Regularization of Grad’s 13 -Moment-Equations in Kinetic Gas Theory

DTIC Science & Technology

2011-01-01

variant of the moment method has been proposed by Eu (1980) and is used, e.g., in Myong (2001). Recently, a maximum- entropy 10-moment system has been used...small amplitude linear waves, the R13 system is linearly stable in time for all modes and wave lengths. The instability of the Burnett system indicates...Boltzmann equation. Related to the problem of global hyperbolicity is the questions of the existence of an entropy law for the R13 system . In the linear

Automatic Control via Thermostats of a Hyperbolic Stefan Problem with Memory

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

Colli, P.; Grasselli, M.; Sprekels, J.

1999-03-15

A hyperbolic Stefan problem based on the linearized Gurtin-Pipkin heat conduction law is considered. The temperature and free boundary are controlled by a thermostat acting on the boundary. This feedback control is based on temperature measurements performed by real thermal sensors located within the domain containing the two-phase system and/or at its boundary. Three different types of thermostats are analyzed: simple switch, relay switch, and a Preisach hysteresis operator. The resulting models lead to integrodifferential hyperbolic Stefan problems with nonlinear and nonlocal boundary conditions. Existence results are proved in all the cases. Uniqueness is also shown, except in the situationmore » corresponding to the ideal switch.« less

On hyperbolicity and Gevrey well-posedness. Part two: Scalar or degenerate transitions

NASA Astrophysics Data System (ADS)

Morisse, Baptiste

2018-04-01

For first-order quasi-linear systems of partial differential equations, we formulate an assumption of a transition from initial hyperbolicity to ellipticity. This assumption bears on the principal symbol of the first-order operator. Under such an assumption, we prove a strong Hadamard instability for the associated Cauchy problem, namely an instantaneous defect of Hölder continuity of the flow from Gσ to L2, with 0 < σ <σ0, the limiting Gevrey index σ0 depending on the nature of the transition. We restrict here to scalar transitions, and non-scalar transitions in which the boundary of the hyperbolic zone satisfies a flatness condition. As in our previous work for initially elliptic Cauchy problems [B. Morisse, On hyperbolicity and Gevrey well-posedness. Part one: the elliptic case, arxiv:arXiv:1611.07225], the instability follows from a long-time Cauchy-Kovalevskaya construction for highly oscillating solutions. This extends recent work of N. Lerner, T. Nguyen, and B. Texier [The onset of instability in first-order systems, to appear in J. Eur. Math. Soc.].

A high-order relaxation method with projective integration for solving nonlinear systems of hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Lafitte, Pauline; Melis, Ward; Samaey, Giovanni

2017-07-01

We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2015-01-01

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

The algebraic-hyperbolic approach to the linearized gravitational constraints on a Minkowski background

NASA Astrophysics Data System (ADS)

Winicour, Jeffrey

2017-08-01

An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to solving the constraints of Einstein’s equations which does not involve elliptic equations and has potential importance for the construction of binary black hole data. In order to shed light on the underpinnings of this approach, we consider its application to obtain solutions of the constraints for linearized perturbations of Minkowski space. In that case, we find the surprising result that there are no suitable Cauchy hypersurfaces in Minkowski space for which the linearized algebraic-hyperbolic constraint problem is well posed.

Linear guided waves in a hyperbolic planar waveguide. Dispersion relations

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

Lyashko, E I; Maimistov, A I

2015-11-30

We have theoretically investigated waveguide modes propagating in a planar waveguide formed by a layer of an isotropic dielectric surrounded by hyperbolic media. The case, when the optical axis of hyperbolic media is perpendicular to the interface, is considered. Dispersion relations are derived for the cases of TE and TM waves. The differences in the characteristics of a hyperbolic and a conventional dielectric waveguide are found. In particular, it is shown that in hyperbolic waveguides for each TM mode there are two cut-off frequencies and the number of propagating modes is always limited. (metamaterials)

A boundary-value problem for a first-order hyperbolic system in a two-dimensional domain

NASA Astrophysics Data System (ADS)

Zhura, N. A.; Soldatov, A. P.

2017-06-01

We consider a strictly hyperbolic first-order system of three equations with constant coefficients in a bounded piecewise-smooth domain. The boundary of the domain is assumed to consist of six smooth non-characteristic arcs. A boundary-value problem in this domain is posed by alternately prescribing one or two linear combinations of the components of the solution on these arcs. We show that this problem has a unique solution under certain additional conditions on the coefficients of these combinations, the boundary of the domain and the behaviour of the solution near the characteristics passing through the corner points of the domain.

Internal friction between fluid particles of MHD tangent hyperbolic fluid with heat generation: Using coefficients improved by Cash and Karp

NASA Astrophysics Data System (ADS)

Salahuddin, T.; Khan, Imad; Malik, M. Y.; Khan, Mair; Hussain, Arif; Awais, Muhammad

2017-05-01

The present work examines the internal resistance between fluid particles of tangent hyperbolic fluid flow due to a non-linear stretching sheet with heat generation. Using similarity transformations, the governing system of partial differential equations is transformed into a coupled non-linear ordinary differential system with variable coefficients. Unlike the current analytical works on the flow problems in the literature, the main concern here is to numerically work out and find the solution by using Runge-Kutta-Fehlberg coefficients improved by Cash and Karp (Naseer et al., Alexandria Eng. J. 53, 747 (2014)). To determine the relevant physical features of numerous mechanisms acting on the deliberated problem, it is sufficient to have the velocity profile and temperature field and also the drag force and heat transfer rate all as given in the current paper.

Fast wavelet based algorithms for linear evolution equations

NASA Technical Reports Server (NTRS)

Engquist, Bjorn; Osher, Stanley; Zhong, Sifen

1992-01-01

A class was devised of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin which they applied to general Calderon-Zygmund type integral operators. A modification of their idea is applied to linear hyperbolic and parabolic equations, with spatially varying coefficients. A significant speedup over standard methods is obtained when applied to hyperbolic equations in one space dimension and parabolic equations in multidimensions.

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza R.; Nishikawa, Hiroaki

2014-01-01

In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.

Modified hyperbolic sine model for titanium dioxide-based memristive thin films

NASA Astrophysics Data System (ADS)

Abu Bakar, Raudah; Syahirah Kamarozaman, Nur; Fazlida Hanim Abdullah, Wan; Herman, Sukreen Hana

2018-03-01

Since the emergence of memristor as the newest fundamental circuit elements, studies on memristor modeling have been evolved. To date, the developed models were based on the linear model, linear ionic drift model using different window functions, tunnelling barrier model and hyperbolic-sine function based model. Although using hyperbolic-sine function model could predict the memristor electrical properties, the model was not well fitted to the experimental data. In order to improve the performance of the hyperbolic-sine function model, the state variable equation was modified. On the one hand, the addition of window function cannot provide an improved fitting. By multiplying the Yakopcic’s state variable model to Chang’s model on the other hand resulted in the closer agreement with the TiO2 thin film experimental data. The percentage error was approximately 2.15%.

Optimal control of coupled parabolic-hyperbolic non-autonomous PDEs: infinite-dimensional state-space approach

NASA Astrophysics Data System (ADS)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2018-04-01

This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.

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

NASA Astrophysics Data System (ADS)

Kumar, Vivek; Raghurama Rao, S. V.

2008-04-01

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

Chosen interval methods for solving linear interval systems with special type of matrix

NASA Astrophysics Data System (ADS)

Szyszka, Barbara

2013-10-01

The paper is devoted to chosen direct interval methods for solving linear interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-point interval arithmetic.

A new method of imposing boundary conditions for hyperbolic equations

NASA Technical Reports Server (NTRS)

Funaro, D.; ative.

1987-01-01

A new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested. This method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions. Stability and convergence results are proven for the Chebyshev approximation of linear scalar hyperbolic equations. The eigenvalues of this method applied to parabolic equations are shown to be real and negative.

Luminescent hyperbolic metasurfaces

NASA Astrophysics Data System (ADS)

Smalley, J. S. T.; Vallini, F.; Montoya, S. A.; Ferrari, L.; Shahin, S.; Riley, C. T.; Kanté, B.; Fullerton, E. E.; Liu, Z.; Fainman, Y.

2017-01-01

When engineered on scales much smaller than the operating wavelength, metal-semiconductor nanostructures exhibit properties unobtainable in nature. Namely, a uniaxial optical metamaterial described by a hyperbolic dispersion relation can simultaneously behave as a reflective metal and an absorptive or emissive semiconductor for electromagnetic waves with orthogonal linear polarization states. Using an unconventional multilayer architecture, we demonstrate luminescent hyperbolic metasurfaces, wherein distributed semiconducting quantum wells display extreme absorption and emission polarization anisotropy. Through normally incident micro-photoluminescence measurements, we observe absorption anisotropies greater than a factor of 10 and degree-of-linear polarization of emission >0.9. We observe the modification of emission spectra and, by incorporating wavelength-scale gratings, show a controlled reduction of polarization anisotropy. We verify hyperbolic dispersion with numerical simulations that model the metasurface as a composite nanoscale structure and according to the effective medium approximation. Finally, we experimentally demonstrate >350% emission intensity enhancement relative to the bare semiconducting quantum wells.

On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

NASA Technical Reports Server (NTRS)

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

1994-01-01

It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

ADER schemes for scalar non-linear hyperbolic conservation laws with source terms in three-space dimensions

NASA Astrophysics Data System (ADS)

Toro, E. F.; Titarev, V. A.

2005-01-01

In this paper we develop non-linear ADER schemes for time-dependent scalar linear and non-linear conservation laws in one-, two- and three-space dimensions. Numerical results of schemes of up to fifth order of accuracy in both time and space illustrate that the designed order of accuracy is achieved in all space dimensions for a fixed Courant number and essentially non-oscillatory results are obtained for solutions with discontinuities. We also present preliminary results for two-dimensional non-linear systems.

Exponential Boundary Observers for Pressurized Water Pipe

NASA Astrophysics Data System (ADS)

Hermine Som, Idellette Judith; Cocquempot, Vincent; Aitouche, Abdel

2015-11-01

This paper deals with state estimation on a pressurized water pipe modeled by nonlinear coupled distributed hyperbolic equations for non-conservative laws with three known boundary measures. Our objective is to estimate the fourth boundary variable, which will be useful for leakage detection. Two approaches are studied. Firstly, the distributed hyperbolic equations are discretized through a finite-difference scheme. By using the Lipschitz property of the nonlinear term and a Lyapunov function, the exponential stability of the estimation error is proven by solving Linear Matrix Inequalities (LMIs). Secondly, the distributed hyperbolic system is preserved for state estimation. After state transformations, a Luenberger-like PDE boundary observer based on backstepping mathematical tools is proposed. An exponential Lyapunov function is used to prove the stability of the resulted estimation error. The performance of the two observers are shown on a water pipe prototype simulated example.

Existence and Regularity Results for the Inviscid Primitive Equations with Lateral Periodicity

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

Hamouda, Makram, E-mail: mahamoud@indiana.edu; Jung, Chang-Yeol, E-mail: changyeoljung@gmail.com; Temam, Roger, E-mail: temam@indiana.edu

2016-06-15

The article is devoted to prove the existence and regularity of the solutions of the 3D inviscid Linearized Primitive Equations (LPEs) in a channel with lateral periodicity. This was assumed in a previous work (Hamouda et al. in Discret Contin Dyn Syst Ser S 6(2):401–422, 2013) which is concerned with the boundary layers generated by the corresponding viscous problem. Although the equations under investigation here are of hyperbolic type, the standard methods do not apply because of the specificity of the hyperbolic system. A set of non-local boundary conditions for the inviscid LPEs has to be imposed at the lateralmore » boundary of the channel making thus the system well-posed.« less

Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models

NASA Astrophysics Data System (ADS)

Giona, M.; Brasiello, A.; Crescitelli, S.

2015-11-01

One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.

Hyperbolic/parabolic development for the GIM-STAR code. [flow fields in supersonic inlets

NASA Technical Reports Server (NTRS)

Spradley, L. W.; Stalnaker, J. F.; Ratliff, A. W.

1980-01-01

Flow fields in supersonic inlet configurations were computed using the eliptic GIM code on the STAR computer. Spillage flow under the lower cowl was calculated to be 33% of the incoming stream. The shock/boundary layer interaction on the upper propulsive surface was computed including separation. All shocks produced by the flow system were captured. Linearized block implicit (LBI) schemes were examined to determine their application to the GIM code. Pure explicit methods have stability limitations and fully implicit schemes are inherently inefficient; however, LBI schemes show promise as an effective compromise. A quasiparabolic version of the GIM code was developed using elastical parabolized Navier-Stokes methods combined with quasitime relaxation. This scheme is referred to as quasiparabolic although it applies equally well to hyperbolic supersonic inviscid flows. Second order windward differences are used in the marching coordinate and either explicit or linear block implicit time relaxation can be incorporated.

Conformal and covariant Z4 formulation of the Einstein equations: Strongly hyperbolic first-order reduction and solution with discontinuous Galerkin schemes

NASA Astrophysics Data System (ADS)

Dumbser, Michael; Guercilena, Federico; Köppel, Sven; Rezzolla, Luciano; Zanotti, Olindo

2018-04-01

We present a strongly hyperbolic first-order formulation of the Einstein equations based on the conformal and covariant Z4 system (CCZ4) with constraint-violation damping, which we refer to as FO-CCZ4. As CCZ4, this formulation combines the advantages of a conformal and traceless formulation, with the suppression of constraint violations given by the damping terms, but being first order in time and space, it is particularly suited for a discontinuous Galerkin (DG) implementation. The strongly hyperbolic first-order formulation has been obtained by making careful use of first and second-order ordering constraints. A proof of strong hyperbolicity is given for a selected choice of standard gauges via an analytical computation of the entire eigenstructure of the FO-CCZ4 system. The resulting governing partial differential equations system is written in nonconservative form and requires the evolution of 58 unknowns. A key feature of our formulation is that the first-order CCZ4 system decouples into a set of pure ordinary differential equations and a reduced hyperbolic system of partial differential equations that contains only linearly degenerate fields. We implement FO-CCZ4 in a high-order path-conservative arbitrary-high-order-method-using-derivatives (ADER)-DG scheme with adaptive mesh refinement and local time-stepping, supplemented with a third-order ADER-WENO subcell finite-volume limiter in order to deal with singularities arising with black holes. We validate the correctness of the formulation through a series of standard tests in vacuum, performed in one, two and three spatial dimensions, and also present preliminary results on the evolution of binary black-hole systems. To the best of our knowledge, these are the first successful three-dimensional simulations of moving punctures carried out with high-order DG schemes using a first-order formulation of the Einstein equations.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

NASA Astrophysics Data System (ADS)

Broche, Rita de Cássia D. S.; de Oliveira, Luiz Augusto F.

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem.

Scientific Activities Pursuant to the Provisions of AFOSR Grant 79-0018.

DTIC Science & Technology

1984-01-01

controllability implies stabilizability n the case of autono- mous finite dimensional linear systems , we are not surprised to find control ...Current Status of the Control Theory of Single Space Dim- ension Hyperbolicr Systems " was presented at the NASA JPL Symposium on Cbntrol and Stabilization ...theory of hyperbolic systems , including controllability , stabilization , control canonical form theory, etc. To allow a unified and not

Pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations

NASA Astrophysics Data System (ADS)

Al-Islam, Najja Shakir

In this Dissertation, the existence of pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations is established. For that, (Al-Islam [4]) is first studied and then obtained under some suitable assumptions. That is, the existence of pseudo almost periodic solutions to a hyperbolic second-order partial differential equation with delay. The second-order partial differential equation (1) represents a mathematical model for the dynamics of gas absorption, given by uxt+a x,tux=Cx,t,u x,t , u0,t=4 t, 1 where a : [0, L] x RR , C : [0, L] x R x RR , and ϕ : RR are (jointly) continuous functions ( t being the greatest integer function) and L > 0. The results in this Dissertation generalize those of Poorkarimi and Wiener [22]. Secondly, a generalization of the above-mentioned system consisting of the non-linear hyperbolic second-order partial differential equation uxt+a x,tux+bx,t ut+cx,tu=f x,t,u, x∈ 0,L,t∈ R, 2 equipped with the boundary conditions ux,0 =40x, u0,t=u 0t, uxx,0=y 0x, x∈0,L, t∈R, 3 where a, b, c : [0, L ] x RR and f : [0, L] x R x RR are (jointly) continuous functions is studied. Under some suitable assumptions, the existence and uniqueness of pseudo almost periodic solutions to particular cases, as well as the general case of the second-order hyperbolic partial differential equation (2) are studied. The results of all studies contained within this text extend those obtained by Aziz and Meyers [6] in the periodic setting.

A New Discretization Method of Order Four for the Numerical Solution of One-Space Dimensional Second-Order Quasi-Linear Hyperbolic Equation

ERIC Educational Resources Information Center

Mohanty, R. K.; Arora, Urvashi

2002-01-01

Three level-implicit finite difference methods of order four are discussed for the numerical solution of the mildly quasi-linear second-order hyperbolic equation A(x, t, u)u[subscript xx] + 2B(x, t, u)u[subscript xt] + C(x, t, u)u[subscript tt] = f(x, t, u, u[subscript x], u[subscript t]), 0 less than x less than 1, t greater than 0 subject to…

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. II - Five-point schemes

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

This paper presents a family of two-level five-point implicit schemes for the solution of one-dimensional systems of hyperbolic conservation laws, which generalized the Crank-Nicholson scheme to fourth order accuracy (4-4) in both time and space. These 4-4 schemes are nondissipative and unconditionally stable. Special attention is given to the system of linear equations associated with these 4-4 implicit schemes. The regularity of this system is analyzed and efficiency of solution-algorithms is examined. A two-datum representation of these 4-4 implicit schemes brings about a compactification of the stencil to three mesh points at each time-level. This compact two-datum representation is particularly useful in deriving boundary treatments. Numerical results are presented to illustrate some properties of the proposed scheme.

