergences when the number of non-compact space-time dimensions is five or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton. We also prove the leading soft graviton theorem for arbitrary number of finite energy external states and arbitrary number of soft gravitons. Since our analysis is based on general properties of one particle irreducible effective action, the results are valid in any theory of quantum gravity that gives finite result for the S-matrix order by order in perturbation theory without violating general coordinate invariance.

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

Renormalization-group theory for finite-size scaling in extreme statistics

NASA Astrophysics Data System (ADS)

Györgyi, G.; Moloney, N. R.; Ozogány, K.; Rácz, Z.; Droz, M.

2010-04-01

We present a renormalization-group (RG) approach to explain universal features of extreme statistics applied here to independent identically distributed variables. The outlines of the theory have been described in a previous paper, the main result being that finite-size shape corrections to the limit distribution can be obtained from a linearization of the RG transformation near a fixed point, leading to the computation of stable perturbations as eigenfunctions. Here we show details of the RG theory which exhibit remarkable similarities to the RG known in statistical physics. Besides the fixed points explaining universality, and the least stable eigendirections accounting for convergence rates and shape corrections, the similarities include marginally stable perturbations which turn out to be generic for the Fisher-Tippett-Gumbel class. Distribution functions containing unstable perturbations are also considered. We find that, after a transitory divergence, they return to the universal fixed line at the same or at a different point depending on the type of perturbation.

Grid sensitivity capability for large scale structures

NASA Technical Reports Server (NTRS)

Nagendra, Gopal K.; Wallerstein, David V.

1989-01-01

The considerations and the resultant approach used to implement design sensitivity capability for grids into a large scale, general purpose finite element system (MSC/NASTRAN) are presented. The design variables are grid perturbations with a rather general linking capability. Moreover, shape and sizing variables may be linked together. The design is general enough to facilitate geometric modeling techniques for generating design variable linking schemes in an easy and straightforward manner. Test cases have been run and validated by comparison with the overall finite difference method. The linking of a design sensitivity capability for shape variables in MSC/NASTRAN with an optimizer would give designers a powerful, automated tool to carry out practical optimization design of real life, complicated structures.

A dimension-wise analysis method for the structural-acoustic system with interval parameters

NASA Astrophysics Data System (ADS)

Xu, Menghui; Du, Jianke; Wang, Chong; Li, Yunlong

2017-04-01

The interval structural-acoustic analysis is mainly accomplished by interval and subinterval perturbation methods. Potential limitations for these intrusive methods include overestimation or interval translation effect for the former and prohibitive computational cost for the latter. In this paper, a dimension-wise analysis method is thus proposed to overcome these potential limitations. In this method, a sectional curve of the system response surface along each input dimensionality is firstly extracted, the minimal and maximal points of which are identified based on its Legendre polynomial approximation. And two input vectors, i.e. the minimal and maximal input vectors, are dimension-wisely assembled by the minimal and maximal points of all sectional curves. Finally, the lower and upper bounds of system response are computed by deterministic finite element analysis at the two input vectors. Two numerical examples are studied to demonstrate the effectiveness of the proposed method and show that, compared to the interval and subinterval perturbation method, a better accuracy is achieved without much compromise on efficiency by the proposed method, especially for nonlinear problems with large interval parameters.

Perturbative two- and three-loop coefficients from large β Monte Carlo

NASA Astrophysics Data System (ADS)

Lepage, G. P.; Mackenzie, P. B.; Shakespeare, N. H.; Trottier, H. D.

Perturbative coefficients for Wilson loops and the static quark self-energy are extracted from Monte Carlo simulations at large β on finite volumes, where all the lattice momenta are large. The Monte Carlo results are in excellent agreement with perturbation theory through second order. New results for third order coefficients are reported. Twisted boundary conditions are used to eliminate zero modes and to suppress Z3 tunneling.

Perturbative two- and three-loop coefficients from large b Monte Carlo

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

G.P. Lepage; P.B. Mackenzie; N.H. Shakespeare

1999-10-18

Perturbative coefficients for Wilson loops and the static quark self-energy are extracted from Monte Carlo simulations at large {beta} on finite volumes, where all the lattice momenta are large. The Monte Carlo results are in excellent agreement with perturbation theory through second order. New results for third order coefficients are reported. Twisted boundary conditions are used to eliminate zero modes and to suppress Z{sub 3} tunneling.

A Renormalisation Group Method. V. A Single Renormalisation Group Step

NASA Astrophysics Data System (ADS)

Brydges, David C.; Slade, Gordon

2015-05-01

This paper is the fifth in a series devoted to the development of a rigorous renormalisation group method applicable to lattice field theories containing boson and/or fermion fields, and comprises the core of the method. In the renormalisation group method, increasingly large scales are studied in a progressive manner, with an interaction parametrised by a field polynomial which evolves with the scale under the renormalisation group map. In our context, the progressive analysis is performed via a finite-range covariance decomposition. Perturbative calculations are used to track the flow of the coupling constants of the evolving polynomial, but on their own perturbative calculations are insufficient to control error terms and to obtain mathematically rigorous results. In this paper, we define an additional non-perturbative coordinate, which together with the flow of coupling constants defines the complete evolution of the renormalisation group map. We specify conditions under which the non-perturbative coordinate is contractive under a single renormalisation group step. Our framework is essentially combinatorial, but its implementation relies on analytic results developed earlier in the series of papers. The results of this paper are applied elsewhere to analyse the critical behaviour of the 4-dimensional continuous-time weakly self-avoiding walk and of the 4-dimensional -component model. In particular, the existence of a logarithmic correction to mean-field scaling for the susceptibility can be proved for both models, together with other facts about critical exponents and critical behaviour.

Global Discontinuity Structure of the Mantle Transition Zone from Finite-Frequency Tomography of SS Precursors

NASA Astrophysics Data System (ADS)

Guo, Z.; Zhou, Y.

2017-12-01

We report global structure of the 410-km and 660-km discontinuities from finite-frequency tomography using frequency-dependent traveltime measurements of SS precursors recorded at the Global Seismological Network (GSN). Finite-frequency sensitivity kernels for discontinuity depth perturbations are calculated in the framework of traveling-wave mode coupling. We parametrize the global discontinuities using a set of spherical triangular grid points and solve the tomographic inverse problem based on singular value decomposition. Our global 410-km and 660-km discontinuity models reveal distinctly different characteristics beneath the oceans and subduction zones. In general, oceanic regions are associated with a thinner mantle transition zone and depth perturbations of the 410-km and 660-km discontinuities are anti-correlated, in agreement with a thermal origin and an overall warm and dry mantle beneath the oceans. The perturbations are not uniform throughout the oceans but show strong small-scale variations, indicating complex processes in the mantle transition zone. In major subduction zones (except for South America where data coverage is sparse), depth perturbations of the 410-km and 660-km discontinuities are correlated, with both the 410-km and the 660-km discontinuities occurring at greater depths. The distributions of the anomalies are consistent with cold stagnant slabs just above the 660-km discontinuity and ascending return flows in a superadiabatic upper mantle.

Finite element structural redesign by large admissible perturbations

NASA Technical Reports Server (NTRS)

Bernitsas, Michael M.; Beyko, E.; Rim, C. W.; Alzahabi, B.

1991-01-01

In structural redesign, two structural states are involved; the baseline (known) State S1 with unacceptable performance, and the objective (unknown) State S2 with given performance specifications. The difference between the two states in performance and design variables may be as high as 100 percent or more depending on the scale of the structure. A Perturbation Approach to Redesign (PAR) is presented to relate any two structural states S1 and S2 that are modeled by the same finite element model and represented by different values of the design variables. General perturbation equations are derived expressing implicitly the natural frequencies, dynamic modes, static deflections, static stresses, Euler buckling loads, and buckling modes of the objective S2 in terms of its performance specifications, and S1 data and Finite Element Analysis (FEA) results. Large Admissible Perturbation (LEAP) algorithms are implemented in code RESTRUCT to define the objective S2 incrementally without trial and error by postprocessing FEA results of S1 with no additional FEAs. Systematic numerical applications in redesign of a 10 element 48 degree of freedom (dof) beam, a 104 element 192 dof offshore tower, a 64 element 216 dof plate, and a 144 element 896 dof cylindrical shell show the accuracy, efficiency, and potential of PAR to find an objective state that may differ 100 percent from the baseline design.

Non-perturbative modelling of energetic particle effects on resistive wall mode: Anisotropy and finite orbit width

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

Liu, Yueqiang, E-mail: yueqiang.liu@ccfe.ac.uk; Chapman, I. T.; Graves, J. P.

2014-05-15

A non-perturbative magnetohydrodynamic-kinetic hybrid formulation is developed and implemented into the MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)] that takes into account the anisotropy and asymmetry [Graves et al., Nature Commun. 3, 624 (2012)] of the equilibrium distribution of energetic particles (EPs) in particle pitch angle space, as well as first order finite orbit width (FOW) corrections for both passing and trapped EPs. Anisotropic models, which affect both the adiabatic and non-adiabatic drift kinetic energy contributions, are implemented for both neutral beam injection and ion cyclotron resonant heating induced EPs. The first order FOW correction does notmore » contribute to the precessional drift resonance of trapped particles, but generally remains finite for the bounce and transit resonance contributions, as well as for the adiabatic contributions from asymmetrically distributed passing particles. Numerical results for a 9MA steady state ITER plasma suggest that (i) both the anisotropy and FOW effects can be important for the resistive wall mode stability in ITER plasmas; and (ii) the non-perturbative approach predicts less kinetic stabilization of the mode, than the perturbative approach, in the presence of anisotropy and FOW effects for the EPs. The latter may partially be related to the modification of the eigenfunction of the mode by the drift kinetic effects.« less

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.

Robust non-fragile finite-frequency H∞ static output-feedback control for active suspension systems

NASA Astrophysics Data System (ADS)

Wang, Gang; Chen, Changzheng; Yu, Shenbo

2017-07-01

This paper deals with the problem of non-fragile H∞ static output-feedback control of vehicle active suspension systems with finite-frequency constraint. The control objective is to improve ride comfort within the given frequency range and ensure the hard constraints in the time-domain. Moreover, in order to enhance the robustness of the controller, the control gain perturbation is also considered in controller synthesis. Firstly, a new non-fragile H∞ finite-frequency control condition is established by using generalized Kalman-Yakubovich-Popov (GKYP) lemma. Secondly, the static output-feedback control gain is directly derived by using a non-iteration algorithm. Different from the existing iteration LMI results, the static output-feedback design is simple and less conservative. Finally, the proposed control algorithm is applied to a quarter-car active suspension model with actuator dynamics, numerical results are made to show the effectiveness and merits of the proposed method.

A stochastic perturbation method to generate inflow turbulence in large-eddy simulation models: Application to neutrally stratified atmospheric boundary layers

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

Muñoz-Esparza, D.; Kosović, B.; Beeck, J. van

2015-03-15

Despite the variety of existing methods, efficient generation of turbulent inflow conditions for large-eddy simulation (LES) models remains a challenging and active research area. Herein, we extend our previous research on the cell perturbation method, which uses a novel stochastic approach based upon finite amplitude perturbations of the potential temperature field applied within a region near the inflow boundaries of the LES domain [Muñoz-Esparza et al., “Bridging the transition from mesoscale to microscale turbulence in numerical weather prediction models,” Boundary-Layer Meteorol., 153, 409–440 (2014)]. The objective was twofold: (i) to identify the governing parameters of the method and their optimummore » values and (ii) to generalize the results over a broad range of atmospheric large-scale forcing conditions, U{sub g} = 5 − 25 m s{sup −1}, where U{sub g} is the geostrophic wind. We identified the perturbation Eckert number, Ec=U{sub g}{sup 2}/ρc{sub p}θ{sup ~}{sub pm}, to be the parameter governing the flow transition to turbulence in neutrally stratified boundary layers. Here, θ{sup ~}{sub pm} is the maximum perturbation amplitude applied, c{sub p} is the specific heat capacity at constant pressure, and ρ is the density. The optimal Eckert number was found for nonlinear perturbations allowed by Ec ≈ 0.16, which instigate formation of hairpin-like vortices that most rapidly transition to a developed turbulent state. Larger Ec numbers (linear small-amplitude perturbations) result in streaky structures requiring larger fetches to reach the quasi-equilibrium solution, while smaller Ec numbers lead to buoyancy dominated perturbations exhibiting difficulties for hairpin-like vortices to emerge. Cell perturbations with wavelengths within the inertial range of three-dimensional turbulence achieved identical quasi-equilibrium values of resolved turbulent kinetic energy, q, and Reynolds-shear stress, . In contrast, large-scale perturbations acting at the production range exhibited reduced levels of , due to the formation of coherent streamwise structures, while q was maintained, requiring larger fetches for the turbulent solution to stabilize. Additionally, the cell perturbation method was compared to a synthetic turbulence generator. The proposed stochastic approach provided at least the same efficiency in developing realistic turbulence, while accelerating the formation of large-scales associated with production of turbulent kinetic energy. Also, it is computationally inexpensive and does not require any turbulent information.« less

From Large Deviations to Semidistances of Transport and Mixing: Coherence Analysis for Finite Lagrangian Data

NASA Astrophysics Data System (ADS)

Koltai, Péter; Renger, D. R. Michiel

2018-06-01

One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given finite Lagrangian trajectory data we derive a discrete-time-and-space semidistance that comes from the "best" approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with time-dependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, and hence they occur as extremal regions on a spanning structure of the state space under this semidistance—in fact, under any distance measure arising from the physical notion of transport. Based on this notion, we develop a tool to analyze the state space (or the finite trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and well-studied standard cases.

Unconditionally stable finite-difference time-domain methods for modeling the Sagnac effect

NASA Astrophysics Data System (ADS)

Novitski, Roman; Scheuer, Jacob; Steinberg, Ben Z.

2013-02-01

We present two unconditionally stable finite-difference time-domain (FDTD) methods for modeling the Sagnac effect in rotating optical microsensors. The methods are based on the implicit Crank-Nicolson scheme, adapted to hold in the rotating system reference frame—the rotating Crank-Nicolson (RCN) methods. The first method (RCN-2) is second order accurate in space whereas the second method (RCN-4) is fourth order accurate. Both methods are second order accurate in time. We show that the RCN-4 scheme is more accurate and has better dispersion isotropy. The numerical results show good correspondence with the expression for the classical Sagnac resonant frequency splitting when using group refractive indices of the resonant modes of a microresonator. Also we show that the numerical results are consistent with the perturbation theory for the rotating degenerate microcavities. We apply our method to simulate the effect of rotation on an entire Coupled Resonator Optical Waveguide (CROW) consisting of a set of coupled microresonators. Preliminary results validate the formation of a rotation-induced gap at the center of a transfer function of a CROW.

Non-perturbative determination of cV, ZV and ZS/ZP in Nf = 3 lattice QCD

NASA Astrophysics Data System (ADS)

Heitger, Jochen; Joswig, Fabian; Vladikas, Anastassios; Wittemeier, Christian

2018-03-01

We report on non-perturbative computations of the improvement coefficient cV and the renormalization factor ZV of the vector current in three-flavour O(a) improved lattice QCD with Wilson quarks and tree-level Symanzik improved gauge action. To reduce finite quark mass effects, our improvement and normalization conditions exploit massive chiral Ward identities formulated in the Schrödinger functional setup, which also allow deriving a new method to extract the ratio ZS/ZP of scalar to pseudoscalar renormalization constants. We present preliminary results of a numerical evaluation of ZV and cV along a line of constant physics with gauge couplings corresponding to lattice spacings of about 0:09 fm and below, relevant for phenomenological applications.

A linear shock cell model for non-circular jets using conformal mapping with a pseudo-spectral hybrid scheme

NASA Technical Reports Server (NTRS)

Bhat, Thonse R. S.; Baty, Roy S.; Morris, Philip J.

1990-01-01

The shock structure in non-circular supersonic jets is predicted using a linear model. This model includes the effects of the finite thickness of the mixing layer and the turbulence in the jet shear layer. A numerical solution is obtained using a conformal mapping grid generation scheme with a hybrid pseudo-spectral discretization method. The uniform pressure perturbation at the jet exit is approximated by a Fourier-Mathieu series. The pressure at downstream locations is obtained from an eigenfunction expansion that is matched to the pressure perturbation at the jet exit. Results are presented for a circular jet and for an elliptic jet of aspect ratio 2.0. Comparisons are made with experimental data.

LIGKA: A linear gyrokinetic code for the description of background kinetic and fast particle effects on the MHD stability in tokamaks

NASA Astrophysics Data System (ADS)

Lauber, Ph.; Günter, S.; Könies, A.; Pinches, S. D.

2007-09-01

In a plasma with a population of super-thermal particles generated by heating or fusion processes, kinetic effects can lead to the additional destabilisation of MHD modes or even to additional energetic particle modes. In order to describe these modes, a new linear gyrokinetic MHD code has been developed and tested, LIGKA (linear gyrokinetic shear Alfvén physics) [Ph. Lauber, Linear gyrokinetic description of fast particle effects on the MHD stability in tokamaks, Ph.D. Thesis, TU München, 2003; Ph. Lauber, S. Günter, S.D. Pinches, Phys. Plasmas 12 (2005) 122501], based on a gyrokinetic model [H. Qin, Gyrokinetic theory and computational methods for electromagnetic perturbations in tokamaks, Ph.D. Thesis, Princeton University, 1998]. A finite Larmor radius expansion together with the construction of some fluid moments and specification to the shear Alfvén regime results in a self-consistent, electromagnetic, non-perturbative model, that allows not only for growing or damped eigenvalues but also for a change in mode-structure of the magnetic perturbation due to the energetic particles and background kinetic effects. Compared to previous implementations [H. Qin, mentioned above], this model is coded in a more general and comprehensive way. LIGKA uses a Fourier decomposition in the poloidal coordinate and a finite element discretisation in the radial direction. Both analytical and numerical equilibria can be treated. Integration over the unperturbed particle orbits is performed with the drift-kinetic HAGIS code [S.D. Pinches, Ph.D. Thesis, The University of Nottingham, 1996; S.D. Pinches et al., CPC 111 (1998) 131] which accurately describes the particles' trajectories. This allows finite-banana-width effects to be implemented in a rigorous way since the linear formulation of the model allows the exchange of the unperturbed orbit integration and the discretisation of the perturbed potentials in the radial direction. Successful benchmarks for toroidal Alfvén eigenmodes (TAEs) and kinetic Alfvén waves (KAWs) with analytical results, ideal MHD codes, drift-kinetic codes and other codes based on kinetic models are reported.

Initial conditions and degrees of freedom of non-local gravity

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca; Modesto, Leonardo; Nardelli, Giuseppe

2018-05-01

We prove the equivalence between non-local gravity with an arbitrary form factor and a non-local gravitational system with an extra rank-2 symmetric tensor. Thanks to this reformulation, we use the diffusion-equation method to transform the dynamics of renormalizable non-local gravity with exponential operators into a higher-dimensional system local in spacetime coordinates. This method, first illustrated with a scalar field theory and then applied to gravity, allows one to solve the Cauchy problem and count the number of initial conditions and of non-perturbative degrees of freedom, which is finite. In particular, the non-local scalar and gravitational theories with exponential operators are both characterized by four initial conditions in any dimension and, respectively, by one and eight degrees of freedom in four dimensions. The fully covariant equations of motion are written in a form convenient to find analytic non-perturbative solutions.

Weakly modulated silicon-dioxide-cladding gratings for silicon waveguide Fabry-Pérot cavities.

PubMed

Grote, Richard R; Driscoll, Jeffrey B; Biris, Claudiu G; Panoiu, Nicolae C; Osgood, Richard M

2011-12-19

We show by theory and experiment that silicon-dioxide-cladding gratings for Fabry-Pérot cavities on silicon-on-insulator channel ("wire") waveguides provide a low-refractive-index perturbation, which is required for several important integrated photonics components. The underlying refractive index perturbation of these gratings is significantly weaker than that of analogous silicon gratings, leading to finer control of the coupling coefficient κ. Our Fabry-Pérot cavities are designed using the transfer-matrix method (TMM) in conjunction with the finite element method (FEM) for calculating the effective index of each waveguide section. Device parameters such as coupling coefficient, κ, Bragg mirror stop band, Bragg mirror reflectivity, and quality factor Q are examined via TMM modeling. Devices are fabricated with representative values of distributed Bragg reflector lengths, cavity lengths, and propagation losses. The measured transmission spectra show excellent agreement with the FEM/TMM calculations.

Lattice dynamics calculations based on density-functional perturbation theory in real space

NASA Astrophysics Data System (ADS)

Shang, Honghui; Carbogno, Christian; Rinke, Patrick; Scheffler, Matthias

2017-06-01

A real-space formalism for density-functional perturbation theory (DFPT) is derived and applied for the computation of harmonic vibrational properties in molecules and solids. The practical implementation using numeric atom-centered orbitals as basis functions is demonstrated exemplarily for the all-electron Fritz Haber Institute ab initio molecular simulations (FHI-aims) package. The convergence of the calculations with respect to numerical parameters is carefully investigated and a systematic comparison with finite-difference approaches is performed both for finite (molecules) and extended (periodic) systems. Finally, the scaling tests and scalability tests on massively parallel computer systems demonstrate the computational efficiency.

On high-order perturbative calculations at finite density

DOE PAGES

Ghisoiu, Ioan; Gorda, Tyler; Kurkela, Aleksi; ...

2016-12-01

We discuss the prospects of performing high-order perturbative calculations in systems characterized by a vanishing temperature but finite density. In particular, we show that the determination of generic Feynman integrals containing fermionic chemical potentials can be reduced to the evaluation of three-dimensional phase space integrals over vacuum on-shell amplitudes — aresult reminiscent of a previously proposed “naive real-time formalism” for vacuum diagrams. Applications of these rules are discussed in the context of the thermodynamics of cold and dense QCD, where it is argued that they facilitate an extension of the Equation of State of cold quark matter to higher perturbativemore » orders.« less

Third-order perturbative lattice and complex Langevin analyses of the finite-temperature equation of state of nonrelativistic fermions in one dimension

NASA Astrophysics Data System (ADS)

Loheac, Andrew C.; Drut, Joaquín E.

2017-05-01

We analyze the pressure and density equations of state of unpolarized nonrelativistic fermions at finite temperature in one spatial dimension with contact interactions. For attractively interacting regimes, we perform a third-order lattice perturbation theory calculation, assess its convergence properties by comparing with hybrid Monte Carlo results (there is no sign problem in this regime), and demonstrate agreement with real Langevin calculations. For repulsive interactions, we present lattice perturbation theory results as well as complex Langevin calculations, with a modified action to prevent uncontrolled excursions in the complex plane. Although perturbation theory is a common tool, our implementation of it is unconventional; we use a Hubbard-Stratonovich transformation to decouple the system and automate the application of Wick's theorem, thus generating the diagrammatic expansion, including symmetry factors, at any desired order. We also present an efficient technique to tackle nested Matsubara frequency sums without relying on contour integration, which is independent of dimension and applies to both relativistic and nonrelativistic systems, as well as all energy-independent interactions. We find exceptional agreement between perturbative and nonperturbative results at weak couplings, and furnish predictions based on complex Langevin at strong couplings. We additionally present perturbative calculations of up to the fifth-order virial coefficient for repulsive and attractive couplings. Both the lattice perturbation theory and complex Langevin formalisms can easily be extended to a variety of situations including polarized systems, bosons, and higher dimension.

Space-time-modulated stochastic processes

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.

A Simple Method for Deriving the Confidence Regions for the Penalized Cox’s Model via the Minimand Perturbation†

PubMed Central

Lin, Chen-Yen; Halabi, Susan

2017-01-01

We propose a minimand perturbation method to derive the confidence regions for the regularized estimators for the Cox’s proportional hazards model. Although the regularized estimation procedure produces a more stable point estimate, it remains challenging to provide an interval estimator or an analytic variance estimator for the associated point estimate. Based on the sandwich formula, the current variance estimator provides a simple approximation, but its finite sample performance is not entirely satisfactory. Besides, the sandwich formula can only provide variance estimates for the non-zero coefficients. In this article, we present a generic description for the perturbation method and then introduce a computation algorithm using the adaptive least absolute shrinkage and selection operator (LASSO) penalty. Through simulation studies, we demonstrate that our method can better approximate the limiting distribution of the adaptive LASSO estimator and produces more accurate inference compared with the sandwich formula. The simulation results also indicate the possibility of extending the applications to the adaptive elastic-net penalty. We further demonstrate our method using data from a phase III clinical trial in prostate cancer. PMID:29326496

A study of fluid-structure problems

NASA Astrophysics Data System (ADS)

Lam, Dennis Kang-Por

The stability of structures with and without fluid load is investigated. A method is developed for determining the fluid load in terms of added structural mass. Finite element methods are employed to study the buckling of a cylindrical shell under axial compression and liquid storage tanks under hydrodynamic load. Both linear and nonlinear analyses are performed. Diamond modes are found to be the possible postbuckling shapes of the cylindrical shell. Local buckling including elephant-foot buckle and diamond buckle are found for the liquid storage tank models. Comparison between the linear and nonlinear results indicates a substantial difference in buckling mode shapes, though the buckling loads are close to each other. The method for determining the hydrodynamic mass is applied to the impeller stage of a centrifugal pump. The method is based on a linear perturbation technique which assumes that the disturbance in the flow boundaries and velocities caused by the motion of the structure is small. A potential method is used to estimate the velocity flow field. The hydrodynamic mass is then obtained by calculating the total force which results from the pressure induced by a perturbation of the structure.

Euler equation computations for the flow over a hovering helicopter rotor

NASA Technical Reports Server (NTRS)

Roberts, Thomas Wesley

1988-01-01

A numerical solution technique is developed for computing the flow field around an isolated helicopter rotor in hover. The flow is governed by the compressible Euler equations which are integrated using a finite volume approach. The Euler equations are coupled to a free wake model of the rotary wing vortical wake. This wake model is incorporated into the finite volume solver using a prescribed flow, or perturbation, technique which eliminates the numerical diffusion of vorticity due to the artificial viscosity of the scheme. The work is divided into three major parts: (1) comparisons of Euler solutions to experimental data for the flow around isolated wings show good agreement with the surface pressures, but poor agreement with the vortical wake structure; (2) the perturbation method is developed and used to compute the interaction of a streamwise vortex with a semispan wing. The rapid diffusion of the vortex when only the basic Euler solver is used is illustrated, and excellent agreement with experimental section lift coefficients is demonstrated when using the perturbation approach; and (3) the free wake solution technique is described and the coupling of the wake to the Euler solver for an isolated rotor is presented. Comparisons with experimental blade load data for several cases show good agreement, with discrepancies largely attributable to the neglect of viscous effects. The computed wake geometries agree less well with experiment, the primary difference being that too rapid a wake contraction is predicted for all the cases.

Determination of aerodynamic sensitivity coefficients in the transonic and supersonic regimes

NASA Technical Reports Server (NTRS)

Elbanna, Hesham M.; Carlson, Leland A.

1989-01-01

The quasi-analytical approach is developed to compute airfoil aerodynamic sensitivity coefficients in the transonic and supersonic flight regimes. Initial investigation verifies the feasibility of this approach as applied to the transonic small perturbation residual expression. Results are compared to those obtained by the direct (finite difference) approach and both methods are evaluated to determine their computational accuracies and efficiencies. The quasi-analytical approach is shown to be superior and worth further investigation.

Finite time convergent learning law for continuous neural networks.

PubMed

Chairez, Isaac

2014-02-01

This paper addresses the design of a discontinuous finite time convergent learning law for neural networks with continuous dynamics. The neural network was used here to obtain a non-parametric model for uncertain systems described by a set of ordinary differential equations. The source of uncertainties was the presence of some external perturbations and poor knowledge of the nonlinear function describing the system dynamics. A new adaptive algorithm based on discontinuous algorithms was used to adjust the weights of the neural network. The adaptive algorithm was derived by means of a non-standard Lyapunov function that is lower semi-continuous and differentiable in almost the whole space. A compensator term was included in the identifier to reject some specific perturbations using a nonlinear robust algorithm. Two numerical examples demonstrated the improvements achieved by the learning algorithm introduced in this paper compared to classical schemes with continuous learning methods. The first one dealt with a benchmark problem used in the paper to explain how the discontinuous learning law works. The second one used the methane production model to show the benefits in engineering applications of the learning law proposed in this paper. Copyright © 2013 Elsevier Ltd. All rights reserved.

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.

Boundary formulations for sensitivity analysis without matrix derivatives

NASA Technical Reports Server (NTRS)

Kane, J. H.; Guru Prasad, K.

1993-01-01

A new hybrid approach to continuum structural shape sensitivity analysis employing boundary element analysis (BEA) is presented. The approach uses iterative reanalysis to obviate the need to factor perturbed matrices in the determination of surface displacement and traction sensitivities via a univariate perturbation/finite difference (UPFD) step. The UPFD approach makes it possible to immediately reuse existing subroutines for computation of BEA matrix coefficients in the design sensitivity analysis process. The reanalysis technique computes economical response of univariately perturbed models without factoring perturbed matrices. The approach provides substantial computational economy without the burden of a large-scale reprogramming effort.

Stress estimation in reservoirs using an integrated inverse method

NASA Astrophysics Data System (ADS)

Mazuyer, Antoine; Cupillard, Paul; Giot, Richard; Conin, Marianne; Leroy, Yves; Thore, Pierre

2018-05-01

Estimating the stress in reservoirs and their surroundings prior to the production is a key issue for reservoir management planning. In this study, we propose an integrated inverse method to estimate such initial stress state. The 3D stress state is constructed with the displacement-based finite element method assuming linear isotropic elasticity and small perturbations in the current geometry of the geological structures. The Neumann boundary conditions are defined as piecewise linear functions of depth. The discontinuous functions are determined with the CMA-ES (Covariance Matrix Adaptation Evolution Strategy) optimization algorithm to fit wellbore stress data deduced from leak-off tests and breakouts. The disregard of the geological history and the simplified rheological assumptions mean that only the stress field, statically admissible and matching the wellbore data should be exploited. The spatial domain of validity of this statement is assessed by comparing the stress estimations for a synthetic folded structure of finite amplitude with a history constructed assuming a viscous response.

Towards the prediction of multiple necking during dynamic extension of round bar : linear stability approach versus finite element calculations

NASA Astrophysics Data System (ADS)

El Maï, S.; Mercier, S.; Petit, J.; Molinari, A.

2014-05-01

The fragmentation of structures subject to dynamic conditions is a matter of interest for civil industries as well as for Defence institutions. Dynamic expansions of structures, such as cylinders or rings, have been performed to obtain crucial information on fragment distributions. Many authors have proposed to capture by FEA the experimental distribution of fragment size by introducing in the FE model a perturbation. Stability and bifurcation analyses have also been proposed to describe the evolution of the perturbation growth rate. In the proposed contribution, the multiple necking of a round bar in dynamic tensile loading is analysed by the FE method. A perturbation on the initial flow stress is introduced in the numerical model to trigger instabilities. The onset time and the dominant mode of necking have been characterized precisely and showed power law evolutions, with the loading velocities and moderately with the amplitudes and the cell sizes of the perturbations. In the second part of the paper, the development of linear stability analysis and the use of salient criteria in terms of the growth rate of perturbations enabled comparisons with the numerical results. A good correlation in terms of onset time of instabilities and of number of necks is shown.

On the nonlinear interaction of Goertler vortices and Tollmien-Schlichting waves in curved channel flows at finite Reynolds numbers

NASA Technical Reports Server (NTRS)

Daudpota, Q. Isa; Zang, Thomas A.; Hall, Philip

1988-01-01

The flow in a two-dimensional curved channel driven by an azimuthal pressure gradient can become linearly unstable due to axisymmetric perturbations and/or nonaxisymmetric perturbations depending on the curvature of the channel and the Reynolds number. For a particular small value of curvature, the critical neighborhood of this curvature value and critical Reynolds number, nonlinear interactions occur between these perturbations. The Stuart-Watson approach is used to derive two coupled Landau equations for the amplitudes of these perturbations. The stability of the various possible states of these perturbations is shown through bifurcation diagrams. Emphasis is given to those cases which have relevance to external flows.

On the nonlinear interaction of Gortler vortices and Tollmien-Schlichting waves in curved channel flows at finite Reynolds numbers

NASA Technical Reports Server (NTRS)

Daudpota, Q. Isa; Hall, Philip; Zang, Thomas A.

1987-01-01

The flow in a two-dimensional curved channel driven by an azimuthal pressure gradient can become linearly unstable due to axisymmetric perturbations and/or nonaxisymmetric perturbations depending on the curvature of the channel and the Reynolds number. For a particular small value of curvature, the critical neighborhood of this curvature value and critical Reynolds number, nonlinear interactions occur between these perturbations. The Stuart-Watson approach is used to derive two coupled Landau equations for the amplitudes of these perturbations. The stability of the various possible states of these perturbations is shown through bifurcation diagrams. Emphasis is given to those cases which have relevance to external flows.

Probabilistic Structures Analysis Methods (PSAM) for select space propulsion system components

NASA Technical Reports Server (NTRS)

1991-01-01

The basic formulation for probabilistic finite element analysis is described and demonstrated on a few sample problems. This formulation is based on iterative perturbation that uses the factorized stiffness on the unperturbed system as the iteration preconditioner for obtaining the solution to the perturbed problem. This approach eliminates the need to compute, store and manipulate explicit partial derivatives of the element matrices and force vector, which not only reduces memory usage considerably, but also greatly simplifies the coding and validation tasks. All aspects for the proposed formulation were combined in a demonstration problem using a simplified model of a curved turbine blade discretized with 48 shell elements, and having random pressure and temperature fields with partial correlation, random uniform thickness, and random stiffness at the root.

Adaptive backstepping sliding mode control with fuzzy monitoring strategy for a kind of mechanical system.

PubMed

Song, Zhankui; Sun, Kaibiao

2014-01-01

A novel adaptive backstepping sliding mode control (ABSMC) law with fuzzy monitoring strategy is proposed for the tracking-control of a kind of nonlinear mechanical system. The proposed ABSMC scheme combining the sliding mode control and backstepping technique ensure that the occurrence of the sliding motion in finite-time and the trajectory of tracking-error converge to equilibrium point. To obtain a better perturbation rejection property, an adaptive control law is employed to compensate the lumped perturbation. Furthermore, we introduce fuzzy monitoring strategy to improve adaptive capacity and soften the control signal. The convergence and stability of the proposed control scheme are proved by using Lyaponov's method. Finally, numerical simulations demonstrate the effectiveness of the proposed control scheme. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Optimal control of singularly perturbed nonlinear systems with state-variable inequality constraints

NASA Technical Reports Server (NTRS)

Calise, A. J.; Corban, J. E.

1990-01-01

The established necessary conditions for optimality in nonlinear control problems that involve state-variable inequality constraints are applied to a class of singularly perturbed systems. The distinguishing feature of this class of two-time-scale systems is a transformation of the state-variable inequality constraint, present in the full order problem, to a constraint involving states and controls in the reduced problem. It is shown that, when a state constraint is active in the reduced problem, the boundary layer problem can be of finite time in the stretched time variable. Thus, the usual requirement for asymptotic stability of the boundary layer system is not applicable, and cannot be used to construct approximate boundary layer solutions. Several alternative solution methods are explored and illustrated with simple examples.

3-D geoelectrical modelling using finite-difference: a new boundary conditions improvement

NASA Astrophysics Data System (ADS)

Maineult, A.; Schott, J.-J.; Ardiot, A.

2003-04-01

Geoelectrical prospecting is a well-known and frequently used method for quantitative and non-destructive subsurface exploration until depths of a few hundreds metres. Thus archeological objects can be efficiently detected as their resistivities often contrast with those of the surrounding media. Nevertheless using the geoelectrical prospecting method has long been restricted due to inhability to model correctly arbitrarily-shaped structures. The one-dimensional modelling and inversion have long been classical, but are of no interest for the majority of field data, since the natural distribution of resistivity is rarely homogeneous or tabular. Since the 1970's some authors developed discrete methods in order to solve the two and three-dimensional problem, using mathematical tools such as finite-element or finite-difference. The finite-difference approach is quite simple, easily understandable and programmable. Since the work of Dey and Morrison (1979), this approach has become quite popular. Nevertheless, one of its major drawbacks is the difficulty to establish satisfying boundary conditions. Recently Lowry et al. (1989) and Zhao and Yedlin (1996) suggested some refinements on the improvement of the boundary problem. We propose a new betterment, based on the splitting of the potential into two terms, the potential due to a reference tabular medium and a secondary potential caused by a disturbance of this medium. The surface response of a tabular medium has long been known (see for example Koefoed 1979). Here we developed the analytical solution for the electrical tabular potential everywhere in the medium, in order to establish more satisfying boundary conditions. The response of the perturbation, that is to say the object of interest, is then solved using volume-difference and preconditioned conjugate gradient. Finally the grid is refined one or more times in the perturbed domain in order to ameliorate the precision. This method of modelling is easy to implement and numerical computations run very fast. Thanks to improved boundary conditions and refinement processes, edges effects are reduced. Moreover, one important conclusion of this work is the necessity to prefer three-dimensional prospecting, since in some cases a unique profile can lead to misinterpretation, as shown by the comparison of transverse profiles through a buried cylinder and through a buried sphere.

Bi-local holography in the SYK model: Perturbations

DOE PAGES

Jevicki, Antal; Suzuki, Kenta

2016-11-08

We continue the study of the Sachdev-Ye-Kitaev model in the Large N limit. Following our formulation in terms of bi-local collective fields with dynamical reparametrization symmetry, we perform perturbative calculations around the conformal IR point. As a result, these are based on an ε expansion which allows for analytical evaluation of correlators and finite temperature quantities.

Analysis and computation of a least-squares method for consistent mesh tying

DOE PAGES

Day, David; Bochev, Pavel

2007-07-10

We report in the finite element method, a standard approach to mesh tying is to apply Lagrange multipliers. If the interface is curved, however, discretization generally leads to adjoining surfaces that do not coincide spatially. Straightforward Lagrange multiplier methods lead to discrete formulations failing a first-order patch test [T.A. Laursen, M.W. Heinstein, Consistent mesh-tying methods for topologically distinct discretized surfaces in non-linear solid mechanics, Internat. J. Numer. Methods Eng. 57 (2003) 1197–1242]. This paper presents a theoretical and computational study of a least-squares method for mesh tying [P. Bochev, D.M. Day, A least-squares method for consistent mesh tying, Internat. J.more » Numer. Anal. Modeling 4 (2007) 342–352], applied to the partial differential equation -∇ 2φ+αφ=f. We prove optimal convergence rates for domains represented as overlapping subdomains and show that the least-squares method passes a patch test of the order of the finite element space by construction. To apply the method to subdomain configurations with gaps and overlaps we use interface perturbations to eliminate the gaps. Finally, theoretical error estimates are illustrated by numerical experiments.« less

Finding Limit Cycles in self-excited oscillators with infinite-series damping functions

NASA Astrophysics Data System (ADS)

Das, Debapriya; Banerjee, Dhruba; Bhattacharjee, Jayanta K.

2015-03-01

In this paper we present a simple method for finding the location of limit cycles of self excited oscillators whose damping functions can be represented by some infinite convergent series. We have used standard results of first-order perturbation theory to arrive at amplitude equations. The approach has been kept pedagogic by first working out the cases of finite polynomials using elementary algebra. Then the method has been extended to various infinite polynomials, where the fixed points of the corresponding amplitude equations cannot be found out. Hopf bifurcations for systems with nonlinear powers in velocities have also been discussed.

Implementing a Matrix-free Analytical Jacobian to Handle Nonlinearities in Models of 3D Lithospheric Deformation

NASA Astrophysics Data System (ADS)

Kaus, B.; Popov, A.

2015-12-01

The analytical expression for the Jacobian is a key component to achieve fast and robust convergence of the nonlinear Newton-Raphson iterative solver. Accomplishing this task in practice often requires a significant algebraic effort. Therefore it is quite common to use a cheap alternative instead, for example by approximating the Jacobian with a finite difference estimation. Despite its simplicity it is a relatively fragile and unreliable technique that is sensitive to the scaling of the residual and unknowns, as well as to the perturbation parameter selection. Unfortunately no universal rule can be applied to provide both a robust scaling and a perturbation. The approach we use here is to derive the analytical Jacobian for the coupled set of momentum, mass, and energy conservation equations together with the elasto-visco-plastic rheology and a marker in cell/staggered finite difference method. The software project LaMEM (Lithosphere and Mantle Evolution Model) is primarily developed for the thermo-mechanically coupled modeling of the 3D lithospheric deformation. The code is based on a staggered grid finite difference discretization in space, and uses customized scalable solvers form PETSc library to efficiently run on the massively parallel machines (such as IBM Blue Gene/Q). Currently LaMEM relies on the Jacobian-Free Newton-Krylov (JFNK) nonlinear solver, which approximates the Jacobian-vector product using a simple finite difference formula. This approach never requires an assembled Jacobian matrix and uses only the residual computation routine. We use an approximate Jacobian (Picard) matrix to precondition the Krylov solver with the Galerkin geometric multigrid. Because of the inherent problems of the finite difference Jacobian estimation, this approach doesn't always result in stable convergence. In this work we present and discuss a matrix-free technique in which the Jacobian-vector product is replaced by analytically-derived expressions and compare results with those obtained with a finite difference approximation of the Jacobian. This project is funded by ERC Starting Grant 258830 and computer facilities were provided by Jülich supercomputer center (Germany).

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.

Resonance Extraction from the Finite Volume

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

Doring, Michael; Molina Peralta, Raquel

2016-06-01

The spectrum of excited hadrons becomes accessible in simulations of Quantum Chromodynamics on the lattice. Extensions of Lüscher's method allow to address multi-channel scattering problems using moving frames or modified boundary conditions to obtain more eigenvalues in finite volume. As these are at different energies, interpolations are needed to relate different eigenvalues and to help determine the amplitude. Expanding the T- or the K-matrix locally provides a controlled scheme by removing the known non-analyticities of thresholds. This can be stabilized by using Chiral Perturbation Theory. Different examples to determine resonance pole parameters and to disentangle resonances from thresholds are dis-more » cussed, like the scalar meson f0(980) and the excited baryons N(1535)1/2^- and Lambda(1405)1/2^-.« less

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

NASA Astrophysics Data System (ADS)

Hollenberg, Sebastian; Päs, Heinrich

2012-01-01

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

Use of source distributions for evaluating theoretical aerodynamics of thin finite wings at supersonic speeds

NASA Technical Reports Server (NTRS)

Evvard, John C

1950-01-01

A series of publications on the source-distribution methods for evaluating the aerodynamics of thin wings at supersonic speeds is summarized, extended, and unified. Included in the first part are the deviations of: (a) the linearized partial-differential equation for unsteady flow at a substantially constant Mach number. b) The source-distribution solution for the perturbation-velocity potential that satisfies the boundary conditions of tangential flow at the surface and in the plane of the wing; and (c) the integral equation for determining the strength and the location of sources to describe the interaction effects (as represented by upwash) of the bottom and top wing surfaces through the region between the finite wing boundary and the foremost Mach wave. The second part deals with steady-state thin-wing problems. The third part of the report approximates the integral equation for unsteady upwash and includes a solution of approximate equation. Expressions are then derived to evaluate the load distributions for time-dependent finite-wing motions.

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

Kaothekar, Sachin, E-mail: sackaothekar@gmail.com

I have studied the effects of finite electron inertia, finite ion Larmor radius (FLR) corrections, and radiative heat-loss function on the thermal instability of an infinite homogeneous, viscous plasma incorporating the effect of thermal conductivity for star formation in interstellar medium (ISM). A general dispersion relation is derived using the normal mode analysis method with the help of relevant linearized perturbation equations of the problem. The wave propagation is discussed for longitudinal and transverse directions to the external magnetic field and the conditions of modified thermal instabilities and stabilities are discussed in different cases. We find that the thermal instabilitymore » criterion is get modified into radiative instability criterion by inclusion of radiative heat-loss functions with thermal conductivity. The viscosity of medium removes the effect of FLR corrections from the condition of radiative instability. Numerical calculation shows stabilizing effect of heat-loss function, viscosity and FLR corrections, and destabilizing effect of finite electron inertia on the thermal instability. Results carried out in this paper shows that stars are formed in interstellar medium mainly due to thermal instability.« less

Gluon and ghost correlation functions of 2-color QCD at finite density

NASA Astrophysics Data System (ADS)

Hajizadeh, Ouraman; Boz, Tamer; Maas, Axel; Skullerud, Jon-Ivar

2018-03-01

2-color QCD, i. e. QCD with the gauge group SU(2), is the simplest non-Abelian gauge theory without sign problem at finite quark density. Therefore its study on the lattice is a benchmark for other non-perturbative approaches at finite density. To provide such benchmarks we determine the minimal-Landau-gauge 2-point and 3-gluon correlation functions of the gauge sector and the running gauge coupling at finite density. We observe no significant effects, except for some low-momentum screening of the gluons at and above the supposed high-density phase transition.

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

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

Velikovich, A. L.; Schmit, P. F.

Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining themore » “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. In the limit of small shell thickness, exact thin-shell perturbation equations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].« less

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

NASA Astrophysics Data System (ADS)

Velikovich, A. L.; Schmit, P. F.

2015-12-01

Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining the "instantaneous growth rate" are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. In the limit of small shell thickness, exact thin-shell perturbation equations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].

Nonperturbative finite-temperature Yang-Mills theory

NASA Astrophysics Data System (ADS)

Cyrol, Anton K.; Mitter, Mario; Pawlowski, Jan M.; Strodthoff, Nils

2018-03-01

We present nonperturbative correlation functions in Landau-gauge Yang-Mills theory at finite temperature. The results are obtained from the functional renormalisation group within a self-consistent approximation scheme. In particular, we compute the magnetic and electric components of the gluon propagator, and the three- and four-gluon vertices. We also show the ghost propagator and the ghost-gluon vertex at finite temperature. Our results for the propagators are confronted with lattice simulations and our Debye mass is compared to hard thermal loop perturbation theory.

Nonlinear effects on the natural modes of oscillation of a finite length inviscid fluid column, supplement 2

NASA Technical Reports Server (NTRS)

Lyell, M. J.; Zhang, L.

1994-01-01

The aspects of nonlinear behavior of a finite length liquid column is investigated with an emphasis on bridge dynamics. The primary objectives are to determine the nonlinear corrections to the interface shape of a naturally oscillating finite length liquid column and to determine the nonlinear corrections to the oscillation frequencies for various modes of oscillation. Application of the Lindstedt-Poincare expansion in conjunction with the domain perturbation techniques results in an hierarchical system of equations.

The Evolution of Finite Amplitude Wavetrains in Plane Channel Flow

NASA Technical Reports Server (NTRS)

Hewitt, R. E.; Hall, P.