Cell-centered high-order hyperbolic finite volume method for diffusion equation on unstructured grids

NASA Astrophysics Data System (ADS)

Lee, Euntaek; Ahn, Hyung Taek; Luo, Hong

2018-02-01

We apply a hyperbolic cell-centered finite volume method to solve a steady diffusion equation on unstructured meshes. This method, originally proposed by Nishikawa using a node-centered finite volume method, reformulates the elliptic nature of viscous fluxes into a set of augmented equations that makes the entire system hyperbolic. We introduce an efficient and accurate solution strategy for the cell-centered finite volume method. To obtain high-order accuracy for both solution and gradient variables, we use a successive order solution reconstruction: constant, linear, and quadratic (k-exact) reconstruction with an efficient reconstruction stencil, a so-called wrapping stencil. By the virtue of the cell-centered scheme, the source term evaluation was greatly simplified regardless of the solution order. For uniform schemes, we obtain the same order of accuracy, i.e., first, second, and third orders, for both the solution and its gradient variables. For hybrid schemes, recycling the gradient variable information for solution variable reconstruction makes one order of additional accuracy, i.e., second, third, and fourth orders, possible for the solution variable with less computational work than needed for uniform schemes. In general, the hyperbolic method can be an effective solution technique for diffusion problems, but instability is also observed for the discontinuous diffusion coefficient cases, which brings necessity for further investigation about the monotonicity preserving hyperbolic diffusion method.

Compatible diagonal-norm staggered and upwind SBP operators

NASA Astrophysics Data System (ADS)

Mattsson, Ken; O'Reilly, Ossian

2018-01-01

The main motivation with the present study is to achieve a provably stable high-order accurate finite difference discretisation of linear first-order hyperbolic problems on a staggered grid. The use of a staggered grid makes it non-trivial to discretise advective terms. To overcome this difficulty we discretise the advective terms using upwind Summation-By-Parts (SBP) operators, while the remaining terms are discretised using staggered SBP operators. The upwind and staggered SBP operators (for each order of accuracy) are compatible, here meaning that they are based on the same diagonal norms, allowing for energy estimates to be formulated. The boundary conditions are imposed using a penalty (SAT) technique, to guarantee linear stability. The resulting SBP-SAT approximations lead to fully explicit ODE systems. The accuracy and stability properties are demonstrated for linear hyperbolic problems in 1D, and for the 2D linearised Euler equations with constant background flow. The newly derived upwind and staggered SBP operators lead to significantly more accurate numerical approximations, compared with the exclusive usage of (previously derived) central-difference first derivative SBP operators.

Impact of hyperbolicity on chimera states in ensembles of nonlocally coupled chaotic oscillators

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

Semenova, N.; Anishchenko, V.; Zakharova, A.

2016-06-08

In this work we analyse nonlocally coupled networks of identical chaotic oscillators. We study both time-discrete and time-continuous systems (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent (synchronous) and incoherent (desynchronized) dynamics coexist, can be obtained only in networks of chaotic non-hyperbolic systems and cannot be found in networks of hyperbolic systems. This hypothesis is supported by numerical simulations for hyperbolic and non-hyperbolic cases.

An improved numerical method for the kernel density functional estimation of disperse flow

NASA Astrophysics Data System (ADS)

Smith, Timothy; Ranjan, Reetesh; Pantano, Carlos

2014-11-01

We present an improved numerical method to solve the transport equation for the one-point particle density function (pdf), which can be used to model disperse flows. The transport equation, a hyperbolic partial differential equation (PDE) with a source term, is derived from the Lagrangian equations for a dilute particle system by treating position and velocity as state-space variables. The method approximates the pdf by a discrete mixture of kernel density functions (KDFs) with space and time varying parameters and performs a global Rayleigh-Ritz like least-square minimization on the state-space of velocity. Such an approximation leads to a hyperbolic system of PDEs for the KDF parameters that cannot be written completely in conservation form. This system is solved using a numerical method that is path-consistent, according to the theory of non-conservative hyperbolic equations. The resulting formulation is a Roe-like update that utilizes the local eigensystem information of the linearized system of PDEs. We will present the formulation of the base method, its higher-order extension and further regularization to demonstrate that the method can predict statistics of disperse flows in an accurate, consistent and efficient manner. This project was funded by NSF Project NSF-DMS 1318161.

Diffusive instabilities in a hyperbolic activator-inhibitor system with superdiffusion

NASA Astrophysics Data System (ADS)

Mvogo, Alain; Macías-Díaz, Jorge E.; Kofané, Timoléon Crépin

2018-03-01

We investigate analytically and numerically the conditions for wave instabilities in a hyperbolic activator-inhibitor system with species undergoing anomalous superdiffusion. In the present work, anomalous superdiffusion is modeled using the two-dimensional Weyl fractional operator, with derivative orders α ∈ [1,2]. We perform a linear stability analysis and derive the conditions for diffusion-driven wave instabilities. Emphasis is placed on the effect of the superdiffusion exponent α , the diffusion ratio d , and the inertial time τ . As the superdiffusive exponent increases, so does the wave number of the Turing instability. Opposite to the requirement for Turing instability, the activator needs to diffuse sufficiently faster than the inhibitor in order for the wave instability to occur. The critical wave number for wave instability decreases with the superdiffusive exponent and increases with the inertial time. The maximum value of the inertial time for a wave instability to occur in the system is τmax=3.6 . As one of the main results of this work, we conclude that both anomalous diffusion and inertial time influence strongly the conditions for wave instabilities in hyperbolic fractional reaction-diffusion systems. Some numerical simulations are conducted as evidence of the analytical predictions derived in this work.

A Model for Displacements Between Parallel Plates That Shows Change of Type from Hyperbolic to Elliptic

NASA Astrophysics Data System (ADS)

Shariati, Maryam; Yortsos, Yannis; Talon, Laurent; Martin, Jerome; Rakotomalala, Nicole; Salin, Dominique

2003-11-01

We consider miscible displacement between parallel plates, where the viscosity is a function of the concentration. By selecting a piece-wise representation, the problem can be considered as ``three-phase'' flow. Assuming a lubrication-type approximation, the mathematical description is in terms of two quasi-linear hyperbolic equations. When the mobility of the middle phase is smaller than its neighbors, the system is genuinely hyperbolic and can be solved analytically. However, when it is larger, an elliptic region develops. This change-of-type behavior is for the first time proved here based on sound physical principles. Numerical solutions with a small diffusion are presented. Good agreement is obtained outside the elliptic region, but not inside, where the numerical results show unstable behavior. We conjecture that for the solution of the real problem in the mixed-type case, the full higher-dimensionality problem must be considered inside the elliptic region, in which the lubrication (parallel-flow) approximation is no longer appropriate. This is discussed in a companion presentation.

Initial value formulation of dynamical Chern-Simons gravity

NASA Astrophysics Data System (ADS)

Delsate, Térence; Hilditch, David; Witek, Helvi

2015-01-01

We derive an initial value formulation for dynamical Chern-Simons gravity, a modification of general relativity involving parity-violating higher derivative terms. We investigate the structure of the resulting system of partial differential equations thinking about linearization around arbitrary backgrounds. This type of consideration is necessary if we are to establish well-posedness of the Cauchy problem. Treating the field equations as an effective field theory we find that weak necessary conditions for hyperbolicity are satisfied. For the full field equations we find that there are states from which subsequent evolution is not determined. Generically the evolution system closes, but is not hyperbolic in any sense that requires a first order pseudodifferential reduction. In a cursory mode analysis we find that the equations of motion contain terms that may cause ill-posedness of the initial value problem.

Time domain convergence properties of Lyapunov stable penalty methods

NASA Technical Reports Server (NTRS)

Kurdila, A. J.; Sunkel, John

1991-01-01

Linear hyperbolic partial differential equations are analyzed using standard techniques to show that a sequence of solutions generated by the Liapunov stable penalty equations approaches the solution of the differential-algebraic equations governing the dynamics of multibody problems arising in linear vibrations. The analysis does not require that the system be conservative and does not impose any specific integration scheme. Variational statements are derived which bound the error in approximation by the norm of the constraint violation obtained in the approximate solutions.

Incorporating inductances in tissue-scale models of cardiac electrophysiology

NASA Astrophysics Data System (ADS)

Rossi, Simone; Griffith, Boyce E.

2017-09-01

In standard models of cardiac electrophysiology, including the bidomain and monodomain models, local perturbations can propagate at infinite speed. We address this unrealistic property by developing a hyperbolic bidomain model that is based on a generalization of Ohm's law with a Cattaneo-type model for the fluxes. Further, we obtain a hyperbolic monodomain model in the case that the intracellular and extracellular conductivity tensors have the same anisotropy ratio. In one spatial dimension, the hyperbolic monodomain model is equivalent to a cable model that includes axial inductances, and the relaxation times of the Cattaneo fluxes are strictly related to these inductances. A purely linear analysis shows that the inductances are negligible, but models of cardiac electrophysiology are highly nonlinear, and linear predictions may not capture the fully nonlinear dynamics. In fact, contrary to the linear analysis, we show that for simple nonlinear ionic models, an increase in conduction velocity is obtained for small and moderate values of the relaxation time. A similar behavior is also demonstrated with biophysically detailed ionic models. Using the Fenton-Karma model along with a low-order finite element spatial discretization, we numerically analyze differences between the standard monodomain model and the hyperbolic monodomain model. In a simple benchmark test, we show that the propagation of the action potential is strongly influenced by the alignment of the fibers with respect to the mesh in both the parabolic and hyperbolic models when using relatively coarse spatial discretizations. Accurate predictions of the conduction velocity require computational mesh spacings on the order of a single cardiac cell. We also compare the two formulations in the case of spiral break up and atrial fibrillation in an anatomically detailed model of the left atrium, and we examine the effect of intracellular and extracellular inductances on the virtual electrode phenomenon.

Applications of Random Differential Equations to Engineering Science. Wave Propagation in Turbulent Media and Random Linear Hyperbolic Systems.

DTIC Science & Technology

1981-11-10

1976), 745-754. 4. (with W. C. Tam) Periodic and traveling wave solutions to Volterra - Lotka equation with diffusion. Bull. Math. Biol. 38 (1976), 643...with applications [17,19,20). (5) A general method for reconstructing the mutual coherent function of a static or moving source from the random

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: An eigenvalue analysis

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1986-01-01

A hyperbolic initial-boundary-value problem can be approximated by a system of ordinary differential equations (ODEs) by replacing the spatial derivatives by finite-difference approximations. The resulting system of ODEs is called a semidiscrete approximation. A complication is the fact that more boundary conditions are required for the spatially discrete approximation than are specified for the partial differential equation. Consequently, additional numerical boundary conditions are required and improper treatment of these additional conditions can lead to instability. For a linear initial-boundary-value problem (IBVP) with homogeneous analytical boundary conditions, the semidiscrete approximation results in a system of ODEs of the form du/dt = Au whose solution can be written as u(t) = exp(At)u(O). Lax-Richtmyer stability requires that the matrix norm of exp(At) be uniformly bounded for O less than or = t less than or = T independent of the spatial mesh size. Although the classical Lax-Richtmyer stability definition involves a conventional vector norm, there is no known algebraic test for the uniform boundedness of the matrix norm of exp(At) for hyperbolic IBVPs. An alternative but more complicated stability definition is used in the theory developed by Gustafsson, Kreiss, and Sundstrom (GKS). The two methods are compared.

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

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

Causal implications of viscous damping in compressible fluid flows

PubMed

Jordan; Meyer; Puri

2000-12-01

Classically, a compressible, isothermal, viscous fluid is regarded as a mathematical continuum and its motion is governed by the linearized continuity, Navier-Stokes, and state equations. Unfortunately, solutions of this system are of a diffusive nature and hence do not satisfy causality. However, in the case of a half-space of fluid set to motion by a harmonically vibrating plate the classical equation of motion can, under suitable conditions, be approximated by the damped wave equation. Since this equation is hyperbolic, the resulting solutions satisfy causal requirements. In this work the Laplace transform and other analytical and numerical tools are used to investigate this apparent contradiction. To this end the exact solutions, as well as their special and limiting cases, are found and compared for the two models. The effects of the physical parameters on the solutions and associated quantities are also studied. It is shown that propagating wave fronts are only possible under the hyperbolic model and that the concept of phase speed has different meanings in the two formulations. In addition, discontinuities and shock waves are noted and a physical system is modeled under both formulations. Overall, it is shown that the hyperbolic form gives a more realistic description of the physical problem than does the classical theory. Lastly, a simple mechanical analog is given and connections to viscoelastic fluids are noted. In particular, the research presented here supports the notion that linear compressible, isothermal, viscous fluids can, at least in terms of causality, be better characterized as a type of viscoelastic fluid.

Triangle based TVD schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Durlofsky, Louis J.; Osher, Stanley; Engquist, Bjorn

1990-01-01

A triangle based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux up to second order accuracy. Numerical results for linear advection and Burgers' equation are presented.

On solvability of boundary value problems for hyperbolic fourth-order equations with nonlocal boundary conditions of integral type

NASA Astrophysics Data System (ADS)

Popov, Nikolay S.

2017-11-01

Solvability of some initial-boundary value problems for linear hyperbolic equations of the fourth order is studied. A condition on the lateral boundary in these problems relates the values of a solution or the conormal derivative of a solution to the values of some integral operator applied to a solution. Nonlocal boundary-value problems for one-dimensional hyperbolic second-order equations with integral conditions on the lateral boundary were considered in the articles by A.I. Kozhanov. Higher-dimensional hyperbolic equations of higher order with integral conditions on the lateral boundary were not studied earlier. The existence and uniqueness theorems of regular solutions are proven. The method of regularization and the method of continuation in a parameter are employed to establish solvability.

Multidimensional FEM-FCT schemes for arbitrary time stepping

NASA Astrophysics Data System (ADS)

Kuzmin, D.; Möller, M.; Turek, S.

2003-05-01

The flux-corrected-transport paradigm is generalized to finite-element schemes based on arbitrary time stepping. A conservative flux decomposition procedure is proposed for both convective and diffusive terms. Mathematical properties of positivity-preserving schemes are reviewed. A nonoscillatory low-order method is constructed by elimination of negative off-diagonal entries of the discrete transport operator. The linearization of source terms and extension to hyperbolic systems are discussed. Zalesak's multidimensional limiter is employed to switch between linear discretizations of high and low order. A rigorous proof of positivity is provided. The treatment of non-linearities and iterative solution of linear systems are addressed. The performance of the new algorithm is illustrated by numerical examples for the shock tube problem in one dimension and scalar transport equations in two dimensions.

The solution of non-linear hyperbolic equation systems by the finite element method

NASA Technical Reports Server (NTRS)

Loehner, R.; Morgan, K.; Zienkiewicz, O. C.

1984-01-01

A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.

13-Moment System with Global Hyperbolicity for Quantum Gas

NASA Astrophysics Data System (ADS)

Di, Yana; Fan, Yuwei; Li, Ruo

2017-06-01

We point out that the quantum Grad's 13-moment system (Yano in Physica A 416:231-241, 2014) is lack of global hyperbolicity, and even worse, the thermodynamic equilibrium is not an interior point of the hyperbolicity region of the system. To remedy this problem, by fully considering Grad's expansion, we split the expansion into the equilibrium part and the non-equilibrium part, and propose a regularization for the system with the help of the new hyperbolic regularization theory developed in Cai et al. (SIAM J Appl Math 75(5):2001-2023, 2015) and Fan et al. (J Stat Phys 162(2):457-486, 2016). This provides us a new model which is hyperbolic for all admissible thermodynamic states, and meanwhile preserves the approximate accuracy of the original system. It should be noted that this procedure is not a trivial application of the hyperbolic regularization theory.

Hyperbolic phonon polaritons in hexagonal boron nitride (Conference Presentation)

NASA Astrophysics Data System (ADS)

Dai, Siyuan; Ma, Qiong; Fei, Zhe; Liu, Mengkun; Goldflam, Michael D.; Andersen, Trond; Garnett, William; Regan, Will; Wagner, Martin; McLeod, Alexander S.; Rodin, Alexandr; Zhu, Shou-En; Watanabe, Kenji; Taniguchi, T.; Dominguez, Gerado; Thiemens, Mark; Castro Neto, Antonio H.; Janssen, Guido C. A. M.; Zettl, Alex; Keilmann, Fritz; Jarillo-Herrero, Pablo; Fogler, Michael M.; Basov, Dmitri N.

2016-09-01

Uniaxial materials whose axial and tangential permittivities have opposite signs are referred to as indefinite or hyperbolic media. While hyperbolic responses are normally achieved with metamaterials, hexagonal boron nitride (hBN) naturally possesses this property due to the anisotropic phonons in the mid-infrared. Using scattering-type scanning near-field optical microscopy, we studied polaritonic phenomena in hBN. We performed infrared nano-imaging of highly confined and low-loss hyperbolic phonon polaritons in hBN. The polariton wavelength was shown to be governed by the hBN thickness according to a linear law persisting down to few atomic layers [1]. Additionally, we carried out the modification of hyperbolic response in meta-structures comprised of a mononlayer graphene deposited on hBN [2]. Electrostatic gating of the top graphene layer allows for the modification of wavelength and intensity of hyperbolic phonon polaritons in bulk hBN. The physics of the modification originates from the plasmon-phonon coupling in the hyperbolic medium. Furthermore, we demonstrated the "hyperlens" for subdiffractional focusing and imaging using a slab of hBN [3]. References [1] S. Dai et al., Science, 343, 1125 (2014). [2] S. Dai et al., Nature Nanotechnology, 10, 682 (2015). [3] S. Dai et al., Nature Communications, 6, 6963 (2015).

Traveling wave to a reaction-hyperbolic system for axonal transport

NASA Astrophysics Data System (ADS)

Huang, Feimin; Li, Xing; Zhang, Yinglong

2017-07-01

In this paper, we study a class of nonlinear reaction-hyperbolic systems modeling the neuronal signal transfer in neuroscience. This reaction-hyperbolic system can be regarded as n × n (n ≥ 2) hyperbolic system with relaxation. We first prove the existence of traveling wave by Gershgorin circle theorem and mathematically describe the neuronal signal transport. Then for a special case n = 2, we show the traveling wave is nonlinearly stable, and obtain the convergence rate simultaneously by a weighted estimate.

Partner symmetries and non-invariant solutions of four-dimensional heavenly equations

NASA Astrophysics Data System (ADS)

Malykh, A. A.; Nutku, Y.; Sheftel, M. B.

2004-07-01

We extend our method of partner symmetries to the hyperbolic complex Monge-Ampère equation and the second heavenly equation of Plebañski. We show the existence of partner symmetries and derive the relations between them. For certain simple choices of partner symmetries the resulting differential constraints together with the original heavenly equations are transformed to systems of linear equations by an appropriate Legendre transformation. The solutions of these linear equations are generically non-invariant. As a consequence we obtain explicitly new classes of heavenly metrics without Killing vectors.

Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

NASA Astrophysics Data System (ADS)

Mabuza, Sibusiso; Shadid, John N.; Kuzmin, Dmitri

2018-05-01

The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. For time discretization, Crank-Nicolson scheme and backward Euler scheme are utilized.

Evolution of finite-amplitude localized vortices in planar homogeneous shear flows

NASA Astrophysics Data System (ADS)

Karp, Michael; Shukhman, Ilia G.; Cohen, Jacob

2017-02-01

An analytical-based method is utilized to follow the evolution of localized initially Gaussian disturbances in flows with homogeneous shear, in which the base velocity components are at most linear functions of the coordinates, including hyperbolic, elliptic, and simple shear. Coherent structures, including counterrotating vortex pairs (CVPs) and hairpin vortices, are formed for the cases where the streamlines of the base flow are open (hyperbolic and simple shear). For hyperbolic base flows, the dominance of shear over rotation leads to elongation of the localized disturbance along the outlet asymptote and formation of CVPs. For simple shear CVPs are formed from linear and nonlinear disturbances, whereas hairpins are observed only for highly nonlinear disturbances. For elliptic base flows CVPs, hairpins and vortex loops form initially, however they do not last and break into various vortical structures that spread in the spanwise direction. The effect of the disturbance's initial amplitude and orientation is examined and the optimal orientation achieving maximal growth is identified.

Chaotic Oscillations of Second Order Linear Hyperbolic Equations with Nonlinear Boundary Conditions: A Factorizable but Noncommutative Case

NASA Astrophysics Data System (ADS)

Li, Liangliang; Huang, Yu; Chen, Goong; Huang, Tingwen

If a second order linear hyperbolic partial differential equation in one-space dimension can be factorized as a product of two first order operators and if the two first order operators commute, with one boundary condition being the van der Pol type and the other being linear, one can establish the occurrence of chaos when the parameters enter a certain regime [Chen et al., 2014]. However, if the commutativity of the two first order operators fails to hold, then the treatment in [Chen et al., 2014] no longer works and significant new challenges arise in determining nonlinear boundary conditions that engenders chaos. In this paper, we show that by incorporating a linear memory effect, a nonlinear van der Pol boundary condition can cause chaotic oscillations when the parameter enters a certain regime. Numerical simulations illustrating chaotic oscillations are also presented.

On the lagrangian 1-form structure of the hyperbolic calogero-moser system

NASA Astrophysics Data System (ADS)

Jairuk, Umpon; Tanasittikosol, Monsit; Yoo-Kong, Sikarin

2017-06-01

In this work, we present the Lagrangian 1-form structure of the hyperbolic Calogero-Moser system in both discrete-time level and continuous-time level. The discrete-time hyperbolic Calogero-Moser system is obtained by considering pole reduction of the semi-discrete Kadomtsev-Petviashvili (KP) equation. Furthermore, it is shown that the hyperbolic Calogero-Moser system possesses the key relation, known as the discrete-time closure relation. This relation is a consequence of the compatibility property of the temporal Lax matrices. The continuous-time hierarchy of the hyperbolic Calogero-Moser system is obtained by taking two successive continuum limits, namely, the skewed limit and full limit. With these successive limits, the continuous-time closure relation is also obtained and is shown to hold at the continuous level.

Synchronization of relativistic particles in the hyperbolic Kuramoto model

NASA Astrophysics Data System (ADS)

Ritchie, Louis M.; Lohe, M. A.; Williams, Anthony G.

2018-05-01

We formulate a noncompact version of the Kuramoto model by replacing the invariance group SO(2) of the plane rotations by the noncompact group SO(1, 1). The N equations of the system are expressed in terms of hyperbolic angles αi and are similar to those of the Kuramoto model, except that the trigonometric functions are replaced by hyperbolic functions. Trajectories are generally unbounded, nevertheless synchronization occurs for any positive couplings κi, arbitrary positive multiplicative parameters λi and arbitrary exponents ωi. There are no critical values for the coupling constants. We measure the onset of synchronization by means of several order and disorder parameters. We show numerically and by means of exact solutions for N = 2 that solutions can develop singularities if the coupling constants are negative, or if the initial values are not suitably restricted. We describe a physical interpretation of the system as a cluster of interacting relativistic particles in 1 + 1 dimensions, subject to linear repulsive forces with space-time trajectories parametrized by the rapidity αi. The trajectories synchronize provided that the particle separations remain predominantly time-like, and the synchronized cluster can be viewed as a bound state of N relativistic particle constituents. We extend the defining equations of the system to higher dimensions by means of vector equations which are covariant with respect to SO(p, q).

A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

NASA Technical Reports Server (NTRS)

Larson, Mats G.; Barth, Timothy J.

1999-01-01

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Investigating the use of a rational Runge Kutta method for transport modelling

NASA Astrophysics Data System (ADS)

Dougherty, David E.

An unconditionally stable explicit time integrator has recently been developed for parabolic systems of equations. This rational Runge Kutta (RRK) method, proposed by Wambecq 1 and Hairer 2, has been applied by Liu et al.3 to linear heat conduction problems in a time-partitioned solution context. An important practical question is whether the method has application for the solution of (nearly) hyperbolic equations as well. In this paper the RRK method is applied to a nonlinear heat conduction problem, the advection-diffusion equation, and the hyperbolic Buckley-Leverett problem. The method is, indeed, found to be unconditionally stable for the linear heat conduction problem and performs satisfactorily for the nonlinear heat flow case. A heuristic limitation on the utility of RRK for the advection-diffusion equation arises in the Courant number; for the second-order accurate one-step two-stage RRK method, a limiting Courant number of 2 applies. First order upwinding is not as effective when used with RRK as with Euler one-step methods. The method is found to perform poorly for the Buckley-Leverett problem.

Discounting of reward sequences: a test of competing formal models of hyperbolic discounting

PubMed Central

Zarr, Noah; Alexander, William H.; Brown, Joshua W.

2014-01-01

Humans are known to discount future rewards hyperbolically in time. Nevertheless, a formal recursive model of hyperbolic discounting has been elusive until recently, with the introduction of the hyperbolically discounted temporal difference (HDTD) model. Prior to that, models of learning (especially reinforcement learning) have relied on exponential discounting, which generally provides poorer fits to behavioral data. Recently, it has been shown that hyperbolic discounting can also be approximated by a summed distribution of exponentially discounted values, instantiated in the μAgents model. The HDTD model and the μAgents model differ in one key respect, namely how they treat sequences of rewards. The μAgents model is a particular implementation of a Parallel discounting model, which values sequences based on the summed value of the individual rewards whereas the HDTD model contains a non-linear interaction. To discriminate among these models, we observed how subjects discounted a sequence of three rewards, and then we tested how well each candidate model fit the subject data. The results show that the Parallel model generally provides a better fit to the human data. PMID:24639662

Dynamics and circuit of a chaotic system with a curve of equilibrium points

NASA Astrophysics Data System (ADS)

Pham, Viet-Thanh; Volos, Christos; Kapitaniak, Tomasz; Jafari, Sajad; Wang, Xiong

2018-03-01

Although chaotic systems have been intensively studied since the 1960s, new systems with mysterious features are still of interest. A novel chaotic system including hyperbolic functions is proposed in this work. Especially, the system has an infinite number of equilibrium points. Dynamics of the system are investigated by using non-linear tools such as phase portrait, bifurcation diagram, and Lyapunov exponent. It is interesting that the system can display coexisting chaotic attractors. An electronic circuit for realising the chaotic system has been implemented. Experimental results show a good agreement with theoretical ones.

Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis

ERIC Educational Resources Information Center

Jeffrey, Alan

1971-01-01

The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)

An approximation theory for nonlinear partial differential equations with applications to identification and control

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1982-01-01

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

The lifespan of 3D radial solutions to the non-isentropic relativistic Euler equations

NASA Astrophysics Data System (ADS)

Wei, Changhua

2017-10-01

This paper investigates the lower bound of the lifespan of three-dimensional spherically symmetric solutions to the non-isentropic relativistic Euler equations, when the initial data are prescribed as a small perturbation with compact support to a constant state. Based on the structure of the hyperbolic system, we show the almost global existence of the smooth solutions to Eulerian flows (polytropic gases and generalized Chaplygin gases) with genuinely nonlinear characteristics. While for the Eulerian flows (Chaplygin gas and stiff matter) with mild linearly degenerate characteristics, we show the global existence of the radial solutions, moreover, for the non-strictly hyperbolic system (pressureless perfect fluid) satisfying the mild linearly degenerate condition, we prove the blowup phenomenon of the radial solutions and show that the lifespan of the solutions is of order O(ɛ ^{-1}), where ɛ denotes the width of the perturbation. This work can be seen as a complement of our work (Lei and Wei in Math Ann 367:1363-1401, 2017) for relativistic Chaplygin gas and can also be seen as a generalization of the classical Eulerian fluids (Godin in Arch Ration Mech Anal 177:497-511, 2005, J Math Pures Appl 87:91-117, 2007) to the relativistic Eulerian fluids.

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

An instability of hyperbolic space under the Yang-Mills flow

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

Gegenberg, Jack; Day, Andrew C.; Liu, Haitao

2014-04-15

We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature configurations, for which the spin connection has zero torsion and the associated Riemannian geometry is one of constant curvature. We analytically solve the linearized flow equations for a large class of perturbations to the fixed point corresponding to hyperbolic 3-space. These can be expressed as a linear superposition of distinct modes, some of which are exponentially growing along the flow. The growing modes imply the divergence ofmore » the (gauge invariant) perturbative torsion for a wide class of initial data, indicating an instability of the background geometry that we confirm with numeric simulations in the partially compactified case. There are stable modes with zero torsion, but all the unstable modes are torsion-full. This leads us to speculate that the instability is induced by the torsion degrees of freedom present in the Yang-Mills flow.« less

A priori error estimates for an hp-version of the discontinuous Galerkin method for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Bey, Kim S.; Oden, J. Tinsley

1993-01-01

A priori error estimates are derived for hp-versions of the finite element method for discontinuous Galerkin approximations of a model class of linear, scalar, first-order hyperbolic conservation laws. These estimates are derived in a mesh dependent norm in which the coefficients depend upon both the local mesh size h(sub K) and a number p(sub k) which can be identified with the spectral order of the local approximations over each element.

Utilizing a Coupled Nonlinear Schrödinger Model to Solve the Linear Modal Problem for Stratified Flows

NASA Astrophysics Data System (ADS)

Liu, Tianyang; Chan, Hiu Ning; Grimshaw, Roger; Chow, Kwok Wing

2017-11-01

The spatial structure of small disturbances in stratified flows without background shear, usually named the `Taylor-Goldstein equation', is studied by employing the Boussinesq approximation (variation in density ignored except in the buoyancy). Analytical solutions are derived for special wavenumbers when the Brunt-Väisälä frequency is quadratic in hyperbolic secant, by comparison with coupled systems of nonlinear Schrödinger equations intensively studied in the literature. Cases of coupled Schrödinger equations with four, five and six components are utilized as concrete examples. Dispersion curves for arbitrary wavenumbers are obtained numerically. The computations of the group velocity, second harmonic, induced mean flow, and the second derivative of the angular frequency can all be facilitated by these exact linear eigenfunctions of the Taylor-Goldstein equation in terms of hyperbolic function, leading to a cubic Schrödinger equation for the evolution of a wavepacket. The occurrence of internal rogue waves can be predicted if the dispersion and cubic nonlinearity terms of the Schrödinger equations are of the same sign. Partial financial support has been provided by the Research Grants Council contract HKU 17200815.

An Obstruction to the Integrability of a Class of Non-linear Wave Equations by 1-Stable Cartan Characteristics

NASA Astrophysics Data System (ADS)

Fackerell, E. D.; Hartley, D.; Tucker, R. W.

We examine in detail the Cauchy problem for a class of non-linear hyperbolic equations in two independent variables. This class is motivated by the analysis of the dynamics of a line of non-linearly coupled particles by Fermi, Pasta, and Ulam and extends the recent investigation of this problem by Gardner and Kamran. We find conditions for the existence of a 1-stable Cartan characteristic of a Pfaffian exterior differential system whose integral curves provide a solution to the Cauchy problem. The same obstruction to involution is exposed in Darboux's method of integration and the two approaches are compared. A class of particular solutions to the obstruction is constructed.

The Linear Quadratic Optimal Control Problem for Infinite Dimensional Systems with Unbounded Input and Output Operators.

DTIC Science & Technology

1984-01-01

5.5) respectively (5.3) and (5.8) which means that u(t) - 0 respectively v(t) - 0 for t > o. The evolution of the systems (5.1) and (5.3) in terms ...input/output delays; and b) the general theory is presented in such a way that it applies to both . . ... ..- Lr parabolic and hyperbolic I P9es as...particular emphasis is placed on the development of the duality theory by means of two different state concepts. The resulting evolution equations

Hyperbolic metamaterials: Novel physics and applications

NASA Astrophysics Data System (ADS)

Smolyaninov, Igor I.; Smolyaninova, Vera N.

2017-10-01

Hyperbolic metamaterials were originally introduced to overcome the diffraction limit of optical imaging. Soon thereafter it was realized that hyperbolic metamaterials demonstrate a number of novel phenomena resulting from the broadband singular behavior of their density of photonic states. These novel phenomena and applications include super resolution imaging, new stealth technologies, enhanced quantum-electrodynamic effects, thermal hyperconductivity, superconductivity, and interesting gravitation theory analogues. Here we briefly review typical material systems, which exhibit hyperbolic behavior and outline important novel applications of hyperbolic metamaterials. In particular, we will describe recent imaging experiments with plasmonic metamaterials and novel VCSEL geometries, in which the Bragg mirrors may be engineered in such a way that they exhibit hyperbolic metamaterial properties in the long wavelength infrared range, so that they may be used to efficiently remove excess heat from the laser cavity. We will also discuss potential applications of three-dimensional self-assembled photonic hypercrystals, which are based on cobalt ferrofluids in external magnetic field. This system bypasses 3D nanofabrication issues, which typically limit metamaterial applications. Photonic hypercrystals combine the most interesting features of hyperbolic metamaterials and photonic crystals.

[Hyperbolic growth of marine and continental biodiversity through the phanerozoic and community evolution].