1996-01-01

We consider a viscous incompressible fluid flow driven between two parallel plates by a constant pressure gradient. The flow is at a finite Reynolds number, with an 0(l) disturbance in the form of a traveling wave. A phase equation approach is used to discuss the evolution of slowly varying fully nonlinear two dimensional wavetrains. We consider uniform wavetrains in detail, showing that the development of a wavenumber perturbation is governed by Burgers equation in most cases. The wavenumber perturbation theory, constructed using the phase equation approach for a uniform wavetrain, is shown to be distinct from an amplitude perturbation expansion about the periodic flow. In fact we show that the amplitude equation contains only linear terms and is simply the heat equation. We review, briefly, the well known dynamics of Burgers equation, which imply that both shock structures and finite time singularities of the wavenumber perturbation can occur with respect to the slow scales. Numerical computations have been performed to identify areas of the (wavenumber, Reynolds number, energy) neutral surface for which each of these possibilities can occur. We note that the evolution equations will breakdown under certain circumstances, in particular for a weakly nonlinear secondary flow. Finally we extend the theory to three dimensions and discuss the limit of a weak spanwise dependence for uniform wavetrains, showing that two functions are required to describe the evolution. These unknowns are a phase and a pressure function which satisfy a pair of linearly coupled partial differential equations. The results obtained from applying the same analysis to the fully three dimensional problem are included as an appendix.

Modelling of the Hypothalamic-Pituitary-Adrenal Axis Perturbations by Externally Induced Cholesterol Pulses of Finite Duration and with Asymmetrically Distributed Concentration Profile

NASA Astrophysics Data System (ADS)

Stanojević, A.; Marković, V. M.; Čupić, Ž.; Vukojević, V.; Kolar-Anić, L.

2017-12-01

A model was developed that can be used to study the effect of gradual cholesterol intake by food on the HPA axis dynamics. Namely, well defined oscillatory dynamics of vital neuroendocrine hypothalamic-pituitary-adrenal (HPA) axis has proven to be necessary for maintaining regular basal physiology and formulating appropriate stress response to various types of perturbations. Cholesterol, as a precursor of all steroid HPA axis hormones, can alter the dynamics of HPA axis. To analyse its particular influence on the HPA axis dynamics we used stoichiometric model of HPA axis activity, and simulate cholesterol perturbations in the form of finite duration pulses, with asymmetrically distributed concentration profile. Our numerical simulations showed that there is a complex, nonlinear dependence between the HPA axis responsiveness and different forms of applied cholesterol concentration pulses, indicating the significance of kinetic modelling, and dynamical systems theory for the understanding of large-scale self-regulatory, and homeostatic processes within this neuroendocrine system.

Nondecoupling of maximal supergravity from the superstring.

PubMed

Green, Michael B; Ooguri, Hirosi; Schwarz, John H

2007-07-27

We consider the conditions necessary for obtaining perturbative maximal supergravity in d dimensions as a decoupling limit of type II superstring theory compactified on a (10-d) torus. For dimensions d=2 and d=3, it is possible to define a limit in which the only finite-mass states are the 256 massless states of maximal supergravity. However, in dimensions d>or=4, there are infinite towers of additional massless and finite-mass states. These correspond to Kaluza-Klein charges, wound strings, Kaluza-Klein monopoles, or branes wrapping around cycles of the toroidal extra dimensions. We conclude that perturbative supergravity cannot be decoupled from string theory in dimensions>or=4. In particular, we conjecture that pure N=8 supergravity in four dimensions is in the Swampland.

Global Culture: A Noise Induced Transition in Finite Systems

NASA Astrophysics Data System (ADS)

Klemm, Konstantin; Eguíluz, Victor M.; Toral, Raúl; San Miguel, Maxi

2003-04-01

We analyze Axelrod's model for the unbiased transmission of culture in the presence of noise. In a one-dimensional lattice, the dynamics is described in terms of a Lyapunov potential, where the disordered configurations are metastable states of the dynamics. In a two-dimensional lattice the dynamics is governed by the average relaxation time T for perturbations to the homogeneous configuration. If the noise rate is smaller than 1/T, the perturbations drive the system to a completely ordered configuration, whereas the system remains disordered for larger noise rates. Based on a mean-field approximation we obtain the average relaxation time T(N) = Nln(N) for system size N. Thus in the limit of infinite system size the system is disordered for any finite noise rate.

Classical stability of sudden and big rip singularities

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

Barrow, John D.; Lip, Sean Z. W.

2009-08-15

We introduce a general characterization of sudden cosmological singularities and investigate the classical stability of homogeneous and isotropic cosmological solutions of all curvatures containing these singularities to small scalar, vector, and tensor perturbations using gauge-invariant perturbation theory. We establish that sudden singularities at which the scale factor, expansion rate, and density are finite are stable except for a set of special parameter values. We also apply our analysis to the stability of Big Rip singularities and find the conditions for their stability against small scalar, vector, and tensor perturbations.

Probing Schrodinger equation with a continued fraction potential

NASA Astrophysics Data System (ADS)

Ahmed, Nasr; Alamri, Sultan Z.; Rassem, M.

2018-06-01

We suggest a new perturbed form of the quantum potential and investigate the possible solutions of Schrodinger equation. The new form can be written as a finite or infinite continued fraction. a comparison has been given between the continued fractional potential and the non-perturbed potential. We suggest the validity of this continued fractional quantum form in some quantum systems. As the order of the continued fraction increases the difference between the perturbed and the ordinary potentials decreases. The physically acceptable solutions critically depend on the values of the continued fraction coefficients αi .

Nonlinear ideal magnetohydrodynamics instabilities

NASA Astrophysics Data System (ADS)

Pfirsch, D.; Sudan, R. N.

1993-07-01

Explosive phenomena such as internal disruptions in toroidal discharges and solar flares are difficult to explain in terms of linear instabilities. A plasma approaching a linear stability limit can, however, become nonlinearly and explosively unstable, with noninfinitesimal perturbations even before the marginal state is reached. For such investigations, a nonlinear extension of the usual MHD (magnetohydrodynamic) energy principle is helpful. (This was obtained by Merkel and Schlüter, Sitzungsberichted. Bayer. Akad. Wiss., Munich, 1976, No. 7, for Cartesian coordinate systems.) A coordinate system independent Eulerian formulation for the Lagrangian allowing for equilibria with flow and with built-in conservation laws for mass, magnetic flux, and entropy is developed in this paper which is similar to Newcomb's Lagrangian method of 1962 [Nucl. Fusion, Suppl., Pt. II, 452 (1962)]. For static equilibria nonlinear stability is completely determined by the potential energy. For a potential energy which contains second- and nth order or some more general contributions only, it is shown in full generality that linearly unstable and marginally stable systems are explosively unstable even for infinitesimal perturbations; linearly absolutely stable systems require finite initial perturbations. For equilibria with Abelian symmetries symmetry breaking initial perturbations are needed, which should be observed in numerical simulations. Nonlinear stability is proved for two simple examples, m=0 perturbations of a Bennet Z-pinch and z-independent perturbations of a θ pinch. The algebra for treating these cases reduces considerably if symmetries are taken into account from the outset, as suggested by M. N. Rosenbluth (private communication, 1992).

Nonperturbative evaluation for anomalous dimension in 2-dimensional O (3 ) sigma model

NASA Astrophysics Data System (ADS)

Calle Jimenez, Sergio; Oka, Makoto; Sasaki, Kiyoshi

2018-06-01

We nonperturbatively calculate the wave-function renormalization in the two-dimensional O (3 ) sigma model. It is evaluated in a box with a finite spatial extent. We determine the anomalous dimension in the finite-volume scheme through an analysis of the step-scaling function. Results are compared with a perturbative evaluation, and reasonable behavior is observed.

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

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

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

2015-11-15

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

Fast state transfer in a Λ-system: a shortcut-to-adiabaticity approach to robust and resource optimized control

NASA Astrophysics Data System (ADS)

Mortensen, Henrik Lund; Sørensen, Jens Jakob W. H.; Mølmer, Klaus; Sherson, Jacob Friis

2018-02-01

We propose an efficient strategy to find optimal control functions for state-to-state quantum control problems. Our procedure first chooses an input state trajectory, that can realize the desired transformation by adiabatic variation of the system Hamiltonian. The shortcut-to-adiabaticity formalism then provides a control Hamiltonian that realizes the reference trajectory exactly but on a finite time scale. As the final state is achieved with certainty, we define a cost functional that incorporates the resource requirements and a perturbative expression for robustness. We optimize this functional by systematically varying the reference trajectory. We demonstrate the method by application to population transfer in a laser driven three-level Λ-system, where we find solutions that are fast and robust against perturbations while maintaining a low peak laser power.

Sensitivities Kernels of Seismic Traveltimes and Amplitudes for Quality Factor and Boundary Topography

NASA Astrophysics Data System (ADS)

Hsieh, M.; Zhao, L.; Ma, K.

2010-12-01

Finite-frequency approach enables seismic tomography to fully utilize the spatial and temporal distributions of the seismic wavefield to improve resolution. In achieving this goal, one of the most important tasks is to compute efficiently and accurately the (Fréchet) sensitivity kernels of finite-frequency seismic observables such as traveltime and amplitude to the perturbations of model parameters. In scattering-integral approach, the Fréchet kernels are expressed in terms of the strain Green tensors (SGTs), and a pre-established SGT database is necessary to achieve practical efficiency for a three-dimensional reference model in which the SGTs must be calculated numerically. Methods for computing Fréchet kernels for seismic velocities have long been established. In this study, we develop algorithms based on the finite-difference method for calculating Fréchet kernels for the quality factor Qμ and seismic boundary topography. Kernels for the quality factor can be obtained in a way similar to those for seismic velocities with the help of the Hilbert transform. The effects of seismic velocities and quality factor on either traveltime or amplitude are coupled. Kernels for boundary topography involve spatial gradient of the SGTs and they also exhibit interesting finite-frequency characteristics. Examples of quality factor and boundary topography kernels will be shown for a realistic model for the Taiwan region with three-dimensional velocity variation as well as surface and Moho discontinuity topography.

Design Optimization Method for Composite Components Based on Moment Reliability-Sensitivity Criteria

NASA Astrophysics Data System (ADS)

Sun, Zhigang; Wang, Changxi; Niu, Xuming; Song, Yingdong

2017-08-01

In this paper, a Reliability-Sensitivity Based Design Optimization (RSBDO) methodology for the design of the ceramic matrix composites (CMCs) components has been proposed. A practical and efficient method for reliability analysis and sensitivity analysis of complex components with arbitrary distribution parameters are investigated by using the perturbation method, the respond surface method, the Edgeworth series and the sensitivity analysis approach. The RSBDO methodology is then established by incorporating sensitivity calculation model into RBDO methodology. Finally, the proposed RSBDO methodology is applied to the design of the CMCs components. By comparing with Monte Carlo simulation, the numerical results demonstrate that the proposed methodology provides an accurate, convergent and computationally efficient method for reliability-analysis based finite element modeling engineering practice.

Numerical solution of the Hele-Shaw equations

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

Whitaker, N.

1987-04-01

An algorithm is presented for approximating the motion of the interface between two immiscible fluids in a Hele-Shaw cell. The interface is represented by a set of volume fractions. We use the Simple Line Interface Calculation method along with the method of fractional steps to transport the interface. The equation of continuity leads to a Poisson equation for the pressure. The Poisson equation is discretized. Near the interface where the velocity field is discontinuous, the discretization is based on a weak formulation of the continuity equation. Interpolation is used on each side of the interface to increase the accuracy ofmore » the algorithm. The weak formulation as well as the interpolation are based on the computed volume fractions. This treatment of the interface is new. The discretized equations are solved by a modified conjugate gradient method. Surface tension is included and the curvature is computed through the use of osculating circles. For perturbations of small amplitude, a surprisingly good agreement is found between the numerical results and linearized perturbation theory. Numerical results are presented for the finite amplitude growth of unstable fingers. 62 refs., 13 figs.« less

Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2007-06-01

In [P.K. Moore, Effects of basis selection and h-refinement on error estimator reliability and solution efficiency for higher-order methods in three space dimensions, Int. J. Numer. Anal. Mod. 3 (2006) 21-51] a fixed, high-order h-refinement finite element algorithm, Href, was introduced for solving reaction-diffusion equations in three space dimensions. In this paper Href is coupled with continuation creating an automatic method for solving regularly and singularly perturbed reaction-diffusion equations. The simple quasilinear Newton solver of Moore, (2006) is replaced by the nonlinear solver NITSOL [M. Pernice, H.F. Walker, NITSOL: a Newton iterative solver for nonlinear systems, SIAM J. Sci. Comput. 19 (1998) 302-318]. Good initial guesses for the nonlinear solver are obtained using continuation in the small parameter ɛ. Two strategies allow adaptive selection of ɛ. The first depends on the rate of convergence of the nonlinear solver and the second implements backtracking in ɛ. Finally a simple method is used to select the initial ɛ. Several examples illustrate the effectiveness of the algorithm.

The effect of delays on filament oscillations and stability

NASA Astrophysics Data System (ADS)

van den Oord, G. H. J.; Schutgens, N. A. J.; Kuperus, M.

1998-11-01

We discuss the linear response of a filament to perturbations, taking the finite communication time between the filament and the photosphere into account. The finite communication time introduces delays in the system. Recently Schutgens (1997ab) investigated the solutions of the delay equation for vertical perturbations. In this paper we expand his analysis by considering also horizontal and coupled oscillations. The latter occur in asymmetric coronal fields. We also discuss the effect of Alfven wave emission on filament oscillations and show that wave emission is important for stabilizing filaments. We introduce a fairly straightforward method to study the solutions of delay equations as a function of the filament-photosphere communication time. A solution can be described by a linear combination of damped harmonic oscillations each characterized by a frequency, a damping/growth time and, accordingly, a quality factor. As a secondary result of our analysis we show that, within the context of line current models, Kippenhahn/Schlüter-type filament equilibria can never be stable in the horizontal and the vertical direction at the same time but we also demonstrate that Kuperus/Raadu-type equilibria can account for both an inverse or a normal polarity signature. The diagnostic value of our analysis for determining, e.g., the filament current from observations of oscillating filaments is discussed.

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.

Wave propagation in a random medium

NASA Technical Reports Server (NTRS)

Lee, R. W.; Harp, J. C.

1969-01-01

A simple technique is used to derive statistical characterizations of the perturbations imposed upon a wave (plane, spherical or beamed) propagating through a random medium. The method is essentially physical rather than mathematical, and is probably equivalent to the Rytov method. The limitations of the method are discussed in some detail; in general they are restrictive only for optical paths longer than a few hundred meters, and for paths at the lower microwave frequencies. Situations treated include arbitrary path geometries, finite transmitting and receiving apertures, and anisotropic media. Results include, in addition to the usual statistical quantities, time-lagged functions, mixed functions involving amplitude and phase fluctuations, angle-of-arrival covariances, frequency covariances, and other higher-order quantities.

The renormalization scale-setting problem in QCD

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

Wu, Xing-Gang; Brodsky, Stanley J.; Mojaza, Matin

2013-09-01

A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this ad hoc procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of the scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scalemore » ambiguity and show how to obtain renormalization scheme- and scale-independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale-dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, i.e., the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky–Lepage–Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance. Using the PMC, all non-conformal terms associated with the β-function in the perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC provides the principle underlying the BLM method, since it gives the general rule for extending BLM up to any perturbative order; in fact, they are equivalent to each other through the PMC–BLM correspondence principle. Thus, all the features previously observed in the BLM literature are also adaptable to the PMC. The PMC scales and the resulting finite-order PMC predictions are to high accuracy independent of the choice of the initial renormalization scale, and thus consistent with RG invariance. The PMC is also consistent with the renormalization scale-setting procedure for QED in the zero-color limit. The use of the PMC thus eliminates a serious systematic scale error in perturbative QCD predictions, greatly improving the precision of empirical tests of the Standard Model and their sensitivity to new physics.« less

Tsunami modelling with adaptively refined finite volume methods

USGS Publications Warehouse

LeVeque, R.J.; George, D.L.; Berger, M.J.

2011-01-01

Numerical modelling of transoceanic tsunami propagation, together with the detailed modelling of inundation of small-scale coastal regions, poses a number of algorithmic challenges. The depth-averaged shallow water equations can be used to reduce this to a time-dependent problem in two space dimensions, but even so it is crucial to use adaptive mesh refinement in order to efficiently handle the vast differences in spatial scales. This must be done in a 'wellbalanced' manner that accurately captures very small perturbations to the steady state of the ocean at rest. Inundation can be modelled by allowing cells to dynamically change from dry to wet, but this must also be done carefully near refinement boundaries. We discuss these issues in the context of Riemann-solver-based finite volume methods for tsunami modelling. Several examples are presented using the GeoClaw software, and sample codes are available to accompany the paper. The techniques discussed also apply to a variety of other geophysical flows. ?? 2011 Cambridge University Press.

Emergence and equilibration of jets in planetary turbulence

NASA Astrophysics Data System (ADS)

Constantinou, Navid; Ioannou, Petros; Farrell, Brian

2013-04-01

Spatially and temporally coherent large scale jets that are not forced directly at the jet scale are prominent feature of rotating turbulence. A familiar example is the midlatitude jet in the Earth's atmosphere and the banded winds of the giants planets. These jets arise and are supported by the systematic organisation of the turbulent Reynolds stresses. Understanding the mechanism producing the required eddy momentum flux convergence, and how the jets and associated eddy field mutually adjust to maintain a steady jet structure at finite amplitude, constitute fundamental theoretical problems. Stochastic Structural Stability Theory (SSST) gives an explanation for jet formation that is fundamentally based on the interaction between jets and their associated field of turbulent eddies. SSST combines the full dynamics of the zonal mean flow with the second order statistics of the turbulent field obtained from a stochastic turbulence model (STM). The quasi-linear (QL) approximation to the full nonlinear dynamics (NL) results when the perturbation-perturbation interactions are parameterized in the perturbation equations, while interaction between the perturbations and the zonal mean flow is retained in the zonal mean equation. SSST consists of an infinite ensemble of perturbations evolving under QL. Therefore, SSST provides a set of dynamical equations for the mean flow and the second order statistics of the second cummulant of the perturbation vorticity field, which are autonomous and fluctuation free and can facilitate analytic study of turbulent equilibria and their stability as a function of parameters. Thus, jet formation in homogeneous beta-turbulence can be identified with an SSST structural instability of a homogeneous (mean flow free) SSTT equilibrium. We investigate the emergence and equilibration of jets from homogeneous barotropic beta-plane turbulence in the absence of coherent external forcing. SSST predicts that infinitesimal perturbations with zonal jet form organise homogeneous turbulence to produce systematic upgradient fluxes, giving rise to exponential jet growth and eventually to the establishment of finite amplitude equilibrium jets. We compare these predictions with simulations of the NL equations and their QL approximation in order to examine further the mechanism of emergence and equilibration of jets from turbulence. We concentrate on the effects of perturbation-perturbation nonlinearity on jet bifurcation and equilibration, and on the influence of perturbations in exciting the manifold of SSST modes with jet structure. We find that the bifurcation structure predicted by SSST for the emergence of zonal jets from a homogeneous turbulent state is confirmed by both QL and NL simulations. Moreover, we show that the finite amplitude equilibrium jets found in NL and QL simulations are as predicted by the fixed point solutions of SSST. Obtaining this agreement between NL and both SSST and QL simulations required in some cases that the modification of the turbulent spectrum caused by the perturbation-perturbation nonlinearity in NL be accounted for in the specification of the stochastic forcing in QL and SSST. These results confirm that jet emergence in barotropic beta-plane turbulence can be traced to the cooperative mean flow/perturbation instability that is captured by SSST.

Performance and Self-Consistency of the Generalized Dielectric Dependent Hybrid Functional

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

Brawand, Nicholas P.; Govoni, Marco; Vörös, Márton

Here, we analyze the performance of the recently proposed screened exchange constant functional (SX) on the GW100 test set, and we discuss results obtained at different levels of self-consistency. The SX functional is a generalization of dielectric dependent hybrid functionals to finite systems; it is nonempirical and depends on the average screening of the exchange interaction. We compare results for ionization potentials obtained with SX to those of CCSD(T) calculations and experiments, and we find excellent agreement, on par with recent state of the art methods based on many body perturbation theory. Applying SX perturbatively to correct PBE eigenvalues yieldsmore » improved results in most cases, except for ionic molecules, for which wave function self-consistency is instead crucial. Calculations where wave functions and the screened exchange constant (α SX) are determined self-consistently, and those where α SX is fixed to the value determined within PBE, yield results of comparable accuracy. Perturbative G 0W 0 corrections of eigenvalues obtained with self-consistent αSX are small on average, for all molecules in the GW100 test set.« less

Performance and Self-Consistency of the Generalized Dielectric Dependent Hybrid Functional

DOE PAGES

Brawand, Nicholas P.; Govoni, Marco; Vörös, Márton; ...

2017-05-24

Here, we analyze the performance of the recently proposed screened exchange constant functional (SX) on the GW100 test set, and we discuss results obtained at different levels of self-consistency. The SX functional is a generalization of dielectric dependent hybrid functionals to finite systems; it is nonempirical and depends on the average screening of the exchange interaction. We compare results for ionization potentials obtained with SX to those of CCSD(T) calculations and experiments, and we find excellent agreement, on par with recent state of the art methods based on many body perturbation theory. Applying SX perturbatively to correct PBE eigenvalues yieldsmore » improved results in most cases, except for ionic molecules, for which wave function self-consistency is instead crucial. Calculations where wave functions and the screened exchange constant (α SX) are determined self-consistently, and those where α SX is fixed to the value determined within PBE, yield results of comparable accuracy. Perturbative G 0W 0 corrections of eigenvalues obtained with self-consistent αSX are small on average, for all molecules in the GW100 test set.« less

Finite-temperature spin dynamics in a perturbed quantum critical Ising chain with an E₈ symmetry.

PubMed

Wu, Jianda; Kormos, Márton; Si, Qimiao

2014-12-12

A spectrum exhibiting E₈ symmetry is expected to arise when a small longitudinal field is introduced in the transverse-field Ising chain at its quantum critical point. Evidence for this spectrum has recently come from neutron scattering measurements in cobalt niobate, a quasi-one-dimensional Ising ferromagnet. Unlike its zero-temperature counterpart, the finite-temperature dynamics of the model has not yet been determined. We study the dynamical spin structure factor of the model at low frequencies and nonzero temperatures, using the form factor method. Its frequency dependence is singular, but differs from the diffusion form. The temperature dependence of the nuclear magnetic resonance (NMR) relaxation rate has an activated form, whose prefactor we also determine. We propose NMR experiments as a means to further test the applicability of the E₈ description for CoNb₂O₆.

Stability and bifurcation analysis of oscillators with piecewise-linear characteristics - A general approach

NASA Technical Reports Server (NTRS)

Noah, S. T.; Kim, Y. B.

1991-01-01

A general approach is developed for determining the periodic solutions and their stability of nonlinear oscillators with piecewise-smooth characteristics. A modified harmonic balance/Fourier transform procedure is devised for the analysis. The procedure avoids certain numerical differentiation employed previously in determining the periodic solutions, therefore enhancing the reliability and efficiency of the method. Stability of the solutions is determined via perturbations of their state variables. The method is applied to a forced oscillator interacting with a stop of finite stiffness. Flip and fold bifurcations are found to occur. This led to the identification of parameter ranges in which chaotic response occurred.

Bridging the Transition from Mesoscale to Microscale Turbulence in Numerical Weather Prediction Models

NASA Astrophysics Data System (ADS)

Muñoz-Esparza, Domingo; Kosović, Branko; Mirocha, Jeff; van Beeck, Jeroen

2014-12-01

With a focus towards developing multiscale capabilities in numerical weather prediction models, the specific problem of the transition from the mesoscale to the microscale is investigated. For that purpose, idealized one-way nested mesoscale to large-eddy simulation (LES) experiments were carried out using the Weather Research and Forecasting model framework. It is demonstrated that switching from one-dimensional turbulent diffusion in the mesoscale model to three-dimensional LES mixing does not necessarily result in an instantaneous development of turbulence in the LES domain. On the contrary, very large fetches are needed for the natural transition to turbulence to occur. The computational burden imposed by these long fetches necessitates the development of methods to accelerate the generation of turbulence on a nested LES domain forced by a smooth mesoscale inflow. To that end, four new methods based upon finite amplitude perturbations of the potential temperature field along the LES inflow boundaries are developed, and investigated under convective conditions. Each method accelerated the development of turbulence within the LES domain, with two of the methods resulting in a rapid generation of production and inertial range energy content associated to microscales that is consistent with non-nested simulations using periodic boundary conditions. The cell perturbation approach, the simplest and most efficient of the best performing methods, was investigated further under neutral and stable conditions. Successful results were obtained in all the regimes, where satisfactory agreement of mean velocity, variances and turbulent fluxes, as well as velocity and temperature spectra, was achieved with reference non-nested simulations. In contrast, the non-perturbed LES solution exhibited important energy deficits associated to a delayed establishment of fully-developed turbulence. The cell perturbation method has negligible computational cost, significantly accelerates the generation of realistic turbulence, and requires minimal parameter tuning, with the necessary information relatable to mean inflow conditions provided by the mesoscale solution.

Inhomogeneous atomic Bose-Fermi mixtures in cubic lattices.

PubMed

Cramer, M; Eisert, J; Illuminati, F

2004-11-05

We determine the ground state properties of inhomogeneous mixtures of bosons and fermions in cubic lattices and parabolic confining potentials. For finite hopping we determine the domain boundaries between Mott-insulator plateaux and hopping-dominated regions for lattices of arbitrary dimension within mean-field and perturbation theory. The results are compared with a new numerical method that is based on a Gutzwiller variational approach for the bosons and an exact treatment for the fermions. The findings can be applied as a guideline for future experiments with trapped atomic Bose-Fermi mixtures in optical lattices.

A limiting analysis for edge effects in angle-ply laminates

NASA Technical Reports Server (NTRS)

Hsu, P. W.; Herakovich, C. T.

1976-01-01

A zeroth order solution for edge effects in angle ply composite laminates using perturbation techniques and a limiting free body approach was developed. The general method of solution for laminates is developed and then applied to the special case of a graphite/epoxy laminate. Interlaminar stress distributions are obtained as a function of the laminate thickness to width ratio h/b and compared to existing numerical results. The solution predicts stable, continuous stress distributions, determines finite maximum tensile interlaminar normal stress for two laminates, and provides mathematical evidence for singular interlaminar shear stresses.

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.

Probing Majorana modes in the tunneling spectra of a resonant level.

PubMed

Korytár, R; Schmitteckert, P

2013-11-27

Unambiguous identification of Majorana physics presents an outstanding problem whose solution could render topological quantum computing feasible. We develop a numerical approach to treat finite-size superconducting chains supporting Majorana modes, which is based on iterative application of a two-site Bogoliubov transformation. We demonstrate the applicability of the method by studying a resonant level attached to the superconductor subject to external perturbations. In the topological phase, we show that the spectrum of a single resonant level allows us to distinguish peaks coming from Majorana physics from the Kondo resonance.

Spatio-temporal evolution of perturbations in ensembles initialized by bred, Lyapunov and singular vectors

NASA Astrophysics Data System (ADS)

Pazó, Diego; Rodríguez, Miguel A.; López, Juan M.

2010-05-01

We study the evolution of finite perturbations in the Lorenz ‘96 model, a meteorological toy model of the atmosphere. The initial perturbations are chosen to be aligned along different dynamic vectors: bred, Lyapunov, and singular vectors. Using a particular vector determines not only the amplification rate of the perturbation but also the spatial structure of the perturbation and its stability under the evolution of the flow. The evolution of perturbations is systematically studied by means of the so-called mean-variance of logarithms diagram that provides in a very compact way the basic information to analyse the spatial structure. We discuss the corresponding advantages of using those different vectors for preparing initial perturbations to be used in ensemble prediction systems, focusing on key properties: dynamic adaptation to the flow, robustness, equivalence between members of the ensemble, etc. Among all the vectors considered here, the so-called characteristic Lyapunov vectors are possibly optimal, in the sense that they are both perfectly adapted to the flow and extremely robust.

Spatio-temporal evolution of perturbations in ensembles initialized by bred, Lyapunov and singular vectors

NASA Astrophysics Data System (ADS)

Pazó, Diego; Rodríguez, Miguel A.; López, Juan M.

2010-01-01

We study the evolution of finite perturbations in the Lorenz `96 model, a meteorological toy model of the atmosphere. The initial perturbations are chosen to be aligned along different dynamic vectors: bred, Lyapunov, and singular vectors. Using a particular vector determines not only the amplification rate of the perturbation but also the spatial structure of the perturbation and its stability under the evolution of the flow. The evolution of perturbations is systematically studied by means of the so-called mean-variance of logarithms diagram that provides in a very compact way the basic information to analyse the spatial structure. We discuss the corresponding advantages of using those different vectors for preparing initial perturbations to be used in ensemble prediction systems, focusing on key properties: dynamic adaptation to the flow, robustness, equivalence between members of the ensemble, etc. Among all the vectors considered here, the so-called characteristic Lyapunov vectors are possibly optimal, in the sense that they are both perfectly adapted to the flow and extremely robust.

Stochastic evaluation of second-order many-body perturbation energies.

PubMed

Willow, Soohaeng Yoo; Kim, Kwang S; Hirata, So

2012-11-28

With the aid of the Laplace transform, the canonical expression of the second-order many-body perturbation correction to an electronic energy is converted into the sum of two 13-dimensional integrals, the 12-dimensional parts of which are evaluated by Monte Carlo integration. Weight functions are identified that are analytically normalizable, are finite and non-negative everywhere, and share the same singularities as the integrands. They thus generate appropriate distributions of four-electron walkers via the Metropolis algorithm, yielding correlation energies of small molecules within a few mE(h) of the correct values after 10(8) Monte Carlo steps. This algorithm does away with the integral transformation as the hotspot of the usual algorithms, has a far superior size dependence of cost, does not suffer from the sign problem of some quantum Monte Carlo methods, and potentially easily parallelizable and extensible to other more complex electron-correlation theories.

Nonlinear ideal magnetohydrodynamics instabilities

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

Pfirsch, D.; Sudan, R.N.

1993-07-01

Explosive phenomena such as internal disruptions in toroidal discharges and solar flares are difficult to explain in terms of linear instabilities. A plasma approaching a linear stability limit can, however, become nonlinearly and explosively unstable, with noninfinitesimal perturbations even before the marginal state is reached. For such investigations, a nonlinear extension of the usual MHD (magnetohydrodynamic) energy principle is helpful. (This was obtained by Merkel and Schlueter, Sitzungsberichted. Bayer. Akad. Wiss., Munich, 1976, No. 7, for Cartesian coordinate systems.) A coordinate system independent Eulerian formulation for the Lagrangian allowing for equilibria with flow and with built-in conservation laws for mass,more » magnetic flux, and entropy is developed in this paper which is similar to Newcomb's Lagrangian method of 1962 [Nucl. Fusion, Suppl., Pt. II, 452 (1962)]. For static equilibria nonlinear stability is completely determined by the potential energy. For a potential energy which contains second- and [ital n]th order or some more general contributions only, it is shown in full generality that linearly unstable and marginally stable systems are explosively unstable even for infinitesimal perturbations; linearly absolutely stable systems require finite initial perturbations. For equilibria with Abelian symmetries symmetry breaking initial perturbations are needed, which should be observed in numerical simulations. Nonlinear stability is proved for two simple examples, [ital m]=0 perturbations of a Bennet Z-pinch and [ital z]-independent perturbations of a [theta] pinch. The algebra for treating these cases reduces considerably if symmetries are taken into account from the outset, as suggested by M. N. Rosenbluth (private communication, 1992).« less

Effects of finite electron temperature on gradient drift instabilities in partially magnetized plasmas

NASA Astrophysics Data System (ADS)

Lakhin, V. P.; Ilgisonis, V. I.; Smolyakov, A. I.; Sorokina, E. A.; Marusov, N. A.

2018-01-01

The gradient-drift instabilities of partially magnetized plasmas in plasma devices with crossed electric and magnetic fields are investigated in the framework of the two-fluid model with finite electron temperature in an inhomogeneous magnetic field. The finite electron Larmor radius (FLR) effects are also included via the gyroviscosity tensor taking into account the magnetic field gradient. This model correctly describes the electron dynamics for k⊥ρe>1 in the sense of Padé approximants (here, k⊥ and ρe are the wavenumber perpendicular to the magnetic field and the electron Larmor radius, respectively). The local dispersion relation for electrostatic plasma perturbations with the frequency in the range between the ion and electron cyclotron frequencies and propagating strictly perpendicular to the magnetic field is derived. The dispersion relation includes the effects of the equilibrium E ×B electron current, finite ion velocity, electron inertia, electron FLR, magnetic field gradients, and Debye length effects. The necessary and sufficient condition of stability is derived, and the stability boundary is found. It is shown that, in general, the electron inertia and FLR effects stabilize the short-wavelength perturbations. In some cases, such effects completely suppress the high-frequency short-wavelength modes so that only the long-wavelength low-frequency (with respect to the lower-hybrid frequency) modes remain unstable.

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.

Non-perturbative quark mass renormalisation and running in N_{f}=3 QCD

NASA Astrophysics Data System (ADS)

Campos, I.; Fritzsch, P.; Pena, C.; Preti, D.; Ramos, A.; Vladikas, A.

2018-05-01

We determine from first principles the quark mass anomalous dimension in N_{f}=3 QCD between the electroweak and hadronic scales. This allows for a fully non-perturbative connection of the perturbative and non-perturbative regimes of the Standard Model in the hadronic sector. The computation is carried out to high accuracy, employing massless O (a)-improved Wilson quarks and finite-size scaling techniques. We also provide the matching factors required in the renormalisation of light quark masses from lattice computations with O (a)-improved Wilson fermions and a tree-level Symanzik improved gauge action. The total uncertainty due to renormalisation and running in the determination of light quark masses in the SM is thus reduced to about 1%.

Finite-volume spectra of the Lee-Yang model

NASA Astrophysics Data System (ADS)

Bajnok, Zoltan; el Deeb, Omar; Pearce, Paul A.

2015-04-01

We consider the non-unitary Lee-Yang minimal model in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels ( r, s) = (1 , 1) , (1 , 2), (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply φ 1,3 integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a Φ1,3 integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated A 4 RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of ( m, n) systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.

Longitudinal structure of MHD perturbations at the boundary of convective stability in the Kruskal-Oberman model

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

Arsenin, V. V.

2010-10-15

It is shown that, in contrast to the MHD model, a perturbation at the boundary of convective stability of a finite-pressure plasma in confinement systems without an averaged minB in the Kruskal-Oberman model is not generally a purely flute one. The reasons for this discrepancy are clarified. The analysis is carried out for axisymmetric configurations formed by a poloidal magnetic field.

Ground-state energies of simple metals

NASA Technical Reports Server (NTRS)

Hammerberg, J.; Ashcroft, N. W.

1974-01-01

A structural expansion for the static ground-state energy of a simple metal is derived. Two methods are presented, one an approach based on single-particle band structure which treats the electron gas as a nonlinear dielectric, the other a more general many-particle analysis using finite-temperature perturbation theory. The two methods are compared, and it is shown in detail how band-structure effects, Fermi-surface distortions, and chemical-potential shifts affect the total energy. These are of special interest in corrections to the total energy beyond third order in the electron-ion interaction and hence to systems where differences in energies for various crystal structures are exceptionally small. Preliminary calculations using these methods for the zero-temperature thermodynamic functions of atomic hydrogen are reported.

Unsteady combustion of solid propellants

NASA Astrophysics Data System (ADS)

Chung, T. J.; Kim, P. K.

The oscillatory motions of all field variables (pressure, temperature, velocity, density, and fuel fractions) in the flame zone of solid propellant rocket motors are calculated using the finite element method. The Arrhenius law with a single step forward chemical reaction is used. Effects of radiative heat transfer, impressed arbitrary acoustic wave incidence, and idealized mean flow velocities are also investigated. Boundary conditions are derived at the solid-gas interfaces and at the flame edges which are implemented via Lagrange multipliers. Perturbation expansions of all governing conservation equations up to and including the second order are carried out so that nonlinear oscillations may be accommodated. All excited frequencies are calculated by means of eigenvalue analyses, and the combustion response functions corresponding to these frequencies are determined. It is shown that the use of isoparametric finite elements, Gaussian quadrature integration, and the Lagrange multiplier boundary matrix scheme offers a convenient approach to two-dimensional calculations.

Probabilistic finite elements for fatigue and fracture analysis

NASA Astrophysics Data System (ADS)

Belytschko, Ted; Liu, Wing Kam

1993-04-01

An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.

Probabilistic finite elements for fatigue and fracture analysis

NASA Technical Reports Server (NTRS)

Belytschko, Ted; Liu, Wing Kam

1993-01-01

An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.

Orbital relaxation effects on Kohn–Sham frontier orbital energies in density functional theory

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

Zhang, DaDi; Zheng, Xiao, E-mail: xz58@ustc.edu.cn; Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026

2015-04-21

We explore effects of orbital relaxation on Kohn–Sham frontier orbital energies in density functional theory by using a nonempirical scaling correction approach developed in Zheng et al. [J. Chem. Phys. 138, 174105 (2013)]. Relaxation of Kohn–Sham orbitals upon addition/removal of a fractional number of electrons to/from a finite system is determined by a systematic perturbative treatment. The information of orbital relaxation is then used to improve the accuracy of predicted Kohn–Sham frontier orbital energies by Hartree–Fock, local density approximation, and generalized gradient approximation methods. The results clearly highlight the significance of capturing the orbital relaxation effects. Moreover, the proposed scalingmore » correction approach provides a useful way of computing derivative gaps and Fukui quantities of N-electron finite systems (N is an integer), without the need to perform self-consistent-field calculations for (N ± 1)-electron systems.« less

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2010-01-01

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC-NN, CC-SA, and CC-FA schemes on all grids and for NC schemes on triangular grids; the discretization errors of the CC-NA scheme without clipping do not converge on irregular grids. Accurate gradient reconstruction can be achieved by introducing a local approximate mapping; without approximate mapping, only the NC scheme with weighted LSQ method provides accurate gradients. Defect correction iterations for the CC-NA scheme without clipping diverge; for the NC scheme with weighted LSQ method, the iterations either diverge or converge very slowly. The best option in curved geometries is the CC-SA scheme that offers low complexity, second-order discretization errors, and fast convergence.

Transit-Time Damping, Landau Damping, and Perturbed Orbits

NASA Astrophysics Data System (ADS)

Simon, A.; Short, R. W.

1997-11-01

Transit-time damping(G.J. Morales and Y.C. Lee, Phys. Rev. Lett. 33), 1534 (1974).*^,*(P.A. Robinson, Phys. Fluids B 3), 545 (1991).** has traditionally been obtained by calculating the net energy gain of transiting electrons, of velocity v, to order E^2* in the amplitude of a localized electric field. This necessarily requires inclusion of the perturbed orbits in the equation of motion. A similar method has been used by others(D.R. Nicholson, Introduction to Plasma Theory) (Wiley, 1983).*^,*(E.M. Lifshitz and L.P. Pitaevskifi, Physical Kinetics) (Pergamon, 1981).** to obtain a ``physical'' picture of Landau damping in a nonlocalized field. The use of perturbed orbits seems odd since the original derivation of Landau (and that of Dawson) never went beyond a linear picture of the dynamics. We introduce a novel method that takes advantage of the time-reversal invariance of the Vlasov equation and requires only the unperturbed orbits to obtain the result. Obviously, there is much reduction in complexity. Application to finite slab geometry yields a simple expression for the damping rate. Equivalence to much more complicated results^2* is demonstrated. This method allows us to calculate damping in more complicated geometries and more complex electric fields, such as occur in SRS in filaments. See accompanying talk.(R.W. Short and A. Simon, this conference.) This work was supported by the U.S. DOE Office of Inertial Confinement Fusion under Co-op Agreement No. DE-FC03-92SF19460.

Excitation of the hydrogen atom by fast-electron impact in the presence of a laser field

NASA Astrophysics Data System (ADS)

Bhattacharya, Manabesh; Sinha, C.; Sil, N. C.

1991-08-01

An approach has been developed to study the excitation of a ground-state H atom to the n=2 level under the simultaneous action of fast-electron impact and a monochromatic, linearly polarized, homogeneous laser beam. The laser frequency is assumed to be low (soft-photon limit) so that a stationary-state perturbation theory can be applied as is done in the adiabatic theory. An elegant method has been developed in the present work to construct the dressed excited-state wave functions of the H atom using first-order perturbation theory in the parabolic coordinate representation. By virtue of this method, the problem arising due to the degeneracy of the excited states of the H atom has been successfully overcome. The main advantage of the present approach is that the dressed wave function has been obtained in terms of a finite number of Laguerre polynomials instead of an infinite summation occurring in the usual perturbative treatment. The amplitude for direct excitation (without exchange) has been obtained in closed form. Numerical results for differential cross sections are presented for individual excitations to different Stark manifolds as well as for excitations to the n=2 level at high energies (100 and 200 eV) and for field directions both parallel and perpendicular to the incident electron momentum. Extension to a higher order of perturbation is also possible in the present approach for the construction of the dressed states, and the electron-exchange effect can also be taken into account without any further approximation.

Modelling and finite-time stability analysis of psoriasis pathogenesis

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Stress and Thermal Analysis of the In-Vessel Resonant Magnetic Perturbation Coils on the J-TEXT Tokamak

NASA Astrophysics Data System (ADS)

Hao, Changduan; Zhang, Ming; Ding, Yonghua; Rao, Bo; Cen, Yishun; Zhuang, Ge

2012-01-01

A set of four in-vessel saddle coils was designed to generate a helical field on the J-TEXT tokamak to study the influences of the external perturbation field on plasma. The coils are fed with alternating current up to 10 kA at frequency up to 10 kHz. Due to the special structure, complex thermal environment and limited space in the vacuum chamber, it is very important to make sure that the coils will not be damaged when undergoing the huge electromagnetic forces in the strong toroidal field, and that their temperatures don't rise too much and destroy the insulation. A 3D finite element model is developed in this paper using the ANSYS code, stresses are analyzed to find the worst condition, and a mounting method is then established. The results of the stress and modal analyses show that the mounting method meets the strength requirements. Finally, a thermal analysis is performed to study the cooling process and the temperature distribution of the coils.

Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

NASA Technical Reports Server (NTRS)

Vaughan, William W.; Friedman, Mark J.; Monteiro, Anand C.

1993-01-01

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem.

Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests

NASA Astrophysics Data System (ADS)

Font, José A.; Stergioulas, Nikolaos; Kokkotas, Kostas D.

2000-04-01

We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different high-resolution shock-capturing (HRSC) finite-difference schemes (based on approximate Riemann solvers) and compare their accuracy in preserving uniformly rotating stationary initial configurations in long-term evolutions. Among these four schemes, we find that the third-order piecewise parabolic method scheme is superior in maintaining the initial rotation law in long-term evolutions, especially near the surface of the star. It is further shown that HRSC schemes are suitable for the evolution of perturbed neutron stars and for the accurate identification (via Fourier transforms) of normal modes of oscillation. This is demonstrated for radial and quadrupolar pulsations in the non-rotating limit, where we find good agreement with frequencies obtained with a linear perturbation code. The code can be used for studying small-amplitude or non-linear pulsations of differentially rotating neutron stars, while our present results serve as testbed computations for three-dimensional general-relativistic evolution codes.

An uncertainty model of acoustic metamaterials with random parameters

NASA Astrophysics Data System (ADS)

He, Z. C.; Hu, J. Y.; Li, Eric

2018-01-01

Acoustic metamaterials (AMs) are man-made composite materials. However, the random uncertainties are unavoidable in the application of AMs due to manufacturing and material errors which lead to the variance of the physical responses of AMs. In this paper, an uncertainty model based on the change of variable perturbation stochastic finite element method (CVPS-FEM) is formulated to predict the probability density functions of physical responses of AMs with random parameters. Three types of physical responses including the band structure, mode shapes and frequency response function of AMs are studied in the uncertainty model, which is of great interest in the design of AMs. In this computation, the physical responses of stochastic AMs are expressed as linear functions of the pre-defined random parameters by using the first-order Taylor series expansion and perturbation technique. Then, based on the linear function relationships of parameters and responses, the probability density functions of the responses can be calculated by the change-of-variable technique. Three numerical examples are employed to demonstrate the effectiveness of the CVPS-FEM for stochastic AMs, and the results are validated by Monte Carlo method successfully.

An Analysis of the Oil-Whirl Instability

NASA Astrophysics Data System (ADS)

Schultz, William W.; Han, Heng-Chu; Boyd, John P.; Schumack, Mark

1997-11-01

We investigate the hydrodynamic stability of a rotating journal translating inside a stationary bearing. A long (two-dimensional) journal bearing separated by a Newtonian non-cavitating lubricant is studied for shaft stability. Spectral element methods, perturbation methods, and linear stability analyses are used. The influences of fluid inertia, eccentricity, ellipticity, shaft mass, and finite gap on hydrodynamic stability are explored. Lubrication theory using Reynolds equation ignoring fluid inertia leads to erroneous conclusions. Without fluid inertia, the shaft is always unstable. However, the journal is conditionally stable even in the limit Rearrow 0 if fluid inertia is included. Increasing eccentricity helps stabilize a whirling shaft. Non-circular shaft bearings, for example elliptical bearings, are observed to have better dynamic stability.

Electronic and optical properties of GaN/AlN quantum dots with adjacent threading dislocations

NASA Astrophysics Data System (ADS)

Ye, Han; Lu, Peng-Fei; Yu, Zhong-Yuan; Yao, Wen-Jie; Chen, Zhi-Hui; Jia, Bo-Yong; Liu, Yu-Min

2010-04-01

We present a theory to simulate a coherent GaN QD with an adjacent pure edge threading dislocation by using a finite element method. The piezoelectric effects and the strain modified band edges are investigated in the framework of multi-band k · p theory to calculate the electron and the heavy hole energy levels. The linear optical absorption coefficients corresponding to the interband ground state transition are obtained via the density matrix approach and perturbation expansion method. The results indicate that the strain distribution of the threading dislocation affects the electronic structure. Moreover, the ground state transition behaviour is also influenced by the position of the adjacent threading dislocation.

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

On the dynamics of approximating schemes for dissipative nonlinear equations

NASA Technical Reports Server (NTRS)

Jones, Donald A.