PubMed

Markov, A V; Korotaev, A V

2008-01-01

Among diverse models that are used to describe and interpret the changes in global biodiversity through the Phanerozoic, the exponential and logistic models (traditionally used in population biology) are the most popular. As we have recently demonstrated (Markov, Korotayev, 2007), the growth of the Phanerozoic marine biodiversity at genus level correlates better with the hyperbolic model (widely used in demography and macrosociology). Here we show that the hyperbolic model is also applicable to the Phanerozoic continental biota at genus and family levels, and to the marine biota at species, genus, and family levels. There are many common features in the evolutionary dynamics of the marine and continental biotas that imply similarity and common nature of the factors and mechanisms underlying the hyperbolic growth. Both marine and continental biotas are characterized by continuous growth of the mean longevity of taxa, by decreasing extinction and origination rates, by similar pattern of replacement of dominant groups, by stepwise accumulation of evolutionary stable, adaptable and "physiologically buffered" taxa with effective mechanisms of parental care, protection of early developmental stages, etc. At the beginning of the development of continental biota, the observed taxonomic diversity was substantially lower than that predicted by the hyperbolic model. We suggest that this is due, firstly, to the fact that, during the earliest stages of the continental biota evolution, the groups that are not preserved in the fossil record (such as soil bacteria, unicellular algae, lichens, etc.) played a fundamental role, and secondly, to the fact that the continental biota initially formed as a marginal portion of the marine biota, rather than a separate system. The hyperbolic dynamics is most prominent when both marine and continental biotas are considered together. This fact can be interpreted as a proof of the integrated nature of the biosphere. In the macrosociological models, the hyperbolic pattern of the world population growth arises from a non-linear second-order positive feedback between the demographic growth and technological development (more people - more potential inventors - faster technological growth - the carrying capacity of the Earth grows faster - faster population growth - more people - more potential inventors, and so on). Based on the analogy with macrosociological models and diverse paleontological data, we suggest that the hyperbolic character of biodiversity growth can be similarly accounted for by a non-linear second-order positive feedback between the diversity growth and community structure complexity. The feedback can work via two parallel mechanisms: 1) decreasing extinction rate (more taxa- higher alpha diversity, or mean number of taxa in a community - communities become more complex and stable - extinction rate decreases - more taxa, and so on) and 2) increasing origination rate (new taxa facilitate niche construction; newly formed niches can be occupied by the next "generation" of taxa). The latter possibility makes the mechanisms underlying the hyperbolic growth of biodiversity and human population even more similar, because the total ecospace of the biota is analogous to the "carrying capacity of the Earth" in demography. As far as new species can increase ecospace and facilitate opportunities for additional species entering the community, they are analogous to the "inventors" of the demographic models whose inventions increase the carrying capacity of the Earth. The hyperbolic growth of the Phanerozoic biodiverstiy suggests that "cooperative" interactions between taxa can play an important role in evolution, along with generally accepted competitive interactions. Due to this "cooperation", the evolution of biodiversity acquires some features of a self-accelerating process. Macroevolutionary "cooperation" reveals itself in: 1) increasing stability of communities that arises from alpha diversity growth; 2) ability of species to facilitate opportunities for additional species entering the community.

Parallel High Order Accuracy Methods Applied to Non-Linear Hyperbolic Equations and to Problems in Materials Sciences

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

Jan Hesthaven

2012-02-06

Final report for DOE Contract DE-FG02-98ER25346 entitled Parallel High Order Accuracy Methods Applied to Non-Linear Hyperbolic Equations and to Problems in Materials Sciences. Principal Investigator Jan S. Hesthaven Division of Applied Mathematics Brown University, Box F Providence, RI 02912 Jan.Hesthaven@Brown.edu February 6, 2012 Note: This grant was originally awarded to Professor David Gottlieb and the majority of the work envisioned reflects his original ideas. However, when Prof Gottlieb passed away in December 2008, Professor Hesthaven took over as PI to ensure proper mentoring of students and postdoctoral researchers already involved in the project. This unusual circumstance has naturally impacted themore » project and its timeline. However, as the report reflects, the planned work has been accomplished and some activities beyond the original scope have been pursued with success. Project overview and main results The effort in this project focuses on the development of high order accurate computational methods for the solution of hyperbolic equations with application to problems with strong shocks. While the methods are general, emphasis is on applications to gas dynamics with strong shocks.« less

Multidimensional Riemann problem with self-similar internal structure - part III - a multidimensional analogue of the HLLI Riemann solver for conservative hyperbolic systems

NASA Astrophysics Data System (ADS)

Balsara, Dinshaw S.; Nkonga, Boniface

2017-10-01

Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The fastest way of endowing such sub-structure consists of making a multidimensional extension of the HLLI Riemann solver for hyperbolic conservation laws. Presenting such a multidimensional analogue of the HLLI Riemann solver with linear sub-structure for use on structured meshes is the goal of this work. The multidimensional MuSIC Riemann solver documented here is universal in the sense that it can be applied to any hyperbolic conservation law. The multidimensional Riemann solver is made to be consistent with constraints that emerge naturally from the Galerkin projection of the self-similar states within the wave model. When the full eigenstructure in both directions is used in the present Riemann solver, it becomes a complete Riemann solver in a multidimensional sense. I.e., all the intermediate waves are represented in the multidimensional wave model. The work also presents, for the very first time, an important analysis of the dissipation characteristics of multidimensional Riemann solvers. The present Riemann solver results in the most efficient implementation of a multidimensional Riemann solver with sub-structure. Because it preserves stationary linearly degenerate waves, it might also help with well-balancing. Implementation-related details are presented in pointwise fashion for the one-dimensional HLLI Riemann solver as well as the multidimensional MuSIC Riemann solver.

Representation of the contextual statistical model by hyperbolic amplitudes

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

Khrennikov, Andrei

We continue the development of a so-called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric cos-interference, there exist contexts producing the hyperbolic cos-interference. Starting with the corresponding interference formula of total probability we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of the Hilbert space. There is obtained a hyperbolic Born's rule. Incompatible observables are represented by noncommutative operators. This paper can be considered as the first step towards hyperbolic quantum probability. Wemore » also discuss possibilities of experimental verification of hyperbolic quantum mechanics: in physics of elementary particles, string theory as well as in experiments with nonphysical systems, e.g., in psychology, cognitive sciences, and economy.« less

Representation of the contextual statistical model by hyperbolic amplitudes

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

2005-06-01

We continue the development of a so-called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric cos-interference, there exist contexts producing the hyperbolic cos-interference. Starting with the corresponding interference formula of total probability we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of the Hilbert space. There is obtained a hyperbolic Born's rule. Incompatible observables are represented by noncommutative operators. This paper can be considered as the first step towards hyperbolic quantum probability. We also discuss possibilities of experimental verification of hyperbolic quantum mechanics: in physics of elementary particles, string theory as well as in experiments with nonphysical systems, e.g., in psychology, cognitive sciences, and economy.

Convergence results for pseudospectral approximations of hyperbolic systems by a penalty type boundary treatment

NASA Technical Reports Server (NTRS)

Funaro, Daniele; Gottlieb, David

1989-01-01

A new method of imposing boundary conditions in the pseudospectral approximation of hyperbolic systems of equations is proposed. It is suggested to collocate the equations, not only at the inner grid points, but also at the boundary points and use the boundary conditions as penalty terms. In the pseudo-spectral Legrendre method with the new boundary treatment, a stability analysis for the case of a constant coefficient hyperbolic system is presented and error estimates are derived.

Doubly stratified MHD tangent hyperbolic nanofluid flow due to permeable stretched cylinder

NASA Astrophysics Data System (ADS)

Nagendramma, V.; Leelarathnam, A.; Raju, C. S. K.; Shehzad, S. A.; Hussain, T.

2018-06-01

An investigation is exhibited to analyze the presence of heat source and sink in doubly stratified MHD incompressible tangent hyperbolic fluid due to stretching of cylinder embedded in porous space under nanoparticles. To develop the mathematical model of tangent hyperbolic nanofluid, movement of Brownian and thermophoretic are accounted. The established equations of continuity, momentum, thermal and solutal boundary layers are reassembled into sets of non-linear expressions. These assembled expressions are executed with the help of Runge-Kutta scheme with MATLAB. The impacts of sundry parameters are illustrated graphically and the engineering interest physical quantities like skin friction, Nusselt and Sherwood number are examined by computing numerical values. It is clear that the power-law index parameter and curvature parameter shows favorable effect on momentum boundary layer thickness whereas Weissennberg number reveals inimical influence.

Hyperbolicity measures democracy in real-world networks

NASA Astrophysics Data System (ADS)

Borassi, Michele; Chessa, Alessandro; Caldarelli, Guido

2015-09-01

In this work, we analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. We provide two improvements in our understanding of this quantity: first of all, in our interpretation, a hyperbolic network is "aristocratic", since few elements "connect" the system, while a non-hyperbolic network has a more "democratic" structure with a larger number of crucial elements. The second contribution is the introduction of the average hyperbolicity of the neighbors of a given node. Through this definition, we outline an "influence area" for the vertices in the graph. We show that in real networks the influence area of the highest degree vertex is small in what we define "local" networks (i.e., social or peer-to-peer networks), and large in "global" networks (i.e., power grid, metabolic networks, or autonomous system networks).

On the boundary treatment in spectral methods for hyperbolic systems

NASA Technical Reports Server (NTRS)

Canuto, C.; Quarteroni, A.

1986-01-01

Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions are clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100.

On the boundary treatment in spectral methods for hyperbolic systems

NASA Technical Reports Server (NTRS)

Canuto, Claudio; Quarteroni, Alfio

1987-01-01

Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions is clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100.

Stability Analysis of Finite Difference Approximations to Hyperbolic Systems,and Problems in Applied and Computational Matrix and Operator Theory

DTIC Science & Technology

1990-12-07

Fundaqao Calouste Gulbenkian, Instituto Gulbenkian de Ci~ncia, Centro de C6lculo Cientifico , Coimbra, 1973. 28, Dirac, P. A. M., Spinors in Hilbert Space...Office of Scientific Research grants 1965 Mathematical Association of America Editorial Prize for the article entitled: "Linear Transformations on...matrices" 1966 L.R. Ford Memorial Prize awarded by the Mathematical Association of America for the article , "Permanents" 1989 Outstanding Computer

Well-posedness, linear perturbations, and mass conservation for the axisymmetric Einstein equations

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

Dain, Sergio; Ortiz, Omar E.; Facultad de Matematica, Astronomia y Fisica, FaMAF, Universidad Nacional de Cordoba, Instituto de Fisica Enrique Gaviola, IFEG, CONICET, Ciudad Universitaria

2010-02-15

For axially symmetric solutions of Einstein equations there exists a gauge which has the remarkable property that the total mass can be written as a conserved, positive definite, integral on the spacelike slices. The mass integral provides a nonlinear control of the variables along the whole evolution. In this gauge, Einstein equations reduce to a coupled hyperbolic-elliptic system which is formally singular at the axis. As a first step in analyzing this system of equations we study linear perturbations on a flat background. We prove that the linear equations reduce to a very simple system of equations which provide, thoughmore » the mass formula, useful insight into the structure of the full system. However, the singular behavior of the coefficients at the axis makes the study of this linear system difficult from the analytical point of view. In order to understand the behavior of the solutions, we study the numerical evolution of them. We provide strong numerical evidence that the system is well-posed and that its solutions have the expected behavior. Finally, this linear system allows us to formulate a model problem which is physically interesting in itself, since it is connected with the linear stability of black hole solutions in axial symmetry. This model can contribute significantly to solve the nonlinear problem and at the same time it appears to be tractable.« less

Second- and third-order upwind difference schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Yang, J. Y.

1984-01-01

Second- and third-order two time-level five-point explicit upwind-difference schemes are described for the numerical solution of hyperbolic systems of conservation laws and applied to the Euler equations of inviscid gas dynamics. Nonliner smoothing techniques are used to make the schemes total variation diminishing. In the method both hyperbolicity and conservation properties of the hyperbolic conservation laws are combined in a very natural way by introducing a normalized Jacobian matrix of the hyperbolic system. Entropy satisfying shock transition operators which are consistent with the upwind differencing are locally introduced when transonic shock transition is detected. Schemes thus constructed are suitable for shockcapturing calculations. The stability and the global order of accuracy of the proposed schemes are examined. Numerical experiments for the inviscid Burgers equation and the compressible Euler equations in one and two space dimensions involving various situations of aerodynamic interest are included and compared.

Plasmons and Polaritons in Low Dimensional Systems

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan

Nearly everything relies on the electromagnetic (EM) force to be in its current form. Therefore, light-matter interaction is both a fundamental and a practical subject in physics. Focusing on the electromagnetic field, the matter degrees of freedom can be encoded into its response to the EM field in the form of charge density and urrent. Reshaped by the EM response, the photons in condensed matter systems appear as various collective modes. In this doctoral dissertation, I present our investigation of the linear and nonlinear EM response theory especially in the hydrodynamic regime of electron systems. Electrons in pristine solids behave as a hydrodynamic fluid in a certain range of temperatures and frequencies. We show that the response of such a fluid to electromagnetic field is different from what is predicted by the usual kinetic theory. Certain aspects of this response are universal, for example, a direct relation between the linear and second-order nonlinear optical conductivities. Discovery of this relation enriches our understanding of the light-matter interaction in diverse electron systems and new materials such as graphene. Subsequently, I study the properties of the charged collective modes, the plasmons and demons in 2D Dirac fluids, e.g., the electron-hole system in graphene. Under non-equilibrium situation, the amplitudes of these collective modes could possibly grow due to an effect of adiabatic amplification. I also present our study of the hyperbolic polaritons, the EM modes in hyperbolic materials. When confined in cavities, they develop isolated eigen modes which could be efficiently predicted by applying semi-classical quantization rules to fictitious particles. We demonstrate this Hamiltonian Optics analytically for cavities of spheroidal shapes, and predict novel geometric patterns of the electric field distribution due to classical periodic orbits.

A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1992-01-01

The present treatment of elliptic regions via hyperbolic flux-splitting and high order methods proposes a flux splitting in which the corresponding Jacobians have real and positive/negative eigenvalues. While resembling the flux splitting used in hyperbolic systems, the present generalization of such splitting to elliptic regions allows the handling of mixed-type systems in a unified and heuristically stable fashion. The van der Waals fluid-dynamics equation is used. Convergence with good resolution to weak solutions for various Riemann problems are observed.

Integrability and Linearizability of the Lotka-Volterra System with a Saddle Point with Rational Hyperbolicity Ratio

NASA Astrophysics Data System (ADS)

Gravel, Simon; Thibault, Pierre

In this paper, we consider normalizability, integrability and linearizability properties of the Lotka-Volterra system in the neighborhood of a singular point with eigenvalues 1 and - λ. The results are obtained by generalizing and expanding two methods already known: the power expansion of the first integral or of the linearizing transformation and the transformation of the saddle into a node. With these methods we find conditions that are valid for λ∈ R+ or λ∈ Q. These conditions will allow us to find all the integrable and linearizable systems for λ= {p}/{2} and {2}/{p} with p∈ N+.

Chimeras and clusters in networks of hyperbolic chaotic oscillators

NASA Astrophysics Data System (ADS)

Cano, A. V.; Cosenza, M. G.

2017-03-01

We show that chimera states, where differentiated subsets of synchronized and desynchronized dynamical elements coexist, can emerge in networks of hyperbolic chaotic oscillators subject to global interactions. As local dynamics we employ Lozi maps, which possess hyperbolic chaotic attractors. We consider a globally coupled system of these maps and use two statistical quantities to describe its collective behavior: the average fraction of elements belonging to clusters and the average standard deviation of state variables. Chimera states, clusters, complete synchronization, and incoherence are thus characterized on the space of parameters of the system. We find that chimera states are related to the formation of clusters in the system. In addition, we show that chimera states arise for a sufficiently long range of interactions in nonlocally coupled networks of these maps. Our results reveal that, under some circumstances, hyperbolicity does not impede the formation of chimera states in networks of coupled chaotic systems, as it had been previously hypothesized.

Links between quantum physics and thought.

PubMed

Robson, Barry

2009-01-01

Quantum mechanics (QM) provides a variety of ideas that can assist in developing Artificial Intelligence for healthcare, and opens the possibility of developing a unified system of Best Practice for inference that will embrace both QM and classical inference. Of particular interest is inference in the hyperbolic-complex plane, the counterpart of the normal i-complex plane of basic QM. There are two reasons. First, QM appears to rotate from i-complex Hilbert space to hyperbolic-complex descriptions when observations are made on wave functions as particles, yielding classical results, and classical laws of probability manipulation (e.g. the law of composition of probabilities) then hold, whereas in the i-complex plane they do not. Second, i-complex Hilbert space is not the whole story in physics. Hyperbolic complex planes arise in extension from the Dirac-Clifford calculus to particle physics, in relativistic correction thereby, and in regard to spinors and twisters. Generalization of these forms resemble grammatical constructions and promote the idea that probability-weighted algebraic elements can be used to hold dimensions of syntactic and semantic meaning. It is also starting to look as though when a solution is reached by an inference system in the hyperbolic-complex, the hyperbolic-imaginary values disappear, while conversely hyperbolic-imaginary values are associated with the un-queried state of a system and goal seeking behavior.

Where the Solar system meets the solar neighbourhood: patterns in the distribution of radiants of observed hyperbolic minor bodies

NASA Astrophysics Data System (ADS)

de la Fuente Marcos, Carlos; de la Fuente Marcos, Raúl; Aarseth, Sverre J.

2018-05-01

Observed hyperbolic minor bodies might have an interstellar origin, but they can be natives of the Solar system as well. Fly-bys with the known planets or the Sun may result in the hyperbolic ejection of an originally bound minor body; in addition, members of the Oort cloud could be forced to follow inbound hyperbolic paths as a result of secular perturbations induced by the Galactic disc or, less frequently, due to impulsive interactions with passing stars. These four processes must leave distinctive signatures in the distribution of radiants of observed hyperbolic objects, both in terms of coordinates and velocity. Here, we perform a systematic numerical exploration of the past orbital evolution of known hyperbolic minor bodies using a full N-body approach and statistical analyses to study their radiants. Our results confirm the theoretical expectations that strong anisotropies are present in the data. We also identify a statistically significant overdensity of high-speed radiants towards the constellation of Gemini that could be due to the closest and most recent known fly-by of a star to the Solar system, that of the so-called Scholz's star. In addition to and besides 1I/2017 U1 (`Oumuamua), we single out eight candidate interstellar comets based on their radiants' velocities.

Summation by parts, projections, and stability

NASA Technical Reports Server (NTRS)

Olsson, Pelle

1993-01-01

We have derived stability results for high-order finite difference approximations of mixed hyperbolic-parabolic initial-boundary value problems (IBVP). The results are obtained using summation by parts and a new way of representing general linear boundary conditions as an orthogonal projection. By slightly rearranging the analytic equations, we can prove strict stability for hyperbolic-parabolic IBVP. Furthermore, we generalize our technique so as to yield strict stability on curvilinear non-smooth domains in two space dimensions. Finally, we show how to incorporate inhomogeneous boundary data while retaining strict stability. Using the same procedure one can prove strict stability in higher dimensions as well.

Accuracy limitations of hyperbolic multilateration systems

DOT National Transportation Integrated Search

1973-03-22

The report is an analysis of the accuracy limitations of hyperbolic multilateration systems. A central result is a demonstration that the inverse of the covariance matrix for positional errors corresponds to the moment of inertia matrix of a simple m...

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.

A dimensionally split Cartesian cut cell method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Gokhale, Nandan; Nikiforakis, Nikos; Klein, Rupert

2018-07-01

We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a full description of its three-dimensional implementation in the dimensionally split framework of Klein et al. [1]. The convergence and stability of the method are proved for the one-dimensional linear advection equation, while its multi-dimensional numerical performance is investigated through the computation of solutions to a number of test problems for the linear advection and Euler equations. When compared to the cut cell flux of Klein et al., it was found that the new flux alleviates the problem of oscillatory boundary solutions produced by the former at higher Courant numbers, and also enables the computation of more accurate solutions near stagnation points. Being dimensionally split, the method is simple to implement and extends readily to multiple dimensions.

Optimal linear-quadratic control of coupled parabolic-hyperbolic PDEs

NASA Astrophysics Data System (ADS)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2017-10-01

This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear-quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ-optimal controller designed in the early portion of the paper is implemented for the original nonlinear model. Numerical simulations are performed to show the controller performances.

Symplectic evolution of Wigner functions in Markovian open systems.

PubMed

Brodier, O; Almeida, A M Ozorio de

2004-01-01

The Wigner function is known to evolve classically under the exclusive action of a quadratic Hamiltonian. If the system also interacts with the environment through Lindblad operators that are complex linear functions of position and momentum, then the general evolution is the convolution of a non-Hamiltonian classical propagation of the Wigner function with a phase space Gaussian that broadens in time. We analyze the consequences of this in the three generic cases of elliptic, hyperbolic, and parabolic Hamiltonians. The Wigner function always becomes positive in a definite time, which does not depend on the initial pure state. We observe the influence of classical dynamics and dissipation upon this threshold. We also derive an exact formula for the evolving linear entropy as the average of a narrowing Gaussian taken over a probability distribution that depends only on the initial state. This leads to a long time asymptotic formula for the growth of linear entropy. We finally discuss the possibility of recovering the initial state.

Hyperbolic chaos in the klystron-type microwave vacuum tube oscillator

NASA Astrophysics Data System (ADS)

Emel'yanov, V. V.; Kuznetsov, S. P.; Ryskin, N. M.

2010-12-01

The ring-loop oscillator consisting of two coupled klystrons which is capable of generating hyperbolic chaotic signal in the microwave band is considered. The system of delayed-differential equations describing the dynamics of the oscillator is derived. This system is further reduced to the two-dimensional return map under the assumption of the instantaneous build-up of oscillations in the cavities. The results of detailed numerical simulation for both models are presented showing that there exists large enough range of control parameters where the sustained regime corresponds to the structurally stable hyperbolic chaos.

Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds

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

Guth, Larry, E-mail: lguth@math.mit.edu; Lubotzky, Alexander, E-mail: alex.lubotzky@mail.huji.ac.il

2014-08-15

Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are low density parity check codes with linear rate and distance n{sup ε}. Their rate is evaluated via Euler characteristic arguments and their distance using Z{sub 2}-systolic geometry. This construction answers a question of Zémor [“On Cayley graphs, surface codes, and the limits of homological coding for quantum error correction,” in Proceedings of Second International Workshop on Coding and Cryptology (IWCC), Lecture Notes in Computer Science Vol. 5557 (2009), pp. 259–273], who asked whether homological codes with such parameters could exist at all.

Scalable Parallel Computation for Extended MHD Modeling of Fusion Plasmas

NASA Astrophysics Data System (ADS)

Glasser, Alan H.

2008-11-01

Parallel solution of a linear system is scalable if simultaneously doubling the number of dependent variables and the number of processors results in little or no increase in the computation time to solution. Two approaches have this property for parabolic systems: multigrid and domain decomposition. Since extended MHD is primarily a hyperbolic rather than a parabolic system, additional steps must be taken to parabolize the linear system to be solved by such a method. Such physics-based preconditioning (PBP) methods have been pioneered by Chac'on, using finite volumes for spatial discretization, multigrid for solution of the preconditioning equations, and matrix-free Newton-Krylov methods for the accurate solution of the full nonlinear preconditioned equations. The work described here is an extension of these methods using high-order spectral element methods and FETI-DP domain decomposition. Application of PBP to a flux-source representation of the physics equations is discussed. The resulting scalability will be demonstrated for simple wave and for ideal and Hall MHD waves.

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

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

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

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

The Shock and Vibration Digest. Volume 16, Number 11

DTIC Science & Technology

1984-11-01

wave [19], a secular equation for Rayleigh waves on ing, seismic risk, and related problems are discussed. the surface of an anisotropic half-space...waves in an !so- tive equation of an elastic-plastic rack medium was....... tropic linear elastic half-space with plane material used; the coefficient...pair of semi-linear hyperbolic partial differential -- " Conditions under which the equations of motion equations governing slow variations in amplitude

Infrared metamaterial by RF magnetron sputtered ZnO/Al:ZnO multilayers

NASA Astrophysics Data System (ADS)

Santiago, Kevin C.; Mundle, Rajeh; White, Curtis; Bahoura, Messaoud; Pradhan, Aswini K.

2018-03-01

Hyperbolic metamaterials create artificial anisotropy using metallic wires suspended in dielectric media or alternating layers of a metal and dielectric (Type I or Type II). In this study we fabricated ZnO/Al:ZnO (AZO) multilayers by the RF magnetron sputtering deposition technique. Our fabricated multilayers satisfy the requirements for a type II hyperbolic metamaterial. The optical response of individual AZO and ZnO films, as well as the multilayered film were investigated via UV-vis-IR transmittance and spectroscopic ellipsometry. The optical response of the multilayered system is calculated using the nonlocal-corrected Effective Medium Approximation (EMA). The spectroscopic ellipsometry data of the multilayered system was modeled using a uniaxial material model and EMA model. Both theoretical and experimental studies validate the fabricated multilayers undergo a hyperbolic transition at a wavelength of 2.2 μm. To our knowledge this is the first AZO/ZnO type II hyperbolic metamaterial system fabricated by magnetron sputtering deposition method.

A chaotic jerk system with non-hyperbolic equilibrium: Dynamics, effect of time delay and circuit realisation

NASA Astrophysics Data System (ADS)

Rajagopal, Karthikeyan; Pham, Viet-Thanh; Tahir, Fadhil Rahma; Akgul, Akif; Abdolmohammadi, Hamid Reza; Jafari, Sajad

2018-04-01

The literature on chaos has highlighted several chaotic systems with special features. In this work, a novel chaotic jerk system with non-hyperbolic equilibrium is proposed. The dynamics of this new system is revealed through equilibrium analysis, phase portrait, bifurcation diagram and Lyapunov exponents. In addition, we investigate the time-delay effects on the proposed system. Realisation of such a system is presented to verify its feasibility.

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

EPA Science Inventory

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

Computational methods for estimation of parameters in hyperbolic systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.; Murphy, K. A.

1983-01-01

Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized.

Optimal disturbance rejecting control of hyperbolic systems

NASA Technical Reports Server (NTRS)

Biswas, Saroj K.; Ahmed, N. U.

1994-01-01

Optimal regulation of hyperbolic systems in the presence of unknown disturbances is considered. Necessary conditions for determining the optimal control that tracks a desired trajectory in the presence of the worst possible perturbations are developed. The results also characterize the worst possible disturbance that the system will be able to tolerate before any degradation of the system performance. Numerical results on the control of a vibrating beam are presented.

An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Bey, Kim S.

1994-01-01

This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

An automatic multigrid method for the solution of sparse linear systems

NASA Technical Reports Server (NTRS)

Shapira, Yair; Israeli, Moshe; Sidi, Avram

1993-01-01

An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.

Existence and Stability of Viscoelastic Shock Profiles

NASA Astrophysics Data System (ADS)

Barker, Blake; Lewicka, Marta; Zumbrun, Kevin

2011-05-01

We investigate existence and stability of viscoelastic shock profiles for a class of planar models including the incompressible shear case studied by Antman and Malek-Madani. We establish that the resulting equations fall into the class of symmetrizable hyperbolic-parabolic systems, hence spectral stability implies linearized and nonlinear stability with sharp rates of decay. The new contributions are treatment of the compressible case, formulation of a rigorous nonlinear stability theory, including verification of stability of small-amplitude Lax shocks, and the systematic incorporation in our investigations of numerical Evans function computations determining stability of large-amplitude and nonclassical type shock profiles.

Hyperbolic Method for Dispersive PDEs: Same High-Order of Accuracy for Solution, Gradient, and Hessian

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Ricchiuto, Mario; Nishikawa, Hiroaki

2016-01-01

In this paper, we introduce a new hyperbolic first-order system for general dispersive partial differential equations (PDEs). We then extend the proposed system to general advection-diffusion-dispersion PDEs. We apply the fourth-order RD scheme of Ref. 1 to the proposed hyperbolic system, and solve time-dependent dispersive equations, including the classical two-soliton KdV and a dispersive shock case. We demonstrate that the predicted results, including the gradient and Hessian (second derivative), are in a very good agreement with the exact solutions. We then show that the RD scheme applied to the proposed system accurately captures dispersive shocks without numerical oscillations. We also verify that the solution, gradient and Hessian are predicted with equal order of accuracy.

Onto the stability analysis of hyperbolic secant-shaped Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Sabari, S.; Murali, R.

2018-05-01

We analyze the stability of the hyperbolic secant-shaped attractive Bose-Einstein condensate in the absence of external trapping potential. The appropriate theoretical model for the system is described by the nonlinear mean-field Gross-Pitaevskii equation with time varying two-body interaction effects. Using the variational method, the stability of the system is analyzed under the influence of time varying two-body interactions. Further we confirm that the stability of the attractive condensate increases by considering the hyperbolic secant-shape profile instead of Gaussian shape. The analytical results are compared with the numerical simulation by employing the split-step Crank-Nicholson method.

High-Order Residual-Distribution Schemes for Discontinuous Problems on Irregular Triangular Grids

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2016-01-01

In this paper, we develop second- and third-order non-oscillatory shock-capturing hyperbolic residual distribution schemes for irregular triangular grids, extending our second- and third-order schemes to discontinuous problems. We present extended first-order N- and Rusanov-scheme formulations for hyperbolic advection-diffusion system, and demonstrate that the hyperbolic diffusion term does not affect the solution of inviscid problems for vanishingly small viscous coefficient. We then propose second- and third-order blended hyperbolic residual-distribution schemes with the extended first-order Rusanov-scheme. We show that these proposed schemes are extremely accurate in predicting non-oscillatory solutions for discontinuous problems. We also propose a characteristics-based nonlinear wave sensor for accurately detecting shocks, compression, and expansion regions. Using this proposed sensor, we demonstrate that the developed hyperbolic blended schemes do not produce entropy-violating solutions (unphysical stocks). We then verify the design order of accuracy of these blended schemes on irregular triangular grids.

Some remarks on the current status of the control theory of single space dimension hyperbolic systems

NASA Technical Reports Server (NTRS)

Russell, D. L.

1983-01-01

Various aspects of the control theory of hyperbolic systems, including controllability, stabilization, control canonical form theory, etc., are reviewed. To allow a unified and not excessively technical treatment, attention is restricted to the case of a single space variable. A newly developed procedure of canonical augmentation is discussed.

Estimation of coefficients and boundary parameters in hyperbolic systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Murphy, K. A.

1984-01-01

Semi-discrete Galerkin approximation schemes are considered in connection with inverse problems for the estimation of spatially varying coefficients and boundary condition parameters in second order hyperbolic systems typical of those arising in 1-D surface seismic problems. Spline based algorithms are proposed for which theoretical convergence results along with a representative sample of numerical findings are given.

Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries

NASA Astrophysics Data System (ADS)

Startsev, Sergey Ya.

2017-05-01

The paper is devoted to hyperbolic (generally speaking, non-Lagrangian and nonlinear) partial differential systems possessing a full set of differential operators that map any function of one independent variable into a symmetry of the corresponding system. We demonstrate that a system has the above property if and only if this system admits a full set of formal integrals (i.e., differential operators which map symmetries into integrals of the system). As a consequence, such systems possess both direct and inverse Noether operators (in the terminology of a work by B. Fuchssteiner and A.S. Fokas who have used these terms for operators that map cosymmetries into symmetries and perform transformations in the opposite direction). Systems admitting Noether operators are not exhausted by Euler-Lagrange systems and the systems with formal integrals. In particular, a hyperbolic system admits an inverse Noether operator if a differential substitution maps this system into a system possessing an inverse Noether operator.

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter Systems

NASA Technical Reports Server (NTRS)

Nguyen, Nhan

2006-01-01

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

Transformations of asymptotically AdS hyperbolic initial data and associated geometric inequalities

NASA Astrophysics Data System (ADS)

Cha, Ye Sle; Khuri, Marcus

2018-01-01

We construct transformations which take asymptotically AdS hyperbolic initial data into asymptotically flat initial data, and which preserve relevant physical quantities. This is used to derive geometric inequalities in the asymptotically AdS hyperbolic setting from counterparts in the asymptotically flat realm, whenever a geometrically motivated system of elliptic equations admits a solution. The inequalities treated here relate mass, angular momentum, charge, and horizon area. Furthermore, new mass-angular momentum inequalities in this setting are conjectured and discussed.

Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change

DOE PAGES

Nourgaliev, R.; Luo, H.; Weston, B.; ...

2015-11-11

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method’s capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing (AM). We focus on the method’s accuracy (in both space and time), as wellmore » as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver.« less

On the coupling of hyperbolic and parabolic systems: Analytical and numerical approach

NASA Technical Reports Server (NTRS)

Gastaldi, Fabio; Quarteroni, Alfio

1988-01-01

The coupling of hyperbolic and parabolic systems is discussed in a domain Omega divided into two distinct subdomains omega(+) and omega(-). The main concern is to find the proper interface conditions to be fulfilled at the surface separating the two domains. Next, they are used in the numerical approximation of the problem. The justification of the interface conditions is based on a singular perturbation analysis, i.e., the hyperbolic system is rendered parabolic by adding a small artifical viscosity. As this goes to zero, the coupled parabolic-parabolic problem degenerates into the original one, yielding some conditions at the interface. These are taken as interface conditions for the hyperbolic-parabolic problem. Actually, two alternative sets of interface conditions are discussed according to whether the regularization procedure is variational or nonvariational. It is shown how these conditions can be used in the frame of a numerical approximation to the given problem. Furthermore, a method of resolution is discussed which alternates the resolution of the hyperbolic problem within omega(-) and of the parabolic one within omega(+). The spectral collocation method is proposed, as an example of space discretization (different methods could be used as well); both explicit and implicit time-advancing schemes are considered. The present study is a preliminary step toward the analysis of the coupling between Euler and Navier-Stokes equations for compressible flows.

Comparing the Performance of Hyperbolic and Circular Rod Quadrupole Mass Spectrometers with Applied Higher Order Auxiliary Excitation

NASA Technical Reports Server (NTRS)

Gershman, D.J.; Block, B.P.; Rubin, M.; Benna, M.; Mahaffy, P. R.; Zurbuchen, T. H.

2012-01-01

This work applies higher order auxiliary excitation techniques to two types of quadrupole mass spectrometers (QMSs): commercial systems and spaceborne instruments. The operational settings of a circular rod geometry commercial system and an engineering test-bed for a hyperbolic rod geometry spaceborne instrument were matched, with the relative performance of each sensor characterized with and without applied excitation using isotopic measurements of Kr+. Each instrument was operated at the limit of the test electronics to determine the effect of auxiliary excitation on extending instrument capabilities. For the circular rod sensor, with applied excitation, a doubling of the mass resolution at 1% of peak transmission resulted from the elimination of the low-mass side peak tail typical of such rod geometries. The mass peak stability and ion rejection efficiency were also increased by factors of 2 and 10, respectively, with voltage scan lines passing through the center of stability islands formed from auxiliary excitation. Auxiliary excitation also resulted in factors of 6 and 2 in peak stability and ion rejection efficiency, respectively, for the hyperbolic rod sensor. These results not only have significant implications for the use of circular rod quadrupoles with applied excitation as a suitable replacement for traditional hyperbolic rod sensors, but also for extending the capabilities of existing hyperbolic rod QMSs for the next generation of spaceborne instruments and low-mass commercial systems.

Algorithm Development and Application of High Order Numerical Methods for Shocked and Rapid Changing Solutions

DTIC Science & Technology

2007-12-06

high order well-balanced schemes to a class of hyperbolic systems with source terms, Boletin de la Sociedad Espanola de Matematica Aplicada, v34 (2006...schemes to a class of hyperbolic systems with source terms, Boletin de la Sociedad Espanola de Matematica Aplicada, v34 (2006), pp.69-80. 39. Y. Xu and C.-W

Computation of Quasi-Periodic Normally Hyperbolic Invariant Tori: Algorithms, Numerical Explorations and Mechanisms of Breakdown

NASA Astrophysics Data System (ADS)

Canadell, Marta; Haro, Àlex

2017-12-01

We present several algorithms for computing normally hyperbolic invariant tori carrying quasi-periodic motion of a fixed frequency in families of dynamical systems. The algorithms are based on a KAM scheme presented in Canadell and Haro (J Nonlinear Sci, 2016. doi: 10.1007/s00332-017-9389-y), to find the parameterization of the torus with prescribed dynamics by detuning parameters of the model. The algorithms use different hyperbolicity and reducibility properties and, in particular, compute also the invariant bundles and Floquet transformations. We implement these methods in several 2-parameter families of dynamical systems, to compute quasi-periodic arcs, that is, the parameters for which 1D normally hyperbolic invariant tori with a given fixed frequency do exist. The implementation lets us to perform the continuations up to the tip of the quasi-periodic arcs, for which the invariant curves break down. Three different mechanisms of breakdown are analyzed, using several observables, leading to several conjectures.