1993-01-01

Since one can rarely write down the analytical solutions to nonlinear dissipative partial differential equations (PDE's), it is important to understand whether, and in what sense, the behavior of approximating schemes to these equations reflects the true dynamics of the original equations. Further, because standard error estimates between approximations of the true solutions coming from spectral methods - finite difference or finite element schemes, for example - and the exact solutions grow exponentially in time, this analysis provides little value in understanding the infinite time behavior of a given approximating scheme. The notion of the global attractor has been useful in quantifying the infinite time behavior of dissipative PDEs, such as the Navier-Stokes equations. Loosely speaking, the global attractor is all that remains of a sufficiently large bounded set in phase space mapped infinitely forward in time under the evolution of the PDE. Though the attractor has been shown to have some nice properties - it is compact, connected, and finite dimensional, for example - it is in general quite complicated. Nevertheless, the global attractor gives a way to understand how the infinite time behavior of approximating schemes such as the ones coming from a finite difference, finite element, or spectral method relates to that of the original PDE. Indeed, one can often show that such approximations also have a global attractor. We therefore only need to understand how the structure of the attractor for the PDE behaves under approximation. This is by no means a trivial task. Several interesting results have been obtained in this direction. However, we will not go into the details. We mention here that approximations generally lose information about the system no matter how accurate they are. There are examples that show certain parts of the attractor may be lost by arbitrary small perturbations of the original equations.

The 1/ N Expansion of Tensor Models Beyond Perturbation Theory

NASA Astrophysics Data System (ADS)

Gurau, Razvan

2014-09-01

We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/ N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/ N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges. As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Borel summable and to prove that the cumulants respect an uniform scaling bound. In particular the quartically perturbed measures fall, in the N→ ∞ limit, in the universality class of Gaussian tensor models.

Selective Transient Cooling by Impulse Perturbations in a Simple Toy Model

NASA Astrophysics Data System (ADS)

Fabrizio, Michele

2018-06-01

We show in a simple exactly solvable toy model that a properly designed impulse perturbation can transiently cool down low-energy degrees of freedom at the expense of high-energy ones that heat up. The model consists of two infinite-range quantum Ising models: one, the high-energy sector, with a transverse field much bigger than the other, the low-energy sector. The finite-duration perturbation is a spin exchange that couples the two Ising models with an oscillating coupling strength. We find a cooling of the low-energy sector that is optimized by the oscillation frequency in resonance with the spin exchange excitation. After the perturbation is turned off, the Ising model with a low transverse field can even develop a spontaneous symmetry breaking despite being initially above the critical temperature.

The AdS3 propagator and the fate of locality

NASA Astrophysics Data System (ADS)

Chen, Hongbin; Fitzpatrick, A. Liam; Kaplan, Jared; Li, Daliang

2018-04-01

We recently used Virasoro symmetry considerations to propose an exact formula for a bulk proto-field ϕ in AdS3. In this paper we study the propagator < ϕϕ>. We show that many techniques from the study of conformal blocks can be generalized to compute it, including the semiclassical monodromy method and both forms of the Zamolodchikov recursion relations. When the results from recursion are expanded at large central charge, they match gravitational perturbation theory for a free scalar field coupled to gravity in our chosen gauge. We find that although the propagator is finite and well-defined at long distances, its perturbative expansion in {G}_N=3/2c exhibits UV/IR mixing effects. If we nevertheless interpret < ϕϕ> as a probe of bulk locality, then when {G}_{N{m}_{φ }}≪ 1 locality breaks down at the new short-distance scale {σ}_{\\ast}˜ √[4]{G_N{R}_{AdS}^3} . For ϕ with very large bulk mass, or at small central charge, bulk locality fails at the AdS length scale. In all cases, locality `breakdown' manifests as singularities or branch cuts at spacelike separation arising from non-perturbative quantum gravitational effects.

Error Field Assessment from Driven Mode Rotation: Results from Extrap-T2R Reversed-Field-Pinch and Perspectives for ITER

NASA Astrophysics Data System (ADS)

Volpe, F. A.; Frassinetti, L.; Brunsell, P. R.; Drake, J. R.; Olofsson, K. E. J.

2012-10-01

A new ITER-relevant non-disruptive error field (EF) assessment technique not restricted to low density and thus low beta was demonstrated at the Extrap-T2R reversed field pinch. Resistive Wall Modes (RWMs) were generated and their rotation sustained by rotating magnetic perturbations. In particular, stable modes of toroidal mode number n=8 and 10 and unstable modes of n=1 were used in this experiment. Due to finite EFs, and in spite of the applied perturbations rotating uniformly and having constant amplitude, the RWMs were observed to rotate non-uniformly and be modulated in amplitude (in the case of unstable modes, the observed oscillation was superimposed to the mode growth). This behavior was used to infer the amplitude and toroidal phase of n=1, 8 and 10 EFs. The method was first tested against known, deliberately applied EFs, and then against actual intrinsic EFs. Applying equal and opposite corrections resulted in longer discharges and more uniform mode rotation, indicating good EF compensation. The results agree with a simple theoretical model. Extensions to tearing modes, to the non-uniform plasma response to rotating perturbations, and to tokamaks, including ITER, will be discussed.

A perturbative correction for electron-inertia in magnetized sheath structures

NASA Astrophysics Data System (ADS)

Gohain, Munmi; Karmakar, Pralay K.

2016-10-01

We propose a hydrodynamic model to study the equilibrium properties of planar plasma sheaths in two-component quasi-neutral magnetized plasmas. It includes weak but finite electron-inertia incorporated via a regular perturbation of the electronic fluid dynamics only relative to a new smallness parameter, δ, assessing the weak inertial-to-electromagnetic strengths. The zeroth-order perturbation around δ leads to the usual Boltzmann distribution law, which describes inertialess thermalized electrons. The forthwith next higher-order yields the modified Boltzmann law describing the putative lowest-order electron-inertial correction, which is applied meticulously to derive the local Bohm criterion for sheath formation. It is found to be influenced jointly by electron-inertial corrective effects, magnetic field and field orientation relative to the bulk plasma flow. We establish that the mutualistic action of electron-inertia amid gyro-kinetic effects slightly enhances the ion-flow Mach threshold value (typically, M i0 ⩾ 1.140), against the normal value of unity, confrontationally towards the sheath entrance. A numerical illustrative scheme is methodically constructed to see the parametric dependence of the new sheath properties on diverse problem arguments. The merits and demerits are highlighted in the light of the existing results conjointly with clear indication to future ameliorations.

van der Waals interactions between nanostructures: Some analytic results from series expansions

NASA Astrophysics Data System (ADS)

Stedman, T.; Drosdoff, D.; Woods, L. M.

2014-01-01

The van der Waals force between objects of nontrivial geometries is considered. A technique based on a perturbation series approach is formulated in the dilute limit. We show that the dielectric response and object size can be decoupled and dominant contributions in terms of object separations can be obtained. This is a powerful method, which enables straightforward calculations of the interaction for different geometries. Our results for planar structures, such as thin sheets, infinitely long ribbons, and ribbons with finite dimensions, may be applicable for nanostructured devices where the van der Waals interaction plays an important role.

SCISEAL: A CFD code for analysis of fluid dynamic forces in seals

NASA Technical Reports Server (NTRS)

Athavale, Mahesh; Przekwas, Andrzej

1994-01-01

A viewgraph presentation is made of the objectives, capabilities, and test results of the computer code SCISEAL. Currently, the seal code has: a finite volume, pressure-based integration scheme; colocated variables with strong conservation approach; high-order spatial differencing, up to third-order; up to second-order temporal differencing; a comprehensive set of boundary conditions; a variety of turbulence models and surface roughness treatment; moving grid formulation for arbitrary rotor whirl; rotor dynamic coefficients calculated by the circular whirl and numerical shaker methods; and small perturbation capabilities to handle centered and eccentric seals.

Higgs-differential cross section at NNLO in dimensional regularisation

DOE PAGES

Dulat, Falko; Lionetti, Simone; Mistlberger, Bernhard; ...

2017-07-05

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.

A double perturbation method of postbuckling analysis in 2D curved beams for assembly of 3D ribbon-shaped structures

NASA Astrophysics Data System (ADS)

Fan, Zhichao; Hwang, Keh-Chih; Rogers, John A.; Huang, Yonggang; Zhang, Yihui

2018-02-01

Mechanically-guided 3D assembly based on controlled, compressive buckling represents a promising, emerging approach for forming complex 3D mesostructures in advanced materials. Due to the versatile applicability to a broad set of material types (including device-grade single-crystal silicon) over length scales from nanometers to centimeters, a wide range of novel applications have been demonstrated in soft electronic systems, interactive bio-interfaces as well as tunable electromagnetic devices. Previously reported 3D designs relied mainly on finite element analyses (FEA) as a guide, but the massive numerical simulations and computational efforts necessary to obtain the assembly parameters for a targeted 3D geometry prevent rapid exploration of engineering options. A systematic understanding of the relationship between a 3D shape and the associated parameters for assembly requires the development of a general theory for the postbuckling process. In this paper, a double perturbation method is established for the postbuckling analyses of planar curved beams, of direct relevance to the assembly of ribbon-shaped 3D mesostructures. By introducing two perturbation parameters related to the initial configuration and the deformation, the highly nonlinear governing equations can be transformed into a series of solvable, linear equations that give analytic solutions to the displacements and curvatures during postbuckling. Systematic analyses of postbuckling in three representative ribbon shapes (sinusoidal, polynomial and arc configurations) illustrate the validity of theoretical method, through comparisons to the results of experiment and FEA. These results shed light on the relationship between the important deformation quantities (e.g., mode ratio and maximum strain) and the assembly parameters (e.g., initial configuration and the applied strain). This double perturbation method provides an attractive route to the inverse design of ribbon-shaped 3D geometries, as demonstrated in a class of helical mesostructures.

Flux density calibration in diffuse optical tomographic systems.

PubMed

Biswas, Samir Kumar; Rajan, Kanhirodan; Vasu, Ram M

2013-02-01

The solution of the forward equation that models the transport of light through a highly scattering tissue material in diffuse optical tomography (DOT) using the finite element method gives flux density (Φ) at the nodal points of the mesh. The experimentally measured flux (Umeasured) on the boundary over a finite surface area in a DOT system has to be corrected to account for the system transfer functions (R) of various building blocks of the measurement system. We present two methods to compensate for the perturbations caused by R and estimate true flux density (Φ) from Umeasuredcal. In the first approach, the measurement data with a homogeneous phantom (Umeasuredhomo) is used to calibrate the measurement system. The second scheme estimates the homogeneous phantom measurement using only the measurement from a heterogeneous phantom, thereby eliminating the necessity of a homogeneous phantom. This is done by statistically averaging the data (Umeasuredhetero) and redistributing it to the corresponding detector positions. The experiments carried out on tissue mimicking phantom with single and multiple inhomogeneities, human hand, and a pork tissue phantom demonstrate the robustness of the approach.

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

Universal entanglement spectra of gapped one-dimensional field theories

NASA Astrophysics Data System (ADS)

Cho, Gil Young; Ludwig, Andreas W. W.; Ryu, Shinsei

2017-03-01

We discuss the entanglement spectrum of the ground state of a (1+1)-dimensional system in a gapped phase near a quantum phase transition. In particular, in proximity to a quantum phase transition described by a conformal field theory (CFT), the system is represented by a gapped Lorentz invariant field theory in the "scaling limit" (correlation length ξ much larger than microscopic "lattice" scale "a "), and can be thought of as a CFT perturbed by a relevant perturbation. We show that for such (1+1) gapped Lorentz invariant field theories in infinite space, the low-lying entanglement spectrum obtained by tracing out, say, left half-infinite space, is precisely equal to the physical spectrum of the unperturbed gapless, i.e., conformal field theory defined on a finite interval of length Lξ=ln(ξ /a ) with certain boundary conditions. In particular, the low-lying entanglement spectrum of the gapped theory is the finite-size spectrum of a boundary conformal field theory, and is always discrete and universal. Each relevant perturbation, and thus each gapped phase in proximity to the quantum phase transition, maps into a particular boundary condition. A similar property has been known to hold for Baxter's corner transfer matrices in a very special class of fine-tuned, namely, integrable off-critical lattice models, for the entire entanglement spectrum and independent of the scaling limit. In contrast, our result applies to completely general gapped Lorentz invariant theories in the scaling limit, without the requirement of integrability, for the low-lying entanglement spectrum. While the entanglement spectrum of the ground state of a gapped theory on a finite interval of length 2 R with suitable boundary conditions, bipartitioned into two equal pieces, turns out to exhibit a crossover between the finite-size spectra of the same CFT with in general different boundary conditions as the system size R crosses the correlation length from the "critical regime'' R ≪ξ to the "gapped regime'' R ≫ξ , the physical spectrum on a finite interval of length R with the same boundary conditions, on the other hand, is known to undergo a dramatic reorganization during the same crossover from being discrete to being continuous.

Comparison of the quadratic configuration interaction and coupled cluster approaches to electron correlation including the effect of triple excitations

NASA Technical Reports Server (NTRS)

Taylor, Peter R.; Lee, Timothy J.; Rendell, Alistair P.

1990-01-01

The recently proposed quadratic configuration interaction (QCI) method is compared with the more rigorous coupled cluster (CC) approach for a variety of chemical systems. Some of these systems are well represented by a single-determinant reference function and others are not. The finite order singles and doubles correlation energy, the perturbational triples correlation energy, and a recently devised diagnostic for estimating the importance of multireference effects are considered. The spectroscopic constants of CuH, the equilibrium structure of cis-(NO)2 and the binding energies of Be3, Be4, Mg3, and Mg4 were calculated using both approaches. The diagnostic for estimating multireference character clearly demonstrates that the QCI method becomes less satisfactory than the CC approach as non-dynamical correlation becomes more important, in agreement with a perturbational analysis of the two methods and the numerical estimates of the triple excitation energies they yield. The results for CuH show that the differences between the two methods become more apparent as the chemical systems under investigation becomes more multireference in nature and the QCI results consequently become less reliable. Nonetheless, when the system of interest is dominated by a single reference determinant both QCI and CC give very similar results.

Self-force via m-mode regularization and 2+1D evolution. II. Scalar-field implementation on Kerr spacetime

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

Dolan, Sam R.; Barack, Leor; Wardell, Barry

2011-10-15

This is the second in a series of papers aimed at developing a practical time-domain method for self-force calculations in Kerr spacetime. The key elements of the method are (i) removal of a singular part of the perturbation field with a suitable analytic 'puncture' based on the Detweiler-Whiting decomposition, (ii) decomposition of the perturbation equations in azimuthal (m-)modes, taking advantage of the axial symmetry of the Kerr background, (iii) numerical evolution of the individual m-modes in 2+1 dimensions with a finite-difference scheme, and (iv) reconstruction of the physical self-force from the mode sum. Here we report an implementation of themore » method to compute the scalar-field self-force along circular equatorial geodesic orbits around a Kerr black hole. This constitutes a first time-domain computation of the self-force in Kerr geometry. Our time-domain code reproduces the results of a recent frequency-domain calculation by Warburton and Barack, but has the added advantage of being readily adaptable to include the backreaction from the self-force in a self-consistent manner. In a forthcoming paper--the third in the series--we apply our method to the gravitational self-force (in the Lorenz gauge).« less

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

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

Velikovich, A. L.; Schmit, P. F.

Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining themore » “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. As a result, in the limit of small shell thickness, exact thin-shell perturbationequations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].« less

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

DOE PAGES

Velikovich, A. L.; Schmit, P. F.

2015-12-28

Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining themore » “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. As a result, in the limit of small shell thickness, exact thin-shell perturbationequations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].« less

ChPT loops for the lattice: pion mass and decay constant, HVP at finite volume and nn̅-oscillations

NASA Astrophysics Data System (ADS)

Bijnens, Johan

2018-03-01

I present higher loop order results for several calculations in Chiral perturbation Theory. 1) Two-loop results at finite volume for hadronic vacuum polarization. 2) A three-loop calculation of the pion mass and decay constant in two-flavour ChPT. For the pion mass all needed auxiliary parameters can be determined from lattice calculations of ππ-scattering. 3) Chiral corrections to neutron-anti-neutron oscillations.

Finite-width Laplace sum rules for 0-+ pseudoscalar glueball in the instanton vacuum model

NASA Astrophysics Data System (ADS)

Wang, Feng; Chen, Junlong; Liu, Jueping

2015-10-01

The correlation function of the 0-+ pseudoscalar glueball current is calculated based on the semiclassical expansion for quantum chromodynamics (QCD) in the instanton liquid background. Besides taking the pure classical contribution from instantons and the perturbative one into account, we calculate the contribution arising from the interaction (or the interference) between instantons and the quantum gluon fields, which is infrared free and more important than the pure perturbative one. Instead of the usual zero-width approximation for the resonances, the Breit-Wigner form with a correct threshold behavior for the spectral function of the finite-width resonance is adopted. The properties of the 0-+ pseudoscalar glueball are investigated via a family of the QCD Laplacian sum rules. A consistency between the subtracted and unsubtracted sum rules is very well justified. The values of the mass, decay width, and coupling constants for the 0-+ resonance in which the glueball fraction is dominant are obtained.

Comparing mass balance and adjoint methods for inverse modeling of nitrogen dioxide columns for global nitrogen oxide emissions

NASA Astrophysics Data System (ADS)

Cooper, Matthew; Martin, Randall V.; Padmanabhan, Akhila; Henze, Daven K.

2017-04-01

Satellite observations offer information applicable to top-down constraints on emission inventories through inverse modeling. Here we compare two methods of inverse modeling for emissions of nitrogen oxides (NOx) from nitrogen dioxide (NO2) columns using the GEOS-Chem chemical transport model and its adjoint. We treat the adjoint-based 4D-Var modeling approach for estimating top-down emissions as a benchmark against which to evaluate variations on the mass balance method. We use synthetic NO2 columns generated from known NOx emissions to serve as "truth." We find that error in mass balance inversions can be reduced by up to a factor of 2 with an iterative process that uses finite difference calculations of the local sensitivity of NO2 columns to a change in emissions. In a simplified experiment to recover local emission perturbations, horizontal smearing effects due to NOx transport are better resolved by the adjoint approach than by mass balance. For more complex emission changes, or at finer resolution, the iterative finite difference mass balance and adjoint methods produce similar global top-down inventories when inverting hourly synthetic observations, both reducing the a priori error by factors of 3-4. Inversions of simulated satellite observations from low Earth and geostationary orbits also indicate that both the mass balance and adjoint inversions produce similar results, reducing a priori error by a factor of 3. As the iterative finite difference mass balance method provides similar accuracy as the adjoint method, it offers the prospect of accurately estimating top-down NOx emissions using models that do not have an adjoint.

Polyakov loop modeling for hot QCD

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

Fukushima, Kenji; Skokov, Vladimir

Here, we review theoretical aspects of quantum chromodynamics (QCD) at finite temperature. The most important physical variable to characterize hot QCD is the Polyakov loop, which is an approximate order parameter for quark deconfinement in a hot gluonic medium. Additionally to its role as an order parameter, the Polyakov loop has rich physical contents in both perturbative and non-perturbative sectors. This review covers a wide range of subjects associated with the Polyakov loop from topological defects in hot QCD to model building with coupling to the Polyakov loop.

Polyakov loop modeling for hot QCD

DOE PAGES

Fukushima, Kenji; Skokov, Vladimir

2017-06-19

Here, we review theoretical aspects of quantum chromodynamics (QCD) at finite temperature. The most important physical variable to characterize hot QCD is the Polyakov loop, which is an approximate order parameter for quark deconfinement in a hot gluonic medium. Additionally to its role as an order parameter, the Polyakov loop has rich physical contents in both perturbative and non-perturbative sectors. This review covers a wide range of subjects associated with the Polyakov loop from topological defects in hot QCD to model building with coupling to the Polyakov loop.

Magnetic field homogeneity perturbations in finite Halbach dipole magnets.

PubMed

Turek, Krzysztof; Liszkowski, Piotr

2014-01-01

Halbach hollow cylinder dipole magnets of a low or relatively low aspect ratio attract considerable attention due to their applications, among others, in compact NMR and MRI systems for investigating small objects. However, a complete mathematical framework for the analysis of magnetic fields in these magnets has been developed only for their infinitely long precursors. In such a case the analysis is reduced to two-dimensions (2D). The paper details the analysis of the 3D magnetic field in the Halbach dipole cylinders of a finite length. The analysis is based on three equations in which the components of the magnetic flux density Bx, By and Bz are expanded to infinite power series of the radial coordinate r. The zeroth term in the series corresponds to a homogeneous magnetic field Bc, which is perturbed by the higher order terms due to a finite magnet length. This set of equations is supplemented with an equation for the field profile B(z) along the magnet axis, presented for the first time. It is demonstrated that the geometrical factors in the coefficients of particular powers of r, defined by intricate integrals are the coefficients of the Taylor expansion of the homogeneity profile (B(z)-Bc)/Bc. As a consequence, the components of B can be easily calculated with an arbitrary accuracy. In order to describe perturbations of the field due to segmentation, two additional equations are borrowed from the 2D theory. It is shown that the 2D approach to the perturbations generated by the segmentation can be applied to the 3D Halbach structures unless r is not too close to the inner radius of the cylinder ri. The mathematical framework presented in the paper was verified with great precision by computations of B by a highly accurate integration of the magnetostatic Coulomb law and utilized to analyze the inhomogeneity of the magnetic field in the magnet with the accuracy better than 1 ppm. Copyright © 2013 Elsevier Inc. All rights reserved.

Fluid and microfluidic dielectric measurement using a cavity perturbation method at microwave C-band

NASA Astrophysics Data System (ADS)

Asghari, Aref

The utilization of cavity perturbation technique in dielectric property measurement of fluid and micro-fluid is investigated in this thesis to better assist the ever-growing needs of science and technology for analysis and characterization of such materials in various applications from genetics, MEMS devices, to consumer product industry. Development of different techniques for measuring complex dielectric properties of fluid and micro-fluids at Giga (10 9)-Hz frequencies is of significant importance as their usage is increasingly coupled with infrared and microwave electromagnetic wavelengths. Conventional cavity perturbation method could provide a sensitive and convenient system for measuring fluids of low (e.g., epsilonr <10) permittivity that meets the assumptions of negligible perturbation to the electromagnetic field distribution in the cavity. Developing a methodology that uses conventional cavity perturbation method that is however suitable for a sensitive, accurate, and reliable measurement of high permittivity polar liquids at microwave C-band is the goal in the current work. Systematic studies are carried out, using de-ionic (DI) water as test specimens, to evaluate the influence of sample's container, volume, dimension, and temperature on the sensitivity and reliability of microwave dielectric measurement. The cavity perturbation measurement of DI water in a 1 mm diameter capillary tube showed well-defined temperature dependence of dielectric permittivity and loss coefficients of water. Observation of a permittivity peak in temperature range tested at 4GHz around -10 °C implies an important relaxation in low temperatures at microwave C-band, which corresponds to a critical slowing down of polarization reorientation in crystallized (icy) H2O. Numerical simulations using Finite Element Analysis (FEA) COMSOL suites were conducted to established the optimum amount of liquid water for cavity perturbation testing at microwave C-band (in perfectly conducting condition). The results showed at TE103 mode the tube D4= 4mm diameter (272 muL liquid volume capacity) provides the best measurement sensitivity in terms of resonant shift and low loss while for TE105 the 2mm 68 (muL liquid volume capacity) tube is the most promising. The experimental results yielded a shape factor of around 2 and 1 for epsilon' and epsilon", respectively. The examination of epsilon' and epsilon" interdependence using Kramers-Kronig concept showed the permittivity loss values is 4 times more dependent to the quality factor of resonant peak than permittivity. On the other hand, the dielectric permittivity dependence to resonant frequency was calculated around 2 times bigger than dielectric loss which signifies the importance of epsilon" in high loss liquid measurement by the cavity resonant perturbation method.

Extraction of gravitational waves in numerical relativity.

PubMed

Bishop, Nigel T; Rezzolla, Luciano

2016-01-01

A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at null infinity and in an appropriate coordinate system, the accurate estimation of the emitted gravitational waves represents an old and non-trivial problem in numerical relativity. A number of methods have been developed over the years to "extract" the radiative part of the solution from a numerical simulation and these include: quadrupole formulas, gauge-invariant metric perturbations, Weyl scalars, and characteristic extraction. We review and discuss each method, in terms of both its theoretical background as well as its implementation. Finally, we provide a brief comparison of the various methods in terms of their inherent advantages and disadvantages.

A numerical study of the thermal stability of low-lying coronal loops

NASA Technical Reports Server (NTRS)

Klimchuk, J. A.; Antiochos, S. K.; Mariska, J. T.

1986-01-01

The nonlinear evolution of loops that are subjected to a variety of small but finite perturbations was studied. Only the low-lying loops are considered. The analysis was performed numerically using a one-dimensional hydrodynamical model developed at the Naval Research Laboratory. The computer codes solve the time-dependent equations for mass, momentum, and energy transport. The primary interest is the active region filaments, hence a geometry appropriate to those structures was considered. The static solutions were subjected to a moderate sized perturbation and allowed to evolve. The results suggest that both hot and cool loops of the geometry considered are thermally stable against amplitude perturbations of all kinds.

Eigenvalue sensitivity analysis of planar frames with variable joint and support locations

NASA Technical Reports Server (NTRS)

Chuang, Ching H.; Hou, Gene J. W.

1991-01-01

Two sensitivity equations are derived in this study based upon the continuum approach for eigenvalue sensitivity analysis of planar frame structures with variable joint and support locations. A variational form of an eigenvalue equation is first derived in which all of the quantities are expressed in the local coordinate system attached to each member. Material derivative of this variational equation is then sought to account for changes in member's length and orientation resulting form the perturbation of joint and support locations. Finally, eigenvalue sensitivity equations are formulated in either domain quantities (by the domain method) or boundary quantities (by the boundary method). It is concluded that the sensitivity equation derived by the boundary method is more efficient in computation but less accurate than that of the domain method. Nevertheless, both of them in terms of computational efficiency are superior to the conventional direct differentiation method and the finite difference method.

Interface and permittivity simultaneous reconstruction in electrical capacitance tomography based on boundary and finite-elements coupling method

PubMed Central

Ren, Shangjie; Dong, Feng

2016-01-01

Electrical capacitance tomography (ECT) is a non-destructive detection technique for imaging the permittivity distributions inside an observed domain from the capacitances measurements on its boundary. Owing to its advantages of non-contact, non-radiation, high speed and low cost, ECT is promising in the measurements of many industrial or biological processes. However, in the practical industrial or biological systems, a deposit is normally seen in the inner wall of its pipe or vessel. As the actual region of interest (ROI) of ECT is surrounded by the deposit layer, the capacitance measurements become weakly sensitive to the permittivity perturbation occurring at the ROI. When there is a major permittivity difference between the deposit and the ROI, this kind of shielding effect is significant, and the permittivity reconstruction becomes challenging. To deal with the issue, an interface and permittivity simultaneous reconstruction approach is proposed. Both the permittivity at the ROI and the geometry of the deposit layer are recovered using the block coordinate descent method. The boundary and finite-elements coupling method is employed to improve the computational efficiency. The performance of the proposed method is evaluated with the simulation tests. This article is part of the themed issue ‘Supersensing through industrial process tomography’. PMID:27185960

Novel Infrared Dynamics of Cold Atoms on Hot Graphene

NASA Astrophysics Data System (ADS)

Sengupta, Sanghita; Kotov, Valeri; Clougherty, Dennis

The low-energy dynamics of cold atoms interacting with macroscopic graphene membranes exhibits severe infrared divergences when treated perturbatively. These infrared problems are even more pronounced at finite temperature due to the (infinitely) many flexural phonons excited in graphene. We have devised a technique to take account (resummation) of such processes in the spirit of the well-known exact solution of the independent boson model. Remarkably, there is also similarity to the infrared problems and their treatment (via the Bloch-Nordsieck scheme) in finite temperature ``hot'' quantum electrodynamics and chromodynamics due to the long-range, unscreened nature of gauge interactions. The method takes into account correctly the strong damping provided by the many emitted phonons at finite temperature. In our case, the inverse membrane size plays the role of an effective low-energy scale, and, unlike the above mentioned field theories, there remains an unusual, highly nontrivial dependence on that scale due to the 2D nature of the problem. We present detailed results for the sticking (atomic damping rate) rate of cold atomic hydrogen as a function of the membrane temperature and size. We find that the rate is very strongly dependent on both quantities.

Direct Numerical Simulation of Fingering Instabilities in Coating Flows

NASA Astrophysics Data System (ADS)

Eres, Murat H.; Schwartz, Leonard W.

1998-11-01

We consider stability and finger formation in free surface flows. Gravity driven downhill drainage and temperature gradient driven climbing flows are two examples of such problems. The former situation occurs when a mound of viscous liquid on a vertical wall is allowed to flow. Constant surface shear stress due to temperature gradients (Marangoni stress) can initiate the latter problem. The evolution equations are derived using the lubrication approximation. We also include the effects of finite-contact angles in the evolution equations using a disjoining pressure model. Evolution equations for both problems are solved using an efficient alternating-direction-implicit method. For both problems a one-dimensional base state is established, that is steady in a moving reference frame. This base state is unstable to transverse perturbations. The transverse wavenumbers for the most rapidly growing modes are found through direct numerical solution of the nonlinear evolution equations, and are compared with published experimental results. For a range of finite equilibrium contact angles, the fingers can grow without limit leading to semi-finite steady fingers in a moving coordinate system. A computer generated movie of the nonlinear simulation results, for several sets of input parameters, will be shown.

Stabilization of lower hybrid drift modes by finite parallel wavenumber and electron temperature gradients in field-reversed configurations

NASA Astrophysics Data System (ADS)

Farengo, R.; Guzdar, P. N.; Lee, Y. C.

1989-08-01

The effect of finite parallel wavenumber and electron temperature gradients on the lower hybrid drift instability is studied in the parameter regime corresponding to the TRX-2 device [Fusion Technol. 9, 48 (1986)]. Perturbations in the electrostatic potential and all three components of the vector potential are considered and finite beta electron orbit modifications are included. The electron temperature gradient decreases the growth rate of the instability but, for kz=0, unstable modes exist for ηe(=T'en0/Ten0)>6. Since finite kz effects completely stabilize the mode at small values of kz/ky(≂5×10-3), magnetic shear could be responsible for stabilizing the lower hybrid drift instability in field-reversed configurations.

Rational approach for assumed stress finite elements

NASA Technical Reports Server (NTRS)

Pian, T. H. H.; Sumihara, K.

1984-01-01

A new method for the formulation of hybrid elements by the Hellinger-Reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element. The equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co-ordinates. The resulting element possesses all the ideal qualities, i.e. it is invariant, it is less sensitive to geometric distortion, it contains a minimum number of stress parameters and it provides accurate stress calculations. For the formulation of a 4-node plane stress element, a small perturbation method is used to determine the equilibrium constraint equations. The element has been proved to be always rank sufficient.

Structural expansions for the ground state energy of a simple metal

NASA Technical Reports Server (NTRS)

Hammerberg, J.; Ashcroft, N. W.

1973-01-01

A structural expansion for the static ground state energy of a simple metal is derived. An approach based on single particle band structure which treats the electron gas as a non-linear dielectric is presented, along with a more general many particle analysis using finite temperature perturbation theory. The two methods are compared, and it is shown in detail how band-structure effects, Fermi surface distortions, and chemical potential shifts affect the total energy. These are of special interest in corrections to the total energy beyond third order in the electron ion interaction, and hence to systems where differences in energies for various crystal structures are exceptionally small. Preliminary calculations using these methods for the zero temperature thermodynamic functions of atomic hydrogen are reported.

Non-perturbative calculation of orbital and spin effects in molecules subject to non-uniform magnetic fields

NASA Astrophysics Data System (ADS)

Sen, Sangita; Tellgren, Erik I.

2018-05-01

External non-uniform magnetic fields acting on molecules induce non-collinear spin densities and spin-symmetry breaking. This necessitates a general two-component Pauli spinor representation. In this paper, we report the implementation of a general Hartree-Fock method, without any spin constraints, for non-perturbative calculations with finite non-uniform fields. London atomic orbitals are used to ensure faster basis convergence as well as invariance under constant gauge shifts of the magnetic vector potential. The implementation has been applied to investigate the joint orbital and spin response to a field gradient—quantified through the anapole moments—of a set of small molecules. The relative contributions of orbital and spin-Zeeman interaction terms have been studied both theoretically and computationally. Spin effects are stronger and show a general paramagnetic behavior for closed shell molecules while orbital effects can have either direction. Basis set convergence and size effects of anapole susceptibility tensors have been reported. The relation of the mixed anapole susceptibility tensor to chirality is also demonstrated.

Ab initio calculation of resonant Raman intensities of transition metal dichalcogenides

NASA Astrophysics Data System (ADS)

Miranda, Henrique; Reichardt, Sven; Molina-Sanchez, Alejandro; Wirtz, Ludger

Raman spectroscopy is used to characterize optical and vibrational properties of materials. Its computational simulation is important for the interpretation of experimental results. Two approaches are the bond polarizability model and density functional perturbation theory. However, both are known to not capture resonance effects. These resonances and quantum interference effects are important to correctly reproduce the intensities as a function of laser energy as, e.g., reported for the case of multi-layer MoTe21.We present two fully ab initio approaches that overcome this limitation. In the first, we calculate finite difference derivatives of the dielectric susceptibility with the phonon displacements2. In the second we calculate electron-light and electron-phonon matrix elements from density functional theory and use them to evaluate expressions for the Raman intensity derived from time-dependent perturbation theory. These expressions are implemented in a computer code that performs the calculations as a post-processing step. We compare both methods and study the case of triple-layer MoTe2. Luxembourg National Research Fund (FNR).

Exploratory Lattice QCD Study of the Rare Kaon Decay K^{+}→π^{+}νν[over ¯].

PubMed

Bai, Ziyuan; Christ, Norman H; Feng, Xu; Lawson, Andrew; Portelli, Antonin; Sachrajda, Christopher T

2017-06-23

We report a first, complete lattice QCD calculation of the long-distance contribution to the K^{+}→π^{+}νν[over ¯] decay within the standard model. This is a second-order weak process involving two four-Fermi operators that is highly sensitive to new physics and being studied by the NA62 experiment at CERN. While much of this decay comes from perturbative, short-distance physics, there is a long-distance part, perhaps as large as the planned experimental error, which involves nonperturbative phenomena. The calculation presented here, with unphysical quark masses, demonstrates that this contribution can be computed using lattice methods by overcoming three technical difficulties: (i) a short-distance divergence that results when the two weak operators approach each other, (ii) exponentially growing, unphysical terms that appear in Euclidean, second-order perturbation theory, and (iii) potentially large finite-volume effects. A follow-on calculation with physical quark masses and controlled systematic errors will be possible with the next generation of computers.

Exploratory Lattice QCD Study of the Rare Kaon Decay K+→π+ν ν ¯

NASA Astrophysics Data System (ADS)

Bai, Ziyuan; Christ, Norman H.; Feng, Xu; Lawson, Andrew; Portelli, Antonin; Sachrajda, Christopher T.; Rbc-Ukqcd Collaboration

2017-06-01

We report a first, complete lattice QCD calculation of the long-distance contribution to the K+→π+ν ν ¯ decay within the standard model. This is a second-order weak process involving two four-Fermi operators that is highly sensitive to new physics and being studied by the NA62 experiment at CERN. While much of this decay comes from perturbative, short-distance physics, there is a long-distance part, perhaps as large as the planned experimental error, which involves nonperturbative phenomena. The calculation presented here, with unphysical quark masses, demonstrates that this contribution can be computed using lattice methods by overcoming three technical difficulties: (i) a short-distance divergence that results when the two weak operators approach each other, (ii) exponentially growing, unphysical terms that appear in Euclidean, second-order perturbation theory, and (iii) potentially large finite-volume effects. A follow-on calculation with physical quark masses and controlled systematic errors will be possible with the next generation of computers.

Optimal perturbations of a finite-width mixing layer near the trailing edge

NASA Astrophysics Data System (ADS)

Gumbart, James C.; Rabchuk, James

2002-03-01

The trailing edge of a surface separating two fluid flows can act as an efficient receptor for acoustic or other disturbances. The incident wave energy is converted by a linear mechanism into incipient flow instabilities which lead further downstream to the transition to turbulence. Understanding this process is essential for analyzing feedback loops and other resonances which can cause unwanted structural vibrations in the surface material or directed acoustic emissions from the mixing region. Previously, the modes of instability in a finite-width mixing layer near the trailing edge were studied as a function of frequency by assuming that vorticity was continually being introduced into the flow at the trailing edge by the forcing field. It was found that the initial amplitude of the growing instability mode was a sharply decreasing function of forcing frequency, and that the initial amplitude was a minimum for the frequency at which the rate of instability growth was a maximum^1. This result has led to a study of the adjoint equation for the perturbation stream function, whose eigensolutions are known to be associated with the optimal perturbation field for the frequency of forcing leading to the greatest instability growth downstream. We have obtained these solutions for a piecewise linear velocity profile near the trailing edge using group-theoretic techniques and have shown that they are indeed optimal. We have also analyzed the nature of the physical forcing field that might produce these optimal perturbations. ^1 Rabchuk, J.A., July 2000, Physics of Fluids.

On the solution of the complex eikonal equation in acoustic VTI media: A perturbation plus optimization scheme

NASA Astrophysics Data System (ADS)

Huang, Xingguo; Sun, Jianguo; Greenhalgh, Stewart

2018-04-01

We present methods for obtaining numerical and analytic solutions of the complex eikonal equation in inhomogeneous acoustic VTI media (transversely isotropic media with a vertical symmetry axis). The key and novel point of the method for obtaining numerical solutions is to transform the problem of solving the highly nonlinear acoustic VTI eikonal equation into one of solving the relatively simple eikonal equation for the background (isotropic) medium and a system of linear partial differential equations. Specifically, to obtain the real and imaginary parts of the complex traveltime in inhomogeneous acoustic VTI media, we generalize a perturbation theory, which was developed earlier for solving the conventional real eikonal equation in inhomogeneous anisotropic media, to the complex eikonal equation in such media. After the perturbation analysis, we obtain two types of equations. One is the complex eikonal equation for the background medium and the other is a system of linearized partial differential equations for the coefficients of the corresponding complex traveltime formulas. To solve the complex eikonal equation for the background medium, we employ an optimization scheme that we developed for solving the complex eikonal equation in isotropic media. Then, to solve the system of linearized partial differential equations for the coefficients of the complex traveltime formulas, we use the finite difference method based on the fast marching strategy. Furthermore, by applying the complex source point method and the paraxial approximation, we develop the analytic solutions of the complex eikonal equation in acoustic VTI media, both for the isotropic and elliptical anisotropic background medium. Our numerical results demonstrate the effectiveness of our derivations and illustrate the influence of the beam widths and the anisotropic parameters on the complex traveltimes.

Numerical and experimental investigation on static electric charge model at stable cone-jet region

NASA Astrophysics Data System (ADS)

Hashemi, Ali Reza; Pishevar, Ahmad Reza; Valipouri, Afsaneh; Pǎrǎu, Emilian I.

2018-03-01

In a typical electro-spinning process, the steady stretching process of the jet beyond the Taylor cone has a significant effect on the dimensions of resulting nanofibers. Also, it sets up the conditions for the onset of the bending instability. The focus of this work is the modeling and simulation of the initial stable jet phase seen during the electro-spinning process. The perturbation method was applied to solve hydrodynamic equations, and the electrostatic equation was solved by a boundary integral method. These equations were coupled with the stress boundary conditions derived appropriate at the fluid-fluid interface. Perturbation equations were discretized by the second-order finite difference method, and the Newton method was implemented to solve the discretized nonlinear system. Also, the boundary element method was utilized to solve the electrostatic equation. In the theoretical study, the fluid is described as a leaky dielectric with charges only on the jet surface in dielectric air. In this study, electric charges were modeled as static. Comparison of numerical and experimental results shows that at low flow rates and high electric field, good agreement was achieved because of the superior importance of the charge transport by conduction rather than convection and charge concentration. In addition, the effect of unevenness of the electric field around the nozzle tip was experimentally studied through plate-plate geometry as well as point-plate geometry.

Spectral algorithms for multiple scale localized eigenfunctions in infinitely long, slightly bent quantum waveguides

NASA Astrophysics Data System (ADS)

Boyd, John P.; Amore, Paolo; Fernández, Francisco M.

2018-03-01

A "bent waveguide" in the sense used here is a small perturbation of a two-dimensional rectangular strip which is infinitely long in the down-channel direction and has a finite, constant width in the cross-channel coordinate. The goal is to calculate the smallest ("ground state") eigenvalue of the stationary Schrödinger equation which here is a two-dimensional Helmholtz equation, ψxx +ψyy + Eψ = 0 where E is the eigenvalue and homogeneous Dirichlet boundary conditions are imposed on the walls of the waveguide. Perturbation theory gives a good description when the "bending strength" parameter ɛ is small as described in our previous article (Amore et al., 2017) and other works cited therein. However, such series are asymptotic, and it is often impractical to calculate more than a handful of terms. It is therefore useful to develop numerical methods for the perturbed strip to cover intermediate ɛ where the perturbation series may be inaccurate and also to check the pertubation expansion when ɛ is small. The perturbation-induced change-in-eigenvalue, δ ≡ E(ɛ) - E(0) , is O(ɛ2) . We show that the computation becomes very challenging as ɛ → 0 because (i) the ground state eigenfunction varies on both O(1) and O(1 / ɛ) length scales and (ii) high accuracy is needed to compute several correct digits in δ, which is itself small compared to the eigenvalue E. The multiple length scales are not geographically separate, but rather are inextricably commingled in the neighborhood of the boundary deformation. We show that coordinate mapping and immersed boundary strategies both reduce the computational domain to the uniform strip, allowing application of pseudospectral methods on tensor product grids with tensor product basis functions. We compared different basis sets; Chebyshev polynomials are best in the cross-channel direction. However, sine functions generate rather accurate analytical approximations with just a single basis function. In the down-channel coordinate, X ∈ [ - ∞ , ∞ ] , Fourier domain truncation using the change of coordinate X = sinh(Lt) is considerably more efficient than rational Chebyshev functions TBn(X ; L) . All the spectral methods, however, yielded the required accuracy on a desktop computer.

Density matrix perturbation theory for magneto-optical response of periodic insulators

NASA Astrophysics Data System (ADS)

Lebedeva, Irina; Tokatly, Ilya; Rubio, Angel

2015-03-01

Density matrix perturbation theory offers an ideal theoretical framework for the description of response of solids to arbitrary electromagnetic fields. In particular, it allows to consider perturbations introduced by uniform electric and magnetic fields under periodic boundary conditions, though the corresponding potentials break the translational invariance of the Hamiltonian. We have implemented the density matrix perturbation theory in the open-source Octopus code on the basis of the efficient Sternheimer approach. The procedures for responses of different order to electromagnetic fields, including electric polarizability, orbital magnetic susceptibility and magneto-optical response, have been developed and tested by comparison with the results for finite systems and for wavefunction-based perturbation theory, which is already available in the code. Additional analysis of the orbital magneto-optical response is performed on the basis of analytical models. Symmetry limitations to observation of the magneto-optical response are discussed. The financial support from the Marie Curie Fellowship PIIF-GA-2012-326435 (RespSpatDisp) is gratefully acknowledged.

Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

NASA Astrophysics Data System (ADS)

Antown, Fadi; Dragičević, Davor; Froyland, Gary

2018-03-01

The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

Effects of the underlying topology on perturbation spreading in the Axelrod model for cultural dissemination

NASA Astrophysics Data System (ADS)

Kim, Yup; Cho, Minsoo; Yook, Soon-Hyung

2011-10-01

We study the effects of the underlying topologies on a single feature perturbation imposed to the Axelrod model of consensus formation. From the numerical simulations we show that there are successive updates which are similar to avalanches in many self-organized criticality systems when a perturbation is imposed. We find that the distribution of avalanche size satisfies the finite-size scaling (FSS) ansatz on two-dimensional lattices and random networks. However, on scale-free networks with the degree exponent γ≤3 we show that the avalanche size distribution does not satisfy the FSS ansatz. The results indicate that the disordered configurations on two-dimensional lattices or on random networks are still stable against the perturbation in the limit N (network size) →∞. However, on scale-free networks with γ≤3 the perturbation always drives the disordered phase into an ordered phase. The possible relationship between the properties of phase transition of the Axelrod model and the avalanche distribution is also discussed.

Interval stability for complex systems

NASA Astrophysics Data System (ADS)

Klinshov, Vladimir V.; Kirillov, Sergey; Kurths, Jürgen; Nekorkin, Vladimir I.

2018-04-01

Stability of dynamical systems against strong perturbations is an important problem of nonlinear dynamics relevant to many applications in various areas. Here, we develop a novel concept of interval stability, referring to the behavior of the perturbed system during a finite time interval. Based on this concept, we suggest new measures of stability, namely interval basin stability (IBS) and interval stability threshold (IST). IBS characterizes the likelihood that the perturbed system returns to the stable regime (attractor) in a given time. IST provides the minimal magnitude of the perturbation capable to disrupt the stable regime for a given interval of time. The suggested measures provide important information about the system susceptibility to external perturbations which may be useful for practical applications. Moreover, from a theoretical viewpoint the interval stability measures are shown to bridge the gap between linear and asymptotic stability. We also suggest numerical algorithms for quantification of the interval stability characteristics and demonstrate their potential for several dynamical systems of various nature, such as power grids and neural networks.

Non-Markovian dynamics of open quantum systems

NASA Astrophysics Data System (ADS)

Fleming, Chris H.

An open quantum system is a quantum system that interacts with some environment whose degrees of freedom have been coarse grained away. This model describes non-equilibrium processes more general than scattering-matrix formulations. Furthermore, the microscopically-derived environment provides a model of noise, dissipation and decoherence far more general than Markovian (white noise) models. The latter are fully characterized by Lindblad equations and can be motivated phenomenologically. Non-Markovian processes consistently account for backreaction with the environment and can incorporate effects such as finite temperature and spatial correlations. We consider linear systems with bilinear coupling to the environment, or quantum Brownian motion, and nonlinear systems with weak coupling to the environment. For linear systems we provide exact solutions with analytical results for a variety of spectral densities. Furthermore, we point out an important mathematical subtlety which led to incorrect master-equation coefficients in earlier derivations, given nonlocal dissipation. For nonlinear systems we provide perturbative solutions by translating the formalism of canonical perturbation theory into the context of master equations. It is shown that unavoidable degeneracy causes an unfortunate reduction in accuracy between perturbative master equations and their solutions. We also extend the famous theorem of Lindblad, Gorini, Kossakowski and Sudarshan on completely positivity to non-Markovian master equations. Our application is primarily to model atoms interacting via a common electromagnetic field. The electromagnetic field contains correlations in both space and time, which are related to its relativistic (photon-mediated) nature. As such, atoms residing in the same field experience different environmental effects depending upon their relative position and orientation. Our more accurate solutions were necessary to assess sudden death of entanglement at zero temperature. In contrast to previous claims, we found that all initial states of two-level atoms undergo finite-time disentanglement. We were also able to access regimes which cannot be described by Lindblad equations and other simpler methods, such as near resonance. Finally we revisit the infamous Abraham-Lorentz force, wherein a single particle in motion experiences backreaction from the electromagnetic field. This leads to a number of well-known problems including pre-acceleration and runaway solutions. We found a more a more-suitable open-system treatment of the nonrelativistic particle to be perfectly causal and dissipative without any extraneous requirements for finite size of the particle, weak coupling to the field, etc..