Handy elementary algebraic properties of the geometry of entanglement

NASA Astrophysics Data System (ADS)

Blair, Howard A.; Alsing, Paul M.

2013-05-01

The space of separable states of a quantum system is a hyperbolic surface in a high dimensional linear space, which we call the separation surface, within the exponentially high dimensional linear space containing the quantum states of an n component multipartite quantum system. A vector in the linear space is representable as an n-dimensional hypermatrix with respect to bases of the component linear spaces. A vector will be on the separation surface iff every determinant of every 2-dimensional, 2-by-2 submatrix of the hypermatrix vanishes. This highly rigid constraint can be tested merely in time asymptotically proportional to d, where d is the dimension of the state space of the system due to the extreme interdependence of the 2-by-2 submatrices. The constraint on 2-by-2 determinants entails an elementary closed formformula for a parametric characterization of the entire separation surface with d-1 parameters in the char- acterization. The state of a factor of a partially separable state can be calculated in time asymptotically proportional to the dimension of the state space of the component. If all components of the system have approximately the same dimension, the time complexity of calculating a component state as a function of the parameters is asymptotically pro- portional to the time required to sort the basis. Metric-based entanglement measures of pure states are characterized in terms of the separation hypersurface.

Elliptical, parabolic, and hyperbolic exchanges of energy in drag reducing plane Couette flows

NASA Astrophysics Data System (ADS)

Pereira, Anselmo S.; Mompean, Gilmar; Thompson, Roney L.; Soares, Edson J.

2017-11-01

In the present paper, we investigate the polymer-turbulence interaction by discriminating between the mechanical responses of this system to three different subdomains: elliptical, parabolic, and hyperbolic, corresponding to regions where the magnitude of vorticity is greater than, equal to, or less than the magnitude of the rate of strain, respectively, in accordance with the Q-criterion. Recently, it was recognized that hyperbolic structures play a crucial role in the drag reduction phenomenon of viscoelastic turbulent flows, thanks to the observation that hyperbolic structures, as well as vortical ones, are weakened by the action of polymers in turbulent flows in a process that can be referred to as flow parabolization. We employ direct numerical simulations of a viscoelastic finite extensible nonlinear elastic model with the Peterlin approximation to examine the transient evolution and statistically steady regimes of a plane Couette flow that has been perturbed from a laminar flow at an initial time and developed a turbulent regime as a result of this perturbation. We have found that even more activity is located within the confines of the hyperbolic structures than in the elliptical ones, which highlights the importance of considering the role of hyperbolic structures in the drag reduction mechanism.

An iterative method for systems of nonlinear hyperbolic equations

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1989-01-01

An iterative algorithm for the efficient solution of systems of nonlinear hyperbolic equations is presented. Parallelism is evident at several levels. In the formation of the iteration, the equations are decoupled, thereby providing large grain parallelism. Parallelism may also be exploited within the solves for each equation. Convergence of the interation is established via a bounding function argument. Experimental results in two-dimensions are presented.

A simple smoothness indicator for the WENO scheme with adaptive order

NASA Astrophysics Data System (ADS)

Huang, Cong; Chen, Li Li

2018-01-01

The fifth order WENO scheme with adaptive order is competent for solving hyperbolic conservation laws, its reconstruction is a convex combination of a fifth order linear reconstruction and three third order linear reconstructions. Note that, on uniform mesh, the computational cost of smoothness indicator for fifth order linear reconstruction is comparable with the sum of ones for three third order linear reconstructions, thus it is too heavy; on non-uniform mesh, the explicit form of smoothness indicator for fifth order linear reconstruction is difficult to be obtained, and its computational cost is much heavier than the one on uniform mesh. In order to overcome these problems, a simple smoothness indicator for fifth order linear reconstruction is proposed in this paper.

Classification of Tidal Disruption Events Based on Stellar Orbital Properties

NASA Astrophysics Data System (ADS)

Hayasaki, Kimitake; Zhong, Shiyan; Li, Shuo; Berczik, Peter; Spurzem, Rainer

2018-03-01

We study the rates of tidal disruption of stars on bound to unbound orbits by intermediate-mass to supermassive black holes using high-accuracy direct N-body experiments. Stars from the star cluster approaching the black hole can have three types of orbit: eccentric, parabolic, and hyperbolic. Since the mass fallback rate shows different variabilities depending on the orbital type, we can classify tidal disruption events (TDEs) into three main categories: eccentric, parabolic, and hyperbolic. The respective TDEs are characterized by two critical values of the orbital eccentricity: the lower critical eccentricity is the one below which stars on eccentric orbits cause finite, intense accretion, and the upper critical eccentricity is the one above which stars on hyperbolic orbits cause no accretion. Moreover, we find that parabolic TDEs can be divided into three subclasses: precisely parabolic, marginally eccentric, and marginally hyperbolic. We analytically derive that the mass fallback rate of marginally eccentric TDEs can be flatter and slightly higher than the standard fallback rate proportional to t ‑5/3, whereas it can be flatter and lower for marginally hyperbolic TDEs. We confirm using N-body experiments that only a few eccentric, precisely parabolic, and hyperbolic TDEs can occur in a spherical stellar system with a single intermediate-mass to supermassive black hole. A substantial fraction of the stars approaching the black hole would cause marginally eccentric or marginally hyperbolic TDEs.

On the hyperbolicity of a two-fluid model for debris flows

NASA Astrophysics Data System (ADS)

Mineo, C.; Torrisi, M.

2010-05-01

We consider the system of partial differential equations associated with the mathematical model for debris flows proposed by E.B. Pitman and L. Le (Phil. Trans. R. Soc. A, 363, 1573-1601, 2005) and analyze the problem of the hyperbolicity of the model.

Cauchy problem as a two-surface based ‘geometrodynamics’

NASA Astrophysics Data System (ADS)

Rácz, István

2015-01-01

Four-dimensional spacetimes foliated by a two-parameter family of homologous two-surfaces are considered in Einstein's theory of gravity. By combining a 1 + (1 + 2) decomposition, the canonical form of the spacetime metric and a suitable specification of the conformal structure of the foliating two-surfaces, a gauge fixing is introduced. It is shown that, in terms of the chosen geometrically distinguished variables, the 1 + 3 Hamiltonian and momentum constraints can be recast into the form of a parabolic equation and a first order symmetric hyperbolic system, respectively. Initial data to this system can be given on one of the two-surfaces foliating the three-dimensional initial data surface. The 1 + 3 reduced Einstein's equations are also determined. By combining the 1 + 3 momentum constraint with the reduced system of the secondary 1 + 2 decomposition, a mixed hyperbolic-hyperbolic system is formed. It is shown that solutions to this mixed hyperbolic-hyperbolic system are also solutions to the full set of Einstein's equations provided that the 1 + 3 Hamiltonian constraint is solved on the initial data surface {{Σ }0} and the 1 + 2 Hamiltonian and momentum type expressions vanish on a world-tube yielded by the Lie transport of one of the two-surfaces foliating {{Σ }0} along the time evolution vector field. Whenever the foliating two-surfaces are compact without boundary in the spacetime and a regular origin exists on the time-slices—this is the location where the foliating two-surfaces smoothly reduce to a point—it suffices to guarantee that the 1 + 3 Hamiltonian constraint holds on the initial data surface. A short discussion on the use of the geometrically distinguished variables in identifying the degrees of freedom of gravity are also included. Dedicated to Zoltán Cseke on the occasion of his 70th birthday.

Four-mirror extreme ultraviolet (EUV) lithography projection system

DOEpatents

Cohen, Simon J; Jeong, Hwan J; Shafer, David R

2000-01-01

The invention is directed to a four-mirror catoptric projection system for extreme ultraviolet (EUV) lithography to transfer a pattern from a reflective reticle to a wafer substrate. In order along the light path followed by light from the reticle to the wafer substrate, the system includes a dominantly hyperbolic convex mirror, a dominantly elliptical concave mirror, spherical convex mirror, and spherical concave mirror. The reticle and wafer substrate are positioned along the system's optical axis on opposite sides of the mirrors. The hyperbolic and elliptical mirrors are positioned on the same side of the system's optical axis as the reticle, and are relatively large in diameter as they are positioned on the high magnification side of the system. The hyperbolic and elliptical mirrors are relatively far off the optical axis and hence they have significant aspherical components in their curvatures. The convex spherical mirror is positioned on the optical axis, and has a substantially or perfectly spherical shape. The spherical concave mirror is positioned substantially on the opposite side of the optical axis from the hyperbolic and elliptical mirrors. Because it is positioned off-axis to a degree, the spherical concave mirror has some asphericity to counter aberrations. The spherical concave mirror forms a relatively large, uniform field on the wafer substrate. The mirrors can be tilted or decentered slightly to achieve further increase in the field size.

Linear dynamics of classical spin as Mobius transformation

DOE PAGES

Galda, Alexey; Vinokur, Valerii М.

2017-04-26

Though the overwhelming majority of natural processes occur far from the equilibrium, general theoretical approaches to non-equilibrium phase transitions remain scarce. Recent breakthroughs introduced a description of open dissipative systems in terms of non-Hermitian quantum mechanics enabling the identification of a class of non-equilibrium phase transitions associated with the loss of combined parity (reflection) and time-reversal symmetries. Here we report that the time evolution of a single classical spin (e.g. monodomain ferromagnet) governed by the Landau-Lifshitz-Gilbert-Slonczewski equation in the absence of magnetic anisotropy terms is described by a Mobius transformation in complex stereographic coordinates. We identify the parity-time symmetry-breaking phasemore » transition occurring in spin-transfer torque-driven linear spin systems as a transition between hyperbolic and loxodromic classes of Mobius transformations, with the critical point of the transition corresponding to the parabolic transformation. However, this establishes the understanding of non-equilibrium phase transitions as topological transitions in configuration space.« less

High Performance Radiation Transport Simulations on TITAN

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

Baker, Christopher G; Davidson, Gregory G; Evans, Thomas M

2012-01-01

In this paper we describe the Denovo code system. Denovo solves the six-dimensional, steady-state, linear Boltzmann transport equation, of central importance to nuclear technology applications such as reactor core analysis (neutronics), radiation shielding, nuclear forensics and radiation detection. The code features multiple spatial differencing schemes, state-of-the-art linear solvers, the Koch-Baker-Alcouffe (KBA) parallel-wavefront sweep algorithm for inverting the transport operator, a new multilevel energy decomposition method scaling to hundreds of thousands of processing cores, and a modern, novel code architecture that supports straightforward integration of new features. In this paper we discuss the performance of Denovo on the 10--20 petaflop ORNLmore » GPU-based system, Titan. We describe algorithms and techniques used to exploit the capabilities of Titan's heterogeneous compute node architecture and the challenges of obtaining good parallel performance for this sparse hyperbolic PDE solver containing inherently sequential computations. Numerical results demonstrating Denovo performance on early Titan hardware are presented.« less

The large discretization step method for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Haras, Zigo; Taasan, Shlomo

1995-01-01

A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

A-Posteriori Error Estimation for Hyperbolic Conservation Laws with Constraint

NASA Technical Reports Server (NTRS)

Barth, Timothy

2004-01-01

This lecture considers a-posteriori error estimates for the numerical solution of conservation laws with time invariant constraints such as those arising in magnetohydrodynamics (MHD) and gravitational physics. Using standard duality arguments, a-posteriori error estimates for the discontinuous Galerkin finite element method are then presented for MHD with solenoidal constraint. From these estimates, a procedure for adaptive discretization is outlined. A taxonomy of Green's functions for the linearized MHD operator is given which characterizes the domain of dependence for pointwise errors. The extension to other constrained systems such as the Einstein equations of gravitational physics are then considered. Finally, future directions and open problems are discussed.

Giant asymmetric self-phase modulation in superconductor thin films

NASA Astrophysics Data System (ADS)

Robson, Charles W.; Biancalana, Fabio

2018-04-01

Self-phase modulation (SPM) of light pulses is found to occur strongly, at low incident intensities, in the coupling of light with superconductors. We develop a theory from a synthesis of the time-dependent Ginzburg-Landau (TDGL) equation and basic electrodynamics which shows the strongly non-linear phase accumulated in the interaction. Unusually, the SPM of the pulse in this system is found to be highly asymmetric, producing a strongly redshifted spectrum when interacting with a superconducting thin film, and it develops in just a few nanometers of propagation. In this paper we present theoretical results and simulations in the THz regime, for both hyperbolic secant and supergaussian-shaped pulses.

Hyperbolic Positioning with Antenna Arrays and Multi-Channel Pseudolite for Indoor Localization

PubMed Central

Fujii, Kenjirou; Sakamoto, Yoshihiro; Wang, Wei; Arie, Hiroaki; Schmitz, Alexander; Sugano, Shigeki

2015-01-01

A hyperbolic positioning method with antenna arrays consisting of proximately-located antennas and a multi-channel pseudolite is proposed in order to overcome the problems of indoor positioning with conventional pseudolites (ground-based GPS transmitters). A two-dimensional positioning experiment using actual devices is conducted. The experimental result shows that the positioning accuracy varies centimeter- to meter-level according to the geometric relation between the pseudolite antennas and the receiver. It also shows that the bias error of the carrier-phase difference observables is more serious than their random error. Based on the size of the bias error of carrier-phase difference that is inverse-calculated from the experimental result, three-dimensional positioning performance is evaluated by computer simulation. In addition, in the three-dimensional positioning scenario, an initial value convergence analysis of the non-linear least squares is conducted. Its result shows that initial values that can converge to a right position exist at least under the proposed antenna setup. The simulated values and evaluation methods introduced in this work can be applied to various antenna setups; therefore, by using them, positioning performance can be predicted in advance of installing an actual system. PMID:26437405

Highly accurate adaptive finite element schemes for nonlinear hyperbolic problems

NASA Astrophysics Data System (ADS)

Oden, J. T.

1992-08-01

This document is a final report of research activities supported under General Contract DAAL03-89-K-0120 between the Army Research Office and the University of Texas at Austin from July 1, 1989 through June 30, 1992. The project supported several Ph.D. students over the contract period, two of which are scheduled to complete dissertations during the 1992-93 academic year. Research results produced during the course of this effort led to 6 journal articles, 5 research reports, 4 conference papers and presentations, 1 book chapter, and two dissertations (nearing completion). It is felt that several significant advances were made during the course of this project that should have an impact on the field of numerical analysis of wave phenomena. These include the development of high-order, adaptive, hp-finite element methods for elastodynamic calculations and high-order schemes for linear and nonlinear hyperbolic systems. Also, a theory of multi-stage Taylor-Galerkin schemes was developed and implemented in the analysis of several wave propagation problems, and was configured within a general hp-adaptive strategy for these types of problems. Further details on research results and on areas requiring additional study are given in the Appendix.

Lateralization of the Huggins pitch

NASA Astrophysics Data System (ADS)

Zhang, Peter Xinya; Hartmann, William M.

2004-05-01

The lateralization of the Huggins pitch (HP) was measured using a direct estimation method. The background noise was initially N0 or Nπ, and then the laterality of the entire stimulus was varied with a frequency-independent interaural delay, ranging from -1 to +1 ms. Two versions of the HP boundary region were used, stepped phase and linear phase. When presented in isolation, without the broadband background, the stepped boundary can be lateralized on its own but the linear boundary cannot. Nevertheless, the lateralizations of both forms of HP were found to be almost identical functions both of the interaural delay and of the boundary frequency over a two-octave range. In a third experiment, the same listeners lateralized sine tones in quiet as a function of interaural delay. Good agreement was found between lateralizations of the HP and of the corresponding sine tones. The lateralization judgments depended on the boundary frequency according to the expected hyperbolic law except when the frequency-independent delay was zero. For the latter case, the dependence on boundary frequency was much slower than hyperbolic. [Work supported by the NIDCD grant DC 00181.

Spectrophotometric evaluation of stability constants of 1:1 weak complexes from continuous variation data.

PubMed

Sayago, Ana; Asuero, Agustin G

2006-09-14

A bilogarithmic hyperbolic cosine method for the spectrophotometric evaluation of stability constants of 1:1 weak complexes from continuous variation data has been devised and applied to literature data. A weighting scheme, however, is necessary in order to take into account the transformation for linearization. The method may be considered a useful alternative to methods in which one variable is involved on both sides of the basic equation (i.e. Heller and Schwarzenbach, Likussar and Adsul and Ramanathan). Classical least squares lead in those instances to biased and approximate stability constants and limiting absorbance values. The advantages of the proposed method are: the method gives a clear indication of the existence of only one complex in solution, it is flexible enough to allow for weighting of measurements and the computation procedure yield the best value of logbeta11 and its limit of error. The agreement between the values obtained by applying the weighted hyperbolic cosine method and the non-linear regression (NLR) method is good, being in both cases the mean quadratic error at a minimum.

Optimal trajectories based on linear equations

NASA Technical Reports Server (NTRS)

Carter, Thomas E.