A perturbation method to the tent map based on Lyapunov exponent and its application

NASA Astrophysics Data System (ADS)

Cao, Lv-Chen; Luo, Yu-Ling; Qiu, Sen-Hui; Liu, Jun-Xiu

2015-10-01

Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-random sequence generated by the tent map is sent to another chaos function — the Chebyshev map for the post processing. If the output value of the Chebyshev map falls into a certain range, it will be sent back to replace the parameter of the tent map. As a result, the parameter of the tent map keeps changing dynamically. The statistical analysis and experimental results prove that the disturbed tent map has a highly random distribution and achieves good cryptographic properties of a pseudo-random sequence. As a result, it weakens the phenomenon of strong correlation caused by the finite precision and effectively compensates for the digital chaos system dynamics degradation. Project supported by the Guangxi Provincial Natural Science Foundation, China (Grant No. 2014GXNSFBA118271), the Research Project of Guangxi University, China (Grant No. ZD2014022), the Fund from Guangxi Provincial Key Laboratory of Multi-source Information Mining & Security, China (Grant No. MIMS14-04), the Fund from the Guangxi Provincial Key Laboratory of Wireless Wideband Communication & Signal Processing, China (Grant No. GXKL0614205), the Education Development Foundation and the Doctoral Research Foundation of Guangxi Normal University, the State Scholarship Fund of China Scholarship Council (Grant No. [2014]3012), and the Innovation Project of Guangxi Graduate Education, China (Grant No. YCSZ2015102).

The Kondo problem. II. Crossover from asymptotic freedom to infrared slavery

NASA Astrophysics Data System (ADS)

Schlottmann, P.

1982-04-01

In the preceding paper we transformed the s-d Hamiltonian onto a resonance level with a large perturbation and derived the scaling equations for the vertices, the invariant coupling, and the resonance width. The scaling equations are integrated under the assumption that the energy dependence of the resonance width can be neglected. The transcendental equation obtained in this way for the renormalized resonance width is solved in the relevant limits and allows a calculation of the static and dynamical susceptibility. At high temperatures the perturbation expansion for the relaxation rate and the susceptibility is reproduced up to third order in Jρ. At low temperatures the lifetime and χ0 remain finite and vary according to a Fermi-liquid theory. The approximation scheme interpolates in this way between the asymptotic freedom and the infrared slavery, yielding a smooth crossover. The present results are in quantitative agreement with previous ones obtained with the relaxation-kernel method by Götze and Schlottmann. The advantages and drawbacks of the method are discussed. The calculation of the dynamical susceptibility is extended to nonzero external magnetic fields. The quasielastic peak of χ''(ω)ω is suppressed at low temperatures and large magnetic fields and shoulders develop at ω=+/-B.

Spatio-temporal correlations in models of collective motion ruled by different dynamical laws.

PubMed

Cavagna, Andrea; Conti, Daniele; Giardina, Irene; Grigera, Tomas S; Melillo, Stefania; Viale, Massimiliano

2016-11-15

Information transfer is an essential factor in determining the robustness of biological systems with distributed control. The most direct way to study the mechanisms ruling information transfer is to experimentally observe the propagation across the system of a signal triggered by some perturbation. However, this method may be inefficient for experiments in the field, as the possibilities to perturb the system are limited and empirical observations must rely on natural events. An alternative approach is to use spatio-temporal correlations to probe the information transfer mechanism directly from the spontaneous fluctuations of the system, without the need to have an actual propagating signal on record. Here we test this method on models of collective behaviour in their deeply ordered phase by using ground truth data provided by numerical simulations in three dimensions. We compare two models characterized by very different dynamical equations and information transfer mechanisms: the classic Vicsek model, describing an overdamped noninertial dynamics and the inertial spin model, characterized by an underdamped inertial dynamics. By using dynamic finite-size scaling, we show that spatio-temporal correlations are able to distinguish unambiguously the diffusive information transfer mechanism of the Vicsek model from the linear mechanism of the inertial spin model.

Concentration of small ring structures in vitreous silica from a first-principles analysis of the Raman spectrum.

PubMed

Umari, P; Gonze, Xavier; Pasquarello, Alfredo

2003-01-17

Using a first-principles approach, we calculate Raman spectra for a model structure of vitreous silica. We develop a perturbational method for calculating the dielectric tensor in an ultrasoft pseudopotential scheme and obtain Raman coupling tensors by finite differences with respect to atomic displacements. For frequencies below 1000 cm(-1), the parallel-polarized Raman spectrum of vitreous silica is dominated by oxygen bending motions, showing a strong sensitivity to the intermediate range structure. By modeling the Raman coupling, we derive estimates for the concentrations of three- and four-membered rings from the experimental intensities of the Raman defect lines.

Effect of fine dust particles and finite electron inertia of rotating magnetized plasma

NASA Astrophysics Data System (ADS)

Kumar, V.; Sutar, D. L.; Pensia, R. K.; Sharma, S.

2018-05-01

A theoretical investigation has been made of the effect of fine dust particles, viscosity and electron inertia on Jeans instability in a self-gravitating magnetized rotating plasma. The MHD model is used to formulate the problem in which a general dispersion relation. A general dispersion relation is obtained from the linearized perturbation equations using the normal mode analysis method. The analytical expressions of the growth rate of Jeans instability are obtained for the longitudinal and transverse mode of propagation. The present result shows that the Jeans criterion of instability is modified due to the presence of viscosity, rotation, and magnetic field.

Fully unsteady subsonic and supersonic potential aerodynamics for complex aircraft configurations for flutter applications

NASA Technical Reports Server (NTRS)

Tseng, K.; Morino, L.

1975-01-01

A general theory for study, oscillatory or fully unsteady potential compressible aerodynamics around complex configurations is presented. Using the finite-element method to discretize the space problem, one obtains a set of differential-delay equations in time relating the potential to its normal derivative which is expressed in terms of the generalized coordinates of the structure. For oscillatory flow, the motion consists of sinusoidal oscillations around a steady, subsonic or supersonic flow. For fully unsteady flow, the motion is assumed to consist of constant subsonic or supersonic speed for time t or = 0 and of small perturbations around the steady state for time t 0.

Visualization of geologic stress perturbations using Mohr diagrams.

PubMed

Crossno, Patricia; Rogers, David H; Brannon, Rebecca M; Coblentz, David; Fredrich, Joanne T

2005-01-01

Huge salt formations, trapping large untapped oil and gas reservoirs, lie in the deepwater region of the Gulf of Mexico. Drilling in this region is high-risk and drilling failures have led to well abandonments, with each costing tens of millions of dollars. Salt tectonics plays a central role in these failures. To explore the geomechanical interactions between salt and the surrounding sand and shale formations, scientists have simulated the stresses in and around salt diapirs in the Gulf of Mexico using nonlinear finite element geomechanical modeling. In this paper, we describe novel techniques developed to visualize the simulated subsurface stress field. We present an adaptation of the Mohr diagram, a traditional paper-and-pencil graphical method long used by the material mechanics community for estimating coordinate transformations for stress tensors, as a new tensor glyph for dynamically exploring tensor variables within three-dimensional finite element models. This interactive glyph can be used as either a probe or a filter through brushing and linking.

Validation of Finite-Element Models of Persistent-Current Effects in Nb 3Sn Accelerator Magnets

DOE PAGES

Wang, X.; Ambrosio, G.; Chlachidze, G.; ...

2015-01-06

Persistent magnetization currents are induced in superconducting filaments during the current ramping in magnets. The resulting perturbation to the design magnetic field leads to field quality degradation, in particular at low field where the effect is stronger relative to the main field. The effects observed in NbTi accelerator magnets were reproduced well with the critical-state model. However, this approach becomes less accurate for the calculation of the persistent-current effects observed in Nb 3Sn accelerator magnets. Here a finite-element method based on the measured strand magnetization is validated against three state-of-art Nb3Sn accelerator magnets featuring different subelement diameters, critical currents, magnetmore » designs and measurement temperatures. The temperature dependence of the persistent-current effects is reproduced. Based on the validated model, the impact of conductor design on the persistent current effects is discussed. The performance, limitations and possible improvements of the approach are also discussed.« less

Stability and perturbations of countable Markov maps

NASA Astrophysics Data System (ADS)

Jordan, Thomas; Munday, Sara; Sahlsten, Tuomas

2018-04-01

Let T and , , be countable Markov maps such that the branches of converge pointwise to the branches of T, as . We study the stability of various quantities measuring the singularity (dimension, Hölder exponent etc) of the topological conjugacy between and T when . This is a well-understood problem for maps with finitely-many branches, and the quantities are stable for small ɛ, that is, they converge to their expected values if . For the infinite branch case their stability might be expected to fail, but we prove that even in the infinite branch case the quantity is stable under some natural regularity assumptions on and T (under which, for instance, the Hölder exponent of fails to be stable). Our assumptions apply for example in the case of Gauss map, various Lüroth maps and accelerated Manneville-Pomeau maps when varying the parameter α. For the proof we introduce a mass transportation method from the cusp that allows us to exploit thermodynamical ideas from the finite branch case. Dedicated to the memory of Bernd O Stratmann

Statistical analysis of effective singular values in matrix rank determination

NASA Technical Reports Server (NTRS)

Konstantinides, Konstantinos; Yao, Kung

1988-01-01

A major problem in using SVD (singular-value decomposition) as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end, conference regions are derived for the perturbed singular values of matrices with noisy observation data. The analysis is based on the theories of perturbations of singular values and statistical significance test. Threshold bounds for perturbation due to finite-precision and i.i.d. random models are evaluated. In random models, the threshold bounds depend on the dimension of the matrix, the noisy variance, and predefined statistical level of significance. Results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered. Various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given.

Perturbations for transient acceleration

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

Vargas, Cristofher Zuñiga; Zimdahl, Winfried; Hipólito-Ricaldi, Wiliam S., E-mail: win_unac@hotmail.com, E-mail: hipolito@ceunes.ufes.br, E-mail: winfried.zimdahl@pq.cnpq.br

2012-04-01

According to the standard ΛCDM model, the accelerated expansion of the Universe will go on forever. Motivated by recent observational results, we explore the possibility of a finite phase of acceleration which asymptotically approaches another period of decelerated expansion. Extending an earlier study on a corresponding homogeneous and isotropic dynamics, in which interactions between dark matter and dark energy are crucial, the present paper also investigates the dynamics of the matter perturbations both on the Newtonian and General Relativistic (GR) levels and quantifies the potential relevance of perturbations of the dark-energy component. In the background, the model is tested againstmore » the Supernova type Ia (SNIa) data of the Constitution set and on the perturbative level against growth rate data, among them those of the WiggleZ survey, and the data of the 2dFGRS project. Our results indicate that a transient phase of accelerated expansion is not excluded by current observations.« less

Large perturbation flow field analysis and simulation for supersonic inlets

NASA Technical Reports Server (NTRS)

Varner, M. O.; Martindale, W. R.; Phares, W. J.; Kneile, K. R.; Adams, J. C., Jr.

1984-01-01

An analysis technique for simulation of supersonic mixed compression inlets with large flow field perturbations is presented. The approach is based upon a quasi-one-dimensional inviscid unsteady formulation which includes engineering models of unstart/restart, bleed, bypass, and geometry effects. Numerical solution of the governing time dependent equations of motion is accomplished through a shock capturing finite difference algorithm, of which five separate approaches are evaluated. Comparison with experimental supersonic wind tunnel data is presented to verify the present approach for a wide range of transient inlet flow conditions.

Numerical simulations of Richtmyer{endash}Meshkov instabilities in finite-thickness fluid layers

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

Mikaelian, K.O.

1996-05-01

Direct numerical simulations of Richtmyer{endash}Meshkov instabilities in shocked fluid layers are reported and compared with analytic theory. To investigate new phenomena such as freeze-out, interface coupling, and feedthrough, several new configurations are simulated on a two-dimensional hydrocode. The basic system is an {ital A}/{ital B}/{ital A} combination, where {ital A} is air and {ital B} is a finite-thickness layer of freon, SF{sub 6}, or helium. The middle layer {ital B} has perturbations either on its upstream or downstream side, or on both sides, in which case the perturbations may be in phase (sinuous) or out of phase (varicose). The evolutionmore » of such perturbations under a Mach 1.5 shock is calculated, including the effect of a reshock. Recently reported gas curtain experiments [J. M. Budzinski {ital et} {ital al}., Phys. Fluids {bold 6}, 3510 (1994)] are also simulated and the code results are found to agree very well with the experiments. A new gas curtain configuration is also considered, involving an initially sinuous SF{sub 6} or helium layer and a new pattern, opposite mushrooms, is predicted to emerge. Upon reshock a relatively simple sinuous gas curtain is found to evolve into a highly complex pattern of nested mushrooms. {copyright} {ital 1996 American Institute of Physics.}« less

Hamiltonian General Relativity in Finite Space and Cosmological Potential Perturbations

NASA Astrophysics Data System (ADS)

Barbashov, B. M.; Pervushin, V. N.; Zakharov, A. F.; Zinchuk, V. A.

The Hamiltonian formulation of general relativity is considered in finite space-time and a specific reference frame given by the diffeo-invariant components of the Fock simplex in terms of the Dirac-ADM variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are constructed by the separation of the cosmological scale factor a(x0) and its identification with the spatial averaging of the metric determinant, so that the dimension of the kinemetric group of diffeomorphisms coincides with the dimension of a set of variables whose velocities are removed by the Gauss-type constraints in accordance with the second Nöther theorem. This coincidence allows us to solve the energy constraint, fulfil Dirac's Hamiltonian reduction, and to describe the potential perturbations in terms of the Lichnerowicz scale-invariant variables distinguished by the absence of the time derivatives of the spatial metric determinant. It was shown that the Hamiltonian version of the cosmological perturbation theory acquires attributes of the theory of superfluid liquid, and it leads to a generalization of the Schwarzschild solution. The astrophysical application of this approach to general relativity is considered under supposition that the Dirac-ADM Hamiltonian frame is identified with that of the Cosmic Microwave Background radiation distinguished by its dipole component in the frame of an Earth observer.

An analysis of the nucleon spectrum from lattice partially-quenched QCD

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

W. Armour; Allton, C. R.; Leinweber, Derek B.

2010-09-01

The chiral extrapolation of the nucleon mass, Mn, is investigated using data coming from 2-flavour partially-quenched lattice simulations. The leading one-loop corrections to the nucleon mass are derived for partially-quenched QCD. A large sample of lattice results from the CP-PACS Collaboration is analysed, with explicit corrections for finite lattice spacing artifacts. The extrapolation is studied using finite range regularised chiral perturbation theory. The analysis also provides a quantitative estimate of the leading finite volume corrections. It is found that the discretisation, finite-volume and partial quenching effects can all be very well described in this framework, producing an extrapolated value ofmore » Mn in agreement with experiment. This procedure is also compared with extrapolations based on polynomial forms, where the results are less encouraging.« less

Relativistic effects on magnetic circular dichroism studied by GUHF/SECI method

NASA Astrophysics Data System (ADS)

Honda, Y.; Hada, M.; Ehara, M.; Nakatsuji, H.; Downing, J.; Michl, J.

2002-04-01

Quasi-relativistic formulation of the Magnetic circular dichroism (MCD) Faraday terms are presented using the generalized unrestricted Hartree-Fock (GUHF)/single excitation configuration interaction (SECI) method combined with the finite perturbation method and applied to the MCD of the three n-σ ∗ states ( 3Q1, 3Q0, 1Q1) of CH 3I. The Faraday B term for the 1Q1 state was 0.1976( Debye) 2( Bohr magneton )/(10 3 cm-1) in the non-relativistic theory, but was dramatically improved by the relativistic effect and became 0.0184 in agreement with the experimental values, 0.014 and 0.0257. This change was mainly due to the one-electron spin-orbit (SO1) term rather than the spin-free relativistic (SFR) and the two-electron spin-orbit (SO2) terms.

Steady and Oscillatory, Subsonic and Supersonic, Aerodynamic Pressure and Generalized Forces for Complex Aircraft Configurations and Applications to Flutter. M.S. Thesis

NASA Technical Reports Server (NTRS)

Chen, L. T.

1975-01-01

A general method for analyzing aerodynamic flows around complex configurations is presented. By applying the Green function method, a linear integral equation relating the unknown, small perturbation potential on the surface of the body, to the known downwash is obtained. The surfaces of the aircraft, wake and diaphragm (if necessary) are divided into small quadrilateral elements which are approximated with hyperboloidal surfaces. The potential and its normal derivative are assumed to be constant within each element. This yields a set of linear algebraic equations and the coefficients are evaluated analytically. By using Gaussian elimination method, equations are solved for the potentials at the centroids of elements. The pressure coefficient is evaluated by the finite different method; the lift and moment coefficients are evaluated by numerical integration. Numerical results are presented, and applications to flutter are also included.

Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs

NASA Astrophysics Data System (ADS)

Ritter, Patxi; Aoudia, Sofiane; Spallicci, Alessandro D. A. M.; Cordier, Stéphane

2016-12-01

The Regge-Wheeler-Zerilli (RWZ) wave-equation describes Schwarzschild-Droste black hole perturbations. The source term contains a Dirac distribution and its derivative. We have previously designed a method of integration in time domain. It consists of a finite difference scheme where analytic expressions, dealing with the wave-function discontinuity through the jump conditions, replace the direct integration of the source and the potential. Herein, we successfully apply the same method to the geodesic generic orbits of EMRI (Extreme Mass Ratio Inspiral) sources, at second order. An EMRI is a Compact Star (CS) captured by a Super-Massive Black Hole (SMBH). These are considered the best probes for testing gravitation in strong regime. The gravitational wave-forms, the radiated energy and angular momentum at infinity are computed and extensively compared with other methods, for different orbits (circular, elliptic, parabolic, including zoom-whirl).

A steady and oscillatory kernel function method for interfering surfaces in subsonic, transonic and supersonic flow. [prediction analysis techniques for airfoils

NASA Technical Reports Server (NTRS)

Cunningham, A. M., Jr.

1976-01-01

The theory, results and user instructions for an aerodynamic computer program are presented. The theory is based on linear lifting surface theory, and the method is the kernel function. The program is applicable to multiple interfering surfaces which may be coplanar or noncoplanar. Local linearization was used to treat nonuniform flow problems without shocks. For cases with imbedded shocks, the appropriate boundary conditions were added to account for the flow discontinuities. The data describing nonuniform flow fields must be input from some other source such as an experiment or a finite difference solution. The results are in the form of small linear perturbations about nonlinear flow fields. The method was applied to a wide variety of problems for which it is demonstrated to be significantly superior to the uniform flow method. Program user instructions are given for easy access.

A Finite Element Framework for Studying the Mechanical Response of Macromolecules: Application to the Gating of the Mechanosensitive Channel MscL

PubMed Central

Tang, Yuye; Cao, Guoxin; Chen, Xi; Yoo, Jejoong; Yethiraj, Arun; Cui, Qiang

2006-01-01

The gating pathways of mechanosensitive channels of large conductance (MscL) in two bacteria (Mycobacterium tuberculosis and Escherichia coli) are studied using the finite element method. The phenomenological model treats transmembrane helices as elastic rods and the lipid membrane as an elastic sheet of finite thickness; the model is inspired by the crystal structure of MscL. The interactions between various continuum components are derived from molecular-mechanics energy calculations using the CHARMM all-atom force field. Both bacterial MscLs open fully upon in-plane tension in the membrane and the variation of pore diameter with membrane tension is found to be essentially linear. The estimated gating tension is close to the experimental value. The structural variations along the gating pathway are consistent with previous analyses based on structural models with experimental constraints and biased atomistic molecular-dynamics simulations. Upon membrane bending, neither MscL opens substantially, although there is notable and nonmonotonic variation in the pore radius. This emphasizes that the gating behavior of MscL depends critically on the form of the mechanical perturbation and reinforces the idea that the crucial gating parameter is lateral tension in the membrane rather than the curvature of the membrane. Compared to popular all-atom-based techniques such as targeted or steered molecular-dynamics simulations, the finite element method-based continuum-mechanics framework offers a unique alternative to bridge detailed intermolecular interactions and biological processes occurring at large spatial scales and long timescales. It is envisioned that such a hierarchical multiscale framework will find great value in the study of a variety of biological processes involving complex mechanical deformations such as muscle contraction and mechanotransduction. PMID:16731564

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).

Three-Dimensional Sensitivity Kernels of Z/H Amplitude Ratios of Surface and Body Waves

NASA Astrophysics Data System (ADS)

Bao, X.; Shen, Y.

2017-12-01

The ellipticity of Rayleigh wave particle motion, or Z/H amplitude ratio, has received increasing attention in inversion for shallow Earth structures. Previous studies of the Z/H ratio assumed one-dimensional (1D) velocity structures beneath the receiver, ignoring the effects of three-dimensional (3D) heterogeneities on wave amplitudes. This simplification may introduce bias in the resulting models. Here we present 3D sensitivity kernels of the Z/H ratio to Vs, Vp, and density perturbations, based on finite-difference modeling of wave propagation in 3D structures and the scattering-integral method. Our full-wave approach overcomes two main issues in previous studies of Rayleigh wave ellipticity: (1) the finite-frequency effects of wave propagation in 3D Earth structures, and (2) isolation of the fundamental mode Rayleigh waves from Rayleigh wave overtones and converted Love waves. In contrast to the 1D depth sensitivity kernels in previous studies, our 3D sensitivity kernels exhibit patterns that vary with azimuths and distances to the receiver. The laterally-summed 3D sensitivity kernels and 1D depth sensitivity kernels, based on the same homogeneous reference model, are nearly identical with small differences that are attributable to the single period of the 1D kernels and a finite period range of the 3D kernels. We further verify the 3D sensitivity kernels by comparing the predictions from the kernels with the measurements from numerical simulations of wave propagation for models with various small-scale perturbations. We also calculate and verify the amplitude kernels for P waves. This study shows that both Rayleigh and body wave Z/H ratios provide vertical and lateral constraints on the structure near the receiver. With seismic arrays, the 3D kernels afford a powerful tool to use the Z/H ratios to obtain accurate and high-resolution Earth models.

Patterns of brittle deformation under extension on Venus

NASA Technical Reports Server (NTRS)

Neumann, G. A.; Zuber, M. T.

1994-01-01

The development of fractures at regular length scales is a widespread feature of Venusian tectonics. Models of lithospheric deformation under extension based on non-Newtonian viscous flow and brittle-plastic flow develop localized failure at preferred wavelengths that depend on lithospheric thickness and stratification. The characteristic wavelengths seen in rift zones and tessera can therefore provide constraints on crustal and thermal structure. Analytic solutions were obtained for growth rates in infinitesimal perturbations imposed on a one-dimensional, layered rheology. Brittle layers were approximated by perfectly-plastic, uniform strength, overlying ductile layers exhibiting thermally-activated power-law creep. This study investigates the formation of faults under finite amounts of extension, employing a finite-element approach. Our model incorporates non-linear viscous rheology and a Coulomb failure envelope. An initial perturbation in crustal thickness gives rise to necking instabilities. A small amount of velocity weakening serves to localize deformation into planar regions of high strain rate. Such planes are analogous to normal faults seen in terrestrial rift zones. These 'faults' evolve to low angle under finite extension. Fault spacing, orientation and location, and the depth to the brittle-ductile transition, depend in a complex way on lateral variations in crustal thickness. In general, we find that multiple wavelengths of deformation can arise from the interaction of crustal and mantle lithosphere.

Global kinetic simulations of neoclassical toroidal viscosity in low-collisional perturbed tokamak plasmas

NASA Astrophysics Data System (ADS)

Matsuoka, Seikichi; Idomura, Yasuhiro; Satake, Shinsuke

2017-10-01

The neoclassical toroidal viscosity (NTV) caused by a non-axisymmetric magnetic field perturbation is numerically studied using two global kinetic simulations with different numerical approaches. Both simulations reproduce similar collisionality ( νb*) dependencies over wide νb * ranges. It is demonstrated that resonant structures in the velocity space predicted by the conventional superbanana-plateau theory exist in the small banana width limit, while the resonances diminish when the banana width becomes large. It is also found that fine scale structures are generated in the velocity space as νb* decreases in the large banana width simulations, leading to the νb* -dependency of the NTV. From the analyses of the particle orbit, it is found that the finite k∥ mode structure along the bounce motion appears owing to the finite orbit width, and it suffers from bounce phase mixing, suggesting the generation of the fine scale structures by the similar mechanism as the parallel phase mixing of passing particles.

Verification and Validation of a Coordinate Transformation Method in Axisymmetric Transient Magnetics.

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

Ashcraft, C. Chace; Niederhaus, John Henry; Robinson, Allen C.

We present a verification and validation analysis of a coordinate-transformation-based numerical solution method for the two-dimensional axisymmetric magnetic diffusion equation, implemented in the finite-element simulation code ALEGRA. The transformation, suggested by Melissen and Simkin, yields an equation set perfectly suited for linear finite elements and for problems with large jumps in material conductivity near the axis. The verification analysis examines transient magnetic diffusion in a rod or wire in a very low conductivity background by first deriving an approximate analytic solution using perturbation theory. This approach for generating a reference solution is shown to be not fully satisfactory. A specializedmore » approach for manufacturing an exact solution is then used to demonstrate second-order convergence under spatial refinement and tem- poral refinement. For this new implementation, a significant improvement relative to previously available formulations is observed. Benefits in accuracy for computed current density and Joule heating are also demonstrated. The validation analysis examines the circuit-driven explosion of a copper wire using resistive magnetohydrodynamics modeling, in comparison to experimental tests. The new implementation matches the accuracy of the existing formulation, with both formulations capturing the experimental burst time and action to within approximately 2%.« less

Nonlinear susceptibilities of finite conjugated organic polymers

NASA Technical Reports Server (NTRS)

Beratan, David N.; Onuchic, Jose Nelson; Perry, Joseph W.

1987-01-01

Tight-binding calculations of the length dependence of the third-order molecular hyperpolarizability for polyenes and polyynes are reported. The pi-electron wave functions were determined by exploiting the limited translational symmetry of the molecules. Perturbation theory was used to calculate the longitudinal component of the electronic nonresonant hyperpolarizability. This is the first two-'band' calculation of third-order hyperpolarizabilities on finite pi-electron systems of varying length. In contrast to the results of the one-'band' models, the hyperpolarizability densities increase rapidly and then, after about 10-15 repeating units, approach an asymptotic value.

Jeans instability of magnetized quantum plasma: Effect of viscosity, rotation and finite Larmor radius corrections

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

Jain, Shweta, E-mail: jshweta09@gmail.com; Sharma, Prerana; Chhajlani, R. K.

2015-07-31

The Jeans instability of self-gravitating quantum plasma is examined considering the effects of viscosity, finite Larmor radius (FLR) corrections and rotation. The analysis is done by normal mode analysis theory with the help of relevant linearized perturbation equations of the problem. The general dispersion relation is obtained using the quantum magneto hydrodynamic model. The modified condition of Jeans instability is obtained and the numerical calculations have been performed to show the effects of various parameters on the growth rate of Jeans instability.

Finite element analysis of periodic transonic flow problems

NASA Technical Reports Server (NTRS)

Fix, G. J.

1978-01-01

Flow about an oscillating thin airfoil in a transonic stream was considered. It was assumed that the flow field can be decomposed into a mean flow plus a periodic perturbation. On the surface of the airfoil the usual Neumman conditions are imposed. Two computer programs were written, both using linear basis functions over triangles for the finite element space. The first program uses a banded Gaussian elimination solver to solve the matrix problem, while the second uses an iterative technique, namely SOR. The only results obtained are for an oscillating flat plate.

Finite-volume effects and the electromagnetic contributions to kaon and pion masses

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

Basak, Subhasish; Bazavov, Alexei; Bernard, Claude

2014-09-25

We report on the MILC Collaboration calculation of electromagnetic effects on light pseudoscalar mesons. The simulations employ asqtad staggered dynamical quarks in QCD plus quenched photons, with lattice spacings varying from 0.12 to 0.06 fm. Finite volume corrections for the MILC realization of lattice electrodynamics have been calculated in chiral perturbation theory and applied to the lattice data. These corrections differ from those calculated by Hayakawa and Uno because our treatment of zero modes differs from theirs. Updated results for the corrections to "Dashen's theorem" are presented.

Thermal imbalance force modelling for a GPS satellite using the finite element method

NASA Technical Reports Server (NTRS)

Vigue, Yvonne; Schutz, Bob E.

1991-01-01

Methods of analyzing the perturbation due to thermal radiation and determining its effects on the orbits of GPS satellites are presented, with emphasis on the FEM technique to calculate satellite solar panel temperatures which are used to determine the magnitude and direction of the thermal imbalance force. Although this force may not be responsible for all of the force mismodeling, conditions may work in combination with the thermal imbalance force to produce such accelerations on the order of 1.e-9 m/sq s. If submeter accurate orbits and centimeter-level accuracy for geophysical applications are desired, a time-dependent model of the thermal imbalance force should be used, especially when satellites are eclipsing, where the observed errors are larger than for satellites in noneclipsing orbits.

PIC simulation of compressive and rarefactive dust ion-acoustic solitary waves

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

Li, Zhong-Zheng; Zhang, Heng; Hong, Xue-Ren

The nonlinear propagations of dust ion-acoustic solitary waves in a collisionless four-component unmagnetized dusty plasma system containing nonextensive electrons, inertial negative ions, Maxwellian positive ions, and negatively charged static dust grains have been investigated by the particle-in-cell method. By comparing the simulation results with those obtained from the traditional reductive perturbation method, it is observed that the rarefactive KdV solitons propagate stably at a low amplitude, and when the amplitude is increased, the prime wave form evolves and then gradually breaks into several small amplitude solitary waves near the tail of soliton structure. The compressive KdV solitons propagate unstably andmore » oscillation arises near the tail of soliton structure. The finite amplitude rarefactive and compressive Gardner solitons seem to propagate stably.« less

Finite volume effects on the electric polarizability of neutral hadrons in lattice QCD

NASA Astrophysics Data System (ADS)

Lujan, M.; Alexandru, A.; Freeman, W.; Lee, F. X.

2016-10-01

We study the finite volume effects on the electric polarizability for the neutron, neutral pion, and neutral kaon using eight dynamically generated two-flavor nHYP-clover ensembles at two different pion masses: 306(1) and 227(2) MeV. An infinite volume extrapolation is performed for each hadron at both pion masses. For the neutral kaon, finite volume effects are relatively mild. The dependence on the quark mass is also mild, and a reliable chiral extrapolation can be performed along with the infinite volume extrapolation. Our result is αK0 phys=0.356 (74 )(46 )×10-4 fm3 . In contrast, for neutron, the electric polarizability depends strongly on the volume. After removing the finite volume corrections, our neutron polarizability results are in good agreement with chiral perturbation theory. For the connected part of the neutral pion polarizability, the negative trend persists, and it is not due to finite volume effects but likely sea quark charging effects.

Topological Defects and Structures in the Early Universe

NASA Astrophysics Data System (ADS)

Zhu, Yong

1997-08-01

This thesis discusses the topological defects generated in the early universe and their contributions to cosmic structure formation. First, we investigate non-Gaussian isocurvature perturbations generated by the evolution of Goldstone modes during inflation. If a global symmetry is broken before inflation, the resulting Goldstone modes are disordered during inflation in a precise and predictable way. After inflation these Goldstone modes order themselves in a self-similar way, much as Goldstone modes in field ordering scenarios based on the Kibble mechanism. For (Hi2/Mpl2)~10- 6, through their gravitational interaction these Goldstone modes generate density perturbations of approximately the right magnitude to explain the cosmic microwave background (CMB) anisotropy and seed the structure seen in the universe today. In such a model non-Gaussian perturbations result because to lowest order density perturbations are sourced by products of Gaussian fields. We explore the issue of phase dispersion and conclude that this non-Gaussian model predicts Doppler peaks in the CMB anisotropy. Topological defects generated from quantum fluctuations during inflation are studied in chapter four. We present a calculation of the power spectrum generated in a classically symmetry-breaking O(N) scalar field through inflationary quantum fluctuations, using the large-N limit. The effective potential of the theory in de Sitter space is obtained from a gap equation which is exact at large N. Quantum fluctuations restore the O(N) symmetry in de Sitter space, but for the finite values of N of interest, there is symmetry breaking and phase ordering after inflation, described by the classical nonlinear sigma model. The scalar field power spectrum is obtained as a function of the scalar field self-coupling. In the second part of the thesis, we investigate non-Abelian topological worm-holes, obtained when winding number one texture field is coupled to Einstein gravity with a conserved global charge. This topological wormhole has the same Euclidean action as axion wormholes and charged scalar wormholes. We find that free topological wormholes are spontaneously generated in the Euclidean space-time with finite density. It is then shown that wormholes with finite density might destroy any long range order in the global fields.

The correlation function for density perturbations in an expanding universe. I - Linear theory

NASA Technical Reports Server (NTRS)

Mcclelland, J.; Silk, J.

1977-01-01

The evolution of the two-point correlation function for adiabatic density perturbations in the early universe is studied. Analytical solutions are obtained for the evolution of linearized spherically symmetric adiabatic density perturbations and the two-point correlation function for these perturbations in the radiation-dominated portion of the early universe. The results are then extended to the regime after decoupling. It is found that: (1) adiabatic spherically symmetric perturbations comparable in scale with the maximum Jeans length would survive the radiation-dominated regime; (2) irregular fluctuations are smoothed out up to the scale of the maximum Jeans length in the radiation era, but regular fluctuations might survive on smaller scales; (3) in general, the only surviving structures for irregularly shaped adiabatic density perturbations of arbitrary but finite scale in the radiation regime are the size of or larger than the maximum Jeans length in that regime; (4) infinite plane waves with a wavelength smaller than the maximum Jeans length but larger than the critical dissipative damping scale could survive the radiation regime; and (5) black holes would also survive the radiation regime and might accrete sufficient mass after decoupling to nucleate the formation of galaxies.

Improvement and performance evaluation of the perturbation source method for an exact Monte Carlo perturbation calculation in fixed source problems

NASA Astrophysics Data System (ADS)

Sakamoto, Hiroki; Yamamoto, Toshihiro

2017-09-01

This paper presents improvement and performance evaluation of the "perturbation source method", which is one of the Monte Carlo perturbation techniques. The formerly proposed perturbation source method was first-order accurate, although it is known that the method can be easily extended to an exact perturbation method. A transport equation for calculating an exact flux difference caused by a perturbation is solved. A perturbation particle representing a flux difference is explicitly transported in the perturbed system, instead of in the unperturbed system. The source term of the transport equation is defined by the unperturbed flux and the cross section (or optical parameter) changes. The unperturbed flux is provided by an "on-the-fly" technique during the course of the ordinary fixed source calculation for the unperturbed system. A set of perturbation particle is started at the collision point in the perturbed region and tracked until death. For a perturbation in a smaller portion of the whole domain, the efficiency of the perturbation source method can be improved by using a virtual scattering coefficient or cross section in the perturbed region, forcing collisions. Performance is evaluated by comparing the proposed method to other Monte Carlo perturbation methods. Numerical tests performed for a particle transport in a two-dimensional geometry reveal that the perturbation source method is less effective than the correlated sampling method for a perturbation in a larger portion of the whole domain. However, for a perturbation in a smaller portion, the perturbation source method outperforms the correlated sampling method. The efficiency depends strongly on the adjustment of the new virtual scattering coefficient or cross section.

New Finite Difference Methods Based on IIM for Inextensible Interfaces in Incompressible Flows

PubMed Central

Li, Zhilin; Lai, Ming-Chih

2012-01-01

In this paper, new finite difference methods based on the augmented immersed interface method (IIM) are proposed for simulating an inextensible moving interface in an incompressible two-dimensional flow. The mathematical models arise from studying the deformation of red blood cells in mathematical biology. The governing equations are incompressible Stokes or Navier-Stokes equations with an unknown surface tension, which should be determined in such a way that the surface divergence of the velocity is zero along the interface. Thus, the area enclosed by the interface and the total length of the interface should be conserved during the evolution process. Because of the nonlinear and coupling nature of the problem, direct discretization by applying the immersed boundary or immersed interface method yields complex nonlinear systems to be solved. In our new methods, we treat the unknown surface tension as an augmented variable so that the augmented IIM can be applied. Since finding the unknown surface tension is essentially an inverse problem that is sensitive to perturbations, our regularization strategy is to introduce a controlled tangential force along the interface, which leads to a least squares problem. For Stokes equations, the forward solver at one time level involves solving three Poisson equations with an interface. For Navier-Stokes equations, we propose a modified projection method that can enforce the pressure jump condition corresponding directly to the unknown surface tension. Several numerical experiments show good agreement with other results in the literature and reveal some interesting phenomena. PMID:23795308

Spectrum of the Wilson Dirac operator at finite lattice spacings

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

Akemann, G.; Damgaard, P. H.; Splittorff, K.

2011-04-15

We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral perturbation theory and chiral random matrix theory. A graded chiral Lagrangian is used to evaluate the microscopic spectral density of the Hermitian Wilson Dirac operator as well as the distribution of the chirality over the real eigenvalues of the Wilson Dirac operator. It is shown that a chiral random matrix theory for the Wilson Dirac operator reproduces the leading zero-momentum terms of Wilson chiral perturbation theory. All results are obtained for a fixed index of the Wilson Dirac operator. The low-energymore » constants of Wilson chiral perturbation theory are shown to be constrained by the Hermiticity properties of the Wilson Dirac operator.« less

Aerodynamic shape optimization using control theory

NASA Technical Reports Server (NTRS)

Reuther, James

1996-01-01

Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.

Numerical and experimental study on the steady cone-jet mode of electro-centrifugal spinning

NASA Astrophysics Data System (ADS)

Hashemi, Ali Reza; Pishevar, Ahmad Reza; Valipouri, Afsaneh; Pǎrǎu, Emilian I.

2018-01-01

This study focuses on a numerical investigation of an initial stable jet through the air-sealed electro-centrifugal spinning process, which is known as a viable method for the mass production of nanofibers. A liquid jet undergoing electric and centrifugal forces, as well as other forces, first travels in a stable trajectory and then goes through an unstable curled path to the collector. In numerical modeling, hydrodynamic equations have been solved using the perturbation method—and the boundary integral method has been implemented to efficiently solve the electric potential equation. Hydrodynamic equations have been coupled with the electric field using stress boundary conditions at the fluid-fluid interface. Perturbation equations were discretized by a second order finite difference method, and the Newton method was implemented to solve the discretized non-linear system. Also, the boundary element method was utilized to solve electrostatic equations. In the theoretical study, the fluid was described as a leaky dielectric with charges only on the surface of the jet traveling in dielectric air. The effect of the electric field induced around the nozzle tip on the jet instability and trajectory deviation was also experimentally studied through plate-plate geometry as well as point-plate geometry. It was numerically found that the centrifugal force prevails on electric force by increasing the rotational speed. Therefore, the alteration of the applied voltage does not significantly affect the jet thinning profile or the jet trajectory.

An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients

NASA Technical Reports Server (NTRS)

Carlson, Leland A.

1994-01-01

The primary accomplishments of the project are as follows: (1) Using the transonic small perturbation equation as a flowfield model, the project demonstrated that the quasi-analytical method could be used to obtain aerodynamic sensitivity coefficients for airfoils at subsonic, transonic, and supersonic conditions for design variables such as Mach number, airfoil thickness, maximum camber, angle of attack, and location of maximum camber. It was established that the quasi-analytical approach was an accurate method for obtaining aerodynamic sensitivity derivatives for airfoils at transonic conditions and usually more efficient than the finite difference approach. (2) The usage of symbolic manipulation software to determine the appropriate expressions and computer coding associated with the quasi-analytical method for sensitivity derivatives was investigated. Using the three dimensional fully conservative full potential flowfield model, it was determined that symbolic manipulation along with a chain rule approach was extremely useful in developing a combined flowfield and quasi-analytical sensitivity derivative code capable of considering a large number of realistic design variables. (3) Using the three dimensional fully conservative full potential flowfield model, the quasi-analytical method was applied to swept wings (i.e. three dimensional) at transonic flow conditions. (4) The incremental iterative technique has been applied to the three dimensional transonic nonlinear small perturbation flowfield formulation, an equivalent plate deflection model, and the associated aerodynamic and structural discipline sensitivity equations; and coupled aeroelastic results for an aspect ratio three wing in transonic flow have been obtained.

Elastic pp-bar and pp scattering up to. sqrt. s = 546 GeV and the flavored perturbative Reggeon field theory

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

Dash, J.W.; Jones, S.T.

We show that the perturbative Reggeon field theory (RFT) with flavoring corrections added reproduces the pp and pp-bar differential cross sections from Fermilab to the CERN SPS collider (Spp-bar S). This completes a long program of phenomenology which is now capable of providing a unified framework for soft hadronic scattering at current energies. Our scenario of data being influenced by finite scales at least up to ..sqrt..s = 546 GeV is compatible with the truly asymptotic limit being described by the critical RFT scaling laws.

Self-similar perturbations of a Friedmann universe

NASA Technical Reports Server (NTRS)

Carr, Bernard J.; Yahil, Amos

1990-01-01

The present analysis of spherically symmetric self-similar solutions to the Einstein equations gives attention to those solutions that are asymptotically k = 0 Friedmann at large z values, and possess finite but perturbed density at the origin. Such solutions represent nonlinear density fluctuations which grow at the same rate as the universe's particle horizon. The overdense solutions span only a narrow range of parameters, and resemble static isothermal gas spheres just within the sonic point; the underdense solutions may have arbitrarily low density at the origin while exhibiting a unique relationship between amplitude and scale. Their relevance to large-scale void formation is considered.

Taste violations in the scalar correlator in mixed action simulations

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

Aubin, C.; /Columbia U. /William-Mary Coll.; Laiho, Jack

2007-10-01

We study the behavior of the isovector scalar correlator, which is particularly sensitive to lattice artifacts, using domain-wall valence quarks on a staggered sea (generated by the MILC collaboration). We analyze this according to the prediction from chiral perturbation theory determined by Prelovsek, which indicates that the leading unitarity violations come from taste breaking effects. We show that our data behaves in the way predicted by Prelovsek, thus verifying that the largest contribution to the violations of unitarity which arise at finite lattice spacing can be described by the mixed-action chiral perturbation theory.

MHD thermal instabilities in cool inhomogeneous atmospheres

NASA Technical Reports Server (NTRS)

Bodo, G.; Ferrari, A.; Massaglia, S.; Rosner, R.

1983-01-01

The formation of a coronal state in a stellar atmosphere is investigated. A numerical code is used to study the effects of atmospheric gradients and finite loop dimension on the scale of unstable perturbations, solving for oscillatory perturbations as eigenfunctions of a boundary value problem. The atmosphere is considered as initially isothermal, with density and pressure having scale heights fixed by the hydrostatic equations. Joule mode instability is found to be an efficient mechanism for current filamentation and subsequent heating in initially cool atmospheres. This instability is mainly effective at the top of magnetic loops and is not suppressed by thermal conduction.

A tensor Banach algebra approach to abstract kinetic equations

NASA Astrophysics Data System (ADS)

Greenberg, W.; van der Mee, C. V. M.

The study deals with a concrete algebraic construction providing the existence theory for abstract kinetic equation boundary-value problems, when the collision operator A is an accretive finite-rank perturbation of the identity operator in a Hilbert space H. An algebraic generalization of the Bochner-Phillips theorem is utilized to study solvability of the abstract boundary-value problem without any regulatory condition. A Banach algebra in which the convolution kernel acts is obtained explicitly, and this result is used to prove a perturbation theorem for bisemigroups, which then plays a vital role in solving the initial equations.

First moments of nucleon generalized parton distributions

DOE PAGES

Wang, P.; Thomas, A. W.

2010-06-01

We extrapolate the first moments of the generalized parton distributions using heavy baryon chiral perturbation theory. The calculation is based on the one loop level with the finite range regularization. The description of the lattice data is satisfactory, and the extrapolated moments at physical pion mass are consistent with the results obtained with dimensional regularization, although the extrapolation in the momentum transfer to t=0 does show sensitivity to form factor effects, which lie outside the realm of chiral perturbation theory. We discuss the significance of the results in the light of modern experiments as well as QCD inspired models.

One-step leapfrog ADI-FDTD method for simulating electromagnetic wave propagation in general dispersive media.

PubMed

Wang, Xiang-Hua; Yin, Wen-Yan; Chen, Zhi Zhang David

2013-09-09

The one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is reformulated for simulating general electrically dispersive media. It models material dispersive properties with equivalent polarization currents. These currents are then solved with the auxiliary differential equation (ADE) and then incorporated into the one-step leapfrog ADI-FDTD method. The final equations are presented in the form similar to that of the conventional FDTD method but with second-order perturbation. The adapted method is then applied to characterize (a) electromagnetic wave propagation in a rectangular waveguide loaded with a magnetized plasma slab, (b) transmission coefficient of a plane wave normally incident on a monolayer graphene sheet biased by a magnetostatic field, and (c) surface plasmon polaritons (SPPs) propagation along a monolayer graphene sheet biased by an electrostatic field. The numerical results verify the stability, accuracy and computational efficiency of the proposed one-step leapfrog ADI-FDTD algorithm in comparison with analytical results and the results obtained with the other methods.

Transmutation of a trans-series: the Gross-Witten-Wadia phase transition

NASA Astrophysics Data System (ADS)

Ahmed, Anees; Dunne, Gerald V.

2017-11-01

We study the change in the resurgent asymptotic properties of a trans-series in two parameters, a coupling g 2 and a gauge index N, as a system passes through a large N phase transition, using the universal example of the Gross-Witten-Wadia third-order phase transition in the unitary matrix model. This transition is well-studied in the immediate vicinity of the transition point, where it is characterized by a double-scaling limit Painlevé II equation, and also away from the transition point using the pre-string difference equation. Here we present a complementary analysis of the transition at all coupling and all finite N, in terms of a differential equation, using the explicit Tracy-Widom mapping of the Gross-Witten-Wadia partition function to a solution of a Painlevé III equation. This mapping provides a simple method to generate trans-series expansions in all parameter regimes, and to study their transmutation as the parameters are varied. For example, at any finite N the weak coupling expansion is divergent, with a non-perturbative trans-series completion; on the other hand, the strong coupling expansion is convergent, and yet there is still a non-perturbative trans-series completion. We show how the different instanton terms `condense' at the transition point to match with the double-scaling limit trans-series. We also define a uniform large N strong-coupling expansion (a non-linear analogue of uniform WKB), which is much more precise than the conventional large N expansion through the transition region, and apply it to the evaluation of Wilson loops.

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

Jevicki, Antal; Suzuki, Kenta

We continue the study of the Sachdev-Ye-Kitaev model in the Large N limit. Following our formulation in terms of bi-local collective fields with dynamical reparametrization symmetry, we perform perturbative calculations around the conformal IR point. As a result, these are based on an ε expansion which allows for analytical evaluation of correlators and finite temperature quantities.

A pseudo energy-invariant method for relativistic wave equations with Riesz space-fractional derivatives

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.; Hendy, A. S.; De Staelen, R. H.

2018-03-01

In this work, we investigate a general nonlinear wave equation with Riesz space-fractional derivatives that generalizes various classical hyperbolic models, including the sine-Gordon and the Klein-Gordon equations from relativistic quantum mechanics. A finite-difference discretization of the model is provided using fractional centered differences. The method is a technique that is capable of preserving an energy-like quantity at each iteration. Some computational comparisons against solutions available in the literature are performed in order to assess the capability of the method to preserve the invariant. Our experiments confirm that the technique yields good approximations to the solutions considered. As an application of our scheme, we provide simulations that confirm, for the first time in the literature, the presence of the phenomenon of nonlinear supratransmission in Riesz space-fractional Klein-Gordon equations driven by a harmonic perturbation at the boundary.

Control theory based airfoil design using the Euler equations

NASA Technical Reports Server (NTRS)

Jameson, Antony; Reuther, James

1994-01-01

This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using the potential flow equation with either a conformal mapping or a general coordinate system. The goal of our present work is to extend the development to treat the Euler equations in two-dimensions by procedures that can readily be generalized to treat complex shapes in three-dimensions. Therefore, we have developed methods which can address airfoil design through either an analytic mapping or an arbitrary grid perturbation method applied to a finite volume discretization of the Euler equations. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented for both the inverse problem and drag minimization problem.

A multiple scales approach to maximal superintegrability

NASA Astrophysics Data System (ADS)

Gubbiotti, G.; Latini, D.

2018-07-01

In this paper we present a simple, algorithmic test to establish if a Hamiltonian system is maximally superintegrable or not. This test is based on a very simple corollary of a theorem due to Nekhoroshev and on a perturbative technique called the multiple scales method. If the outcome is positive, this test can be used to suggest maximal superintegrability, whereas when the outcome is negative it can be used to disprove it. This method can be regarded as a finite dimensional analog of the multiple scales method as a way to produce soliton equations. We use this technique to show that the real counterpart of a mechanical system found by Jules Drach in 1935 is, in general, not maximally superintegrable. We give some hints on how this approach could be applied to classify maximally superintegrable systems by presenting a direct proof of the well-known Bertrand’s theorem.

Transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation under the influence of nonlinear gain and higher-order effects

NASA Astrophysics Data System (ADS)

Uzunov, Ivan M.; Georgiev, Zhivko D.; Arabadzhiev, Todor N.

2018-05-01

In this paper we study the transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation (CCQGLE) under the influence of nonlinear gain, its saturation, and higher-order effects: self-steepening, third-order of dispersion, and intrapulse Raman scattering in the anomalous dispersion region. The variation method and the method of moments are applied in order to obtain the dynamic models with finite degrees of freedom for the description of stationary and pulsating solutions. Having applied the first model and its bifurcation analysis we have discovered the existence of families of subcritical Poincaré-Andronov-Hopf bifurcations due to the intrapulse Raman scattering, as well as some small nonlinear gain and the saturation of the nonlinear gain. A phenomenon of nonlinear stability has been studied and it has been shown that long living pulsating solutions with relatively small fluctuations of amplitude and frequencies exist at the bifurcation point. The numerical analysis of the second model has revealed the existence of Poincaré-Andronov-Hopf bifurcations of Raman dissipative soliton under the influence of the self-steepening effect and large nonlinear gain. All our theoretical predictions have been confirmed by the direct numerical solution of the full perturbed CCQGLE. The detailed comparison between the results obtained by both dynamic models and the direct numerical solution of the perturbed CCQGLE has proved the applicability of the proposed models in the investigation of the solutions of the perturbed CCQGLE.

Topological bound states of a quantum walk with cold atoms

NASA Astrophysics Data System (ADS)

Mugel, Samuel; Celi, Alessio; Massignan, Pietro; Asbóth, János K.; Lewenstein, Maciej; Lobo, Carlos

2016-08-01

We suggest a method for engineering a quantum walk, with cold atoms as walkers, which presents topologically nontrivial properties. We derive the phase diagram, and show that we are able to produce a boundary between topologically distinct phases using the finite beam width of the applied lasers. A topologically protected bound state can then be observed, which is pinned to the interface and is robust to perturbations. We show that it is possible to identify this bound state by averaging over spin sensitive measures of the atom's position, based on the spin distribution that these states display. Interestingly, there exists a parameter regime in which our system maps on to the Creutz ladder.

Hybrid control of the Neimark-Sacker bifurcation in a delayed Nicholson's blowflies equation.

PubMed

Wang, Yuanyuan; Wang, Lisha

In this article, for delayed Nicholson's blowflies equation, we propose a hybrid control nonstandard finite-difference (NSFD) scheme in which state feedback and parameter perturbation are used to control the Neimark-Sacker bifurcation. Firstly, the local stability of the positive equilibria for hybrid control delay differential equation is discussed according to Hopf bifurcation theory. Then, for any step-size, a hybrid control numerical algorithm is introduced to generate the Neimark-Sacker bifurcation at a desired point. Finally, numerical simulation results confirm that the control strategy is efficient in controlling the Neimark-Sacker bifurcation. At the same time, the results show that the NSFD control scheme is better than the Euler control method.

Investigation of the effects of external current systems on the MAGSAT data utilizing grid cell modeling techniques

NASA Technical Reports Server (NTRS)

Klumpar, D. M. (Principal Investigator)

1982-01-01

The feasibility of modeling magnetic fields due to certain electrical currents flowing in the Earth's ionosphere and magnetosphere was investigated. A method was devised to carry out forward modeling of the magnetic perturbations that arise from space currents. The procedure utilizes a linear current element representation of the distributed electrical currents. The finite thickness elements are combined into loops which are in turn combined into cells having their base in the ionosphere. In addition to the extensive field modeling, additional software was developed for the reduction and analysis of the MAGSAT data in terms of the external current effects. Direct comparisons between the models and the MAGSAT data are possible.

Infrared dynamics of cold atoms on hot graphene membranes

NASA Astrophysics Data System (ADS)

Sengupta, Sanghita; Kotov, Valeri N.; Clougherty, Dennis P.

2016-06-01

We study the infrared dynamics of low-energy atoms interacting with a sample of suspended graphene at finite temperature. The dynamics exhibits severe infrared divergences order by order in perturbation theory as a result of the singular nature of low-energy flexural phonon emission. Our model can be viewed as a two-channel generalization of the independent boson model with asymmetric atom-phonon coupling. This allows us to take advantage of the exact nonperturbative solution of the independent boson model in the stronger channel while treating the weaker one perturbatively. In the low-energy limit, the exact solution can be viewed as a resummation (exponentiation) of the most divergent diagrams in the perturbative expansion. As a result of this procedure, we obtain the atom's Green function which we use to calculate the atom damping rate, a quantity equal to the quantum sticking rate. A characteristic feature of our results is that the Green's function retains a weak, infrared cutoff dependence that reflects the reduced dimensionality of the problem. As a consequence, we predict a measurable dependence of the sticking rate on graphene sample size. We provide detailed predictions for the sticking rate of atomic hydrogen as a function of temperature and sample size. The resummation yields an enhanced sticking rate relative to the conventional Fermi golden rule result (equivalent to the one-loop atom self-energy), as higher-order processes increase damping at finite temperature.

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

NASA Astrophysics Data System (ADS)

Velikovich, A. L.; Schmit, P. F.

2015-11-01

Bell-Plesset effects accounting for the time dependence of the radius, velocity and acceleration of the Rayleigh-Taylor-unstable surface are ubiquitous in the instability of spherical laser targets and magnetically driven cylindrical liners. We present an analytical model that, for an ideal incompressible fluid and small perturbation amplitudes, exactly accounts for the Bell-Plesset effects in finite-thickness targets and liners through acceleration and deceleration phases. We derive the time-dependent dispersion equations determining the ``instantaneous growth rate'' and demonstrate that by integrating this growth rate over time (the WKB approximation) we accurately evaluate the number of perturbation e-foldings during the acceleration phase. In the limit of the small target/liner thickness, we obtain the exact thin-shell perturbation equations and approximate thin-shell dispersion relations, generalizing the earlier results of Harris (1962), Ott (1972) and Bud'ko et al. (1989). This research was supported by the US DOE/NNSA (A.L.V.), and in part by appointment to the Sandia National Laboratories Truman Fellowship in National Security Science and Engineering (P.F.S.), which is part of the Laboratory Directed Research and Development (LDRD) Program, Project No. 165746, and sponsored by Sandia Corporation (a wholly owned subsidiary of Lockheed Martin Corporation) as Operator of Sandia National Laboratories under its U.S. Department of Energy Contract No. DE-AC04-94AL85000.

Relativistic bound-state problem in the light-front Yukawa model

NASA Astrophysics Data System (ADS)

Głazek, Stanisław; Harindranath, Avaroth; Pinsky, Stephen; Shigemitsu, Junko; Wilson, Kenneth

1993-02-01

We study the renormalization problem on the light front for the two-fermion bound state in the (3+1)-dimensional Yukawa model, working within the lowest-order Tamm-Dancoff approximation. In addition to traditional mass and wave-function renormalization, new types of counterterms are required. These are nonlocal and involve arbitrary functions of the longitudinal momenta. Their appearance is consistent with general power-counting arguments on the light front. We estimate the ``arbitrary function'' in two ways: (1) by using perturbation theory as a guide and (2) by considering the asymptotic large transverse momentum behavior of the kernel in the bound-state equations. The latter method, as it is currently implemented, is applicable only to the helicity-zero sector of the theory. Because of triviality, in the Yukawa model one must retain a finite cutoff Λ in order to have a nonvanishing renormalized coupling. For the range of renormalized couplings (and cutoffs) allowed by triviality, one finds that the perturbative counterterm does a good job in eliminating cutoff dependence in the low-energy spectrum (masses <<Λ).

Large-eddy simulation of a spatially-evolving turbulent mixing layer

NASA Astrophysics Data System (ADS)

Capuano, Francesco; Catalano, Pietro; Mastellone, Andrea

2015-11-01

Large-eddy simulations of a spatially-evolving turbulent mixing layer have been performed. The flow conditions correspond to those of a documented experimental campaign (Delville, Appl. Sci. Res. 1994). The flow evolves downstream of a splitter plate separating two fully turbulent boundary layers, with Reθ = 2900 on the high-speed side and Reθ = 1200 on the low-speed side. The computational domain starts at the trailing edge of the splitter plate, where experimental mean velocity profiles are prescribed; white-noise perturbations are superimposed to mimic turbulent fluctuations. The fully compressible Navier-Stokes equations are solved by means of a finite-volume method implemented into the in-house code SPARK-LES. The results are mainly checked in terms of the streamwise evolution of the vorticity thickness and averaged velocity profiles. The combined effects of inflow perturbations, numerical accuracy and subgrid-scale model are discussed. It is found that excessive levels of dissipation may damp inlet fluctuations and delay the virtual origin of the turbulent mixing layer. On the other hand, non-dissipative, high-resolution computations provide results that are in much better agreement with experimental data.

High-beta analytic equilibria in circular, elliptical, and D-shaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows

NASA Astrophysics Data System (ADS)

López, O. E.; Guazzotto, L.

2017-03-01

The Grad-Shafranov-Bernoulli system of equations is a single fluid magnetohydrodynamical description of axisymmetric equilibria with mass flows. Using a variational perturbative approach [E. Hameiri, Phys. Plasmas 20, 024504 (2013)], analytic approximations for high-beta equilibria in circular, elliptical, and D-shaped cross sections in the high aspect ratio approximation are found, which include finite toroidal and poloidal flows. Assuming a polynomial dependence of the free functions on the poloidal flux, the equilibrium problem is reduced to an inhomogeneous Helmholtz partial differential equation (PDE) subject to homogeneous Dirichlet conditions. An application of the Green's function method leads to a closed form for the circular solution and to a series solution in terms of Mathieu functions for the elliptical case, which is valid for arbitrary elongations. To extend the elliptical solution to a D-shaped domain, a boundary perturbation in terms of the triangularity is used. A comparison with the code FLOW [L. Guazzotto et al., Phys. Plasmas 11(2), 604-614 (2004)] is presented for relevant scenarios.

Large displacement behavior of double parallelogram flexure mechanisms with underconstraint eliminators

DOE PAGES

Panas, Robert M.

2016-06-23

This paper presents a new analytical method for predicting the large displacement behavior of flexural double parallelogram (DP) bearings with underconstraint eliminator (UE) linkages. This closed-form perturbative Euler analysis method is able to – for the first time – directly incorporate the elastomechanics of a discrete UE linkage, which is a hybrid flexure element that is linked to ground as well as both stages on the bearing. The models are used to understand a nested linkage UE design, however the method is extensible to other UE linkages. Design rules and figures-of-merit are extracted from the analysis models, which provide powerfulmore » tools for accelerating the design process. The models, rules and figures-of-merit enable the rapid design of a UE for a desired large displacement behavior, as well as providing a means for determining the limits of UE and DP structures. This will aid in the adoption of UE linkages into DP bearings for precision mechanisms. Models are generated for a nested linkage UE design, and the performance of this DP with UE structure is compared to a DP-only bearing. As a result, the perturbative Euler analysis is shown to match existing theories for DP-only bearings with distributed compliance within ≈2%, and Finite Element Analysis for the DP with UE bearings within an average 10%.« less

Large displacement behavior of double parallelogram flexure mechanisms with underconstraint eliminators

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

Panas, Robert M.

This paper presents a new analytical method for predicting the large displacement behavior of flexural double parallelogram (DP) bearings with underconstraint eliminator (UE) linkages. This closed-form perturbative Euler analysis method is able to – for the first time – directly incorporate the elastomechanics of a discrete UE linkage, which is a hybrid flexure element that is linked to ground as well as both stages on the bearing. The models are used to understand a nested linkage UE design, however the method is extensible to other UE linkages. Design rules and figures-of-merit are extracted from the analysis models, which provide powerfulmore » tools for accelerating the design process. The models, rules and figures-of-merit enable the rapid design of a UE for a desired large displacement behavior, as well as providing a means for determining the limits of UE and DP structures. This will aid in the adoption of UE linkages into DP bearings for precision mechanisms. Models are generated for a nested linkage UE design, and the performance of this DP with UE structure is compared to a DP-only bearing. As a result, the perturbative Euler analysis is shown to match existing theories for DP-only bearings with distributed compliance within ≈2%, and Finite Element Analysis for the DP with UE bearings within an average 10%.« less

Learning from ISS-modular adaptive NN control of nonlinear strict-feedback systems.

PubMed

Wang, Cong; Wang, Min; Liu, Tengfei; Hill, David J

2012-10-01

This paper studies learning from adaptive neural control (ANC) for a class of nonlinear strict-feedback systems with unknown affine terms. To achieve the purpose of learning, a simple input-to-state stability (ISS) modular ANC method is first presented to ensure the boundedness of all the signals in the closed-loop system and the convergence of tracking errors in finite time. Subsequently, it is proven that learning with the proposed stable ISS-modular ANC can be achieved. The cascade structure and unknown affine terms of the considered systems make it very difficult to achieve learning using existing methods. To overcome these difficulties, the stable closed-loop system in the control process is decomposed into a series of linear time-varying (LTV) perturbed subsystems with the appropriate state transformation. Using a recursive design, the partial persistent excitation condition for the radial basis function neural network (NN) is established, which guarantees exponential stability of LTV perturbed subsystems. Consequently, accurate approximation of the closed-loop system dynamics is achieved in a local region along recurrent orbits of closed-loop signals, and learning is implemented during a closed-loop feedback control process. The learned knowledge is reused to achieve stability and an improved performance, thereby avoiding the tremendous repeated training process of NNs. Simulation studies are given to demonstrate the effectiveness of the proposed method.

Large-angle slewing maneuvers for flexible spacecraft

NASA Technical Reports Server (NTRS)

Chun, Hon M.; Turner, James D.

1988-01-01

A new class of closed-form solutions for finite-time linear-quadratic optimal control problems is presented. The solutions involve Potter's solution for the differential matrix Riccati equation, which assumes the form of a steady-state plus transient term. Illustrative examples are presented which show that the new solutions are more computationally efficient than alternative solutions based on the state transition matrix. As an application of the closed-form solutions, the neighboring extremal path problem is presented for a spacecraft retargeting maneuver where a perturbed plant with off-nominal boundary conditions now follows a neighboring optimal trajectory. The perturbation feedback approach is further applied to three-dimensional slewing maneuvers of large flexible spacecraft. For this problem, the nominal solution is the optimal three-dimensional rigid body slew. The perturbation feedback then limits the deviations from this nominal solution due to the flexible body effects. The use of frequency shaping in both the nominal and perturbation feedback formulations reduces the excitation of high-frequency unmodeled modes. A modified Kalman filter is presented for estimating the plant states.

Determination of Spatio-Temporal Characteristics of D-region Electron Density during Annular Solar Eclipse from VLF Network Observations

NASA Astrophysics Data System (ADS)

Basak, T.; Hobara, Y.

2015-12-01

A major part of the path of the annular solar eclipse of May 20, 2012 (magnitude 0.9439) was over southern Japan. The D-region ionospheric changes associated with that eclipse, led to several degree of observable perturbations of sub-ionospheric very low frequency (VLF) radio signal. The University of Electro-Communications (UEC) operates VLF observation network over Japan. The solar eclipse associated signal changes were recorded in several receiving stations (Rx) simultaneously for the VLF signals coming from NWC/19.8kHz, JJI/22.2kHz, JJY/40.0kHz, NLK/24.8kHz and other VLF transmitters (Tx). These temporal dependences of VLF signal perturbation have been analyzed and the spatio-temporal characteristics of respective sub-ionospheric perturbations has already been studied by earlier workers using 2D-Finite Difference Time Domain method of simulation. In this work, we determine the spatial scale, depth and temporal dependence of lower ionospheric perturbation in consistence with umbral and penumbral motion. We considered the 2-parameter D-region ionospheric model with exponential electron density profile. To model the solar obscuration effect over it, we assumed a generalized space-time dependent 2-dimensional elliptical Gaussian distribution for ionospheric parameters, such as, effective reflection height (h') and sharpness factor (β). The depth (△hmax, △βmax), center of shadow (lato(t), lono(t)) and spatial scale (σlat,lon) of that Gaussian distribution are used as model parameters. In the vicinity of the eclipse zone, we compute the VLF signal perturbations using Long Wave Propagation Capability (LWPC) code for several signal propagation paths. The propagation path characteristics, such as, ground and water conductivity and geomagnetic effect on ionosphere are considered from standard LWPC prescriptions. The model parameters are tuned to set an optimum agreement between our computation and observed positive and negative type of VLF perturbations. Thus, appropriate set of parameters lead us to the possible determination of spatial scale, depth and temporal dependence of eclipse associated D-region electron density perturbation solely from the VLF-network observations coupled with theoretical modeling.

Linear and nonlinear pattern selection in Rayleigh-Benard stability problems

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

1993-01-01

A new algorithm is introduced to compute finite-amplitude states using primitive variables for Rayleigh-Benard convection on relatively coarse meshes. The algorithm is based on a finite-difference matrix-splitting approach that separates all physical and dimensional effects into one-dimensional subsets. The nonlinear pattern selection process for steady convection in an air-filled square cavity with insulated side walls is investigated for Rayleigh numbers up to 20,000. The internalization of disturbances that evolve into coherent patterns is investigated and transient solutions from linear perturbation theory are compared with and contrasted to the full numerical simulations.

Rapid magnetic reconnection caused by finite amplitude fluctuations

NASA Technical Reports Server (NTRS)

Matthaeus, W. H.; Lamkin, S. L.

1985-01-01

The nonlinear dynamics of the magnetohydrodynamic sheet pinch have been investigated as an unforced initial value problem for large scale Reynolds numbers up to 1000. Reconnection is triggered by adding to the sheet pinch a small but finite level of broadband random perturbations. Effects of turbulence in the solutions include the production of reconnected magnetic islands at rates that are insensitive to resistivity at early times. This is explained by noting that electric field fluctuations near the X point produce irregularities in the vector potential, sometimes taking the form of 'magnetic bubbles', which allow rapid change of field topology.

Features of sound propagation through and stability of a finite shear layer

NASA Technical Reports Server (NTRS)

Koutsoyannis, S. P.

1976-01-01

The plane wave propagation, the stability and the rectangular duct mode problems of a compressible inviscid linearly sheared parallel, but otherwise homogeneous flow, are shown to be governed by Whittaker's equation. The exact solutions for the perturbation quantities are essentially Whittaker M-functions. A number of known results are obtained as limiting cases of exact solutions. For the compressible finite thickness shear layer it is shown that no resonances and no critical angles exist for all Mach numbers, frequencies and shear layer velocity profile slopes except in the singular case of the vortex sheet.

Quantum statistical mechanics of nonrelativistic membranes: crumpling transition at finite temperature

NASA Astrophysics Data System (ADS)

Borelli, M. E. S.; Kleinert, H.; Schakel, Adriaan M. J.

2000-03-01

The effect of quantum fluctuations on a nearly flat, nonrelativistic two-dimensional membrane with extrinsic curvature stiffness and tension is investigated. The renormalization group analysis is carried out in first-order perturbative theory. In contrast to thermal fluctuations, which soften the membrane at large scales and turn it into a crumpled surface, quantum fluctuations are found to stiffen the membrane, so that it exhibits a Hausdorff dimension equal to two. The large-scale behavior of the membrane is further studied at finite temperature, where a nontrivial fixed point is found, signaling a crumpling transition.

Edge effects in angle-ply composite laminates

NASA Technical Reports Server (NTRS)

Hsu, P. W.; Herakovich, C. T.

1977-01-01

This paper presents the results of a zeroth-order solution for edge effects in angle-ply composite laminates obtained using perturbation techniques and a limiting free body approach. The general solution for edge effects in laminates of arbitrary angle ply is applied to the special case of a (+ or - 45)s graphite/epoxy laminate. Interlaminar stress distributions are obtained as a function of the laminate thickness-to-width ratio and compared to finite difference results. The solution predicts stable, continuous stress distributions, determines finite maximum tensile interlaminar normal stress and provides mathematical evidence for singular interlaminar shear stresses in (+ or - 45) graphite/epoxy laminates.

Bi-stability resistant to fluctuations

NASA Astrophysics Data System (ADS)

Caruel, M.; Truskinovsky, L.

2017-12-01

We study a simple micro-mechanical device that does not lose its snap-through behavior in an environment dominated by fluctuations. The main idea is to have several degrees of freedom that can cooperatively resist the de-synchronizing effect of random perturbations. As an inspiration we use the power stroke machinery of skeletal muscles, which ensures at sub-micron scales and finite temperatures a swift recovery of an abruptly applied slack. In addition to hypersensitive response at finite temperatures, our prototypical Brownian snap spring also exhibits criticality at special values of parameters which is another potentially interesting property for micro-scale engineering applications.

A finite-element-based perturbation model for the rotordynamic analysis of shrouded pump impellers: Part 1: Model development and applications

NASA Technical Reports Server (NTRS)

Baskharone, Erian A.

1993-01-01

This study concerns the rotor dynamic characteristics of fluid-encompassed rotors, with special emphasis on shrouded pump impellers. The core of the study is a versatile and categorically new finite-element-based perturbation model, which is based on a rigorous flow analysis and what we have generically termed the 'virtually' deformable finite-element approach. The model is first applied to the case of a smooth annular seal for verification purposes. The rotor excitation components, in this sample problem, give rise to a purely cylindrical, purely conical, and a simultaneous cylindrical/conical rotor whirl around the housing centerline. In all cases, the computed results are compared to existing experimental and analytical data involving the same seal geometry and operating conditions. Next, two labyrinth-seal configurations, which share the same tooth-to-tooth chamber geometry but differ in the total number of chambers, were investigated. The results, in this case, are compared to experimental measurements for both seal configurations. The focus is finally shifted to the shrouded-impeller problem, where the stability effects of the leakage flow in the shroud-to-housing secondary passage are investigated. To this end, the computational model is applied to a typical shrouded-impeller pump stage, fabricated and rotor dynamically tested by Sulzer Bros., and the results compared to those of a simplified 'bulk-flow' analysis and Sulzer Bros.' test data. In addition to assessing the computed rotor dynamic coefficients, the shrouded-impeller study also covers a controversial topic, namely that of the leakage-passage inlet swirl, which was previously cited as the origin of highly unconventional (resonance-like) trends of the fluid-exerted forces. In order to validate this claim, a 'microscopic' study of the fluid/shroud interaction mechanism is conducted, with the focus being on the structure of the perturbed flow field associated with the impeller whirl. The conclusions of this study were solidified by the outcome of a numerical-certainty exercise, where the grid dependency of the numerical results is objectively examined. The final phase of the shrouded-impeller investigation involves the validation of a built-in assumption, in all other perturbation models, whereby single-harmonic tangential distributions of all the flow thermophysical properties are imposed. The last phase of the investigation course is aimed at verifying the fine details of the perturbed flow field in light of recent set of detailed LDA measurements in a smooth annular seal. Grid dependency of the fluid-induced forces is also investigated, and specific recommendations are made.

High speed flow past wings

NASA Technical Reports Server (NTRS)

Norstrud, H.

1973-01-01

The analytical solution to the transonic small perturbation equation which describes steady compressible flow past finite wings at subsonic speeds can be expressed as a nonlinear integral equation with the perturbation velocity potential as the unknown function. This known formulation is substituted by a system of nonlinear algebraic equations to which various methods are applicable for its solution. Due to the presence of mathematical discontinuities in the flow solutions, however, a main computational difficulty was to ensure uniqueness of the solutions when local velocities on the wing exceeded the speed of sound. For continuous solutions this was achieved by embedding the algebraic system in an one-parameter operator homotopy in order to apply the method of parametric differentiation. The solution to the initial system of equations appears then as a solution to a Cauchy problem where the initial condition is related to the accompanying incompressible flow solution. In using this technique, however, a continuous dependence of the solution development on the initial data is lost when the solution reaches the minimum bifurcation point. A steepest descent iteration technique was therefore, added to the computational scheme for the calculation of discontinuous flow solutions. Results for purely subsonic flows and supersonic flows with and without compression shocks are given and compared with other available theoretical solutions.

Investigation of the local stress perturbation in Long Valley, California, by coupling seismic analyses and FEM numerical modeling

NASA Astrophysics Data System (ADS)

Lin, G.; Albino, F.; Amelung, F.

2017-12-01

Long Valley Caldera in eastern California is well known for producing numerous volcanic eruptions over the past 3 Myr. There has been a stress perturbation in the vicinity of the caldera with respect to the regional stress field. In this study, we combine seismic analyses and finite-element numerical modeling to investigate this local stress anomaly. We first compute focal mechanisms for earthquakes relocated by using a three-dimensional (3-D) seismic velocity model and waveform cross-correlation data. The final 42,000 good-quality focal solutions show that the mechanisms are dominated by approximately the same amount of normal faulting and strike-slip and much fewer reverse focal types. These focal mechanisms are then used to invert for the stress field in the study area by applying the SATSI algorithm. The orientations of the inverted minimum horizontal principal stress (ShMIN) greatly agree with those in previous studies based on analyses of focal mechanisms, borehole breakouts, and fault offsets. The NE-SW oriented ShMIN in the resurgent dome and south moat of the caldera is in contrast to the dominating E-W orientation in the western Basin and Range province and Mammoth Mountain. We then investigate which mechanism most likely causes this local stress perturbation by applying 3-D Finite Element Modeling (FEM). Mechanical properties (e.g., density, Poisson's ratio, and Young's Modulus) used in the model are derived from the latest 3-D seismic tomography model. Taking into account an initial stress field, we examine stress perturbations resulting from different sources: (1) pressurization of a magma reservoir, (2) dyking event, and (3) tectonic faulting; and compute the corresponding stress field orientation for each and compare it with the observations.

A non-perturbative exploration of the high energy regime in Nf=3 QCD. ALPHA Collaboration

NASA Astrophysics Data System (ADS)

Dalla Brida, Mattia; Fritzsch, Patrick; Korzec, Tomasz; Ramos, Alberto; Sint, Stefan; Sommer, Rainer

2018-05-01

Using continuum extrapolated lattice data we trace a family of running couplings in three-flavour QCD over a large range of scales from about 4 to 128 GeV. The scale is set by the finite space time volume so that recursive finite size techniques can be applied, and Schrödinger functional (SF) boundary conditions enable direct simulations in the chiral limit. Compared to earlier studies we have improved on both statistical and systematic errors. Using the SF coupling to implicitly define a reference scale 1/L_0≈ 4 GeV through \\bar{g}^2(L_0) =2.012, we quote L_0 Λ ^{N_f=3}_{{\\overline{MS}}} =0.0791(21). This error is dominated by statistics; in particular, the remnant perturbative uncertainty is negligible and very well controlled, by connecting to infinite renormalization scale from different scales 2^n/L_0 for n=0,1,\\ldots ,5. An intermediate step in this connection may involve any member of a one-parameter family of SF couplings. This provides an excellent opportunity for tests of perturbation theory some of which have been published in a letter (ALPHA collaboration, M. Dalla Brida et al. in Phys Rev Lett 117(18):182001, 2016). The results indicate that for our target precision of 3 per cent in L_0 Λ ^{N_f=3}_{{\\overline{MS}}}, a reliable estimate of the truncation error requires non-perturbative data for a sufficiently large range of values of α _s=\\bar{g}^2/(4π ). In the present work we reach this precision by studying scales that vary by a factor 2^5= 32, reaching down to α _s≈ 0.1. We here provide the details of our analysis and an extended discussion.

Spectral properties from Matsubara Green's function approach: Application to molecules

NASA Astrophysics Data System (ADS)

Schüler, M.; Pavlyukh, Y.

2018-03-01

We present results for many-body perturbation theory for the one-body Green's function at finite temperatures using the Matsubara formalism. Our method relies on the accurate representation of the single-particle states in standard Gaussian basis sets, allowing to efficiently compute, among other observables, quasiparticle energies and Dyson orbitals of atoms and molecules. In particular, we challenge the second-order treatment of the Coulomb interaction by benchmarking its accuracy for a well-established test set of small molecules, which includes also systems where the usual Hartree-Fock treatment encounters difficulties. We discuss different schemes how to extract quasiparticle properties and assess their range of applicability. With an accurate solution and compact representation, our method is an ideal starting point to study electron dynamics in time-resolved experiments by the propagation of the Kadanoff-Baym equations.

Maxwell-Wagner relaxation in electrical imaging.

PubMed

Korjenevsky, A V

2005-04-01

The electric field tomography (EFT) method exploits interaction of high-frequency electric field with an inhomogeneous conductive medium without contact with the electrodes. The interaction is accompanied by a high-frequency redistribution of free charges inside the medium and leads to small and regular phase shifts of the field in the area surrounding an object. Such a kind of phenomenon is referred to as the Maxwell-Wagner relaxation. Measuring the perturbations of the field using the set of electrodes placed around the object enables us to reconstruct the internal structure of the medium, generally the spatial distribution of a nonlinear combination of permittivity and resistivity. In the case of biomedical applications the result of measurements is determined mainly by the resistivity of the tissues. Three-dimensional simulation based on the finite element method has demonstrated the feasibility of the technique.

A new method to study he effective shear modulus of shocked material

NASA Astrophysics Data System (ADS)

Xiaojuan, Ma; Fusheng, Liu

2013-06-01

Shear modulus is a crucial material parameter for description of mechanical behavior. However, at strong shock compression, it is generally deduced from the longitudinal and bulk sound velocity evaluated by unloading wave profile measurement. Here, a new method called the disturbed amplitude damping method of shock wave is presented, that can directly measure the shear modulus of material. This method relies on the correlation between the shear modulus of shock compressed state and amplitude damping and oscillation of an initial sinusoidal disturbance on shock front in concerned substance. Two important steps are required to determine the shear modulus of material. The first is to measure the damping and oscillation feature of disturbance by the flyer impacted method. The second is to find the quantitative relationship between the disturbed amplitude damping and shear modulus by the finite difference method which is applied to obtain the numerical solutions for disturbance amplitude damping behavior of sinusoidal shock front in flyer impacted flow field. When aluminum shocked to 80 GPa is taken as an example, the shape of perturbed shock front and its disturbed amplitude development with propagation distance, are approximately mapped out. The figure shows an oscillatory damping characteristic. At the early stage the perturbation amplitude on the shock front experiences a decaying process until to zero point, then it rises to a maximum but in reverse phase, and then it decays again. Comparing these data with those simulated using the SCG constitutive model, the effective shear modulus for aluminum shocked to 80 GPa is determined to be about 90 GPa, which is higher than the result given by Yu.

Phase dynamics of single long Josephson junction in MgB2 superconductor

NASA Astrophysics Data System (ADS)

Chimouriya, Shanker Pd.; Ghimire, Bal Ram; Kim, Ju H.

2018-05-01

A system of perturbed sine Gordon equations is derived to a superconductor-insulator-superconductor (SIS) long Joseph-son junction as an extension of the Ambegaokar-Baratoff relation, following the long route of path integral formalism. A computer simulation is performed by discretizing the equations using finite difference approximation and applied to the MgB2 superconductor with SiO2 as the junction material. The solution of unperturbed sG equation is taken as the initial profile for the simulation and observed how the perturbation terms play the role to modify it. It is found initial profile deformed as time goes on. The variation of total Josephson current has also been observed. It is found that, the perturbation terms play the role for phase frustration. The phase frustration achieves quicker for high tunneling current.

Renormalization of the inflationary perturbations revisited

NASA Astrophysics Data System (ADS)

Markkanen, Tommi

2018-05-01

In this work we clarify aspects of renormalization on curved backgrounds focussing on the potential ramifications on the amplitude of inflationary perturbations. We provide an alternate view of the often used adiabatic prescription by deriving a correspondence between the adiabatic subtraction terms and traditional renormalization. Specifically, we show how adiabatic subtraction can be expressed as a set of counter terms that are introduced by redefining the bare parameters of the action. Our representation of adiabatic subtraction then allows us to easily find other renormalization prescriptions differing only in the finite parts of the counter terms. As our main result, we present for quadratic inflation how one may consistently express the renormalization of the spectrum of perturbations from inflation as a redefinition of the bare cosmological constant and Planck mass such that the observable predictions coincide with the unrenormalized result.

Structure theorems for game trees

PubMed Central

Govindan, Srihari; Wilson, Robert

2002-01-01

Kohlberg and Mertens [Kohlberg, E. & Mertens, J. (1986) Econometrica 54, 1003–1039] proved that the graph of the Nash equilibrium correspondence is homeomorphic to its domain when the domain is the space of payoffs in normal-form games. A counterexample disproves the analog for the equilibrium outcome correspondence over the space of payoffs in extensive-form games, but we prove an analog when the space of behavior strategies is perturbed so that every path in the game tree has nonzero probability. Without such perturbations, the graph is the closure of the union of a finite collection of its subsets, each diffeomorphic to a corresponding path-connected open subset of the space of payoffs. As an application, we construct an algorithm for computing equilibria of an extensive-form game with a perturbed strategy space, and thus approximate equilibria of the unperturbed game. PMID:12060702

Structure theorems for game trees.

PubMed

Govindan, Srihari; Wilson, Robert

2002-06-25

Kohlberg and Mertens [Kohlberg, E. & Mertens, J. (1986) Econometrica 54, 1003-1039] proved that the graph of the Nash equilibrium correspondence is homeomorphic to its domain when the domain is the space of payoffs in normal-form games. A counterexample disproves the analog for the equilibrium outcome correspondence over the space of payoffs in extensive-form games, but we prove an analog when the space of behavior strategies is perturbed so that every path in the game tree has nonzero probability. Without such perturbations, the graph is the closure of the union of a finite collection of its subsets, each diffeomorphic to a corresponding path-connected open subset of the space of payoffs. As an application, we construct an algorithm for computing equilibria of an extensive-form game with a perturbed strategy space, and thus approximate equilibria of the unperturbed game.

Finite element models of earthquake cycles in mature strike-slip fault zones

NASA Astrophysics Data System (ADS)

Lynch, John Charles

The research presented in this dissertation is on the subject of strike-slip earthquakes and the stresses that build and release in the Earth's crust during earthquake cycles. Numerical models of these cycles in a layered elastic/viscoelastic crust are produced using the finite element method. A fault that alternately sticks and slips poses a particularly challenging problem for numerical implementation, and a new contact element dubbed the "Velcro" element was developed to address this problem (Appendix A). Additionally, the finite element code used in this study was bench-marked against analytical solutions for some simplified problems (Chapter 2), and the resolving power was tested for the fault region of the models (Appendix B). With the modeling method thus developed, there are two main questions posed. First, in Chapter 3, the effect of a finite-width shear zone is considered. By defining a viscoelastic shear zone beneath a periodically slipping fault, it is found that shear stress concentrates at the edges of the shear zone and thus causes the stress tensor to rotate into non-Andersonian orientations. Several methods are used to examine the stress patterns, including the plunge angles of the principal stresses and a new method that plots the stress tensor in a manner analogous to seismic focal mechanism diagrams. In Chapter 4, a simple San Andreas-like model is constructed, consisting of two great earthquake producing faults separated by a freely-slipping shorter fault. The model inputs of lower crustal viscosity, fault separation distance, and relative breaking strengths are examined for their effect on fault communication. It is found that with a lower crustal viscosity of 1018 Pa s (in the lower range of estimates for California), the two faults tend to synchronize their earthquake cycles, even in the cases where the faults have asymmetric breaking strengths. These models imply that postseismic stress transfer over hundreds of kilometers may play a significant roll in the variability of earthquake repeat times. Specifically, small perturbations in the model parameters can lead to results similar to such observed phenomena as earthquake clustering and disruptions to so-called "characteristic" earthquake cycles.

Marine Controlled-Source Electromagnetic 2D Inversion for synthetic models.

NASA Astrophysics Data System (ADS)

Liu, Y.; Li, Y.

2016-12-01

We present a 2D inverse algorithm for frequency domain marine controlled-source electromagnetic (CSEM) data, which is based on the regularized Gauss-Newton approach. As a forward solver, our parallel adaptive finite element forward modeling program is employed. It is a self-adaptive, goal-oriented grid refinement algorithm in which a finite element analysis is performed on a sequence of refined meshes. The mesh refinement process is guided by a dual error estimate weighting to bias refinement towards elements that affect the solution at the EM receiver locations. With the use of the direct solver (MUMPS), we can effectively compute the electromagnetic fields for multi-sources and parametric sensitivities. We also implement the parallel data domain decomposition approach of Key and Ovall (2011), with the goal of being able to compute accurate responses in parallel for complicated models and a full suite of data parameters typical of offshore CSEM surveys. All minimizations are carried out by using the Gauss-Newton algorithm and model perturbations at each iteration step are obtained by using the Inexact Conjugate Gradient iteration method. Synthetic test inversions are presented.

Finite density two color chiral perturbation theory revisited

NASA Astrophysics Data System (ADS)

Adhikari, Prabal; Beleznay, Soma B.; Mannarelli, Massimo

2018-06-01

We revisit two-color, two-flavor chiral perturbation theory at finite isospin and baryon density. We investigate the phase diagram obtained varying the isospin and the baryon chemical potentials, focusing on the phase transition occurring when the two chemical potentials are equal and exceed the pion mass (which is degenerate with the diquark mass). In this case, there is a change in the order parameter of the theory that does not lend itself to the standard picture of first order transitions. We explore this phase transition both within a Ginzburg-Landau framework valid in a limited parameter space and then by inspecting the full chiral Lagrangian in all the accessible parameter space. Across the phase transition between the two broken phases the order parameter becomes an SU(2) doublet, with the ground state fixing the expectation value of the sum of the magnitude squared of the pion and the diquark fields. Furthermore, we find that the Lagrangian at equal chemical potentials is invariant under global SU(2) transformations and construct the effective Lagrangian of the three Goldstone degrees of freedom by integrating out the radial fluctuations.

Sensitivity of charge transport measurements to local inhomogeneities

NASA Astrophysics Data System (ADS)

Koon, Daniel; Wang, Fei; Hjorth Petersen, Dirch; Hansen, Ole

2012-02-01

We derive analytic expressions for the sensitivity of resistive and Hall measurements to local variations in a specimen's material properties in the combined linear limit of both small magnetic fields and small perturbations, presenting exact, algebraic expressions both for four-point probe measurements on an infinite plane and for symmetric, circular van der Pauw discs. We then generalize the results to obtain corrections to the sensitivities both for finite magnetic fields and for finite perturbations. Calculated functions match published results and computer simulations, and provide an intuitive, visual explanation for experimental misassignment of carrier type in n-type ZnO and agree with published experimental results for holes in a uniform material. These results simplify calculation and plotting of the sensitivities on an NxN grid from a problem of order N^5 to one of order N^3 in the arbitrary case and of order N^2 in the handful of cases that can be solved exactly, putting a powerful tool for inhomogeneity analysis in the hands of the researcher: calculation of the sensitivities requires little more than the solution of Laplace's equation on the specimen geometry.

Effective gravitational couplings for cosmological perturbations in generalized Proca theories

NASA Astrophysics Data System (ADS)

De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li

2016-08-01

We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling Geff with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing Geff. In fact, within the parameter space, Geff can be even smaller than the Newton gravitational constant G at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter η and the evolution of the growth rate f σ8 are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the Λ CDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.

Mathematical construction and perturbation analysis of Zernike discrete orthogonal points.

PubMed

Shi, Zhenguang; Sui, Yongxin; Liu, Zhenyu; Peng, Ji; Yang, Huaijiang

2012-06-20

Zernike functions are orthogonal within the unit circle, but they are not over the discrete points such as CCD arrays or finite element grids. This will result in reconstruction errors for loss of orthogonality. By using roots of Legendre polynomials, a set of points within the unit circle can be constructed so that Zernike functions over the set are discretely orthogonal. Besides that, the location tolerances of the points are studied by perturbation analysis, and the requirements of the positioning precision are not very strict. Computer simulations show that this approach provides a very accurate wavefront reconstruction with the proposed sampling set.

SMD-based numerical stochastic perturbation theory

NASA Astrophysics Data System (ADS)

Dalla Brida, Mattia; Lüscher, Martin

2017-05-01

The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schrödinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit.

Non-Perturbative Renormalization of the Lattice Heavy Quark Classical Velocity

NASA Astrophysics Data System (ADS)

Mandula, Jeffrey E.; Ogilvie, Michael C.

1997-02-01

We discuss the renormalization of the lattice formulation of the Heavy Quark Effective Theory (LHQET). In addition to wave function and composite operator renormalizations, on the lattice the classical velocity is also renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. We present results of a new, direct lattice simulation of this finite renormalization, and compare the results to the perturbative (one loop) result. The simulation results are obtained with the use of a variationally optimized heavy-light meson operator, using an ensemble of lattices provided by the Fermilab ACP-MAPS collaboration.

Renormalization of the Lattice Heavy Quark Classical Velocity

NASA Astrophysics Data System (ADS)

Mandula, Jeffrey E.; Ogilvie, Michael C.

1996-03-01

In the lattice formulation of the Heavy Quark Effective Theory (LHQET), the "classical velocity" v becomes renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. The renormalization is finite and depends on the form of the decretization of the reduced heavy quark Dirac equation. For the Forward Time — Centered Space discretization, the renormalization is computed both perturbatively, to one loop, and non-perturbatively using two ensembles of lattices, one at β = 5.7 and the other at β = 6.1 The estimates agree, and indicate that for small classical velocities, ν→ is reduced by about 25-30%.

Linear analysis of the Richtmyer-Meshkov instability in shock-flame interactions

NASA Astrophysics Data System (ADS)

Massa, L.; Jha, P.

2012-05-01

Shock-flame interactions enhance supersonic mixing and detonation formation. Therefore, their analysis is important to explosion safety, internal combustion engine performance, and supersonic combustor design. The fundamental process at the basis of the interaction is the Richtmyer-Meshkov instability supported by the density difference between burnt and fresh mixtures. In the present study we analyze the effect of reactivity on the Richtmyer-Meshkov instability with particular emphasis on combustion lengths that typify the scaling between perturbation growth and induction. The results of the present linear analysis study show that reactivity changes the perturbation growth rate by developing a pressure gradient at the flame surface. The baroclinic torque based on the density gradient across the flame acts to slow down the instability growth of high wave-number perturbations. A gasdynamic flame representation leads to the definition of a Peclet number representing the scaling between perturbation and thermal diffusion lengths within the flame. Peclet number effects on perturbation growth are observed to be marginal. The gasdynamic model also considers a finite flame Mach number that supports a separation between flame and contact discontinuity. Such a separation destabilizes the interface growth by augmenting the tangential shear.

Surface passivation for tight-binding calculations of covalent solids.

PubMed

Bernstein, N

2007-07-04

Simulation of a cluster representing a finite portion of a larger covalently bonded system requires the passivation of the cluster surface. We compute the effects of an explicit hybrid orbital passivation (EHOP) on the atomic structure in a model bulk, three-dimensional, narrow gap semiconductor, which is very different from the wide gap, quasi-one-dimensional organic molecules where most passivation schemes have been studied in detail. The EHOP approach is directly applicable to minimal atomic orbital basis methods such as tight-binding. Each broken bond is passivated by a hybrid created from an explicitly expressed linear combination of basis orbitals, chosen to represent the contribution of the missing neighbour, e.g. a sp(3) hybrid for a single bond. The method is tested by computing the forces on atoms near a point defect as a function of cluster geometry. We show that, compared to alternatives such as pseudo-hydrogen passivation, the force on an atom converges to the correct bulk limit more quickly as a function of cluster radius, and that the force is more stable with respect to perturbations in the position of the cluster centre. The EHOP method also obviates the need for parameterizing the interactions between the system atoms and the passivating atoms. The method is useful for cluster calculations of non-periodic defects in large systems and for hybrid schemes that simulate large systems by treating finite regions with a quantum-mechanical model, coupled to an interatomic potential description of the rest of the system.

Surface passivation for tight-binding calculations of covalent solids

NASA Astrophysics Data System (ADS)

Bernstein, N.