1990-01-01

The Principal results of a recent theory of fuel optimal space trajectories for linear differential equations are presented. Both impulsive and bounded-thrust problems are treated. A new form of the Lawden Primer vector is found that is identical for both problems. For this reason, starting iteratives from the solution of the impulsive problem are highly effective in the solution of the two-point boundary-value problem associated with bounded thrust. These results were applied to the problem of fuel optimal maneuvers of a spacecraft near a satellite in circular orbit using the Clohessy-Wiltshire equations. For this case two-point boundary-value problems were solved using a microcomputer, and optimal trajectory shapes displayed. The results of this theory can also be applied if the satellite is in an arbitrary Keplerian orbit through the use of the Tschauner-Hempel equations. A new form of the solution of these equations has been found that is identical for elliptical, parabolic, and hyperbolic orbits except in the way that a certain integral is evaluated. For elliptical orbits this integral is evaluated through the use of the eccentric anomaly. An analogous evaluation is performed for hyperbolic orbits.

Time-stable overset grid method for hyperbolic problems using summation-by-parts operators

NASA Astrophysics Data System (ADS)

Sharan, Nek; Pantano, Carlos; Bodony, Daniel J.

2018-05-01

A provably time-stable method for solving hyperbolic partial differential equations arising in fluid dynamics on overset grids is presented in this paper. The method uses interface treatments based on the simultaneous approximation term (SAT) penalty method and derivative approximations that satisfy the summation-by-parts (SBP) property. Time-stability is proven using energy arguments in a norm that naturally relaxes to the standard diagonal norm when the overlap reduces to a traditional multiblock arrangement. The proposed overset interface closures are time-stable for arbitrary overlap arrangements. The information between grids is transferred using Lagrangian interpolation applied to the incoming characteristics, although other interpolation schemes could also be used. The conservation properties of the method are analyzed. Several one-, two-, and three-dimensional, linear and non-linear numerical examples are presented to confirm the stability and accuracy of the method. A performance comparison between the proposed SAT-based interface treatment and the commonly-used approach of injecting the interpolated data onto each grid is performed to highlight the efficacy of the SAT method.

The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

NASA Technical Reports Server (NTRS)

Cockburn, Bernardo; Shu, Chi-Wang

1997-01-01

In this paper, we study the Local Discontinuous Galerkin methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L(sup 2)-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.

On the Theory of the Laval Nozzle

NASA Technical Reports Server (NTRS)

Falkovich, S. V.

1949-01-01

In the present paper, the motion of a gas in a plane-parallel Laval nozzle in the neighborhood of the transition from subsonic to supersonic velocities is studied. In a recently published paper, F. I. Frankl, applying the holograph method of Chaplygin, undertook a detailed investigation of the character of the flow near the line of transition from subsonic to supersonic velocities. From the results of Tricomi's investigation on the theory of differential equations of the mixed elliptic-hyperbolic type, Frankl introduced as one of the independent variables in place of the modulus of the velocity, a certain specially chosen function of this modulus. He thereby succeeded in explaining the character of the flow at the point of intersection of the transition line and the axis of symmetry (center of the nozzle) and in studying the behavior of the stream function in the neighborhood of this point by separating out the principal term having, together with its derivatives, the maximum value as compared with the corresponding corrections. This principal term is represented in Frankl's paper in the form of a linear combination of two hypergeometric functions. In order to find this linear combination, it is necessary to solve a number of boundary problems, which results in a complex analysis. In the investigation of the flow with which this paper is concerned, a second method is applied. This method is based on the transformation of the equations of motion to a form that may be called canonical for the system of differential equations of the mixed elliptic-hyperbolic type to which the system of equations of the motion of an ideal compressible fluid refers. By studying the behavior of the integrals of this system in the neighborhood of the parabolic line, the principal term of the solution is easily separated out in the form of a polynomial of the third degree. As a result, the computation of the transitional part of the nozzle is considerably simplified.

An Eigenvalue Analysis of finite-difference approximations for hyperbolic IBVPs

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1989-01-01

The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L(sub 2) stability on a finite domain.

Policy Effects in Hyperbolic vs. Exponential Models of Consumption and Retirement

PubMed Central

Gustman, Alan L.; Steinmeier, Thomas L.

2012-01-01

This paper constructs a structural retirement model with hyperbolic preferences and uses it to estimate the effect of several potential Social Security policy changes. Estimated effects of policies are compared using two models, one with hyperbolic preferences and one with standard exponential preferences. Sophisticated hyperbolic discounters may accumulate substantial amounts of wealth for retirement. We find it is frequently difficult to distinguish empirically between models with the two types of preferences on the basis of asset accumulation paths or consumption paths around the period of retirement. Simulations suggest that, despite the much higher initial time preference rate, individuals with hyperbolic preferences may actually value a real annuity more than individuals with exponential preferences who have accumulated roughly equal amounts of assets. This appears to be especially true for individuals with relatively high time preference rates or who have low assets for whatever reason. This affects the tradeoff between current benefits and future benefits on which many of the retirement incentives of the Social Security system rest. Simulations involving increasing the early entitlement age and increasing the delayed retirement credit do not show a great deal of difference whether exponential or hyperbolic preferences are used, but simulations for eliminating the earnings test show a non-trivially greater effect when exponential preferences are used. PMID:22711946

Policy Effects in Hyperbolic vs. Exponential Models of Consumption and Retirement.

PubMed

Gustman, Alan L; Steinmeier, Thomas L

2012-06-01

This paper constructs a structural retirement model with hyperbolic preferences and uses it to estimate the effect of several potential Social Security policy changes. Estimated effects of policies are compared using two models, one with hyperbolic preferences and one with standard exponential preferences. Sophisticated hyperbolic discounters may accumulate substantial amounts of wealth for retirement. We find it is frequently difficult to distinguish empirically between models with the two types of preferences on the basis of asset accumulation paths or consumption paths around the period of retirement. Simulations suggest that, despite the much higher initial time preference rate, individuals with hyperbolic preferences may actually value a real annuity more than individuals with exponential preferences who have accumulated roughly equal amounts of assets. This appears to be especially true for individuals with relatively high time preference rates or who have low assets for whatever reason. This affects the tradeoff between current benefits and future benefits on which many of the retirement incentives of the Social Security system rest.Simulations involving increasing the early entitlement age and increasing the delayed retirement credit do not show a great deal of difference whether exponential or hyperbolic preferences are used, but simulations for eliminating the earnings test show a non-trivially greater effect when exponential preferences are used.

A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model

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

Samet Y. Kadioglu; Robert Nourgaliev; Nam Dinh

2011-10-01

We introduce a novel approach for the hyperbolization of the well-known two-phase six equation flow model. The six-equation model has been frequently used in many two-phase flow applications such as bubbly fluid flows in nuclear reactors. One major drawback of this model is that it can be arbitrarily non-hyperbolic resulting in difficulties such as numerical instability issues. Non-hyperbolic behavior can be associated with complex eigenvalues that correspond to characteristic matrix of the system. Complex eigenvalues are often due to certain flow parameter choices such as the definition of inter-facial pressure terms. In our method, we prevent the characteristic matrix receivingmore » complex eigenvalues by fine tuning the inter-facial pressure terms with an iterative procedure. In this way, the characteristic matrix possesses all real eigenvalues meaning that the characteristic wave speeds are all real therefore the overall two-phase flowmodel becomes hyperbolic. The main advantage of this is that one can apply less diffusive highly accurate high resolution numerical schemes that often rely on explicit calculations of real eigenvalues. We note that existing non-hyperbolic models are discretized mainly based on low order highly dissipative numerical techniques in order to avoid stability issues.« less

Reactive transport in a partially molten system with binary solid solution

NASA Astrophysics Data System (ADS)

Jordan, J.; Hesse, M. A.

2017-12-01

Melt extraction from the Earth's mantle through high-porosity channels is required to explain the composition of the oceanic crust. Feedbacks from reactive melt transport are thought to localize melt into a network of high-porosity channels. Recent studies invoke lithological heterogeneities in the Earth's mantle to seed the localization of partial melts. Therefore, it is necessary to understand the reaction fronts that form as melt flows across the lithological interface of a heterogeneity and the background mantle. Simplified melting models of such systems aide in the interpretation and formulation of larger scale mantle models. Motivated by the aforementioned facts, we present a chromatographic analysis of reactive melt transport across lithological boundaries, using theory for hyperbolic conservation laws. This is an extension of well-known linear trace element chromatography to the coupling of major elements and energy transport. Our analysis allows the prediction of the feedbacks that arise in reactive melt transport due to melting, freezing, dissolution and precipitation for frontal reactions. This study considers the simplified case of a rigid, partially molten porous medium with binary solid solution. As melt traverses a lithological contact-modeled as a Riemann problem-a rich set of features arise, including a reacted zone between an advancing reaction front and partial chemical preservation of the initial contact. Reactive instabilities observed in this study originate at the lithological interface rather than along a chemical gradient as in most studies of mantle dynamics. We present a regime diagram that predicts where reaction fronts become unstable, thereby allowing melt localization into high-porosity channels through reactive instabilities. After constructing the regime diagram, we test the one-dimensional hyperbolic theory against two-dimensional numerical experiments. The one-dimensional hyperbolic theory is sufficient for predicting the qualitative behavior of reactive melt transport simulations conducted in two-dimensions. The theoretical framework presented can be extended to more complex and realistic phase behavior, and is therefore a useful tool for understanding nonlinear feedbacks in reactive melt transport problems relevant to mantle dynamics.

Geometry in a dynamical system without space: Hyperbolic Geometry in Kuramoto Oscillator Systems

NASA Astrophysics Data System (ADS)

Engelbrecht, Jan; Chen, Bolun; Mirollo, Renato

Kuramoto oscillator networks have the special property that their time evolution is constrained to lie on 3D orbits of the Möbius group acting on the N-fold torus TN which explains the N - 3 constants of motion discovered by Watanabe and Strogatz. The dynamics for phase models can be further reduced to 2D invariant sets in T N - 1 which have a natural geometry equivalent to the unit disk Δ with hyperbolic metric. We show that the classic Kuramoto model with order parameter Z1 (the first moment of the oscillator configuration) is a gradient flow in this metric with a unique fixed point on each generic 2D invariant set, corresponding to the hyperbolic barycenter of an oscillator configuration. This gradient property makes the dynamics especially easy to analyze. We exhibit several new families of Kuramoto oscillator models which reduce to gradient flows in this metric; some of these have a richer fixed point structure including non-hyperbolic fixed points associated with fixed point bifurcations. Work Supported by NSF DMS 1413020.

Kinetics of Bacteriophage λ Deoxyribonucleic Acid Infection of Escherichia coli

PubMed Central

Barnhart, Benjamin J.

1965-01-01

Barnhart, Benjamin J. (Los Alamos Scientific Laboratory, University of California, Los Alamos, N.M.). Kinetics of bacteriophage λ deoxyribonucleic acid infection of Escherichia coli. J. Bacteriol. 90:1617–1623. 1965.—The kinetics of Escherichia coli K-12 infection by phage λ deoxyribonucleic acid (DNA) were determined. An initial lag of 55 to 80 sec was found to be the time required for infecting DNA to become deoxyribonuclease-insensitive at 33 C. When cell-DNA interactions were stopped by washing away unbound DNA, the already bound DNA continued to infect the cell at rates described by linear kinetics with no apparent lag. Whereas the lag period was relatively insensitive to DNA and cell concentrations, both the lag and the subsequent linear portions of the rate curves were temperature-sensitive. Cell and DNA dose-response curves prescribed hyperbolic functions. Similarities between λ DNA infection of E. coli and bacterial transformation systems are discussed. PMID:5322721

On the construction and application of implicit factored schemes for conservation laws. [in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Warming, R. F.; Beam, R. M.

1978-01-01

Efficient, noniterative, implicit finite difference algorithms are systematically developed for nonlinear conservation laws including purely hyperbolic systems and mixed hyperbolic parabolic systems. Utilization of a rational fraction or Pade time differencing formulas, yields a direct and natural derivation of an implicit scheme in a delta form. Attention is given to advantages of the delta formation and to various properties of one- and two-dimensional algorithms.

Design and fabrication of a basic mass analyzer and vacuum system

NASA Technical Reports Server (NTRS)

Judson, C. M.; Josias, C.; Lawrence, J. L., Jr.

1977-01-01

A two-inch hyperbolic rod quadrupole mass analyzer with a mass range of 400 to 200 amu and a sensitivity exceeding 100 packs per billion has been developed and tested. This analyzer is the basic hardware portion of a microprocessor-controlled quadrupole mass spectrometer for a Gas Analysis and Detection System (GADS). The development and testing of the hyperbolic-rod quadrupole mass spectrometer and associated hardware are described in detail.

Discontinuous Galerkin finite element method for the nonlinear hyperbolic problems with entropy-based artificial viscosity stabilization

NASA Astrophysics Data System (ADS)

Zingan, Valentin Nikolaevich

This work develops a discontinuous Galerkin finite element discretization of non- linear hyperbolic conservation equations with efficient and robust high order stabilization built on an entropy-based artificial viscosity approximation. The solutions of equations are represented by elementwise polynomials of an arbitrary degree p > 0 which are continuous within each element but discontinuous on the boundaries. The discretization of equations in time is done by means of high order explicit Runge-Kutta methods identified with respective Butcher tableaux. To stabilize a numerical solution in the vicinity of shock waves and simultaneously preserve the smooth parts from smearing, we add some reasonable amount of artificial viscosity in accordance with the physical principle of entropy production in the interior of shock waves. The viscosity coefficient is proportional to the local size of the residual of an entropy equation and is bounded from above by the first-order artificial viscosity defined by a local wave speed. Since the residual of an entropy equation is supposed to be vanishingly small in smooth regions (of the order of the Local Truncation Error) and arbitrarily large in shocks, the entropy viscosity is almost zero everywhere except the shocks, where it reaches the first-order upper bound. One- and two-dimensional benchmark test cases are presented for nonlinear hyperbolic scalar conservation laws and the system of compressible Euler equations. These tests demonstrate the satisfactory stability properties of the method and optimal convergence rates as well. All numerical solutions to the test problems agree well with the reference solutions found in the literature. We conclude that the new method developed in the present work is a valuable alternative to currently existing techniques of viscous stabilization.

Distributions of Orbital Elements for Meteoroids on Near-Parabolic Orbits According to Radar Observational Data

NASA Technical Reports Server (NTRS)

Kolomiyets, S. V.

2011-01-01

Some results of the International Heliophysical Year (IHY) Coordinated Investigation Program (CIP) number 65 Meteors in the Earth Atmosphere and Meteoroids in the Solar System are presented. The problem of hyperbolic and near-parabolic orbits is discussed. Some possibilities for the solution of this problem can be obtained from the radar observation of faint meteors. The limiting magnitude of the Kharkov, Ukraine, radar observation program in the 1970 s was +12, resulting in a very large number of meteors being detected. 250,000 orbits down to even fainter limiting magnitude were determined in the 1972-78 period in Kharkov (out of them 7,000 are hyperbolic). The hypothesis of hyperbolic meteors was confirmed. In some radar meteor observations 1 10% of meteors are hyperbolic meteors. Though the Advanced Meteor Orbit Radar (AMOR, New Zealand) and Canadian Meteor Orbit Radar (CMOR, Canada) have accumulated millions of meteor orbits, there are difficulties in comparing the radar observational data obtained from these three sites (New Zealand, Canada, Kharkov). A new global program International Space Weather Initiative (ISWI) has begun in 2010 (http://www.iswi-secretariat.org). Today it is necessary to create the unified radar catalogue of nearparabolic and hyperbolic meteor orbits in the framework of the ISWI, or any other different way, in collaboration of Ukraine, Canada, New Zealand, the USA and, possibly, Japan. Involvement of the Virtual Meteor Observatory (Netherlands) and Meteor Data Centre (Slovakia) is desirable too. International unified radar catalogue of near-parabolic and hyperbolic meteor orbits will aid to a major advance in our understanding of the ecology of meteoroids within the Solar System and beyond.

Development of an Integrated Modeling Framework for Simulations of Coastal Processes in Deltaic Environments Using High-Performance Computing

DTIC Science & Technology

2008-01-01

exceeds the local water depth. The approximation eliminates the vertical dimension of the elliptic equation that is normally required for the fully non...used for vertical resolution. The shallow water equations (SWE) are a set of non-linear hyperbolic equations. As the equations are derived under...linear standing wave with a wavelength of 10 m in a square 10 m by 10 m basin. The still water depth is 0.5 m. In order to compare with the analytical

[Not Available].

PubMed

Bernard, A M; Burgot, J L

1981-12-01

The variation in heat capacity and the thermal shifts which accompany a thermometric determination make the thermogram, even in the case of a very rapid and irreversible reaction, hyperbolic instead of formed of straight segments. These departures from linearity, which are inconvenient in the interpretation and exploitation of the thermograms, can be calculated as a function of the degree of titration. The relation obtained introduces a parameter which the authors call the apparent change of capacity at the equivalence point, and which takes into account the two causes of deviation from linearity. This relationship is confirmed experimentally.

Filling of a Poisson trap by a population of random intermittent searchers.