2007-07-01

Simulation of a cluster representing a finite portion of a larger covalently bonded system requires the passivation of the cluster surface. We compute the effects of an explicit hybrid orbital passivation (EHOP) on the atomic structure in a model bulk, three-dimensional, narrow gap semiconductor, which is very different from the wide gap, quasi-one-dimensional organic molecules where most passivation schemes have been studied in detail. The EHOP approach is directly applicable to minimal atomic orbital basis methods such as tight-binding. Each broken bond is passivated by a hybrid created from an explicitly expressed linear combination of basis orbitals, chosen to represent the contribution of the missing neighbour, e.g. a sp3 hybrid for a single bond. The method is tested by computing the forces on atoms near a point defect as a function of cluster geometry. We show that, compared to alternatives such as pseudo-hydrogen passivation, the force on an atom converges to the correct bulk limit more quickly as a function of cluster radius, and that the force is more stable with respect to perturbations in the position of the cluster centre. The EHOP method also obviates the need for parameterizing the interactions between the system atoms and the passivating atoms. The method is useful for cluster calculations of non-periodic defects in large systems and for hybrid schemes that simulate large systems by treating finite regions with a quantum-mechanical model, coupled to an interatomic potential description of the rest of the system.

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.

Finite plate thickness effects on the Rayleigh-Taylor instability in elastic-plastic materials

NASA Astrophysics Data System (ADS)

Polavarapu, Rinosh; Banerjee, Arindam

2017-11-01

The majority of theoretical studies have tackled the Rayleigh-Taylor instability (RTI) problem in solids using an infinitely thick plate. Recent theoretical studies by Piriz et al. (PRE 95, 053108, 2017) have explored finite thickness effects. We seek to validate this recent theoretical estimate experimentally using our rotating wheel RTI experiment in an accelerated elastic-plastic material. The test section consists of a container filled with air and mayonnaise (a non-Newtonian emulsion) with an initial perturbation between two materials. The plate thickness effects are studied by varying the depth of the soft-solid. A set of experiments is run by employing different initial conditions with different container dimensions. Additionally, the effect of acceleration rate (driving pressure rise time) on the instability threshold with reference to the finite thickness will also be inspected. Furthermore, the experimental results are compared to the analytical strength models related to finite thickness effects on RTI. Authors acknowledge financial support from DOE-SSAA Grant # DE-NA0003195 and LANL subcontract #370333.

The Relation of Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Vinokur, M.

1976-01-01

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

A method for the geometrically nonlinear analysis of compressively loaded prismatic composite structures

NASA Technical Reports Server (NTRS)

Stoll, Frederick; Gurdal, Zafer; Starnes, James H., Jr.

1991-01-01

A method was developed for the geometrically nonlinear analysis of the static response of thin-walled stiffened composite structures loaded in uniaxial or biaxial compression. The method is applicable to arbitrary prismatic configurations composed of linked plate strips, such as stiffened panels and thin-walled columns. The longitudinal ends of the structure are assumed to be simply supported, and geometric shape imperfections can be modeled. The method can predict the nonlinear phenomena of postbuckling strength and imperfection sensitivity which are exhibited by some buckling-dominated structures. The method is computer-based and is semi-analytic in nature, making it computationally economical in comparison to finite element methods. The method uses a perturbation approach based on the use of a series of buckling mode shapes to represent displacement contributions associated with nonlinear response. Displacement contributions which are of second order in the model amplitudes are incorported in addition to the buckling mode shapes. The principle of virtual work is applied using a finite basis of buckling modes, and terms through the third order in the model amplitudes are retained. A set of cubic nonlinear algebraic equations are obtained, from which approximate equilibrium solutions are determined. Buckling mode shapes for the general class of structure are obtained using the VIPASA analysis code within the PASCO stiffened-panel design code. Thus, subject to some additional restrictions in loading and plate anisotropy, structures which can be modeled with respect to buckling behavior by VIPASA can be analyzed with respect to nonlinear response using the new method. Results obtained using the method are compared with both experimental and analytical results in the literature. The configurations investigated include several different unstiffened and blade-stiffening panel configurations, featuring both homogeneous, isotropic materials, and laminated composite material.

Top-quark decay at next-to-next-to-leading order in QCD.

PubMed

Gao, Jun; Li, Chong Sheng; Zhu, Hua Xing

2013-01-25

We present the complete calculation of the top-quark decay width at next-to-next-to-leading order in QCD, including next-to-leading electroweak corrections as well as finite bottom quark mass and W boson width effects. In particular, we also show the first results of the fully differential decay rates for the top-quark semileptonic decay t → W(+)(l(+)ν)b at next-to-next-to-leading order in QCD. Our method is based on the understanding of the invariant mass distribution of the final-state jet in the singular limit from effective field theory. Our result can be used to study arbitrary infrared-safe observables of top-quark decay with the highest perturbative accuracy.

The effects of vortex like distributed electron in magnetized multi-ion dusty plasmas

NASA Astrophysics Data System (ADS)

Haider, Md. Masum; Ferdous, Tahmina; Duha, Syed S.

2014-09-01

The nonlinear propagation of small but finite amplitude dust-ion-acoustic solitary waves in a magnetized, collisionless dusty plasma is investigated theoretically. It has been assumed that the electrons are trapped following the vortex-like distribution and that the negatively and positively charged ions are mobile with the presence of charge fluctuating stationary dusts, where ions mass provide the inertia and restoring forces are provided by the thermal pressure of hot electrons. A reductive perturbation method was employed to obtain a modified Korteweg-de Vries (mK-dV) equation for the first-order potential and a stationary solution is obtained. The effect of the presence of trapped electrons, negatively and positively charged ions and arbitrary charged dust grains are discussed.

Electromagnetic nonlinear gyrokinetics with polarization drift

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

Duthoit, F.-X.; Hahm, T. S., E-mail: tshahm@snu.ac.kr; Wang, Lu

2014-08-15

A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lie-transform perturbation method in toroidal geometry. For the first time, we recover the drift-kinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediate-mode-number toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen,more » Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete.« less

Electromagnetic nonlinear gyrokinetics with polarization drift

NASA Astrophysics Data System (ADS)

Duthoit, F.-X.; Hahm, T. S.; Wang, Lu

2014-08-01

A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lie-transform perturbation method in toroidal geometry. For the first time, we recover the drift-kinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediate-mode-number toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen, Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete.

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

NASA Astrophysics Data System (ADS)

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

1989-09-01

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

Near-threshold NN→dπ reaction in chiral perturbation theory

NASA Astrophysics Data System (ADS)

Gårdestig, A.; Phillips, D. R.; Elster, Ch.

2006-02-01

The near-threshold np→dπ0 cross section is calculated in chiral perturbation theory to next-to-leading order in the expansion parameter √(Mmπ)/Λχ. At this order irreducible pion loops contribute to the relevant pion-production operator. Although their contribution to this operator is finite, considering initial- and final-state distortions produces a linear divergence in its matrix elements. We renormalize this divergence by introducing a counterterm, whose value we choose to reproduce the threshold np→dπ0 cross section measured at TRIUMF. The energy dependence of this cross section is then predicted in chiral perturbation theory, being determined by the production of p-wave pions, and also by energy dependence in the amplitude for the production of s-wave pions. With an appropriate choice of the counterterm, the chiral prediction for this energy dependence converges well.

Relativistic Bose-Einstein condensates thin-shell wormholes

NASA Astrophysics Data System (ADS)

Richarte, M. G.; Salako, I. G.; Graça, J. P. Morais; Moradpour, H.; Övgün, Ali

2017-10-01

We construct traversable thin-shell wormholes which are asymptotically Ads/dS applying the cut and paste procedure for the case of an acoustic metric created by a relativistic Bose-Einstein condensate. We examine several definitions of the flare-out condition along with the violation or not of the energy conditions for such relativistic geometries. Under reasonable assumptions about the equation of state of the matter located at the shell, we concentrate on the mechanical stability of wormholes under radial perturbation preserving the original spherical symmetry. To do so, we consider linearized perturbations around static solutions. We obtain that dS acoustic wormholes remain stable under radial perturbations as long as they have small radius; such wormholes with finite radius do not violate the strong/null energy condition. Besides, we show that stable Ads wormhole satisfy some of the energy conditions whereas unstable Ads wormhole with large radii violate them.

Optimum performance of hovering rotors

NASA Technical Reports Server (NTRS)

Wu, J. C.; Goorjian, P. M.

1972-01-01

A theory for the optimum performance of a rotor hovering out of ground effect is developed. The performance problem is formulated using general momentum theory for an infinitely bladed rotor, and the effect of a finite number of blades is estimated. The analysis takes advantage of the fact that a simple relation exists between the radial distributions of static pressure and angular velocity in the ultimate wake, far downstream of the rotor, since the radial velocity vanishes there. This relation permits the establishment of an optimum performance criterion in terms of the ultimate wake velocities by introducing a small local perturbation of the rotational velocity and requiring the resulting ratio of thrust and power changes to be independent of the radial location of the perturbation. This analysis fully accounts for the changes in static pressure distribution and axial velocity distribution throughout the wake as the result of the local perturbation of the rotational velocity component.

A System of ODEs for a Perturbation of a Minimal Mass Soliton

NASA Astrophysics Data System (ADS)

Marzuola, Jeremy L.; Raynor, Sarah; Simpson, Gideon

2010-08-01

We study soliton solutions to the nonlinear Schrödinger equation (NLS) with a saturated nonlinearity. NLS with such a nonlinearity is known to possess a minimal mass soliton. We consider a small perturbation of a minimal mass soliton and identify a system of ODEs extending the work of Comech and Pelinovsky (Commun. Pure Appl. Math. 56:1565-1607, 2003), which models the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, in accord with the conclusions of Pelinovsky et al. (Phys. Rev. E 53(2):1940-1953, 1996). Generically, initial data which supports a soliton structure appears to oscillate, with oscillations centered on a stable soliton. For initial data which is expected to disperse, the finite dimensional dynamics initially follow the unstable portion of the soliton curve.

Probabilistic Structural Analysis of SSME Turbopump Blades: Probabilistic Geometry Effects

NASA Technical Reports Server (NTRS)

Nagpal, V. K.

1985-01-01

A probabilistic study was initiated to evaluate the precisions of the geometric and material properties tolerances on the structural response of turbopump blades. To complete this study, a number of important probabilistic variables were identified which are conceived to affect the structural response of the blade. In addition, a methodology was developed to statistically quantify the influence of these probabilistic variables in an optimized way. The identified variables include random geometric and material properties perturbations, different loadings and a probabilistic combination of these loadings. Influences of these probabilistic variables are planned to be quantified by evaluating the blade structural response. Studies of the geometric perturbations were conducted for a flat plate geometry as well as for a space shuttle main engine blade geometry using a special purpose code which uses the finite element approach. Analyses indicate that the variances of the perturbations about given mean values have significant influence on the response.

Viscous-enstrophy scaling law for Navier-Stokes reconnection

NASA Astrophysics Data System (ADS)

Kerr, Robert M.

2017-11-01

Simulations of perturbed, helical trefoil vortex knots and anti-parallel vortices find ν-independent collapse of temporally scaled (√{ ν} Z) - 1 / 2, Z enstrophy, between when the loops first touch at tΓ, and when reconnection ends at tx for the viscosity ν varying by 256. Due to mathematical bounds upon higher-order norms, this collapse requires that the domain increase as ν decreases, possibly to allow large-scale negative helicity to grow as compensation for small-scale positive helicity and enstrophy growth. This mechanism could be a step towards explaining how smooth solutions of the Navier-Stokes can generate finite-energy dissipation in a finite time as ν -> 0 .

Temporal and spatiotemporal correlation functions for trapped Bose gases

NASA Astrophysics Data System (ADS)

Kohnen, M.; Nyman, R. A.

2015-03-01

Density correlations unambiguously reveal the quantum nature of matter. Here, we study correlations between measurements of density in cold-atom clouds at different times at one position, and also at two separated positions. We take into account the effects of finite-size and -duration measurements made by light beams passing through the atom cloud. We specialize to the case of Bose gases in harmonic traps above critical temperature, for weakly perturbative measurements. For overlapping measurement regions, shot-noise correlations revive after a trap oscillation period. For nonoverlapping regions, bosonic correlations dominate at long times, and propagate at finite speeds. Finally, we give a realistic measurement protocol for performing such experiments.

Features of sound propagation through and stability of a finite shear layer

NASA Technical Reports Server (NTRS)

Koutsoyannis, S. P.

1977-01-01

The plane wave propagation, the stability, and the rectangular duct mode problems of a compressible, inviscid, linearly sheared, parallel, homogeneous flow are shown to be governed by Whittaker's equation. The exact solutions for the perturbation quantities are essentially the Whittaker M-functions where the nondimensional quantities have precise physical meanings. A number of known results are obtained as limiting cases of the exact solutions. For the compressible finite thickness shear layer it is shown that no resonances and no critical angles exist for all Mach numbers, frequencies, and shear layer velocity profile slopes except in the singular case of the vortex sheet.

Parametric instabilities of finite-amplitude, circularly polarized Alfven waves in an anisotropic plasma

NASA Technical Reports Server (NTRS)

Hamabata, Hiromitsu

1993-01-01

A class of parametric instabilities of finite-amplitude, circularly polarized Alfven waves in a plasma with pressure anisotropy is studied by application of the CGL equations. A linear perturbation analysis is used to find the dispersion relation governing the instabilities, which is a fifth-order polynomial and is solved numerically. A large-amplitude, circularly polarized wave is unstable with respect to decay into three waves: one sound-like wave and two side-band Alfven-like waves. It is found that, in addition to the decay instability, two new instabilities that are absent in the framework of the MHD equations can occur, depending on the plasma parameters.

VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport

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

Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

1975-10-01

The computer code block VENTURE, designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P$sub 1$) in up to three- dimensional geometry is described. A variety of types of problems may be solved: the usual eigenvalue problem, a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations, or an indirect criticality search on nuclide concentrations, or on dimensions. First- order perturbation analysis capability is available at the macroscopic cross section level. (auth)

Singular perturbation, state aggregation and nonlinear filtering

NASA Technical Reports Server (NTRS)

Hijab, O.; Sastry, S.

1981-01-01

Consideration is given to a state process evolving in R(n), whose motion is that of a pure jump process in R(n) in the 0(1) time scale, upon which is superimposed a continuous motion along the orbits of a gradient-like vector field g in R(n) in the 0(1/epsilon) time scale. The infinitesimal generator of the state process is, in other words, of the form L + (1/epsilon)g. It follows from the main results presented that the projected filters converge to the finite state Wonham filter corresponding to the problem of estimating the finite state process in the presence of additive white noise.

Equilibrium finite-frequency noise of an interacting mesoscopic capacitor studied in time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Dittmann, Niklas; Splettstoesser, Janine; Helbig, Nicole

2018-03-01

We calculate the frequency-dependent equilibrium noise of a mesoscopic capacitor in time-dependent density functional theory (TDDFT). The capacitor is modeled as a single-level quantum dot with on-site Coulomb interaction and tunnel coupling to a nearby reservoir. The noise spectra are derived from linear-response conductances via the fluctuation-dissipation theorem. Thereby, we analyze the performance of a recently derived exchange-correlation potential with time-nonlocal density dependence in the finite-frequency linear-response regime. We compare our TDDFT noise spectra with real-time perturbation theory and find excellent agreement for noise frequencies below the reservoir temperature.

Non-Fermi-liquid superconductivity: Eliashberg approach versus the renormalization group

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

Wang, Huajia; Raghu, Srinivas; Torroba, Gonzalo

Here, we address the problem of superconductivity for non-Fermi liquids using two commonly adopted, yet apparently distinct, methods: (1) the renormalization group (RG) and (2) Eliashberg theory. The extent to which both methods yield consistent solutions for the low-energy behavior of quantum metals has remained unclear. We show that the perturbative RG beta function for the 4-Fermi coupling can be explicitly derived from the linearized Eliashberg equations, under the assumption that quantum corrections are approximately local across energy scales. We apply our analysis to the test case of phonon-mediated superconductivity and show the consistency of both the Eliashberg and RGmore » treatments. We next study superconductivity near a class of quantum critical points and find a transition between superconductivity and a “naked” metallic quantum critical point with finite, critical BCS couplings. We speculate on the applications of our theory to the phenomenology of unconventional metals.« less

A new scenario-based approach to damage detection using operational modal parameter estimates

NASA Astrophysics Data System (ADS)

Hansen, J. B.; Brincker, R.; López-Aenlle, M.; Overgaard, C. F.; Kloborg, K.

2017-09-01

In this paper a vibration-based damage localization and quantification method, based on natural frequencies and mode shapes, is presented. The proposed technique is inspired by a damage assessment methodology based solely on the sensitivity of mass-normalized experimental determined mode shapes. The present method differs by being based on modal data extracted by means of Operational Modal Analysis (OMA) combined with a reasonable Finite Element (FE) representation of the test structure and implemented in a scenario-based framework. Besides a review of the basic methodology this paper addresses fundamental theoretical as well as practical considerations which are crucial to the applicability of a given vibration-based damage assessment configuration. Lastly, the technique is demonstrated on an experimental test case using automated OMA. Both the numerical study as well as the experimental test case presented in this paper are restricted to perturbations concerning mass change.

Non-Fermi-liquid superconductivity: Eliashberg approach versus the renormalization group

DOE PAGES

Wang, Huajia; Raghu, Srinivas; Torroba, Gonzalo

2017-04-15

Here, we address the problem of superconductivity for non-Fermi liquids using two commonly adopted, yet apparently distinct, methods: (1) the renormalization group (RG) and (2) Eliashberg theory. The extent to which both methods yield consistent solutions for the low-energy behavior of quantum metals has remained unclear. We show that the perturbative RG beta function for the 4-Fermi coupling can be explicitly derived from the linearized Eliashberg equations, under the assumption that quantum corrections are approximately local across energy scales. We apply our analysis to the test case of phonon-mediated superconductivity and show the consistency of both the Eliashberg and RGmore » treatments. We next study superconductivity near a class of quantum critical points and find a transition between superconductivity and a “naked” metallic quantum critical point with finite, critical BCS couplings. We speculate on the applications of our theory to the phenomenology of unconventional metals.« less

Special class of nonlinear damping models in flexible space structures

NASA Technical Reports Server (NTRS)

Hu, Anren; Singh, Ramendra P.; Taylor, Lawrence W.

1991-01-01

A special class of nonlinear damping models is investigated in which the damping force is proportional to the product of positive integer or the fractional power of the absolute values of displacement and velocity. For a one-degree-of-freedom system, the classical Krylov-Bogoliubov 'averaging' method is used, whereas for a distributed system, both an ad hoc perturbation technique and the finite difference method are employed to study the effects of nonlinear damping. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on the damping ratio but also on the initial amplitude, the time to measure the response, the frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce the energy of the system and to pass energy to lower modes.

Accurate ω-ψ Spectral Solution of the Singular Driven Cavity Problem

NASA Astrophysics Data System (ADS)

Auteri, F.; Quartapelle, L.; Vigevano, L.

2002-08-01

This article provides accurate spectral solutions of the driven cavity problem, calculated in the vorticity-stream function representation without smoothing the corner singularities—a prima facie impossible task. As in a recent benchmark spectral calculation by primitive variables of Botella and Peyret, closed-form contributions of the singular solution for both zero and finite Reynolds numbers are subtracted from the unknown of the problem tackled here numerically in biharmonic form. The method employed is based on a split approach to the vorticity and stream function equations, a Galerkin-Legendre approximation of the problem for the perturbation, and an evaluation of the nonlinear terms by Gauss-Legendre numerical integration. Results computed for Re=0, 100, and 1000 compare well with the benchmark steady solutions provided by the aforementioned collocation-Chebyshev projection method. The validity of the proposed singularity subtraction scheme for computing time-dependent solutions is also established.

Design of an adaptive super-twisting decoupled terminal sliding mode control scheme for a class of fourth-order systems.

PubMed

Ashtiani Haghighi, Donya; Mobayen, Saleh

2018-04-01

This paper proposes an adaptive super-twisting decoupled terminal sliding mode control technique for a class of fourth-order systems. The adaptive-tuning law eliminates the requirement of the knowledge about the upper bounds of external perturbations. Using the proposed control procedure, the state variables of cart-pole system are converged to decoupled terminal sliding surfaces and their equilibrium points in the finite time. Moreover, via the super-twisting algorithm, the chattering phenomenon is avoided without affecting the control performance. The numerical results demonstrate the high stabilization accuracy and lower performance indices values of the suggested method over the other ones. The simulation results on the cart-pole system as well as experimental validations demonstrate that the proposed control technique exhibits a reasonable performance in comparison with the other methods. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

A hybrid-perturbation-Galerkin technique which combines multiple expansions

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1989-01-01

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Stability of Local Quantum Dissipative Systems

NASA Astrophysics Data System (ADS)

Cubitt, Toby S.; Lucia, Angelo; Michalakis, Spyridon; Perez-Garcia, David

2015-08-01

Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Lindbladians. In the setting of quantum many-body systems on a lattice it is natural to consider Lindbladians that decompose into a sum of local interactions with decreasing strength with respect to the size of their support. For both practical and theoretical reasons, it is crucial to estimate the impact that perturbations in the generating Lindbladian, arising as noise or errors, can have on the evolution. These local perturbations are potentially unbounded, but constrained to respect the underlying lattice structure. We show that even for polynomially decaying errors in the Lindbladian, local observables and correlation functions are stable if the unperturbed Lindbladian has a unique fixed point and a mixing time that scales logarithmically with the system size. The proof relies on Lieb-Robinson bounds, which describe a finite group velocity for propagation of information in local systems. As a main example, we prove that classical Glauber dynamics is stable under local perturbations, including perturbations in the transition rates, which may not preserve detailed balance.

Renormalization-group flow of the effective action of cosmological large-scale structures

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

Floerchinger, Stefan; Garny, Mathias; Tetradis, Nikolaos

Following an approach of Matarrese and Pietroni, we derive the functional renormalization group (RG) flow of the effective action of cosmological large-scale structures. Perturbative solutions of this RG flow equation are shown to be consistent with standard cosmological perturbation theory. Non-perturbative approximate solutions can be obtained by truncating the a priori infinite set of possible effective actions to a finite subspace. Using for the truncated effective action a form dictated by dissipative fluid dynamics, we derive RG flow equations for the scale dependence of the effective viscosity and sound velocity of non-interacting dark matter, and we solve them numerically. Physically,more » the effective viscosity and sound velocity account for the interactions of long-wavelength fluctuations with the spectrum of smaller-scale perturbations. We find that the RG flow exhibits an attractor behaviour in the IR that significantly reduces the dependence of the effective viscosity and sound velocity on the input values at the UV scale. This allows for a self-contained computation of matter and velocity power spectra for which the sensitivity to UV modes is under control.« less

FIRST-ORDER COSMOLOGICAL PERTURBATIONS ENGENDERED BY POINT-LIKE MASSES

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

Eingorn, Maxim, E-mail: maxim.eingorn@gmail.com

2016-07-10

In the framework of the concordance cosmological model, the first-order scalar and vector perturbations of the homogeneous background are derived in the weak gravitational field limit without any supplementary approximations. The sources of these perturbations (inhomogeneities) are presented in the discrete form of a system of separate point-like gravitating masses. The expressions found for the metric corrections are valid at all (sub-horizon and super-horizon) scales and converge at all points except at the locations of the sources. The average values of these metric corrections are zero (thus, first-order backreaction effects are absent). Both the Minkowski background limit and the Newtonianmore » cosmological approximation are reached under certain well-defined conditions. An important feature of the velocity-independent part of the scalar perturbation is revealed: up to an additive constant, this part represents a sum of Yukawa potentials produced by inhomogeneities with the same finite time-dependent Yukawa interaction range. The suggested connection between this range and the homogeneity scale is briefly discussed along with other possible physical implications.« less

Energy gap states and tunneling currents in semiconducting graphene

NASA Astrophysics Data System (ADS)

Szczesniak, Dominik; Hoehn, Ross; Kais, Sabre

It has been predicted that when graphene is supported on a substrate or doped with foreign atom species, the inherent linear electronic dispersion of its pristine form can be strongly altered. Worthy of special attention is the situation when the interactions between graphene and the substrate or dopants lead to an opening of the finite electronic gap in the fermionic spectrum of this nano-material, and strongly influence its transport and optical properties. Herein, the fundamental electronic transport properties of such perturbed graphene are discussed in the framework of the complex band structure analysis, which not only accounts for the propagating but also the evanescent electronic states. Various scenarios responsible for the band gap opening and manipulation of its characteristics are considered, these considerations may entirely account for the aforementioned perturbations to the pristine graphene. It is shown, that the these perturbations are responsible for inducing gap states which allow electrons to directly tunnel between the conduction and valence bands in perturbed graphene. The resulting tunneling states are analyzed in a comprehensive manner, suggesting their great importance for the transport processes across graphene-based semiconducting nanostructures.

Perturbative instability of inflationary cosmology from quantum potentials

NASA Astrophysics Data System (ADS)

Tawfik, A.; Diab, A.; Abou El Dahab, E.

2017-09-01

It was argued that the Raychaudhuri equation with a quantum correction term seems to avoid the Big Bang singularity and to characterize an everlasting Universe (Ali and Das in Phys Lett B 741:276, 2015). Critical comments on both conclusions and on the correctness of the key expressions of this work were discussed in literature (Lashin in Mod Phys Lett 31:1650044, 2016). In the present work, we have analyzed the perturbative (in)stability conditions in the inflationary era of the early Universe. We conclude that both unstable and stable modes are incompatible with the corresponding ones obtained in the standard FLRW Universe. We have shown that unstable modes do exist at small (an)isotropic perturbation and for different equations of state. Inequalities for both unstable and stable solutions with the standard FLRW space were derived. They reveal that in the FLRW flat Universe both perturbative instability and stability are likely. While negative stability modes have been obtained for radiation- and matter-dominated eras, merely, instability modes exist in case of a finite cosmological constant and also if the vacuum energy dominates the cosmic background geometry.

Computational helioseismology in the frequency domain: acoustic waves in axisymmetric solar models with flows

NASA Astrophysics Data System (ADS)

Gizon, Laurent; Barucq, Hélène; Duruflé, Marc; Hanson, Chris S.; Leguèbe, Michael; Birch, Aaron C.; Chabassier, Juliette; Fournier, Damien; Hohage, Thorsten; Papini, Emanuele

2017-04-01

Context. Local helioseismology has so far relied on semi-analytical methods to compute the spatial sensitivity of wave travel times to perturbations in the solar interior. These methods are cumbersome and lack flexibility. Aims: Here we propose a convenient framework for numerically solving the forward problem of time-distance helioseismology in the frequency domain. The fundamental quantity to be computed is the cross-covariance of the seismic wavefield. Methods: We choose sources of wave excitation that enable us to relate the cross-covariance of the oscillations to the Green's function in a straightforward manner. We illustrate the method by considering the 3D acoustic wave equation in an axisymmetric reference solar model, ignoring the effects of gravity on the waves. The symmetry of the background model around the rotation axis implies that the Green's function can be written as a sum of longitudinal Fourier modes, leading to a set of independent 2D problems. We use a high-order finite-element method to solve the 2D wave equation in frequency space. The computation is embarrassingly parallel, with each frequency and each azimuthal order solved independently on a computer cluster. Results: We compute travel-time sensitivity kernels in spherical geometry for flows, sound speed, and density perturbations under the first Born approximation. Convergence tests show that travel times can be computed with a numerical precision better than one millisecond, as required by the most precise travel-time measurements. Conclusions: The method presented here is computationally efficient and will be used to interpret travel-time measurements in order to infer, e.g., the large-scale meridional flow in the solar convection zone. It allows the implementation of (full-waveform) iterative inversions, whereby the axisymmetric background model is updated at each iteration.

Schwarzschild black hole encircled by a rotating thin disc: Properties of perturbative solution

NASA Astrophysics Data System (ADS)

Kotlařík, P.; Semerák, O.; Čížek, P.

2018-04-01

Will [Astrophys. J. 191, 521 (1974), 10.1086/152992] solved the perturbation of a Schwarzschild black hole due to a slowly rotating light concentric thin ring, using Green's functions expressed as infinite-sum expansions in multipoles and in the small mass and rotational parameters. In a previous paper [P. Čížek and O. Semerák, Astrophys. J. Suppl. Ser. 232, 14 (2017), 10.3847/1538-4365/aa876b], we expressed the Green functions in closed form containing elliptic integrals, leaving just summation over the mass expansion. Such a form is more practical for numerical evaluation, but mainly for generalizing the problem to extended sources where the Green functions have to be integrated over the source. We exemplified the method by computing explicitly the first-order perturbation due to a slowly rotating thin disc lying between two finite radii. After finding basic parameters of the system—mass and angular momentum of the black hole and of the disc—we now add further properties, namely those which reveal how the disc gravity influences geometry of the black-hole horizon and those of circular equatorial geodesics (specifically, radii of the photon, marginally bound and marginally stable orbits). We also realize that, in the linear order, no ergosphere occurs and the central singularity remains pointlike, and check the implications of natural physical requirements (energy conditions and subluminal restriction on orbital speed) for the single-stream as well as counter-rotating double-stream interpretations of the disc.

Two approaches for the gravitational self-force in black hole spacetime: Comparison of numerical results

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

Sago, Norichika; Barack, Leor; Detweiler, Steven

2008-12-15

Recently, two independent calculations have been presented of finite-mass ('self-force') effects on the orbit of a point mass around a Schwarzschild black hole. While both computations are based on the standard mode-sum method, they differ in several technical aspects, which makes comparison between their results difficult--but also interesting. Barack and Sago [Phys. Rev. D 75, 064021 (2007)] invoke the notion of a self-accelerated motion in a background spacetime, and perform a direct calculation of the local self-force in the Lorenz gauge (using numerical evolution of the perturbation equations in the time domain); Detweiler [Phys. Rev. D 77, 124026 (2008)] describesmore » the motion in terms a geodesic orbit of a (smooth) perturbed spacetime, and calculates the metric perturbation in the Regge-Wheeler gauge (using frequency-domain numerical analysis). Here we establish a formal correspondence between the two analyses, and demonstrate the consistency of their numerical results. Specifically, we compare the value of the conservative O({mu}) shift in u{sup t} (where {mu} is the particle's mass and u{sup t} is the Schwarzschild t component of the particle's four-velocity), suitably mapped between the two orbital descriptions and adjusted for gauge. We find that the two analyses yield the same value for this shift within mere fractional differences of {approx}10{sup -5}-10{sup -7} (depending on the orbital radius)--comparable with the estimated numerical error.« less

Biomechanics and dynamics of red blood cells probed by optical tweezers and digital holographic microscopy

NASA Astrophysics Data System (ADS)

Cardenas, Nelson; Thomas, Pattrick; Yu, Lingfeng; Mohanty, Samarendra

2011-03-01

Red blood cells (RBC), with their unique viscoelastic properties, can undergo large deformations during interaction with fluid flow and migration through narrow capillaries. Both local and overall viscoelastic property is important for cellular function and change in these properties indicate diseased condition. Though biomechanics of the cells have been studied using variety of physical techniques (AFM, optically-trapped anchoring beads and microcapilary aspiration) in force regime 10pN, little is studied at low force regime <1pN. Such perturbations are not only hard to exercise on the cell membrane, but quantification of such deformations becomes extremely difficult. By application of low power optical tweezers directly on cell membrane, we could locally perturb discotic RBC along the axial direction, which was monitored dynamically by digital holographic microscopy-a real time, wide-field imaging method having nm axial resolution. The viscoelastic property of the RBC at low force regime was found to be significantly different from that of high-force regime. The results were found to be in good agreement with the simulation results obtained using finite element model of the axially-stretched RBC. The simulations and results of viscoelestic measurements will be presented.

Evolution of midplate hotspot swells: Numerical solutions

NASA Technical Reports Server (NTRS)

Liu, Mian; Chase, Clement G.

1990-01-01

The evolution of midplate hotspot swells on an oceanic plate moving over a hot, upwelling mantle plume is numerically simulated. The plume supplies a Gaussian-shaped thermal perturbation and thermally-induced dynamic support. The lithosphere is treated as a thermal boundary layer with a strongly temperature-dependent viscosity. The two fundamental mechanisms of transferring heat, conduction and convection, during the interaction of the lithosphere with the mantle plume are considered. The transient heat transfer equations, with boundary conditions varying in both time and space, are solved in cylindrical coordinates using the finite difference ADI (alternating direction implicit) method on a 100 x 100 grid. The topography, geoid anomaly, and heat flow anomaly of the Hawaiian swell and the Bermuda rise are used to constrain the models. Results confirm the conclusion of previous works that the Hawaiian swell can not be explained by conductive heating alone, even if extremely high thermal perturbation is allowed. On the other hand, the model of convective thinning predicts successfully the topography, geoid anomaly, and the heat flow anomaly around the Hawaiian islands, as well as the changes in the topography and anomalous heat flow along the Hawaiian volcanic chain.

Nonlocal quantum effective actions in Weyl-Flat spacetimes

NASA Astrophysics Data System (ADS)

Bautista, Teresa; Benevides, André; Dabholkar, Atish

2018-06-01

Virtual massless particles in quantum loops lead to nonlocal effects which can have interesting consequences, for example, for primordial magnetogenesis in cosmology or for computing finite N corrections in holography. We describe how the quantum effective actions summarizing these effects can be computed efficiently for Weyl-flat metrics by integrating the Weyl anomaly or, equivalently, the local renormalization group equation. This method relies only on the local Schwinger-DeWitt expansion of the heat kernel and allows for a re-summation of the anomalous leading large logarithms of the scale factor, log a( x), in situations where the Weyl factor changes by several e-foldings. As an illustration, we obtain the quantum effective action for the Yang-Mills field coupled to massless matter, and the self-interacting massless scalar field. Our action reduces to the nonlocal action obtained using the Barvinsky-Vilkovisky covariant perturbation theory in the regime R 2 ≪ ∇2 R for a typical curvature scale R, but has a greater range of validity effectively re-summing the covariant perturbation theory to all orders in curvatures. In particular, it is applicable also in the opposite regime R 2 ≫ ∇2 R, which is often of interest in cosmology.

Uncertainty Quantification of Non-linear Oscillation Triggering in a Multi-injector Liquid-propellant Rocket Combustion Chamber

NASA Astrophysics Data System (ADS)

Popov, Pavel; Sideris, Athanasios; Sirignano, William

2014-11-01

We examine the non-linear dynamics of the transverse modes of combustion-driven acoustic instability in a liquid-propellant rocket engine. Triggering can occur, whereby small perturbations from mean conditions decay, while larger disturbances grow to a limit-cycle of amplitude that may compare to the mean pressure. For a deterministic perturbation, the system is also deterministic, computed by coupled finite-volume solvers at low computational cost for a single realization. The randomness of the triggering disturbance is captured by treating the injector flow rates, local pressure disturbances, and sudden acceleration of the entire combustion chamber as random variables. The combustor chamber with its many sub-fields resulting from many injector ports may be viewed as a multi-scale complex system wherein the developing acoustic oscillation is the emergent structure. Numerical simulation of the resulting stochastic PDE system is performed using the polynomial chaos expansion method. The overall probability of unstable growth is assessed in different regions of the parameter space. We address, in particular, the seven-injector, rectangular Purdue University experimental combustion chamber. In addition to the novel geometry, new features include disturbances caused by engine acceleration and unsteady thruster nozzle flow.

Spectro-spatial analysis of wave packet propagation in nonlinear acoustic metamaterials

NASA Astrophysics Data System (ADS)

Zhou, W. J.; Li, X. P.; Wang, Y. S.; Chen, W. Q.; Huang, G. L.

2018-01-01

The objective of this work is to analyze wave packet propagation in weakly nonlinear acoustic metamaterials and reveal the interior nonlinear wave mechanism through spectro-spatial analysis. The spectro-spatial analysis is based on full-scale transient analysis of the finite system, by which dispersion curves are generated from the transmitted waves and also verified by the perturbation method (the L-P method). We found that the spectro-spatial analysis can provide detailed information about the solitary wave in short-wavelength region which cannot be captured by the L-P method. It is also found that the optical wave modes in the nonlinear metamaterial are sensitive to the parameters of the nonlinear constitutive relation. Specifically, a significant frequency shift phenomenon is found in the middle-wavelength region of the optical wave branch, which makes this frequency region behave like a band gap for transient waves. This special frequency shift is then used to design a direction-biased waveguide device, and its efficiency is shown by numerical simulations.

Accuracy of topological entanglement entropy on finite cylinders.

PubMed

Jiang, Hong-Chen; Singh, Rajiv R P; Balents, Leon

2013-09-06

Topological phases are unique states of matter which support nonlocal excitations which behave as particles with fractional statistics. A universal characterization of gapped topological phases is provided by the topological entanglement entropy (TEE). We study the finite size corrections to the TEE by focusing on systems with a Z2 topological ordered state using density-matrix renormalization group and perturbative series expansions. We find that extrapolations of the TEE based on the Renyi entropies with a Renyi index of n≥2 suffer from much larger finite size corrections than do extrapolations based on the von Neumann entropy. In particular, when the circumference of the cylinder is about ten times the correlation length, the TEE obtained using von Neumann entropy has an error of order 10(-3), while for Renyi entropies it can even exceed 40%. We discuss the relevance of these findings to previous and future searches for topological ordered phases, including quantum spin liquids.

Renormalizability of the gradient flow in the 2D O(N) non-linear sigma model

NASA Astrophysics Data System (ADS)

Makino, Hiroki; Suzuki, Hiroshi

2015-03-01

It is known that the gauge field and its composite operators evolved by the Yang-Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D O(N) non-linear sigma model possesses a similar property: The flowed N-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a (2+1)-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance without gauge field. As an application of the UV finiteness of the gradient flow, we construct the energy-momentum tensor in the lattice formulation of the O(N) non-linear sigma model that automatically restores the correct normalization and the conservation law in the continuum limit.

spsann - optimization of sample patterns using spatial simulated annealing

NASA Astrophysics Data System (ADS)

Samuel-Rosa, Alessandro; Heuvelink, Gerard; Vasques, Gustavo; Anjos, Lúcia

2015-04-01

There are many algorithms and computer programs to optimize sample patterns, some private and others publicly available. A few have only been presented in scientific articles and text books. This dispersion and somewhat poor availability is holds back to their wider adoption and further development. We introduce spsann, a new R-package for the optimization of sample patterns using spatial simulated annealing. R is the most popular environment for data processing and analysis. Spatial simulated annealing is a well known method with widespread use to solve optimization problems in the soil and geo-sciences. This is mainly due to its robustness against local optima and easiness of implementation. spsann offers many optimizing criteria for sampling for variogram estimation (number of points or point-pairs per lag distance class - PPL), trend estimation (association/correlation and marginal distribution of the covariates - ACDC), and spatial interpolation (mean squared shortest distance - MSSD). spsann also includes the mean or maximum universal kriging variance (MUKV) as an optimizing criterion, which is used when the model of spatial variation is known. PPL, ACDC and MSSD were combined (PAN) for sampling when we are ignorant about the model of spatial variation. spsann solves this multi-objective optimization problem scaling the objective function values using their maximum absolute value or the mean value computed over 1000 random samples. Scaled values are aggregated using the weighted sum method. A graphical display allows to follow how the sample pattern is being perturbed during the optimization, as well as the evolution of its energy state. It is possible to start perturbing many points and exponentially reduce the number of perturbed points. The maximum perturbation distance reduces linearly with the number of iterations. The acceptance probability also reduces exponentially with the number of iterations. R is memory hungry and spatial simulated annealing is a computationally intensive method. As such, many strategies were used to reduce the computation time and memory usage: a) bottlenecks were implemented in C++, b) a finite set of candidate locations is used for perturbing the sample points, and c) data matrices are computed only once and then updated at each iteration instead of being recomputed. spsann is available at GitHub under a licence GLP Version 2.0 and will be further developed to: a) allow the use of a cost surface, b) implement other sensitive parts of the source code in C++, c) implement other optimizing criteria, d) allow to add or delete points to/from an existing point pattern.

Where is the continuum in lattice quantum chromodynamics?

NASA Technical Reports Server (NTRS)

Kennedy, A. D.; Pendleton, B. J.; Kuti, J.; Meyer, S.

1985-01-01

A Monte Carlo calculation of the quark-liberating phase transition in lattice quantum chromodynamics is presented. The transition temperature as a function of the lattice coupling g does not scale according to the perturbative beta function for 6/g-squared less than 6.1. Finite-size scaling is used in analyzing the properties of the lattice system near the transition point.

Influence of Finite Span and Sweep on Active Flow Control Efficacy

NASA Technical Reports Server (NTRS)

Greenblatt, David; Washburn, Anthony E.

2008-01-01

Active flow control efficacy was investigated by means of leading-edge and flap-shoulder zero mass-flux blowing slots on a semispan wing model that was tested in unswept (standard) and swept configurations. On the standard configuration, stall commenced inboard, but with sweep the wing stalled initially near the tip. On both configurations, leading-edge perturbations increased CL,max and post stall lift, both with and without deflected flaps. Without sweep, the effect of control was approximately uniform across the wing span but remained effective to high angles of attack near the tip; when sweep was introduced a significant effect was noted inboard, but this effect degraded along the span and produced virtually no meaningful lift enhancement near the tip, irrespective of the tip configuration. In the former case, control strengthened the wingtip vortex; in the latter case, a simple semi-empirical model, based on the trajectory or "streamline" of the evolving perturbation, served to explain the observations. In the absence of sweep, control on finite-span flaps did not differ significantly from their nominally twodimensional counterpart. Control from the flap produced expected lift enhancement and CL,max improvements in the absence of sweep, but these improvements degraded with the introduction of sweep.

Scalar and vector perturbations in a universe with discrete and continuous matter sources

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

Eingorn, Maxim; Kiefer, Claus; Zhuk, Alexander, E-mail: maxim.eingorn@gmail.com, E-mail: kiefer@thp.uni-koeln.de, E-mail: ai.zhuk2@gmail.com

We study a universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies and their groups and clusters) and two sets of perfect fluids with linear and nonlinear equations of state, respectively. The background spacetime geometry is defined by the FLRW metric. In the weak gravitational field limit, we develop the first-order scalar and vector cosmological perturbation theory. Our approach works at all cosmological scales (i.e. sub-horizon and super-horizon ones) and incorporates linear and nonlinear effects with respect to energy density fluctuations. We demonstrate that the scalar perturbation (i.e. the gravitational potential) as well as the vectormore » perturbation can be split into individual contributions from each matter source. Each of these contributions satisfies its own equation. The velocity-independent parts of the individual gravitational potentials are characterized by a finite time-dependent Yukawa interaction range being the same for each individual contribution. We also obtain the exact form of the gravitational potential and vector perturbation related to the discrete matter sources. The self-consistency of our approach is thoroughly checked. The derived equations can form the theoretical basis for numerical simulations for a wide class of cosmological models.« less

Continued-fraction representation of the Kraus map for non-Markovian reservoir damping

NASA Astrophysics Data System (ADS)

van Wonderen, A. J.; Suttorp, L. G.

2018-04-01

Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In the lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In the lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes–Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field.

Shortcuts to adiabaticity from linear response theory

DOE PAGES

Acconcia, Thiago V.; Bonança, Marcus V. S.; Deffner, Sebastian

2015-10-23

A shortcut to adiabaticity is a finite-time process that produces the same final state as would result from infinitely slow driving. We show that such shortcuts can be found for weak perturbations from linear response theory. Moreover, with the help of phenomenological response functions, a simple expression for the excess work is found—quantifying the nonequilibrium excitations. For two specific examples, i.e., the quantum parametric oscillator and the spin 1/2 in a time-dependent magnetic field, we show that finite-time zeros of the excess work indicate the existence of shortcuts. We finally propose a degenerate family of protocols, which facilitates shortcuts tomore » adiabaticity for specific and very short driving times.« less

An efficient finite element technique for sound propagation in axisymmetric hard wall ducts carrying high subsonic Mach number flows

NASA Technical Reports Server (NTRS)

Tag, I. A.; Lumsdaine, E.

1978-01-01

The general non-linear three-dimensional equation for acoustic potential is derived by using a perturbation technique. The linearized axisymmetric equation is then solved by using a finite element algorithm based on the Galerkin formulation for a harmonic time dependence. The solution is carried out in complex number notation for the acoustic velocity potential. Linear, isoparametric, quadrilateral elements with non-uniform distribution across the duct section are implemented. The resultant global matrix is stored in banded form and solved by using a modified Gauss elimination technique. Sound pressure levels and acoustic velocities are calculated from post element solutions. Different duct geometries are analyzed and compared with experimental results.

The complexity of divisibility.

PubMed

Bausch, Johannes; Cubitt, Toby

2016-09-01

We address two sets of long-standing open questions in linear algebra and probability theory, from a computational complexity perspective: stochastic matrix divisibility, and divisibility and decomposability of probability distributions. We prove that finite divisibility of stochastic matrices is an NP-complete problem, and extend this result to nonnegative matrices, and completely-positive trace-preserving maps, i.e. the quantum analogue of stochastic matrices. We further prove a complexity hierarchy for the divisibility and decomposability of probability distributions, showing that finite distribution divisibility is in P, but decomposability is NP-hard. For the former, we give an explicit polynomial-time algorithm. All results on distributions extend to weak-membership formulations, proving that the complexity of these problems is robust to perturbations.

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.

Chiral tunneling modulated by a time-periodic potential on the surface states of a topological insulator

PubMed Central

Li, Yuan; Jalil, Mansoor B. A.; Tan, S. G.; Zhao, W.; Bai, R.; Zhou, G. H.

2014-01-01

Time-periodic perturbation can be used to modify the transport properties of the surface states of topological insulators, specifically their chiral tunneling property. Using the scattering matrix method, we study the tunneling transmission of the surface states of a topological insulator under the influence of a time-dependent potential and finite gate bias voltage. It is found that perfect transmission is obtained for electrons which are injected normally into the time-periodic potential region in the absence of any bias voltage. However, this signature of Klein tunneling is destroyed when a bias voltage is applied, with the transmission probability of normally incident electrons decreasing with increasing gate bias voltage. Likewise, the overall conductance of the system decreases significantly when a gate bias voltage is applied. The characteristic left-handed helicity of the transmitted spin polarization is also broken by the finite gate bias voltage. In addition, the time-dependent potential modifies the large-angle transmission profile, which exhibits an oscillatory or resonance-like behavior. Finally, time-dependent transport modes (with oscillating potential in the THz frequency) can result in enhanced overall conductance, irrespective of the presence or absence of the gate bias voltage. PMID:24713634

Finite element method (FEM) model of the mechanical stress on phospholipid membranes from shock waves produced in nanosecond electric pulses (nsEP)

NASA Astrophysics Data System (ADS)

Barnes, Ronald; Roth, Caleb C.; Shadaram, Mehdi; Beier, Hope; Ibey, Bennett L.

2015-03-01

The underlying mechanism(s) responsible for nanoporation of phospholipid membranes by nanosecond pulsed electric fields (nsEP) remains unknown. The passage of a high electric field through a conductive medium creates two primary contributing factors that may induce poration: the electric field interaction at the membrane and the shockwave produced from electrostriction of a polar submersion medium exposed to an electric field. Previous work has focused on the electric field interaction at the cell membrane, through such models as the transport lattice method. Our objective is to model the shock wave cell membrane interaction induced from the density perturbation formed at the rising edge of a high voltage pulse in a polar liquid resulting in a shock wave propagating away from the electrode toward the cell membrane. Utilizing previous data from cell membrane mechanical parameters, and nsEP generated shockwave parameters, an acoustic shock wave model based on the Helmholtz equation for sound pressure was developed and coupled to a cell membrane model with finite-element modeling in COMSOL. The acoustic structure interaction model was developed to illustrate the harmonic membrane displacements and stresses resulting from shockwave and membrane interaction based on Hooke's law. Poration is predicted by utilizing membrane mechanical breakdown parameters including cortical stress limits and hydrostatic pressure gradients.

Nonlinear damping model for flexible structures. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Zang, Weijian

1990-01-01

The study of nonlinear damping problem of flexible structures is addressed. Both passive and active damping, both finite dimensional and infinite dimensional models are studied. In the first part, the spectral density and the correlation function of a single DOF nonlinear damping model is investigated. A formula for the spectral density is established with O(Gamma(sub 2)) accuracy based upon Fokker-Planck technique and perturbation. The spectral density depends upon certain first order statistics which could be obtained if the stationary density is known. A method is proposed to find the approximate stationary density explicitly. In the second part, the spectral density of a multi-DOF nonlinear damping model is investigated. In the third part, energy type nonlinear damping model in an infinite dimensional setting is studied.

A finite difference solution for the propagation of sound in near sonic flows

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Lester, H. C.

1983-01-01

An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift acoustical energy to higher harmonics. With increased source strengths, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at at higher sound pressure level as the throat Mach number aproaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory.

Investigation of surface wave amplitudes in 3-D velocity and 3-D Q models

NASA Astrophysics Data System (ADS)

Ruan, Y.; Zhou, Y.

2010-12-01

It has been long recognized that seismic amplitudes depend on both wave speed structures and anelasticity (Q) structures. However, the effects of lateral heterogeneities in wave speed and Q structures on seismic amplitudes has not been well understood. We investigate the effects of 3-D wave speed and 3-D anelasticity (Q) structures on surface-wave amplitudes based upon wave propagation simulations of twelve globally-distributed earthquakes and 801 stations in Earth models with and without lateral heterogeneities in wave speed and anelasticity using a Spectral Element Method (SEM). Our tomographic-like 3-D Q models are converted from a velocity model S20RTS using a set of reasonable mineralogical parameters, assuming lateral perturbations in both velocity and Q are due to temperature perturbations. Surface-wave amplitude variations of SEM seismograms are measured in the period range of 50--200 s using boxcar taper, cosine taper and Slepian multi-tapers. We calculate ray-theoretical predictions of surface-wave amplitude perturbations due to elastic focusing, attenuation, and anelastic focusing which respectively depend upon the second spatial derivative (''roughness'') of perturbations in phase velocity, 1/Q, and the roughness of perturbations in 1/Q. Both numerical experiments and theoretical calculations show that (1) for short-period (~ 50 s) surface waves, the effects of amplitude attenuation due to 3-D Q structures are comparable with elastic focusing effects due to 3-D wave speed structures; and (2) for long-period (> 100 s) surface waves, the effects of attenuation become much weaker than elastic focusing; and (3) elastic focusing effects are correlated with anelastic focusing at all periods due to the correlation between velocity and Q models; and (4) amplitude perturbations are depend on measurement techniques and therefore cannot be directly compared with ray-theoretical predictions because ray theory does not account for the effects of measurement techniques. We calculate 3-D finite-frequency sensitivity of surface-wave amplitude to perturbations in wave speed and anelasticity (Q) which fully account for the effects of elastic focusing, attenuation, anelastic focusing as well as measurement techniques. We show that amplitude perturbations calculated using wave speed and Q sensitivity kernels agree reasonably well with SEM measurements and therefore the sensitivity kernels can be used in a joint inversion of seismic phase delays and amplitudes to simultaneously image high resolution 3-D wave speed and 3-D Q structures in the upper mantle.

2D instabilities of surface gravity waves on a linear shear current

NASA Astrophysics Data System (ADS)

Francius, Marc; Kharif, Christian

2016-04-01

Periodic 2D surface water waves propagating steadily on a rotational current have been studied by many authors (see [1] and references therein). Although the recent important theoretical developments have confirmed that periodic waves can exist over flows with arbitrary vorticity, their stability and their nonlinear evolution have not been much studied extensively so far. In fact, even in the rather simple case of uniform vorticity (linear shear), few papers have been published on the effect of a vertical shear current on the side-band instability of a uniform wave train over finite depth. In most of these studies [2-5], asymptotic expansions and multiple scales method have been used to obtain envelope evolution equations, which allow eventually to formulate a condition of (linear) instability to long modulational perturbations. It is noted here that this instability is often referred in the literature as the Benjamin-Feir or modulational instability. In the present study, we consider the linear stability of finite amplitude two-dimensional, periodic water waves propagating steadily on the free surface of a fluid with constant vorticity and finite depth. First, the steadily propagating surface waves are computed with steepness up to very close to the highest, using a Fourier series expansions and a collocation method, which constitutes a simple extension of Fenton's method [6] to the cases with a linear shear current. Then, the linear stability of these permanent waves to infinitesimal 2D perturbations is developed from the fully nonlinear equations in the framework of normal modes analysis. This linear stability analysis is an extension of [7] to the case of waves in the presence of a linear shear current and permits the determination of the dominant instability as a function of depth and vorticity for a given steepness. The numerical results are used to assess the accuracy of the vor-NLS equation derived in [5] for the characteristics of modulational instabilities due to resonant four-wave interactions, as well as to study the influence of vorticity and nonlinearity on the characteristics of linear instabilities due to resonant five-wave and six-wave interactions. Depending on the dimensionless depth, superharmonic instabilities due to five-wave interactions can become dominant with increasing positive vorticiy. Acknowledgments: This work was supported by the Direction Générale de l'Armement and funded by the ANR project n°. ANR-13-ASTR-0007. References [1] A. Constantin, Two-dimensionality of gravity water flows of constant non-zero vorticity beneath a surface wave train, Eur. J. Mech. B/Fluids, 2011, 30, 12-16. [2] R. S. Johnson, On the modulation of water waves on shear flows, Proc. Royal Soc. Lond. A., 1976, 347, 537-546. [3] M. Oikawa, K. Chow, D. J. Benney, The propagation of nonlinear wave packets in a shear flow with a free surface, Stud. Appl. Math., 1987, 76, 69-92. [4] A. I Baumstein, Modulation of gravity waves with shear in water, Stud. Appl. Math., 1998, 100, 365-90. [5] R. Thomas, C. Kharif, M. Manna, A nonlinear Schrödinger equation for water waves on finite depth with constant vorticity, Phys. Fluids, 2012, 24, 127102. [6] M. M Rienecker, J. D Fenton, A Fourier approximation method for steady water waves , J. Fluid Mech., 1981, 104, 119-137 [7] M. Francius, C. Kharif, Three-dimensional instabilities of periodic gravity waves in shallow water, J. Fluid Mech., 2006, 561, 417-437

Asymptotically flat, stable black hole solutions in Einstein-Yang-Mills-Chern-Simons theory.

PubMed

Brihaye, Yves; Radu, Eugen; Tchrakian, D H

2011-02-18

We construct finite mass, asymptotically flat black hole solutions in d=5 Einstein-Yang-Mills-Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordström solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations.

Scattering theory for graphs isomorphic to a regular tree at infinity

NASA Astrophysics Data System (ADS)

Colin de Verdière, Yves; Truc, Françoise

2013-06-01

We describe the spectral theory of the adjacency operator of a graph which is isomorphic to a regular tree at infinity. Using some combinatorics, we reduce the problem to a scattering problem for a finite rank perturbation of the adjacency operator on a regular tree. We develop this scattering theory using the classical recipes for Schrödinger operators in Euclidian spaces.

Characterization of thunderstorm induced Maxwell current densities in the middle atmosphere

NASA Technical Reports Server (NTRS)

Baginski, Michael Edward

1989-01-01

Middle atmospheric transient Maxwell current densities generated by lightning induced charge perturbations are investigated via a simulation of Maxwell's equations. A time domain finite element analysis is employed for the simulations. The atmosphere is modeled as a region contained within a right circular cylinder with a height of 110 km and radius of 80 km. A composite conductivity profile based on measured data is used when charge perturbations are centered about the vertical axis at altitudes of 6 and 10 km. The simulations indicate that the temporal structure of the Maxwell current density is relatively insensitive to altitude variation within the region considered. It is also shown that the electric field and Maxwell current density are not generally aligned.

Phase structure of completely asymptotically free SU(Nc) models with quarks and scalar quarks

NASA Astrophysics Data System (ADS)

Hansen, F. F.; Janowski, T.; Langæble, K.; Mann, R. B.; Sannino, F.; Steele, T. G.; Wang, Z. W.

2018-03-01

We determine the phase diagram of completely asymptotically free SU (Nc) gauge theories featuring Ns complex scalars and Nf Dirac quarks transforming according to the fundamental representation of the gauge group. The analysis is performed at the maximum known order in perturbation theory. We unveil a very rich dynamics and associated phase structure. Intriguingly, we discover that the completely asymptotically free conditions guarantee that the infrared dynamics displays long-distance conformality, and in a regime when perturbation theory is applicable. We conclude our analysis by determining the quantum corrected potential of the model and summarizing the possible patterns of radiative symmetry breaking. These models are of potential phenomenological interest as either elementary or composite ultraviolet finite extensions of the standard model.

On the singular perturbations for fractional differential equation.

PubMed

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

Scaling relations for watersheds

NASA Astrophysics Data System (ADS)

Fehr, E.; Kadau, D.; Araújo, N. A. M.; Andrade, J. S., Jr.; Herrmann, H. J.

2011-09-01

We study the morphology of watersheds in two and three dimensional systems subjected to different degrees of spatial correlations. The response of these objects to small, local perturbations is also investigated with extensive numerical simulations. We find the fractal dimension of the watersheds to generally decrease with the Hurst exponent, which quantifies the degree of spatial correlations. Moreover, in two dimensions, our results match the range of fractal dimensions 1.10≤df≤1.15 observed for natural landscapes. We report that the watershed is strongly affected by local perturbations. For perturbed two and three dimensional systems, we observe a power-law scaling behavior for the distribution of areas (volumes) enclosed by the original and the displaced watershed and for the distribution of distances between outlets. Finite-size effects are analyzed and the resulting scaling exponents are shown to depend significantly on the Hurst exponent. The intrinsic relation between watershed and invasion percolation, as well as relations between exponents conjectured in previous studies with two dimensional systems, are now confirmed by our results in three dimensions.

NIMROD Modeling of HIT-SI and HIT-SI3

NASA Astrophysics Data System (ADS)

Morgan, Kyle; Jarboe, Tom; Hossack, Aaron

2016-10-01

The HIT-SI and HIT-SI3 devices are spheromaks formed and sustained via a set of Steady Inductive Helicity Injectors (SIHI) that are operated in AC. The experiment explores the formation and sustain of stable spheromaks with a variety of perturbation mode structures. The HIT-SI device consisted of two injectors with primarily n = 1 toroidal symmetry while the HIT-SI3 device has three injectors capable of a mixture of n = 1 and n = 2 perturbations or a primarily n = 3 perturbation, depending on the relative phase of the injectors. Using the NIMROD code to model these devices, we are able to validate with experimental results (previously only done on HIT-SI) and examine the interaction between the injectors and the spheromak. Simulations are performed with both finite and zero- β models to gain an understanding of the thermal properties of the device. Additionally, a set of extrapolation simulations has been performed illustrating the spontaneous formation of closed flux surfaces at high current amplification. Work supported by the US DOE.

A hybrid perturbation Galerkin technique with applications to slender body theory

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1989-01-01

A two-step hybrid perturbation-Galerkin method to solve a variety of applied mathematics problems which involve a small parameter is presented. The method consists of: (1) the use of a regular or singular perturbation method to determine the asymptotic expansion of the solution in terms of the small parameter; (2) construction of an approximate solution in the form of a sum of the perturbation coefficient functions multiplied by (unknown) amplitudes (gauge functions); and (3) the use of the classical Bubnov-Galerkin method to determine these amplitudes. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is applied to some singular perturbation problems in slender body theory. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the degree of applicability of the hybrid method to broader problem areas is discussed.

A hybrid perturbation Galerkin technique with applications to slender body theory

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1987-01-01

A two step hybrid perturbation-Galerkin method to solve a variety of applied mathematics problems which involve a small parameter is presented. The method consists of: (1) the use of a regular or singular perturbation method to determine the asymptotic expansion of the solution in terms of the small parameter; (2) construction of an approximate solution in the form of a sum of the perturbation coefficient functions multiplied by (unknown) amplitudes (gauge functions); and (3) the use of the classical Bubnov-Galerkin method to determine these amplitudes. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is applied to some singular perturbation problems in slender body theory. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the degree of applicability of the hybrid method to broader problem areas is discussed.

Projector Augmented-Wave formulation of response to strain and electric field perturbation within the density-functional perturbation theory

NASA Astrophysics Data System (ADS)

Martin, Alexandre; Torrent, Marc; Caracas, Razvan

2015-03-01

A formulation of the response of a system to strain and electric field perturbations in the pseudopotential-based density functional perturbation theory (DFPT) has been proposed by D.R Hamman and co-workers. It uses an elegant formalism based on the expression of DFT total energy in reduced coordinates, the key quantity being the metric tensor and its first and second derivatives. We propose to extend this formulation to the Projector Augmented-Wave approach (PAW). In this context, we express the full elastic tensor including the clamped-atom tensor, the atomic-relaxation contributions (internal stresses) and the response to electric field change (piezoelectric tensor and effective charges). With this we are able to compute the elastic tensor for all materials (metals and insulators) within a fully analytical formulation. The comparison with finite differences calculations on simple systems shows an excellent agreement. This formalism has been implemented in the plane-wave based DFT ABINIT code. We apply it to the computation of elastic properties and seismic-wave velocities of iron with impurity elements. By analogy with the materials contained in meteorites, tested impurities are light elements (H, O, C, S, Si).

Finite Moment Tensors of Southern California Earthquakes

NASA Astrophysics Data System (ADS)

Jordan, T. H.; Chen, P.; Zhao, L.

2003-12-01

We have developed procedures for inverting broadband waveforms for the finite moment tensors (FMTs) of regional earthquakes. The FMT is defined in terms of second-order polynomial moments of the source space-time function and provides the lowest order representation of a finite fault rupture; it removes the fault-plane ambiguity of the centroid moment tensor (CMT) and yields several additional parameters of seismological interest: the characteristic length L{c}, width W{c}, and duration T{c} of the faulting, as well as the directivity vector {v}{d} of the fault slip. To formulate the inverse problem, we follow and extend the methods of McGuire et al. [2001, 2002], who have successfully recovered the second-order moments of large earthquakes using low-frequency teleseismic data. We express the Fourier spectra of a synthetic point-source waveform in its exponential (Rytov) form and represent the observed waveform relative to the synthetic in terms two frequency-dependent differential times, a phase delay δ τ {p}(ω ) and an amplitude-reduction time δ τ {q}(ω ), which we measure using Gee and Jordan's [1992] isolation-filter technique. We numerically calculate the FMT partial derivatives in terms of second-order spatiotemporal gradients, which allows us to use 3D finite-difference seismograms as our isolation filters. We have applied our methodology to a set of small to medium-sized earthquakes in Southern California. The errors in anelastic structure introduced perturbations larger than the signal level caused by finite source effect. We have therefore employed a joint inversion technique that recovers the CMT parameters of the aftershocks, as well as the CMT and FMT parameters of the mainshock, under the assumption that the source finiteness of the aftershocks can be ignored. The joint system of equations relating the δ τ {p} and δ τ {q} data to the source parameters of the mainshock-aftershock cluster is denuisanced for path anomalies in both observables; this projection operation effectively corrects the mainshock data for path-related amplitude anomalies in a way similar to, but more flexible than, empirical Green function (EGF) techniques.

AxiSEM3D: a new fast method for global wave propagation in 3-D Earth models with undulating discontinuities

NASA Astrophysics Data System (ADS)

Leng, K.; Nissen-Meyer, T.; van Driel, M.; Al-Attar, D.

2016-12-01

We present a new, computationally efficient numerical method to simulate global seismic wave propagation in realistic 3-D Earth models with laterally heterogeneous media and finite boundary perturbations. Our method is a hybrid of pseudo-spectral and spectral element methods (SEM). We characterize the azimuthal dependence of 3-D wavefields in terms of Fourier series, such that the 3-D equations of motion reduce to an algebraic system of coupled 2-D meridional equations, which can be solved by a 2-D spectral element method (based on www.axisem.info). Computational efficiency of our method stems from lateral smoothness of global Earth models (with respect to wavelength) as well as axial singularity of seismic point sources, which jointly confine the Fourier modes of wavefields to a few lower orders. All boundary perturbations that violate geometric spherical symmetry, including Earth's ellipticity, topography and bathymetry, undulations of internal discontinuities such as Moho and CMB, are uniformly considered by means of a Particle Relabeling Transformation.The MPI-based high performance C++ code AxiSEM3D, is now available for forward simulations upon 3-D Earth models with fluid outer core, ellipticity, and both mantle and crustal structures. We show novel benchmarks for global wave solutions in 3-D mantle structures between our method and an independent, fully discretized 3-D SEM with remarkable agreement. Performance comparisons are carried out on three state-of-the-art tomography models, with seismic period going down to 5s. It is shown that our method runs up to two orders of magnitude faster than the 3-D SEM for such settings, and such computational advantage scales favourably with seismic frequency. By examining wavefields passing through hypothetical Gaussian plumes of varying sharpness, we identify in model-wavelength space the limits where our method may lose its advantage.

Strong dynamics and lattice gauge theory

NASA Astrophysics Data System (ADS)

Schaich, David

In this dissertation I use lattice gauge theory to study models of electroweak symmetry breaking that involve new strong dynamics. Electroweak symmetry breaking (EWSB) is the process by which elementary particles acquire mass. First proposed in the 1960s, this process has been clearly established by experiments, and can now be considered a law of nature. However, the physics underlying EWSB is still unknown, and understanding it remains a central challenge in particle physics today. A natural possibility is that EWSB is driven by the dynamics of some new, strongly-interacting force. Strong interactions invalidate the standard analytical approach of perturbation theory, making these models difficult to study. Lattice gauge theory is the premier method for obtaining quantitatively-reliable, nonperturbative predictions from strongly-interacting theories. In this approach, we replace spacetime by a regular, finite grid of discrete sites connected by links. The fields and interactions described by the theory are likewise discretized, and defined on the lattice so that we recover the original theory in continuous spacetime on an infinitely large lattice with sites infinitesimally close together. The finite number of degrees of freedom in the discretized system lets us simulate the lattice theory using high-performance computing. Lattice gauge theory has long been applied to quantum chromodynamics, the theory of strong nuclear interactions. Using lattice gauge theory to study dynamical EWSB, as I do in this dissertation, is a new and exciting application of these methods. Of particular interest is non-perturbative lattice calculation of the electroweak S parameter. Experimentally S ≈ -0.15(10), which tightly constrains dynamical EWSB. On the lattice, I extract S from the momentum-dependence of vector and axial-vector current correlators. I created and applied computer programs to calculate these correlators and analyze them to determine S. I also calculated the masses and other properties of the new particles predicted by these theories. I find S ≳ 0.1 in the specific theories I study. Although this result still disagrees with experiment, it is much closer to the experimental value than is the conventional wisdom S ≳ 0.3. These results encourage further lattice studies to search for experimentally viable strongly-interacting theories of EWSB.

Groundwater withdrawal in the Central Valley, California: implications for San Andreas Fault stressing and lithosphere rheology

NASA Astrophysics Data System (ADS)

Lundgren, P.; Liu, Z.; Ali, S. T.; Farr, T.; Faunt, C. C.

2016-12-01

Anthropogenic perturbations to crustal loading due to groundwater pumping are increasingly recognized as causing changes in nearby fault stresses. We present preliminary analysis of crustal unloading in the Central Valley (CV), California, for the period 2006-2010 to infer Coulomb stress changes on the central San Andreas Fault (CSAF), lithospheric rheology, and system memory due to more than a century of groundwater withdrawal in the southern CV. We use data-driven unloading estimates to drive three-dimensional (3-D) finite element method models and compare model vertical surface deformation rates with observed GPS uplift rates outside the CV. Groundwater level changes are observed through well water elevation changes and through the resultant surface deformation (subsidence) by interferometric synthetic aperture radar (InSAR) and through broader scale changes in gravity from the GRACE satellite time variable gravity data [Famiglietti et al., 2011] that constrain the overall water volume changes. Combining InSAR with well-water data we are able to estimate the aquifer skeletal elastic and inelastic response and through a linear inversion derive the water volume (load) changes across the Central Valley and compare them with GRACE-inferred groundwater changes. Preliminary 3-D finite element method modeling that considers elastic and viscosity structure in the lithosphere gives three interesting results: 1) elastic models poorly fit the uplift rates near the SAF; 2) viscoelastic models that simulate different unloading histories show the past history of groundwater unloading has significant residual uplift rates and fault stress changes; 3) Coulomb stress change varies from inhibited on the locked (Carrizo) section to promoted on the creeping section of the SAF north of Parkfield. Thus, 3D models that account for lithosphere rheology, loading history viscous relaxation, have significant implications for longer-term time-dependent deformation, stress perturbation, and earthquake hazard on the nearby faults. Reference: Famiglietti, J. S., M. Lo, S. L. Ho, J. Bethune, K. J. Anderson, T. H. Syed, S. C. Swenson, C. R. de Linage, and M. Rodell, 2011, Satellites measure recent rates of groundwater depletion in California's Central Valley, Geophys. Res. Lett., 38, L03403, doi:10.1029/2010GL046442.

Wigner phase space distribution via classical adiabatic switching

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

Bose, Amartya; Makri, Nancy; Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, Illinois 61801

2015-09-21

Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if themore » perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations.« less

Solution of Fifth-order Korteweg and de Vries Equation by Homotopy perturbation Transform Method using He's Polynomial

NASA Astrophysics Data System (ADS)

Sharma, Dinkar; Singh, Prince; Chauhan, Shubha

2017-06-01

In this paper, a combined form of the Laplace transform method with the homotopy perturbation method is applied to solve nonlinear fifth order Korteweg de Vries (KdV) equations. The method is known as homotopy perturbation transform method (HPTM). The nonlinear terms can be easily handled by the use of He's polynomials. Two test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM).

On the Singular Perturbations for Fractional Differential Equation

PubMed Central

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method. PMID:24683357

Thin layer model for nonlinear evolution of the Rayleigh-Taylor instability

NASA Astrophysics Data System (ADS)

Zhao, K. G.; Wang, L. F.; Xue, C.; Ye, W. H.; Wu, J. F.; Ding, Y. K.; Zhang, W. Y.

2018-03-01

On the basis of the thin layer approximation [Ott, Phys. Rev. Lett. 29, 1429 (1972)], a revised thin layer model for incompressible Rayleigh-Taylor instability has been developed to describe the deformation and nonlinear evolution of the perturbed interface. The differential equations for motion are obtained by analyzing the forces (the gravity and pressure difference) of fluid elements (i.e., Newton's second law). The positions of the perturbed interface are obtained from the numerical solution of the motion equations. For the case of vacuum on both sides of the layer, the positions of the upper and lower interfaces obtained from the revised thin layer approximation agree with that from the weakly nonlinear (WN) model of a finite-thickness fluid layer [Wang et al., Phys. Plasmas 21, 122710 (2014)]. For the case considering the fluids on both sides of the layer, the bubble-spike amplitude from the revised thin layer model agrees with that from the WN model [Wang et al., Phys. Plasmas 17, 052305 (2010)] and the expanded Layzer's theory [Goncharov, Phys. Rev. Lett. 88, 134502 (2002)] in the early nonlinear growth regime. Note that the revised thin layer model can be applied to investigate the perturbation growth at arbitrary Atwood numbers. In addition, the large deformation (the large perturbed amplitude and the arbitrary perturbed distributions) in the initial stage can also be described by the present model.

Estimation of metal strength at very high rates using free-surface Richtmyer–Meshkov Instabilities

DOE PAGES

Prime, Michael Bruce; Buttler, William Tillman; Buechler, Miles Allen; ...

2017-03-08

Recently, Richtmyer–Meshkov Instabilities (RMI) have been proposed for studying the average strength at strain rates up to at least 10 7/s. RMI experiments involve shocking a metal interface that has initial sinusoidal perturbations. The perturbations invert and grow subsequent to shock and may arrest because of strength effects. In this work we present new RMI experiments and data on a copper target that had five regions with different perturbation amplitudes on the free surface opposite the shock. We estimate the high-rate, low-pressure copper strength by comparing experimental data with Lagrangian numerical simulations. From a detailed computational study we find thatmore » mesh convergence must be carefully addressed to accurately compare with experiments, and numerical viscosity has a strong influence on convergence. We also find that modeling the as-built perturbation geometry rather than the nominal makes a significant difference. Because of the confounding effect of tensile damage on total spike growth, which has previously been used as the metric for estimating strength, we instead use a new strength metric: the peak velocity during spike growth. Furthermore, this new metric also allows us to analyze a broader set of experimental results that are sensitive to strength because some larger initial perturbations grow unstably to failure and so do not have a finite total spike growth.« less

Estimation of metal strength at very high rates using free-surface Richtmyer–Meshkov Instabilities

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

Prime, Michael Bruce; Buttler, William Tillman; Buechler, Miles Allen

Recently, Richtmyer–Meshkov Instabilities (RMI) have been proposed for studying the average strength at strain rates up to at least 10 7/s. RMI experiments involve shocking a metal interface that has initial sinusoidal perturbations. The perturbations invert and grow subsequent to shock and may arrest because of strength effects. In this work we present new RMI experiments and data on a copper target that had five regions with different perturbation amplitudes on the free surface opposite the shock. We estimate the high-rate, low-pressure copper strength by comparing experimental data with Lagrangian numerical simulations. From a detailed computational study we find thatmore » mesh convergence must be carefully addressed to accurately compare with experiments, and numerical viscosity has a strong influence on convergence. We also find that modeling the as-built perturbation geometry rather than the nominal makes a significant difference. Because of the confounding effect of tensile damage on total spike growth, which has previously been used as the metric for estimating strength, we instead use a new strength metric: the peak velocity during spike growth. Furthermore, this new metric also allows us to analyze a broader set of experimental results that are sensitive to strength because some larger initial perturbations grow unstably to failure and so do not have a finite total spike growth.« less

Vertical Propagation and Temporal Growth of Perturbations in the Winter Atmosphere

NASA Astrophysics Data System (ADS)

Christiansen, B.

2001-12-01

We present a general circulation model study of the temporal growth and vertically propagation of perturbations following vertical confined forcings. Both transient and sustained forcings are considered. The motivation for the study is the recent recognition of downward propagation of anomalies from the stratosphere to the troposphere and its implications both for medium range forecasts and for a possible physical mechanism for stratospheric impacts on weather and climate. The dynamical link might also offer a mechanism for changes in the upper atmosphere to affect the tropospheric climate. Here we are thinking of changes in trace gases such as ozone, but also of modulations of the upper atmospheric structure related to the 11-year solar cycle. The model atmosphere is chaotic and shows growth of perturbations no matter which level is forced. The perturbations grow to a size comparable to the variability of the unperturbed atmosphere on a time-scale of 20 - 25 days in the troposphere and 30 - 40 days in the stratosphere. After the initial period of growth the perturbations have the same structure as the unperturbed atmosphere. Although the forcing is restricted to the northern hemisphere the perturbations encompass the whole atmosphere and develop on the same time scale on both hemispheres. Perturbations grow with time squared both when zonal mean and single cell values are considered. Such a power law growth suggest the existence of a finite predictability time which is independent of the initial perturbation as long as it is small. In the unperturbed atmosphere the stratospheric variability has the form of downward propagating stratospheric vacillations. However, in the initial period of growth the perturbations do not propagate downward and seem in general uncoupled to the background vacillations. This suggests that the downward propagation is a robust feature determined more by the processes in the troposphere than the state of the stratosphere. We note that downward propagation may still be a source for enhanced predictability of near-surface weather.

BMS supertranslation symmetry implies Faddeev-Kulish amplitudes

NASA Astrophysics Data System (ADS)

Choi, Sangmin; Akhoury, Ratindranath

2018-02-01

We show explicitly that, among the scattering amplitudes constructed from eigenstates of the BMS supertranslation charge, the ones that conserve this charge, are equal to those constructed from Faddeev-Kulish states. Thus, Faddeev-Kulish states naturally arise as a consequence of the asymptotic symmetries of perturbative gravity and all charge conserving amplitudes are infrared finite. In the process we show an important feature of the Faddeev-Kulish clouds dressing the external hard particles: these clouds can be moved from the incoming states to the outgoing ones, and vice-versa, without changing the infrared finiteness properties of S matrix elements. We also apply our discussion to the problem of the decoherence of momentum configurations of hard particles due to soft boson effects.

Theory of cavitons in complex plasmas.

PubMed

Shukla, P K; Eliasson, B; Sandberg, I

2003-08-15

Nonlinear coupling between Langmuir waves with finite amplitude dispersive dust acoustic perturbations is considered. It is shown that the interaction is governed by a pair of coupled nonlinear differential equations. Numerical results reveal the formation of Langmuir envelope solitons composed of the dust density depression created by the ponderomotive force of bell-shaped Langmuir wave envelops. The associated ambipolar potential is positive. The present nonlinear theory should be able to account for the trapping of large amplitude Langmuir waves in finite amplitude dust density holes. This scenario may appear in Saturn's dense rings, and the Cassini spacecraft should be able to observe fully nonlinear cavitons, as presented herein. Furthermore, we propose that new electron-beam plasma experiments should be conducted to verify our theoretical prediction.

Magnetic Chern bands and triplon Hall effect in an extended Shastry-Sutherland model

NASA Astrophysics Data System (ADS)

Malki, M.; Schmidt, K. P.

2017-05-01

We study topological properties of one-triplon bands in an extended Shastry-Sutherland model relevant for the frustrated quantum magnet SrCu2(BO3)2 . To this end perturbative continuous unitary transformations are applied about the isolated dimer limit allowing us to calculate the one-triplon dispersion up to high order in various couplings including intra- and interdimer Dzyaloshinskii-Moriya interactions and a general uniform magnetic field. We determine the Berry curvature and the Chern number of the different one-triplon bands. We demonstrate the occurrence of Chern numbers ±1 and ±2 for the case that two components of the magnetic field are finite. Finally, we also calculate the triplon Hall effect arising at finite temperatures.

Sensitivity kernels for viscoelastic loading based on adjoint methods

NASA Astrophysics Data System (ADS)

Al-Attar, David; Tromp, Jeroen

2014-01-01

Observations of glacial isostatic adjustment (GIA) allow for inferences to be made about mantle viscosity, ice sheet history and other related parameters. Typically, this inverse problem can be formulated as minimizing the misfit between the given observations and a corresponding set of synthetic data. When the number of parameters is large, solution of such optimization problems can be computationally challenging. A practical, albeit non-ideal, solution is to use gradient-based optimization. Although the gradient of the misfit required in such methods could be calculated approximately using finite differences, the necessary computation time grows linearly with the number of model parameters, and so this is often infeasible. A far better approach is to apply the `adjoint method', which allows the exact gradient to be calculated from a single solution of the forward problem, along with one solution of the associated adjoint problem. As a first step towards applying the adjoint method to the GIA inverse problem, we consider its application to a simpler viscoelastic loading problem in which gravitationally self-consistent ocean loading is neglected. The earth model considered is non-rotating, self-gravitating, compressible, hydrostatically pre-stressed, laterally heterogeneous and possesses a Maxwell solid rheology. We determine adjoint equations and Fréchet kernels for this problem based on a Lagrange multiplier method. Given an objective functional J defined in terms of the surface deformation fields, we show that its first-order perturbation can be written δ J = int _{MS}K_{η }δ ln η dV +int _{t0}^{t1}int _{partial M}K_{dot{σ }} δ dot{σ } dS dt, where δ ln η = δη/η denotes relative viscosity variations in solid regions MS, dV is the volume element, δ dot{σ } is the perturbation to the time derivative of the surface load which is defined on the earth model's surface ∂M and for times [t0, t1] and dS is the surface element on ∂M. The `viscosity kernel' Kη determines the linearized sensitivity of J to viscosity perturbations defined with respect to a laterally heterogeneous reference earth model, while the `rate-of-loading kernel' K_{dot{σ }} determines the sensitivity to variations in the time derivative of the surface load. By restricting attention to spherically symmetric viscosity perturbations, we also obtain a `radial viscosity kernel' overline{K}_{η } such that the associated contribution to δJ can be written int _{IS}overline{K}_{η }δ ln η dr, where IS denotes the subset of radii lying in solid regions. In order to illustrate this theory, we describe its numerical implementation in the case of a spherically symmetric earth model using a 1-D spectral element method, and calculate sensitivity kernels for a range of realistic observables.

Lattice dynamics and electron-phonon coupling calculations using nondiagonal supercells

NASA Astrophysics Data System (ADS)

Lloyd-Williams, Jonathan; Monserrat, Bartomeu

Quantities derived from electron-phonon coupling matrix elements require a fine sampling of the vibrational Brillouin zone. Converged results are typically not obtainable using the direct method, in which a perturbation is frozen into the system and the total energy derivatives are calculated using a finite difference approach, because the size of simulation cell needed is prohibitively large. We show that it is possible to determine the response of a periodic system to a perturbation characterized by a wave vector with reduced fractional coordinates (m1 /n1 ,m2 /n2 ,m3 /n3) using a supercell containing a number of primitive cells equal to the least common multiple of n1, n2, and n3. This is accomplished by utilizing supercell matrices containing nonzero off-diagonal elements. We present the results of electron-phonon coupling calculations using the direct method to sample the vibrational Brillouin zone with grids of unprecedented size for a range of systems, including the canonical example of diamond. We also demonstrate that the use of nondiagonal supercells reduces by over an order of magnitude the computational cost of obtaining converged vibrational densities of states and phonon dispersion curves. J.L.-W. is supported by the Engineering and Physical Sciences Research Council (EPSRC). B.M. is supported by Robinson College, Cambridge, and the Cambridge Philosophical Society. This work was supported by EPSRC Grants EP/J017639/1 and EP/K013564/1.

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

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

1978-01-01

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

Magnetohydrodynamics and Plasma Cosmology

NASA Astrophysics Data System (ADS)

Kleidis, Kostas; Kuiroukidis, Apostolos; Papadopoulos, Demetrios; Vlahos, Loukas

2007-09-01

We study the linear magnetohydrodynamic (MHD) equations, both in the Newtonian and the general-relativistic limit, as regards a viscous magnetized fluid of finite conductivity and discuss instability criteria. In addition, we explore the excitation of cosmological perturbations in anisotropic spacetimes, in the presence of an ambient magnetic field. Acoustic, electromagnetic (e/m) and fast-magnetosonic modes, propagating normal to the magnetic field, can be excited, resulting in several implications of cosmological significance.

Dynamic characteristics of a vibrating beam with periodic variation in bending stiffness

NASA Technical Reports Server (NTRS)

Townsend, John S.

1987-01-01

A detailed dynamic analysis is performed of a vibrating beam with bending stiffness periodic in the spatial coordinate. The effects of system parameters on beam response are explored with a perturbation expansion technique. It is found that periodic stiffness acts to modulate the modal displacements from the characteristic shape of a simple sine wave. The results are verified by a finite element solution and through experimental testing.

Developments in Impeller/Seal Secondary Flow Path Modeling for Dynamic Force Coefficients and Leakage

NASA Technical Reports Server (NTRS)

Palazzolo, Alan; Bhattacharya, Avijit; Athavale, Mahesh; Venkataraman, Balaji; Ryan, Steve; Funston, Kerry

1997-01-01

This paper highlights bulk flow and CFD-based models prepared to calculate force and leakage properties for seals and shrouded impeller leakage paths. The bulk flow approach uses a Hir's based friction model and the CFD approach solves the Navier Stoke's (NS) equation with a finite whirl orbit or via analytical perturbation. The results show good agreement in most instances with available benchmarks.

One-dimensional "atom" with zero-range potential perturbed by finite sequence of zero-duration laser pulses

NASA Astrophysics Data System (ADS)

Gusev, A. A.; Chuluunbaatar, O.; Popov, Yu. V.; Vinitsky, S. I.; Derbov, V. L.; Lovetskiy, K. P.

2018-04-01

The exactly soluble model of a train of zero-duration electromagnetic pulses interacting with a 1D atom with short-range interaction potential modelled by a δ-function is considered. The model is related to the up-to-date laser techniques providing the duration of pulses as short as a few attoseconds and the intensities higher than 1014 W/cm2.

Remarks on Chern-Simons Invariants

NASA Astrophysics Data System (ADS)

Cattaneo, Alberto S.; Mnëv, Pavel

2010-02-01

The perturbative Chern-Simons theory is studied in a finite-dimensional version or assuming that the propagator satisfies certain properties (as is the case, e.g., with the propagator defined by Axelrod and Singer). It turns out that the effective BV action is a function on cohomology (with shifted degrees) that solves the quantum master equation and is defined modulo certain canonical transformations that can be characterized completely. Out of it one obtains invariants.

Statistics of cosmic density profiles from perturbation theory

NASA Astrophysics Data System (ADS)

Bernardeau, Francis; Pichon, Christophe; Codis, Sandrine

2014-11-01

The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre transform of a function directly built in terms of the initial moments. In the context of the upcoming generation of large-scale structure surveys, it is conjectured that this result correctly models such a function for finite values of the variance. Detailed consequences of this assumption are explored. In particular the corresponding one-cell density probability distribution at finite variance is computed for realistic power spectra, taking into account its scale variation. It is found to be in agreement with Λ -cold dark matter simulations at the few percent level for a wide range of density values and parameters. Related explicit analytic expansions at the low and high density tails are given. The conditional (at fixed density) and marginal probability of the slope—the density difference between adjacent cells—and its fluctuations is also computed from the two-cell joint PDF; it also compares very well to simulations. It is emphasized that this could prove useful when studying the statistical properties of voids as it can serve as a statistical indicator to test gravity models and/or probe key cosmological parameters.

Quantum correlations in non-inertial cavity systems

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

Harsij, Zeynab, E-mail: z.harsij@ph.iut.ac.ir; Mirza, Behrouz, E-mail: b.mirza@cc.iut.ac.ir

2016-10-15

Non-inertial cavities are utilized to store and send Quantum Information between mode pairs. A two-cavity system is considered where one is inertial and the other accelerated in a finite time. Maclaurian series are applied to expand the related Bogoliubov coefficients and the problem is treated perturbatively. It is shown that Quantum Discord, which is a measure of quantumness of correlations, is degraded periodically. This is almost in agreement with previous results reached in accelerated systems where increment of acceleration decreases the degree of quantum correlations. As another finding of the study, it is explicitly shown that degradation of Quantum Discordmore » disappears when the state is in a single cavity which is accelerated for a finite time. This feature makes accelerating cavities useful instruments in Quantum Information Theory. - Highlights: • Non-inertial cavities are utilized to store and send information in Quantum Information Theory. • Cavities include boundary conditions which will protect the entanglement once it has been created. • The problem is treated perturbatively and the maclaurian series are applied to expand the related Bogoliubov coefficients. • When two cavities are considered degradation in the degree of quantum correlation happens and it appears periodically. • The interesting issue is when a single cavity is studied and the degradation in quantum correlations disappears.« less

Synaptic efficacy shapes resource limitations in working memory.

PubMed

Krishnan, Nikhil; Poll, Daniel B; Kilpatrick, Zachary P

2018-06-01

Working memory (WM) is limited in its temporal length and capacity. Classic conceptions of WM capacity assume the system possesses a finite number of slots, but recent evidence suggests WM may be a continuous resource. Resource models typically assume there is no hard upper bound on the number of items that can be stored, but WM fidelity decreases with the number of items. We analyze a neural field model of multi-item WM that associates each item with the location of a bump in a finite spatial domain, considering items that span a one-dimensional continuous feature space. Our analysis relates the neural architecture of the network to accumulated errors and capacity limitations arising during the delay period of a multi-item WM task. Networks with stronger synapses support wider bumps that interact more, whereas networks with weaker synapses support narrower bumps that are more susceptible to noise perturbations. There is an optimal synaptic strength that both limits bump interaction events and the effects of noise perturbations. This optimum shifts to weaker synapses as the number of items stored in the network is increased. Our model not only provides a circuit-based explanation for WM capacity, but also speaks to how capacity relates to the arrangement of stored items in a feature space.

Viscous-resistive layer in Rayleigh-Taylor instability

NASA Astrophysics Data System (ADS)

Silveira, F. E. M.; Orlandi, H. I.

2017-03-01

In this work, new scaling laws of the time growth rate γ of the Rayleigh-Taylor instability with the plasma resistivity η, kinematic viscosity ν, and electron number density ne are derived. A viscosity scale is defined in terms of the time decay of the perturbative fluid flow perpendicular to the equilibrium magnetic field, at the quasi-static approximation. Such a scale provides the identification of a viscous layer that can be combined with the resistive layer to produce a viscous-resistive layer. The latter, in turn, is found to satisfy an algebraic biquadratic equation. When viscous effects are negligible, it is shown that the viscous-resistive layer is given by the resistive layer. Somewhat surprisingly, when viscous effects cannot be neglected, it is shown that the viscous-resistive layer is given by the geometric mean of the resistive and viscous layers. A dispersion relation for the time growth rate is derived in terms of the viscous-resistive layer. When viscous effects cannot be neglected, two new scaling laws are found. At the quasi-static approximation, it is shown that γ ˜ (ην)1/4. However, on account of a finite electron mass, it is shown that γ˜(ν/ne ) 1 /3 . Further developments of our formulation are addressed in connection with a finite compressibility in the perturbative flow.

Temporal evolution of a Current Sheet with Initial Finite Perturbations by Three-dimensional MHD Simulations

NASA Astrophysics Data System (ADS)

Yokoyama, Takaaki

Temporal evolution of a current sheet with initial perturbations is studied by using the threedimensional resistive magnetohydrodynamic (MHD) simulations. The magnetic reconnection is considered to be the main engine of the energy rele ase in solar flares. The structure of the diffusion region is, however, not stil l understood under the circumstances with enormously large magnetic Reynolds num ber as the solar corona. In particular, the relationship between the flare's macroscopic physics and the microscopic ones are unclear. It is generally believed that the MHD turbulence s hould play a role in the intermediate scale. The initial current sheet is in an approximately hydromagnetic equilibrium with anti-parallel magnetic field in the y-direction. We imposed a finite-amplitude perturbations (=50ee what happens. Special attention is paid upon the evolution of a three-dimens ional structure in the direction along the initial electric current (z-direction ). Our preliminary results are as follows: (1) In the early phase of the evolut ion, high wavenumber modes in the z-direction are excited and grow. (2) Many "X "-type neutral points (lines) are generated along the magnetic neutral line (pla ne) in the current sheet. When they evolve into the non-linear phase, three-dime nsional structures in the z-direction also evolve. The spatial scale in the z-di rection seems to be almost comparable with that in the xy-plane. (3) The energy release rate is reduced in case of 3D simulations compared with 2D ones probably because of the reduction of the inflow cross sections by the formation of pattc hy structures in the current sheet.

Dirac Quasinormal Modes of Static f(R) de Sitter Black Holes

NASA Astrophysics Data System (ADS)

Ma, Hong

2018-02-01

Quasinormal modes (QNMs) for Dirac perturbations of f(R) black holes (BHs) are described in this paper, involving two types of f(R) solution: f(R) (Schwarzschild) BHs and f(R) (Maxwell) BHs. With the finite difference method, the stability of the f(R) black holes (BHs) is analysed and the threshold range of f(R) (Schwarzschild) BHs and f(R) (Maxwell) BHs is defined respectively. The results show that due to the presence of the correction factor R0, the damping rate of Dirac field decreases. Meanwhile, the influence of angular quantum number values |k| on the f(R) BHs is investigated. The results indicate that the QNMs oscillation becomes tenser and damping speed slowly decreases with |k| increasing. Furthermore, under the Dirac perturbation, the stability of f(R) solutions can be reflected in the manner of Dirac QNMs. The relationships between the QNMs and the parameters (|k|, charge Q and mass m) are discussed in massless, and massive cases, by contrast to the classical BHs. Supported by FAPESP No. 2012/08934-0, National Natural Science Foundation of China under Grant Nos. 11205254, 11178018, 11375279, 11605015, and the Natural Science Foundation Project of CQ CSTC 2011BB0052, and the Fundamental Research Funds for the Central Universities 106112016CDJXY300002 and CDJRC10300003

Methods for High-Order Multi-Scale and Stochastic Problems Analysis, Algorithms, and Applications

DTIC Science & Technology

2016-10-17

finite volume schemes, discontinuous Galerkin finite element method, and related methods, for solving computational fluid dynamics (CFD) problems and...approximation for finite element methods. (3) The development of methods of simulation and analysis for the study of large scale stochastic systems of...laws, finite element method, Bernstein-Bezier finite elements , weakly interacting particle systems, accelerated Monte Carlo, stochastic networks 16

Geometric integration in Born-Oppenheimer molecular dynamics.

PubMed

Odell, Anders; Delin, Anna; Johansson, Börje; Cawkwell, Marc J; Niklasson, Anders M N

2011-12-14

Geometric integration schemes for extended Lagrangian self-consistent Born-Oppenheimer molecular dynamics, including a weak dissipation to remove numerical noise, are developed and analyzed. The extended Lagrangian framework enables the geometric integration of both the nuclear and electronic degrees of freedom. This provides highly efficient simulations that are stable and energy conserving even under incomplete and approximate self-consistent field (SCF) convergence. We investigate three different geometric integration schemes: (1) regular time reversible Verlet, (2) second order optimal symplectic, and (3) third order optimal symplectic. We look at energy conservation, accuracy, and stability as a function of dissipation, integration time step, and SCF convergence. We find that the inclusion of dissipation in the symplectic integration methods gives an efficient damping of numerical noise or perturbations that otherwise may accumulate from finite arithmetics in a perfect reversible dynamics. © 2011 American Institute of Physics

Comparison of two perturbation methods to estimate the land surface modeling uncertainty

NASA Astrophysics Data System (ADS)

Su, H.; Houser, P.; Tian, Y.; Kumar, S.; Geiger, J.; Belvedere, D.

2007-12-01

In land surface modeling, it is almost impossible to simulate the land surface processes without any error because the earth system is highly complex and the physics of the land processes has not yet been understood sufficiently. In most cases, people want to know not only the model output but also the uncertainty in the modeling, to estimate how reliable the modeling is. Ensemble perturbation is an effective way to estimate the uncertainty in land surface modeling, since land surface models are highly nonlinear which makes the analytical approach not applicable in this estimation. The ideal perturbation noise is zero mean Gaussian distribution, however, this requirement can't be satisfied if the perturbed variables in land surface model have physical boundaries because part of the perturbation noises has to be removed to feed the land surface models properly. Two different perturbation methods are employed in our study to investigate their impact on quantifying land surface modeling uncertainty base on the Land Information System (LIS) framework developed by NASA/GSFC land team. One perturbation method is the built-in algorithm named "STATIC" in LIS version 5; the other is a new perturbation algorithm which was recently developed to minimize the overall bias in the perturbation by incorporating additional information from the whole time series for the perturbed variable. The statistical properties of the perturbation noise generated by the two different algorithms are investigated thoroughly by using a large ensemble size on a NASA supercomputer and then the corresponding uncertainty estimates based on the two perturbation methods are compared. Their further impacts on data assimilation are also discussed. Finally, an optimal perturbation method is suggested.

Jointly reconstructing ground motion and resistivity for ERT-based slope stability monitoring

NASA Astrophysics Data System (ADS)

Boyle, Alistair; Wilkinson, Paul B.; Chambers, Jonathan E.; Meldrum, Philip I.; Uhlemann, Sebastian; Adler, Andy

2018-02-01

Electrical resistivity tomography (ERT) is increasingly being used to investigate unstable slopes and monitor the hydrogeological processes within. But movement of electrodes or incorrect placement of electrodes with respect to an assumed model can introduce significant resistivity artefacts into the reconstruction. In this work, we demonstrate a joint resistivity and electrode movement reconstruction algorithm within an iterative Gauss-Newton framework. We apply this to ERT monitoring data from an active slow-moving landslide in the UK. Results show fewer resistivity artefacts and suggest that electrode movement and resistivity can be reconstructed at the same time under certain conditions. A new 2.5-D formulation for the electrode position Jacobian is developed and is shown to give accurate numerical solutions when compared to the adjoint method on 3-D models. On large finite element meshes, the calculation time of the newly developed approach was also proven to be orders of magnitude faster than the 3-D adjoint method and addressed modelling errors in the 2-D perturbation and adjoint electrode position Jacobian.

2-D Model for Normal and Sickle Cell Blood Microcirculation

NASA Astrophysics Data System (ADS)

Tekleab, Yonatan; Harris, Wesley

2011-11-01

Sickle cell disease (SCD) is a genetic disorder that alters the red blood cell (RBC) structure and function such that hemoglobin (Hb) cannot effectively bind and release oxygen. Previous computational models have been designed to study the microcirculation for insight into blood disorders such as SCD. Our novel 2-D computational model represents a fast, time efficient method developed to analyze flow dynamics, O2 diffusion, and cell deformation in the microcirculation. The model uses a finite difference, Crank-Nicholson scheme to compute the flow and O2 concentration, and the level set computational method to advect the RBC membrane on a staggered grid. Several sets of initial and boundary conditions were tested. Simulation data indicate a few parameters to be significant in the perturbation of the blood flow and O2 concentration profiles. Specifically, the Hill coefficient, arterial O2 partial pressure, O2 partial pressure at 50% Hb saturation, and cell membrane stiffness are significant factors. Results were found to be consistent with those of Le Floch [2010] and Secomb [2006].

Digital lattice gauge theories

NASA Astrophysics Data System (ADS)

Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio

2017-02-01

We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with 2 +1 dimensions and higher are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through perturbative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a Z3 lattice gauge theory with dynamical fermionic matter in 2 +1 dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge, and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.

Properties of Solutions to the Irving-Mullineux Oscillator Equation

NASA Astrophysics Data System (ADS)

Mickens, Ronald E.

2002-10-01

A nonlinear differential equation is given in the book by Irving and Mullineux to model certain oscillatory phenomena.^1 They use a regular perturbation method^2 to obtain a first-approximation to the assumed periodic solution. However, their result is not uniformly valid and this means that the obtained solution is not periodic because of the presence of secular terms. We show their way of proceeding is not only incorrect, but that in fact the actual solution to this differential equation is a damped oscillatory function. Our proof uses the method of averaging^2,3 and the qualitative theory of differential equations for 2-dim systems. A nonstandard finite-difference scheme is used to calculate numerical solutions for the trajectories in phase-space. References: ^1J. Irving and N. Mullineux, Mathematics in Physics and Engineering (Academic, 1959); section 14.1. ^2R. E. Mickens, Nonlinear Oscillations (Cambridge University Press, 1981). ^3D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations (Oxford, 1987).

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Robustness against parametric noise of nonideal holonomic gates

NASA Astrophysics Data System (ADS)

Lupo, Cosmo; Aniello, Paolo; Napolitano, Mario; Florio, Giuseppe

2007-07-01

Holonomic gates for quantum computation are commonly considered to be robust against certain kinds of parametric noise, the cause of this robustness being the geometric character of the transformation achieved in the adiabatic limit. On the other hand, the effects of decoherence are expected to become more and more relevant when the adiabatic limit is approached. Starting from the system described by Florio [Phys. Rev. A 73, 022327 (2006)], here we discuss the behavior of nonideal holonomic gates at finite operational time, i.e., long before the adiabatic limit is reached. We have considered several models of parametric noise and studied the robustness of finite-time gates. The results obtained suggest that the finite-time gates present some effects of cancellation of the perturbations introduced by the noise which mimic the geometrical cancellation effect of standard holonomic gates. Nevertheless, a careful analysis of the results leads to the conclusion that these effects are related to a dynamical instead of a geometrical feature.

High order finite volume WENO schemes for the Euler equations under gravitational fields

NASA Astrophysics Data System (ADS)

Li, Gang; Xing, Yulong

2016-07-01

Euler equations with gravitational source terms are used to model many astrophysical and atmospheric phenomena. This system admits hydrostatic balance where the flux produced by the pressure is exactly canceled by the gravitational source term, and two commonly seen equilibria are the isothermal and polytropic hydrostatic solutions. Exact preservation of these equilibria is desirable as many practical problems are small perturbations of such balance. High order finite difference weighted essentially non-oscillatory (WENO) schemes have been proposed in [22], but only for the isothermal equilibrium state. In this paper, we design high order well-balanced finite volume WENO schemes, which can preserve not only the isothermal equilibrium but also the polytropic hydrostatic balance state exactly, and maintain genuine high order accuracy for general solutions. The well-balanced property is obtained by novel source term reformulation and discretization, combined with well-balanced numerical fluxes. Extensive one- and two-dimensional simulations are performed to verify well-balanced property, high order accuracy, as well as good resolution for smooth and discontinuous solutions.

The Stabilizing Effect of Spacetime Expansion on Relativistic Fluids With Sharp Results for the Radiation Equation of State

NASA Astrophysics Data System (ADS)

Speck, Jared

2013-07-01

In this article, we study the 1 + 3-dimensional relativistic Euler equations on a pre-specified conformally flat expanding spacetime background with spatial slices that are diffeomorphic to {R}^3. We assume that the fluid verifies the equation of state {p = c2s ρ,} where {0 ≤ cs ≤ √{1/3}} is the speed of sound. We also assume that the reciprocal of the scale factor associated with the expanding spacetime metric verifies a c s -dependent time-integrability condition. Under these assumptions, we use the vector field energy method to prove that an explicit family of physically motivated, spatially homogeneous, and spatially isotropic fluid solutions are globally future-stable under small perturbations of their initial conditions. The explicit solutions corresponding to each scale factor are analogs of the well-known spatially flat Friedmann-Lemaître-Robertson-Walker family. Our nonlinear analysis, which exploits dissipative terms generated by the expansion, shows that the perturbed solutions exist for all future times and remain close to the explicit solutions. This work is an extension of previous results, which showed that an analogous stability result holds when the spacetime is exponentially expanding. In the case of the radiation equation of state p = (1/3)ρ, we also show that if the time-integrability condition for the reciprocal of the scale factor fails to hold, then the explicit fluid solutions are unstable. More precisely, we show the existence of an open family of initial data such that (i) it contains arbitrarily small smooth perturbations of the explicit solutions' data and (ii) the corresponding perturbed solutions necessarily form shocks in finite time. The shock formation proof is based on the conformal invariance of the relativistic Euler equations when {c2s = 1/3,} which allows for a reduction to a well-known result of Christodoulou.

On bifurcation delay: An alternative approach using Geometric Singular Perturbation Theory

NASA Astrophysics Data System (ADS)

Hsu, Ting-Hao

2017-02-01

To explain the phenomenon of bifurcation delay, which occurs in planar systems of the form x ˙ = ɛf (x , z , ɛ), z ˙ = g (x , z , ɛ) z, where f (x , 0 , 0) > 0 and g (x , 0 , 0) changes sign at least once on the x-axis, we use the Exchange Lemma in Geometric Singular Perturbation Theory to track the limiting behavior of the solutions. Using the trick of extending dimension to overcome the degeneracy at the turning point, we show that the limiting attracting and repulsion points are given by the well-known entry-exit function, and the minimum of z on the trajectory is of order exp ⁡ (- 1 / ɛ). Also we prove smoothness of the return map up to arbitrary finite order in ɛ.

Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers

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

Zhang, H.; Betti, R.; Gopalaswamy, V.

Small-scale perturbations in the ablative Rayleigh-Taylor instability (ARTI) are often neglected because they are linearly stable when their wavelength is shorter than a linear cutoff. Using 2D and 3D numerical simulations, it is shown that linearly stable modes of any wavelength can be destabilized. This instability regime requires finite amplitude initial perturbations and linearly stable ARTI modes are more easily destabilized in 3D than in 2D. In conclusion, it is shown that for conditions found in laser fusion targets, short wavelength ARTI modes are more efficient at driving mixing of ablated material throughout the target since the nonlinear bubble densitymore » increases with the wave number and small scale bubbles carry a larger mass flux of mixed material.« less

Fast and slow coherent cascades in anti-de Sitter spacetime

NASA Astrophysics Data System (ADS)

Dimitrakopoulos, Fotios V.; Freivogel, Ben; Pedraza, Juan F.

2018-06-01

We study the phase and amplitude dynamics of small perturbations in 3  +  1 dimensional anti-de Sitter spacetime using the truncated resonant approximation, also known as the two time framework. We analyse the phase spectrum for different classes of initial data and find that higher frequency modes turn on with coherently aligned phases. Combining numerical and analytical results, we conjecture that there is a class of initial conditions that collapse in infinite slow time and to which the well-studied case of the two-mode, equal energy initial data belongs. We additionally study perturbations that collapse in finite time, and find that the energy spectrum approaches a power law, with the energy per mode scaling approximately as the inverse first power of the frequency.

From Faddeev-Kulish to LSZ. Towards a non-perturbative description of colliding electrons

NASA Astrophysics Data System (ADS)

Dybalski, Wojciech

2017-12-01

In a low energy approximation of the massless Yukawa theory (Nelson model) we derive a Faddeev-Kulish type formula for the scattering matrix of N electrons and reformulate it in LSZ terms. To this end, we perform a decomposition of the infrared finite Dollard modifier into clouds of real and virtual photons, whose infrared divergencies mutually cancel. We point out that in the original work of Faddeev and Kulish the clouds of real photons are omitted, and consequently their wave-operators are ill-defined on the Fock space of free electrons. To support our observations, we compare our final LSZ expression for N = 1 with a rigorous non-perturbative construction due to Pizzo. While our discussion contains some heuristic steps, they can be formulated as clear-cut mathematical conjectures.

Stability of anti-de sitter space in Einstein-Gauss-Bonnet gravity.

PubMed

Deppe, Nils; Kolly, Allison; Frey, Andrew; Kunstatter, Gabor

2015-02-20

Recently it has been argued that in Einstein gravity anti-de Sitter spacetime is unstable against the formation of black holes for a large class of arbitrarily small perturbations. We examine the effects of including a Gauss-Bonnet term. In five dimensions, spherically symmetric Einstein-Gauss-Bonnet gravity has two key features: Choptuik scaling exhibits a radius gap, and the mass function goes to a finite value as the horizon radius vanishes. These suggest that black holes will not form dynamically if the total mass-energy content of the spacetime is too small, thereby restoring the stability of anti-de Sitter spacetime in this context. We support this claim with numerical simulations and uncover a rich structure in horizon radii and formation times as a function of perturbation amplitude.

Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers

DOE PAGES

Zhang, H.; Betti, R.; Gopalaswamy, V.; ...

2018-01-16

Small-scale perturbations in the ablative Rayleigh-Taylor instability (ARTI) are often neglected because they are linearly stable when their wavelength is shorter than a linear cutoff. Using 2D and 3D numerical simulations, it is shown that linearly stable modes of any wavelength can be destabilized. This instability regime requires finite amplitude initial perturbations and linearly stable ARTI modes are more easily destabilized in 3D than in 2D. In conclusion, it is shown that for conditions found in laser fusion targets, short wavelength ARTI modes are more efficient at driving mixing of ablated material throughout the target since the nonlinear bubble densitymore » increases with the wave number and small scale bubbles carry a larger mass flux of mixed material.« less

Double power series method for approximating cosmological perturbations

NASA Astrophysics Data System (ADS)

Wren, Andrew J.; Malik, Karim A.

2017-04-01

We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a noncosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on subhorizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well-known growing and decaying Mészáros solutions, these oscillating modes provide a complete set of subhorizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online.

Field Theoretical Methods in Cosmology

NASA Astrophysics Data System (ADS)

Singh, Anupam

1995-01-01

To optimally utilize all the exciting cosmological data coming in we need to sharpen also the theoretical tools available to cosmologists. One such indispensible tool to understand hot big bang cosmology is finite temperature field theory. We review and summarise the efforts made by us to use finite temperature field theory to address issues of current interest to cosmologists. An introduction to both the real time and the imaginary time formalisms is provided. The imaginary time formalism is illustrated by applying it to understand the interesting possibility of late Time Phase Transitions. Recent observations of the space distribution of quasars indicate a very notable peak in space density at a redshift of 2 to 3. It is pointed out that this may be the result of a phase transition which has a critical temperature of roughly a few meV (in the cosmological units, h = c = k = 1), which is natural in the context of massive neutrinos. In fact, the neutrino masses required for quasar production and those required to solve the solar neutrino problem by the MSW mechanism are consistent with each other. As a bonus, the cosmological constant implied by this model may also help resolve the discrepancy between the recently measured value of the Hubble Constant and the age of the universe. We illustrate the real time formalism by studying one of the most important time-dependent and non-equilibrium phenomena associated with phase transitions. The non-equilibrium dynamics of the first stage of the reheating process, that is dissipation via particle production is studied in scalar field theories. We show that a complete understanding of the mechanism of dissipation via particle production requires a non-perturbative resummation. We then study a Hartree approximation and clearly exhibit dissipative effects related to particle production. The effect of dissipation by Goldstone bosons is studied non-perturbatively in the large N limit in an O(N) theory. We also place our work in perspective and point out some of the related issues which clearly need further exploration.

A normal mode treatment of semi-diurnal body tides on an aspherical, rotating and anelastic Earth

NASA Astrophysics Data System (ADS)

Lau, Harriet C. P.; Yang, Hsin-Ying; Tromp, Jeroen; Mitrovica, Jerry X.; Latychev, Konstantin; Al-Attar, David

2015-08-01

Normal mode treatments of the Earth's body tide response were developed in the 1980s to account for the effects of Earth rotation, ellipticity, anelasticity and resonant excitation within the diurnal band. Recent space-geodetic measurements of the Earth's crustal displacement in response to luni-solar tidal forcings have revealed geographical variations that are indicative of aspherical deep mantle structure, thus providing a novel data set for constraining deep mantle elastic and density structure. In light of this, we make use of advances in seismic free oscillation literature to develop a new, generalized normal mode theory for the tidal response within the semi-diurnal and long-period tidal band. Our theory involves a perturbation method that permits an efficient calculation of the impact of aspherical structure on the tidal response. In addition, we introduce a normal mode treatment of anelasticity that is distinct from both earlier work in body tides and the approach adopted in free oscillation seismology. We present several simple numerical applications of the new theory. First, we compute the tidal response of a spherically symmetric, non-rotating, elastic and isotropic Earth model and demonstrate that our predictions match those based on standard Love number theory. Second, we compute perturbations to this response associated with mantle anelasticity and demonstrate that the usual set of seismic modes adopted for this purpose must be augmented by a family of relaxation modes to accurately capture the full effect of anelasticity on the body tide response. Finally, we explore aspherical effects including rotation and we benchmark results from several illustrative case studies of aspherical Earth structure against independent finite-volume numerical calculations of the semi-diurnal body tide response. These tests confirm the accuracy of the normal mode methodology to at least the level of numerical error in the finite-volume predictions. They also demonstrate that full coupling of normal modes, rather than group coupling, is necessary for accurate predictions of the body tide response.

Influence of geometric and material properties on artifacts generated by interventional MRI devices: Relevance to PRF-shift thermometry

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

Tatebe, Ken, E-mail: Ken.Tatebe@gmail.com; Ramsay, Elizabeth; Kazem, Mohammad

2016-01-15

Purpose: Magnetic resonance imaging (MRI) is capable of providing valuable real-time feedback during medical procedures, partly due to the excellent soft-tissue contrast available. Several technical hurdles still exist to seamless integration of medical devices with MRI due to incompatibility of most conventional devices with this imaging modality. In this study, the effect of local perturbations in the magnetic field caused by the magnetization of medical devices was examined using finite element analysis modeling. As an example, the influence of the geometric and material characteristics of a transurethral high-intensity ultrasound applicator on temperature measurements using proton resonance frequency (PRF)-shift thermometry wasmore » investigated. Methods: The effect of local perturbations in the magnetic field, caused by the magnetization of medical device components, was examined using finite element analysis modeling. The thermometry artifact generated by a transurethral ultrasound applicator was simulated, and these results were validated against analytic models and scans of an applicator in a phantom. Several parameters were then varied to identify which most strongly impacted the level of simulated thermometry artifact, which varies as the applicator moves over the course of an ablative high-intensity ultrasound treatment. Results: Key design parameters identified as having a strong influence on the magnitude of thermometry artifact included the susceptibility of materials and their volume. The location of components was also important, particularly when positioned to maximize symmetry of the device. Finally, the location of component edges and the inclination of the device relative to the magnetic field were also found to be important factors. Conclusions: Previous design strategies to minimize thermometry artifact were validated, and novel design strategies were identified that substantially reduce PRF-shift thermometry artifacts for a variety of device orientations. These new strategies are being incorporated into the next generation of applicators. The general strategy described in this study can be applied to the design of other interventional devices intended for use with MRI.« less

Algorithmic vs. finite difference Jacobians for infrared atmospheric radiative transfer

NASA Astrophysics Data System (ADS)

Schreier, Franz; Gimeno García, Sebastián; Vasquez, Mayte; Xu, Jian

2015-10-01

Jacobians, i.e. partial derivatives of the radiance and transmission spectrum with respect to the atmospheric state parameters to be retrieved from remote sensing observations, are important for the iterative solution of the nonlinear inverse problem. Finite difference Jacobians are easy to implement, but computationally expensive and possibly of dubious quality; on the other hand, analytical Jacobians are accurate and efficient, but the implementation can be quite demanding. GARLIC, our "Generic Atmospheric Radiation Line-by-line Infrared Code", utilizes algorithmic differentiation (AD) techniques to implement derivatives w.r.t. atmospheric temperature and molecular concentrations. In this paper, we describe our approach for differentiation of the high resolution infrared and microwave spectra and provide an in-depth assessment of finite difference approximations using "exact" AD Jacobians as a reference. The results indicate that the "standard" two-point finite differences with 1 K and 1% perturbation for temperature and volume mixing ratio, respectively, can exhibit substantial errors, and central differences are significantly better. However, these deviations do not transfer into the truncated singular value decomposition solution of a least squares problem. Nevertheless, AD Jacobians are clearly recommended because of the superior speed and accuracy.

Electroosmosis over charge-modulated surfaces with finite electrical double layer thicknesses: Asymptotic and numerical investigations

NASA Astrophysics Data System (ADS)

Ghosh, Uddipta; Mandal, Shubhadeep; Chakraborty, Suman

2017-06-01

Here we attempt to solve the fully coupled Poisson-Nernst-Planck-Navier-Stokes equations, to ascertain the influence of finite electric double layer (EDL) thickness on coupled charge and fluid dynamics over patterned charged surfaces. We go beyond the well-studied "weak-field" limit and obtain numerical solutions for a wide range of EDL thicknesses, applied electric field strengths, and the surface potentials. Asymptotic solutions to the coupled system are also derived using a combination of singular and regular perturbation, for thin EDLs and low surface potential, and good agreement between the two solutions is observed. Counterintuitively to common arguments, our analysis reveals that finite EDL thickness may either increase or decrease the "free-stream velocity" (equivalent to net throughput), depending on the strength of the applied electric field. We also unveil a critical EDL thickness for which the effect of finite EDL thickness on the free-stream velocity is the most prominent. Finally, we demonstrate that increasing the surface potential and the applied field tends to influence the overall flow patterns in the contrasting manners. These results may be of profound importance in developing a comprehensive theoretical basis for designing electro-osmotically actuated microfluidic mixtures.

Finite Frequency Traveltime Tomography of Lithospheric and Upper Mantle Structures beneath the Cordillera-Craton Transition in Southwestern Canada

NASA Astrophysics Data System (ADS)

Chen, Y.; Gu, Y. J.; Hung, S. H.

2014-12-01

Based on finite-frequency theory and cross-correlation teleseismic relative traveltime data from the USArray, Canadian National Seismograph Network (CNSN) and Canadian Rockies and Alberta Network (CRANE), we present a new tomographic model of P-wave velocity perturbations for the lithosphere and upper mantle beneath the Cordillera-cration transition region in southwestern Canada. The inversion procedure properly accounts for the finite-volume sensitivities of measured travel time residuals, and the resulting model shows a greater resolution of upper mantle velocity heterogeneity beneath the study area than earlier approaches based on the classical ray-theoretical approach. Our model reveals a lateral change of P velocities from -0.5% to 0.5% down to ~200-km depth in a 50-km wide zone between the Alberta Basin and the foothills of the Rocky Mountains, which suggests a sharp structural gradient along the Cordillera deformation front. The stable cratonic lithosphere, delineated by positive P-velocity perturbations of 0.5% and greater, extends down to a maximum depth of ~180 km beneath the Archean Loverna Block (LB). In comparison, the mantle beneath the controversial Medicine Hat Block (MHB) exhibits significantly higher velocities in the uppermost mantle and a shallower (130-150 km depth) root, generally consistent with the average depth of the lithosphere-asthenosphere boundary beneath Southwest Western Canada Sedimentary Basin (WCSB). The complex shape of the lithospheric velocities under the MHB may be evidence of extensive erosion or a partial detachment of the Precambrian lithospheric root. Furthermore, distinct high velocity anomalies in LB and MHB, which are separated by 'normal' mantle block beneath the Vulcan structure (VS), suggest different Archean assembly and collision histories between these two tectonic blocks.

High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

NASA Technical Reports Server (NTRS)

Barth, Timothy (Editor); Deconinck, Herman (Editor)

1999-01-01

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Solution of the Time-Dependent Schrödinger Equation by the Laplace Transform Method

PubMed Central

Lin, S. H.; Eyring, H.

1971-01-01

The time-dependent Schrödinger equation for two quite general types of perturbation has been solved by introducing the Laplace transforms to eliminate the time variable. The resulting time-independent differential equation can then be solved by the perturbation method, the variation method, the variation-perturbation method, and other methods. PMID:16591898

Holographic stress-energy tensor near the Cauchy horizon inside a rotating black hole

NASA Astrophysics Data System (ADS)

Ishibashi, Akihiro; Maeda, Kengo; Mefford, Eric

2017-07-01

We investigate a stress-energy tensor for a conformal field theory (CFT) at strong coupling inside a small five-dimensional rotating Myers-Perry black hole with equal angular momenta by using the holographic method. As a gravitational dual, we perturbatively construct a black droplet solution by applying the "derivative expansion" method, generalizing the work of Haddad [Classical Quantum Gravity 29, 245001 (2012), 10.1088/0264-9381/29/24/245001] and analytically compute the holographic stress-energy tensor for our solution. We find that the stress-energy tensor is finite at both the future and past outer (event) horizons and that the energy density is negative just outside the event horizons due to the Hawking effect. Furthermore, we apply the holographic method to the question of quantum instability of the Cauchy horizon since, by construction, our black droplet solution also admits a Cauchy horizon inside. We analytically show that the null-null component of the holographic stress-energy tensor negatively diverges at the Cauchy horizon, suggesting that a singularity appears there, in favor of strong cosmic censorship.

Examining the accuracy of the infinite order sudden approximation using sensitivity analysis

NASA Astrophysics Data System (ADS)

Eno, Larry; Rabitz, Herschel

1981-08-01

A method is developed for assessing the accuracy of scattering observables calculated within the framework of the infinite order sudden (IOS) approximation. In particular, we focus on the energy sudden assumption of the IOS method and our approach involves the determination of the sensitivity of the IOS scattering matrix SIOS with respect to a parameter which reintroduces the internal energy operator ?0 into the IOS Hamiltonian. This procedure is an example of sensitivity analysis of missing model components (?0 in this case) in the reference Hamiltonian. In contrast to simple first-order perturbation theory a finite result is obtained for the effect of ?0 on SIOS. As an illustration, our method of analysis is applied to integral state-to-state cross sections for the scattering of an atom and rigid rotor. Results are generated within the He+H2 system and a comparison is made between IOS and coupled states cross sections and the corresponding IOS sensitivities. It is found that the sensitivity coefficients are very useful indicators of the accuracy of the IOS results. Finally, further developments and applications are discussed.

Improved perturbation method for gadolinia worth calculation

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

Chiang, R.T.; Congdon, S.P.

1986-01-01

Gadolinia is utilized in light water power reactors as burnable poison for reserving excess reactivity. Good gadolinia worth estimation is useful for evaluating fuel bundle designs, core operating strategies, and fuel cycle economics. The authors have developed an improved perturbation method based on exact perturbation theory for gadolinia worth calculations in fuel bundles. The method predicts much more accurate gadolinia worth than the first-order perturbation method (commonly used to estimate nuclide worths) for bundles containing fresh or partly burned gadolinia.

Adaptive Modeling Procedure Selection by Data Perturbation.

PubMed

Zhang, Yongli; Shen, Xiaotong

2015-10-01

Many procedures have been developed to deal with the high-dimensional problem that is emerging in various business and economics areas. To evaluate and compare these procedures, modeling uncertainty caused by model selection and parameter estimation has to be assessed and integrated into a modeling process. To do this, a data perturbation method estimates the modeling uncertainty inherited in a selection process by perturbing the data. Critical to data perturbation is the size of perturbation, as the perturbed data should resemble the original dataset. To account for the modeling uncertainty, we derive the optimal size of perturbation, which adapts to the data, the model space, and other relevant factors in the context of linear regression. On this basis, we develop an adaptive data-perturbation method that, unlike its nonadaptive counterpart, performs well in different situations. This leads to a data-adaptive model selection method. Both theoretical and numerical analysis suggest that the data-adaptive model selection method adapts to distinct situations in that it yields consistent model selection and optimal prediction, without knowing which situation exists a priori. The proposed method is applied to real data from the commodity market and outperforms its competitors in terms of price forecasting accuracy.

Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity

NASA Astrophysics Data System (ADS)

Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael

2018-06-01

In this work, we present a novel second-order accurate well-balanced arbitrary Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gas dynamics with gravity in cylindrical coordinates. The main feature of the proposed algorithm is the capability of preserving many of the physical properties of the system exactly also on the discrete level: besides being conservative for mass, momentum and total energy, also any known steady equilibrium between pressure gradient, centrifugal force, and gravity force can be exactly maintained up to machine precision. Perturbations around such equilibrium solutions are resolved with high accuracy and with minimal dissipation on moving contact discontinuities even for very long computational times. This is achieved by the novel combination of well-balanced path-conservative finite volume schemes, which are expressly designed to deal with source terms written via non-conservative products, with ALE schemes on moving grids, which exhibit only very little numerical dissipation on moving contact waves. In particular, we have formulated a new HLL-type and a novel Osher-type flux that are both able to guarantee the well balancing in a gas cloud rotating around a central object. Moreover, to maintain a high level of quality of the moving mesh, we have adopted a nonconforming treatment of the sliding interfaces that appear due to the differential rotation. A large set of numerical tests has been carried out in order to check the accuracy of the method close and far away from the equilibrium, both, in one- and two-space dimensions.

Stochastic theory of photon flow in homogeneous and heterogeneous anisotropic biological and artificial material

NASA Astrophysics Data System (ADS)

Miller, Steven D.

1995-05-01

Standard Monte Carlo methods used in photon diffusion score absorbed photons or statistical weight deposited within voxels comprising a mesh. An alternative approach to a stochastic description is considered for rapid surface flux calculations and finite medias. Matrix elements are assigned to a spatial lattice whose function is to score vector intersections of scattered photons making transitions into either the forward or back solid angle half spaces. These complete matrix elements can be related to the directional fluxes within the lattice space. This model differentiates between ballistic, quasi-ballistic, and highly diffuse photon contributions, and effectively models the subsurface generation of a scattered light flux from a ballistic source. The connection between a path integral and diffusion is illustrated. Flux perturbations can be effectively illustrated for tissue-tumor-tissue and for 3 layer systems with strong absorption in one or more layers. For conditions where the diffusion theory has difficulties such as strong absorption, highly collimated sources, small finite volumes, and subsurface regions, the computation time of the algorithm is rapid with good accuracy and compliments other description of photon diffusion. The model has the potential to do computations relevant to photodynamic therapy (PDT) and analysis of laser beam interaction with tissues.

Nonlinear propagation of ion-acoustic waves in electron-positron-ion plasma with trapped electrons

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

Alinejad, H.; Sobhanian, S.; Mahmoodi, J.

2006-01-15

A theoretical investigation has been made for ion-acoustic waves in an unmagnetized electron-positron-ion plasma. A more realistic situation in which plasma consists of a negatively charged ion fluid, free positrons, and trapped as well as free electrons is considered. The properties of stationary structures are studied by the reductive perturbation method, which is valid for small but finite amplitude limit, and by pseudopotential approach, which is valid for large amplitude. With an appropriate modified form of the electron number density, two new equations for the ion dynamics have been found. When deviations from isothermality are finite, the modified Korteweg-deVries equationmore » has been found, and for the case that deviations from isothermality are small, calculations lead to a generalized Korteweg-deVries equation. It is shown from both weakly and highly nonlinear analysis that the presence of the positrons may allow solitary waves to exist. It is found that the effect of the positron density changes the maximum value of the amplitude and M (Mach number) for which solitary waves can exist. The present theory is applicable to analyze arbitrary amplitude ion-acoustic waves associated with positrons which may occur in space plasma.« less

A More Accurate and Efficient Technique Developed for Using Computational Methods to Obtain Helical Traveling-Wave Tube Interaction Impedance

NASA Technical Reports Server (NTRS)

Kory, Carol L.

1999-01-01

The phenomenal growth of commercial communications has created a great demand for traveling-wave tube (TWT) amplifiers. Although the helix slow-wave circuit remains the mainstay of the TWT industry because of its exceptionally wide bandwidth, until recently it has been impossible to accurately analyze a helical TWT using its exact dimensions because of the complexity of its geometrical structure. For the first time, an accurate three-dimensional helical model was developed that allows accurate prediction of TWT cold-test characteristics including operating frequency, interaction impedance, and attenuation. This computational model, which was developed at the NASA Lewis Research Center, allows TWT designers to obtain a more accurate value of interaction impedance than is possible using experimental methods. Obtaining helical slow-wave circuit interaction impedance is an important part of the design process for a TWT because it is related to the gain and efficiency of the tube. This impedance cannot be measured directly; thus, conventional methods involve perturbing a helical circuit with a cylindrical dielectric rod placed on the central axis of the circuit and obtaining the difference in resonant frequency between the perturbed and unperturbed circuits. A mathematical relationship has been derived between this frequency difference and the interaction impedance (ref. 1). However, because of the complex configuration of the helical circuit, deriving this relationship involves several approximations. In addition, this experimental procedure is time-consuming and expensive, but until recently it was widely accepted as the most accurate means of determining interaction impedance. The advent of an accurate three-dimensional helical circuit model (ref. 2) made it possible for Lewis researchers to fully investigate standard approximations made in deriving the relationship between measured perturbation data and interaction impedance. The most prominent approximations made in the analysis were addressed and fully investigated for their accuracy by using the three-dimensional electromagnetic simulation code MAFIA (Solution of Maxwell's Equations by the Finite Integration Algorithm) (refs. 3 and 4). We found that several approximations introduced significant error (ref. 5).

Rayleigh-Bloch waves trapped by a periodic perturbation: exact solutions

NASA Astrophysics Data System (ADS)

Merzon, A.; Zhevandrov, P.; Romero Rodríguez, M. I.; De la Paz Méndez, J. E.

2018-06-01

Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction and of finite support in the other. These solutions are quasiperiodic along the structure and exponentially decay in the orthogonal direction. A simple formula for the dispersion relation of these waves is obtained.

Application of Classical and Lie Transform Methods to Zonal Perturbation in the Artificial Satellite

NASA Astrophysics Data System (ADS)

San-Juan, J. F.; San-Martin, M.; Perez, I.; Lopez-Ochoa, L. M.

2013-08-01

A scalable second-order analytical orbit propagator program is being carried out. This analytical orbit propagator combines modern perturbation methods, based on the canonical frame of the Lie transform, and classical perturbation methods in function of orbit types or the requirements needed for a space mission, such as catalog maintenance operations, long period evolution, and so on. As a first step on the validation of part of our orbit propagator, in this work we only consider the perturbation produced by zonal harmonic coefficients in the Earth's gravity potential, so that it is possible to analyze the behaviour of the perturbation methods involved in the corresponding analytical theories.

Modal Test/Analysis Correlation of Space Station Structures Using Nonlinear Sensitivity

NASA Technical Reports Server (NTRS)

Gupta, Viney K.; Newell, James F.; Berke, Laszlo; Armand, Sasan

1992-01-01

The modal correlation problem is formulated as a constrained optimization problem for validation of finite element models (FEM's). For large-scale structural applications, a pragmatic procedure for substructuring, model verification, and system integration is described to achieve effective modal correlation. The space station substructure FEM's are reduced using Lanczos vectors and integrated into a system FEM using Craig-Bampton component modal synthesis. The optimization code is interfaced with MSC/NASTRAN to solve the problem of modal test/analysis correlation; that is, the problem of validating FEM's for launch and on-orbit coupled loads analysis against experimentally observed frequencies and mode shapes. An iterative perturbation algorithm is derived and implemented to update nonlinear sensitivity (derivatives of eigenvalues and eigenvectors) during optimizer iterations, which reduced the number of finite element analyses.

Modal test/analysis correlation of Space Station structures using nonlinear sensitivity

NASA Technical Reports Server (NTRS)

Gupta, Viney K.; Newell, James F.; Berke, Laszlo; Armand, Sasan

1992-01-01

The modal correlation problem is formulated as a constrained optimization problem for validation of finite element models (FEM's). For large-scale structural applications, a pragmatic procedure for substructuring, model verification, and system integration is described to achieve effective modal correlations. The space station substructure FEM's are reduced using Lanczos vectors and integrated into a system FEM using Craig-Bampton component modal synthesis. The optimization code is interfaced with MSC/NASTRAN to solve the problem of modal test/analysis correlation; that is, the problem of validating FEM's for launch and on-orbit coupled loads analysis against experimentally observed frequencies and mode shapes. An iterative perturbation algorithm is derived and implemented to update nonlinear sensitivity (derivatives of eigenvalues and eigenvectors) during optimizer iterations, which reduced the number of finite element analyses.

Direct Numerical Simulation of Acoustic Waves Interacting with a Shock Wave in a Quasi-1D Convergent-Divergent Nozzle Using an Unstructured Finite Volume Algorithm

NASA Technical Reports Server (NTRS)

Bui, Trong T.; Mankbadi, Reda R.

1995-01-01

Numerical simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle is performed using an unstructured finite volume algorithm with a piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for steady flows with and without the normal shock by running the simulation with a sequence of successively finer meshes. Then the accuracy of the Roe flux difference splitting near the sonic transition point is examined for different reconstruction schemes. Finally, the unsteady numerical solutions with the acoustic perturbation are presented and compared with linear theory results.

Suppression of the Saffman-Taylor instability through injection of a finite slug of polymer

NASA Astrophysics Data System (ADS)

Beeson-Jones, Timothy H.; Woods, Andrew W.

2014-11-01

During secondary oil recovery, relatively mobile water can channel through oil owing to the Saffman-Taylor instability. Injection of a finite slug of polymer solution from a central well prior to the water flood suppresses the growth of the instability by reducing the adverse mobility ratio at the leading interface. A linear stability analysis of an axisymmetric base state identifies how perturbations on the leading and trailing interfaces become coupled. It also reveals the dependence of the long-time algebraic growth of each mode on the mobility ratios across the two interfaces. The viscosity of the polymer solution which minimizes the growth rate of the instability is identified, and the impact of different slug sizes on this growth is described. Funded by EPSRC & BP.

Singular perturbations with boundary conditions and the Casimir effect in the half space

NASA Astrophysics Data System (ADS)

Albeverio, S.; Cognola, G.; Spreafico, M.; Zerbini, S.

2010-06-01

We study the self-adjoint extensions of a class of nonmaximal multiplication operators with boundary conditions. We show that these extensions correspond to singular rank 1 perturbations (in the sense of Albeverio and Kurasov [Singular Perturbations of Differential Operaters (Cambridge University Press, Cambridge, 2000)]) of the Laplace operator, namely, the formal Laplacian with a singular delta potential, on the half space. This construction is the appropriate setting to describe the Casimir effect related to a massless scalar field in the flat space-time with an infinite conducting plate and in the presence of a pointlike "impurity." We use the relative zeta determinant (as defined in the works of Müller ["Relative zeta functions, relative determinants and scattering theory," Commun. Math. Phys. 192, 309 (1998)] and Spreafico and Zerbini ["Finite temperature quantum field theory on noncompact domains and application to delta interactions," Rep. Math. Phys. 63, 163 (2009)]) in order to regularize the partition function of this model. We study the analytic extension of the associated relative zeta function, and we present explicit results for the partition function and for the Casimir force.

Shock waves on complex networks

NASA Astrophysics Data System (ADS)

Mones, Enys; Araújo, Nuno A. M.; Vicsek, Tamás; Herrmann, Hans J.

2014-05-01

Power grids, road maps, and river streams are examples of infrastructural networks which are highly vulnerable to external perturbations. An abrupt local change of load (voltage, traffic density, or water level) might propagate in a cascading way and affect a significant fraction of the network. Almost discontinuous perturbations can be modeled by shock waves which can eventually interfere constructively and endanger the normal functionality of the infrastructure. We study their dynamics by solving the Burgers equation under random perturbations on several real and artificial directed graphs. Even for graphs with a narrow distribution of node properties (e.g., degree or betweenness), a steady state is reached exhibiting a heterogeneous load distribution, having a difference of one order of magnitude between the highest and average loads. Unexpectedly we find for the European power grid and for finite Watts-Strogatz networks a broad pronounced bimodal distribution for the loads. To identify the most vulnerable nodes, we introduce the concept of node-basin size, a purely topological property which we show to be strongly correlated to the average load of a node.

Negative running can prevent eternal inflation

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

Kinney, William H.; Freese, Katherine, E-mail: whkinney@buffalo.edu, E-mail: ktfreese@umich.edu

Current data from the Planck satellite and the BICEP2 telescope favor, at around the 2 σ level, negative running of the spectral index of curvature perturbations from inflation. We show that for negative running α < 0, the curvature perturbation amplitude has a maximum on scales larger than our current horizon size. A condition for the absence of eternal inflation is that the curvature perturbation amplitude always remain below unity on superhorizon scales. For current bounds on n{sub S} from Planck, this corresponds to an upper bound of the running α < −9 × 10{sup −5}, so that even tiny running of the scalar spectral index ismore » sufficient to prevent eternal inflation from occurring, as long as the running remains negative on scales outside the horizon. In single-field inflation models, negative running is associated with a finite duration of inflation: we show that eternal inflation may not occur even in cases where inflation lasts as long as 10{sup 4} e-folds.« less

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

The Blended Finite Element Method for Multi-fluid Plasma Modeling

DTIC Science & Technology

2016-07-01

Briefing Charts 3. DATES COVERED (From - To) 07 June 2016 - 01 July 2016 4. TITLE AND SUBTITLE The Blended Finite Element Method for Multi-fluid Plasma...BLENDED FINITE ELEMENT METHOD FOR MULTI-FLUID PLASMA MODELING Éder M. Sousa1, Uri Shumlak2 1ERC INC., IN-SPACE PROPULSION BRANCH (RQRS) AIR FORCE RESEARCH...MULTI-FLUID PLASMA MODEL 2 BLENDED FINITE ELEMENT METHOD Blended Finite Element Method Nodal Continuous Galerkin Modal Discontinuous Galerkin Model

Spark formation as a moving boundary process

NASA Astrophysics Data System (ADS)

Ebert, Ute

2006-03-01

The growth process of spark channels recently becomes accessible through complementary methods. First, I will review experiments with nanosecond photographic resolution and with fast and well defined power supplies that appropriately resolve the dynamics of electric breakdown [1]. Second, I will discuss the elementary physical processes as well as present computations of spark growth and branching with adaptive grid refinement [2]. These computations resolve three well separated scales of the process that emerge dynamically. Third, this scale separation motivates a hierarchy of models on different length scales. In particular, I will discuss a moving boundary approximation for the ionization fronts that generate the conducting channel. The resulting moving boundary problem shows strong similarities with classical viscous fingering. For viscous fingering, it is known that the simplest model forms unphysical cusps within finite time that are suppressed by a regularizing condition on the moving boundary. For ionization fronts, we derive a new condition on the moving boundary of mixed Dirichlet-Neumann type (φ=ɛnφ) that indeed regularizes all structures investigated so far. In particular, we present compact analytical solutions with regularization, both for uniformly translating shapes and for their linear perturbations [3]. These solutions are so simple that they may acquire a paradigmatic role in the future. Within linear perturbation theory, they explicitly show the convective stabilization of a curved front while planar fronts are linearly unstable against perturbations of arbitrary wave length. [1] T.M.P. Briels, E.M. van Veldhuizen, U. Ebert, TU Eindhoven. [2] C. Montijn, J. Wackers, W. Hundsdorfer, U. Ebert, CWI Amsterdam. [3] B. Meulenbroek, U. Ebert, L. Schäfer, Phys. Rev. Lett. 95, 195004 (2005).

Generalized Autobalanced Ramsey Spectroscopy of Clock Transitions

NASA Astrophysics Data System (ADS)

Yudin, V. I.; Taichenachev, A. V.; Basalaev, M. Yu.; Zanon-Willette, T.; Pollock, J. W.; Shuker, M.; Donley, E. A.; Kitching, J.

2018-05-01

When performing precision measurements, the quantity being measured is often perturbed by the measurement process itself. Such measurements include precision frequency measurements for atomic clock applications carried out with Ramsey spectroscopy. With the aim of eliminating probe-induced perturbations, a method of generalized autobalanced Ramsey spectroscopy (GABRS) is presented and rigorously substantiated. The usual local-oscillator frequency control loop is augmented with a second control loop derived from secondary Ramsey sequences interspersed with the primary sequences and with a different Ramsey period. This second loop feeds back to a secondary clock variable and ultimately compensates for the perturbation of the clock frequency caused by the measurements in the first loop. We show that such a two-loop scheme can lead to perfect compensation for measurement-induced light shifts and does not suffer from the effects of relaxation, time-dependent pulse fluctuations and phase-jump modulation errors that are typical of other hyper-Ramsey schemes. Several variants of GABRS are explored based on different secondary variables including added relative phase shifts between Ramsey pulses, external frequency-step compensation, and variable second-pulse duration. We demonstrate that a universal antisymmetric error signal, and hence perfect compensation at a finite modulation amplitude, is generated only if an additional frequency step applied during both Ramsey pulses is used as the concomitant variable parameter. This universal technique can be applied to the fields of atomic clocks, high-resolution molecular spectroscopy, magnetically induced and two-photon probing schemes, Ramsey-type mass spectrometry, and the field of precision measurements. Some variants of GABRS can also be applied for rf atomic clocks using coherent-population-trapping-based Ramsey spectroscopy of the two-photon dark resonance.

Discontinuous finite element space-angle treatment of the first order linear Boltzmann transport equation with magnetic fields: Application to MRI-guided radiotherapy

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

St Aubin, J., E-mail: joel.st.aubin@albertahealthservices.ca; Keyvanloo, A.; Fallone, B. G.

Purpose: The advent of magnetic resonance imaging (MRI) guided radiotherapy systems demands the incorporation of the magnetic field into dose calculation algorithms of treatment planning systems. This is due to the fact that the Lorentz force of the magnetic field perturbs the path of the relativistic electrons, hence altering the dose deposited by them. Building on the previous work, the authors have developed a discontinuous finite element space-angle treatment of the linear Boltzmann transport equation to accurately account for the effects of magnetic fields on radiotherapy doses. Methods: The authors present a detailed description of their new formalism and comparemore » its accuracy to GEANT4 Monte Carlo calculations for magnetic fields parallel and perpendicular to the radiation beam at field strengths of 0.5 and 3 T for an inhomogeneous 3D slab geometry phantom comprising water, bone, and air or lung. The accuracy of the authors’ new formalism was determined using a gamma analysis with a 2%/2 mm criterion. Results: Greater than 98.9% of all points analyzed passed the 2%/2 mm gamma criterion for the field strengths and orientations tested. The authors have benchmarked their new formalism against Monte Carlo in a challenging radiation transport problem with a high density material (bone) directly adjacent to a very low density material (dry air at STP) where the effects of the magnetic field dominate collisions. Conclusions: A discontinuous finite element space-angle approach has been proven to be an accurate method for solving the linear Boltzmann transport equation with magnetic fields for cases relevant to MRI guided radiotherapy. The authors have validated the accuracy of this novel technique against GEANT4, even in cases of strong magnetic field strengths and low density air.« less