PubMed

Bressloff, Paul C; Newby, Jay M

2012-03-01

We extend the continuum theory of random intermittent search processes to the case of N independent searchers looking to deliver cargo to a single hidden target located somewhere on a semi-infinite track. Each searcher randomly switches between a stationary state and either a leftward or rightward constant velocity state. We assume that all of the particles start at one end of the track and realize sample trajectories independently generated from the same underlying stochastic process. The hidden target is treated as a partially absorbing trap in which a particle can only detect the target and deliver its cargo if it is stationary and within range of the target; the particle is removed from the system after delivering its cargo. As a further generalization of previous models, we assume that up to n successive particles can find the target and deliver its cargo. Assuming that the rate of target detection scales as 1/N, we show that there exists a well-defined mean-field limit N→∞, in which the stochastic model reduces to a deterministic system of linear reaction-hyperbolic equations for the concentrations of particles in each of the internal states. These equations decouple from the stochastic process associated with filling the target with cargo. The latter can be modeled as a Poisson process in which the time-dependent rate of filling λ(t) depends on the concentration of stationary particles within the target domain. Hence, we refer to the target as a Poisson trap. We analyze the efficiency of filling the Poisson trap with n particles in terms of the waiting time density f(n)(t). The latter is determined by the integrated Poisson rate μ(t)=∫(0)(t)λ(s)ds, which in turn depends on the solution to the reaction-hyperbolic equations. We obtain an approximate solution for the particle concentrations by reducing the system of reaction-hyperbolic equations to a scalar advection-diffusion equation using a quasisteady-state analysis. We compare our analytical results for the mean-field model with Monte Carlo simulations for finite N. We thus determine how the mean first passage time (MFPT) for filling the target depends on N and n.

High-Order Energy Stable WENO Schemes

NASA Technical Reports Server (NTRS)

Yamaleev, Nail K.; Carpenter, Mark H.

2009-01-01

A third-order Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference scheme developed by Yamaleev and Carpenter was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables 'energy stable' modifications for existing WENO schemes of any order. The technique is demonstrated by developing a one-parameter family of fifth-order upwind-biased ESWENO schemes; ESWENO schemes up to eighth order are presented in the appendix. New weight functions are also developed that provide (1) formal consistency, (2) much faster convergence for smooth solutions with an arbitrary number of vanishing derivatives, and (3) improved resolution near strong discontinuities.

Canonical forms of multidimensional steady inviscid flows

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1993-01-01

Canonical forms and canonical variables for inviscid flow problems are derived. In these forms the components of the system governed by different types of operators (elliptic and hyperbolic) are separated. Both the incompressible and compressible cases are analyzed, and their similarities and differences are discussed. The canonical forms obtained are block upper triangular operator form in which the elliptic and non-elliptic parts reside in different blocks. The full nonlinear equations are treated without using any linearization process. This form enables a better analysis of the equations as well as better numerical treatment. These forms are the analog of the decomposition of the one dimensional Euler equations into characteristic directions and Riemann invariants.

A novel grid multiwing chaotic system with only non-hyperbolic equilibria

NASA Astrophysics Data System (ADS)

Zhang, Sen; Zeng, Yicheng; Li, Zhijun; Wang, Mengjiao; Xiong, Le

2018-05-01

The structure of the chaotic attractor of a system is mainly determined by the nonlinear functions in system equations. By using a new saw-tooth wave function and a new stair function, a novel complex grid multiwing chaotic system which belongs to non-Shil'nikov chaotic system with non-hyperbolic equilibrium points is proposed in this paper. It is particularly interesting that the complex grid multiwing attractors are generated by increasing the number of non-hyperbolic equilibrium points, which are different from the traditional methods of realising multiwing attractors by adding the index-2 saddle-focus equilibrium points in double-wing chaotic systems. The basic dynamical properties of the new system, such as dissipativity, phase portraits, the stability of the equilibria, the time-domain waveform, power spectrum, bifurcation diagram, Lyapunov exponents, and so on, are investigated by theoretical analysis and numerical simulations. Furthermore, the corresponding electronic circuit is designed and simulated on the Multisim platform. The Multisim simulation results and the hardware experimental results are in good agreement with the numerical simulations of the same system on Matlab platform, which verify the feasibility of this new grid multiwing chaotic system.

High order ADER schemes for a unified first order hyperbolic formulation of Newtonian continuum mechanics coupled with electro-dynamics

NASA Astrophysics Data System (ADS)

Dumbser, Michael; Peshkov, Ilya; Romenski, Evgeniy; Zanotti, Olindo

2017-11-01

In this paper, we propose a new unified first order hyperbolic model of Newtonian continuum mechanics coupled with electro-dynamics. The model is able to describe the behavior of moving elasto-plastic dielectric solids as well as viscous and inviscid fluids in the presence of electro-magnetic fields. It is actually a very peculiar feature of the proposed PDE system that viscous fluids are treated just as a special case of elasto-plastic solids. This is achieved by introducing a strain relaxation mechanism in the evolution equations of the distortion matrix A, which in the case of purely elastic solids maps the current configuration to the reference configuration. The model also contains a hyperbolic formulation of heat conduction as well as a dissipative source term in the evolution equations for the electric field given by Ohm's law. Via formal asymptotic analysis we show that in the stiff limit, the governing first order hyperbolic PDE system with relaxation source terms tends asymptotically to the well-known viscous and resistive magnetohydrodynamics (MHD) equations. Furthermore, a rigorous derivation of the model from variational principles is presented, together with the transformation of the Euler-Lagrange differential equations associated with the underlying variational problem from Lagrangian coordinates to Eulerian coordinates in a fixed laboratory frame. The present paper hence extends the unified first order hyperbolic model of Newtonian continuum mechanics recently proposed in [110,42] to the more general case where the continuum is coupled with electro-magnetic fields. The governing PDE system is symmetric hyperbolic and satisfies the first and second principle of thermodynamics, hence it belongs to the so-called class of symmetric hyperbolic thermodynamically compatible systems (SHTC), which have been studied for the first time by Godunov in 1961 [61] and later in a series of papers by Godunov and Romenski [67,69,119]. An important feature of the proposed model is that the propagation speeds of all physical processes, including dissipative processes, are finite. The model is discretized using high order accurate ADER discontinuous Galerkin (DG) finite element schemes with a posteriori subcell finite volume limiter and using high order ADER-WENO finite volume schemes. We show numerical test problems that explore a rather large parameter space of the model ranging from ideal MHD, viscous and resistive MHD over pure electro-dynamics to moving dielectric elastic solids in a magnetic field.

A new adaptively central-upwind sixth-order WENO scheme

NASA Astrophysics Data System (ADS)

Huang, Cong; Chen, Li Li

2018-03-01

In this paper, we propose a new sixth-order WENO scheme for solving one dimensional hyperbolic conservation laws. The new WENO reconstruction has three properties: (1) it is central in smooth region for low dissipation, and is upwind near discontinuities for numerical stability; (2) it is a convex combination of four linear reconstructions, in which one linear reconstruction is sixth order, and the others are third order; (3) its linear weights can be any positive numbers with requirement that their sum equals one. Furthermore, we propose a simple smoothness indicator for the sixth-order linear reconstruction, this smooth indicator not only can distinguish the smooth region and discontinuities exactly, but also can reduce the computational cost, thus it is more efficient than the classical one.

Corridengum: Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables (2017 Nonlinearity 30 1204)

NASA Astrophysics Data System (ADS)

Baladi, Viviane; Kuna, Tobias; Lucarini, Valerio

2017-08-01

The first main result of Baladi et al (2017 Nonlinearity 30 1204-20) is modified as follows: For any θ in the Sobolev space H^r_p(M) , with 1 and 0, the map t\\mapsto \\int θ dρt is α-Hölder continuous for all \

Time-dependent boundary conditions for hyperbolic systems. II

NASA Technical Reports Server (NTRS)

Thompson, Kevin W.

1990-01-01

A general boundary condition formalism is developed for all types of boundary conditions to which hyperbolic systems are subject; the formalism makes possible a 'cookbook' approach to boundary conditions, by means of which novel boundary 'recipes' may be derived and previously devised ones may be consulted as required. Numerous useful conditions are derived for such CFD problems as subsonic and supersonic inflows and outflows, nonreflecting boundaries, force-free boundaries, constant pressure boundaries, and constant mass flux. Attention is given to the computation and integration of time derivatives.

Time-dependent boundary conditions for hyperbolic systems. II

NASA Astrophysics Data System (ADS)

Thompson, Kevin W.

1990-08-01

A general boundary condition formalism is developed for all types of boundary conditions to which hyperbolic systems are subject; the formalism makes possible a 'cookbook' approach to boundary conditions, by means of which novel boundary 'recipes' may be derived and previously devised ones may be consulted as required. Numerous useful conditions are derived for such CFD problems as subsonic and supersonic inflows and outflows, nonreflecting boundaries, force-free boundaries, constant pressure boundaries, and constant mass flux. Attention is given to the computation and integration of time derivatives.

Ruijsenaars-Schneider three-body models with N = 2 supersymmetry

NASA Astrophysics Data System (ADS)

Galajinsky, Anton

2018-04-01

The Ruijsenaars-Schneider models are conventionally regarded as relativistic generalizations of the Calogero integrable systems. Surprisingly enough, their supersymmetric generalizations escaped attention. In this work, N = 2 supersymmetric extensions of the rational and hyperbolic Ruijsenaars-Schneider three-body models are constructed within the framework of the Hamiltonian formalism. It is also known that the rational model can be described by the geodesic equations associated with a metric connection. We demonstrate that the hyperbolic systems are linked to non-metric connections.

The surface-induced spatial-temporal structures in confined binary alloys

NASA Astrophysics Data System (ADS)

Krasnyuk, Igor B.; Taranets, Roman M.; Chugunova, Marina

2014-12-01

This paper examines surface-induced ordering in confined binary alloys. The hyperbolic initial boundary value problem (IBVP) is used to describe a scenario of spatiotemporal ordering in a disordered phase for concentration of one component of binary alloy and order parameter with non-linear dynamic boundary conditions. This hyperbolic model consists of two coupled second order differential equations for order parameter and concentration. It also takes into account effects of the “memory” on the ordering of atoms and their densities in the alloy. The boundary conditions characterize surface velocities of order parameter and concentration changing which is due to surface (super)cooling on walls confining the binary alloy. It is shown that for large times there are three classes of dynamic non-linear boundary conditions which lead to three different types of attractor’s elements for the IBVP. Namely, the elements of attractor are the limit periodic simple shock waves with fronts of “discontinuities” Γ. If Γ is finite, then the attractor contains spatiotemporal functions of relaxation type. If Γ is infinite and countable then we observe the functions of pre-turbulent type. If Γ is infinite and uncountable then we obtain the functions of turbulent type.

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

Cololla, P.

This review describes a structured approach to adaptivity. The Automated Mesh Refinement (ARM) algorithms developed by M Berger are described, touching on hyperbolic and parabolic applications. Adaptivity is achieved by overlaying finer grids only in areas flagged by a generalized error criterion. The author discusses some of the issues involved in abutting disparate-resolution grids, and demonstrates that suitable algorithms exist for dissipative as well as hyperbolic systems.

Collision Index and Stability of Elliptic Relative Equilibria in Planar {n}-body Problem

NASA Astrophysics Data System (ADS)

Hu, Xijun; Ou, Yuwei

2016-12-01

It is well known that a planar central configuration of the {n}-body problem gives rise to solutions where each particle moves on a specific Keplerian orbit while the totality of the particles move on a homographic motion. When the eccentricity {e} of the Keplerian orbit belongs in {[0,1)}, following Meyer and Schmidt, we call such solutions elliptic relative equilibria (shortly, ERE). In order to study the linear stability of ERE in the near-collision case, namely when {1-e} is small enough, we introduce the collision index for planar central configurations. The collision index is a Maslov-type index for heteroclinic orbits and orbits parametrised by half-lines that, according to the definition given by Hu and Portaluri (An index theory for unbounded motions of Hamiltonian systems, Hu and Portaluri (2015, preprint)), we shall refer to as half-clinic orbits and whose definition in this context, is essentially based on a blow up technique in the case {e=1}. We get the fundamental properties of collision index and approximation theorems. As applications, we give some new hyperbolic criteria and prove that, generically, the ERE of minimal central configurations are hyperbolic in the near-collision case, and we give a detailed analysis of Euler collinear orbits in the near-collision case.

Interference figures of polarimetric interferometry analysis of the human corneal stroma

PubMed Central

Mastropasqua, Rodolfo; Nubile, Mario; Salgari, Niccolò; Lanzini, Manuela; Calienno, Roberta; Mattei, Peter A.; Sborgia, Alessandra; Agnifili, Luca

2017-01-01

A rotating polarimetric 90°-cross linear-filter interferometry system was used to detect the morphological characteristics and features of interference patterns produced in in-vivo corneal stroma in healthy human corneas of 23 subjects. The characteristic corneal isogyres presenting with an evident cross-shaped pattern, grossly aligned with the fixation axis, were observed in all patients with centers within the pupillary dark area, impeding the exact determination of the center point. During the rotational scan in 78.3% of the eyes the cross-shaped pattern of the isogyre gradually separated to form two distinct hyperbolic arcs in opposite quadrants, reaching their maximal separation at 45 degrees with respect to angle of cross-shaped pattern formation. The corneal cross and hyperbolic-pattern repeated every 90° throughout the 360° rotational scan. While the interpretation of the isogyres presents particular difficulties, two summary parameters can be extracted for each cornea: the presence/orientation of a single or two dark areas in post-processed images and isochromes. However, the development of dedicated software for semi-quantitative analysis of these parameters and enantiomorphism may become available in the near future. The possible application of polarimetric interferometry in the field of both corneal pathologies and corneal surgery may be of great interest for clinical purposes. PMID:28570631

Interference figures of polarimetric interferometry analysis of the human corneal stroma.

PubMed

Mastropasqua, Rodolfo; Nubile, Mario; Salgari, Niccolò; Lanzini, Manuela; Calienno, Roberta; Mattei, Peter A; Sborgia, Alessandra; Agnifili, Luca

2017-01-01

A rotating polarimetric 90°-cross linear-filter interferometry system was used to detect the morphological characteristics and features of interference patterns produced in in-vivo corneal stroma in healthy human corneas of 23 subjects. The characteristic corneal isogyres presenting with an evident cross-shaped pattern, grossly aligned with the fixation axis, were observed in all patients with centers within the pupillary dark area, impeding the exact determination of the center point. During the rotational scan in 78.3% of the eyes the cross-shaped pattern of the isogyre gradually separated to form two distinct hyperbolic arcs in opposite quadrants, reaching their maximal separation at 45 degrees with respect to angle of cross-shaped pattern formation. The corneal cross and hyperbolic-pattern repeated every 90° throughout the 360° rotational scan. While the interpretation of the isogyres presents particular difficulties, two summary parameters can be extracted for each cornea: the presence/orientation of a single or two dark areas in post-processed images and isochromes. However, the development of dedicated software for semi-quantitative analysis of these parameters and enantiomorphism may become available in the near future. The possible application of polarimetric interferometry in the field of both corneal pathologies and corneal surgery may be of great interest for clinical purposes.

The Geometry of the Universe: Part 2

ERIC Educational Resources Information Center

Francis, Stephanie

2009-01-01

Hyperbolic geometry occurs on hyperbolic planes--the most commonly cited one being a saddle shape. In this article, the author explores negative hyperbolic curvature, and provides a detailed description of how she constructed two hyperbolic paraboloids. Hyperbolic geometry occurs on surfaces that have negative curvature. (Contains 11 figures and 4…

Single qubit operations using microwave hyperbolic secant pulses

NASA Astrophysics Data System (ADS)

Ku, H. S.; Long, J. L.; Wu, X.; Bal, M.; Lake, R. E.; Barnes, Edwin; Economou, Sophia E.; Pappas, D. P.

2017-10-01

It has been known since the early days of quantum mechanics that hyperbolic secant pulses possess the unique property that they can perform full-cycle Rabi oscillations on two-level quantum systems independently of the pulse detuning. More recently, it was realized that they induce detuning-controlled phases without changing state populations. Here, we experimentally demonstrate the properties of hyperbolic secant pulses on superconducting transmon qubits and contrast them with the more commonly used Gaussian and square waves. We further show that these properties can be exploited to implement phase gates, nominally without exiting the computational subspace. This enables us to demonstrate a microwave-driven Z rotation with a single control parameter, the detuning.

Lagrangian Coherent Structures, Hyperbolicity, and Lyapunov Exponents

NASA Astrophysics Data System (ADS)

Haller, George

2010-05-01

We review the fundamental physical motivation behind the definition of Lagrangian Coherent Structures (LCS) and show how it leads to the concept of finite-time hyperbolicity in non-autonomous dynamical systems. Using this concept of hyperbolicity, we obtain a self-consistent criterion for the existence of attracting and repelling material surfaces in unsteady fluid flows, such as those in the atmosphere and the ocean. The existence of LCS is often postulated in terms of features of the Finite-Time Lyapunov Exponent (FTLE) field associated with the system. As simple examples show, however, the FTLE field does not necessarily highlight LCS, or may ighlight structures that are not LCS. Under appropriate nondegeneracy conditions, we show that ridges of the FTLE field indeed coincide with LCS in volume-preserving flows. For general flows, we obtain a more general scalar field whose ridges correspond to LCS. We finally review recent applications of LCS techniques to flight safety analysis at Hong Kong International Airport.

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

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio

1989-01-01

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

Singularities and non-hyperbolic manifolds do not coincide

NASA Astrophysics Data System (ADS)

Simányi, Nándor

2013-06-01

We consider the billiard flow of elastically colliding hard balls on the flat ν-torus (ν ⩾ 2), and prove that no singularity manifold can even locally coincide with a manifold describing future non-hyperbolicity of the trajectories. As a corollary, we obtain the ergodicity (actually the Bernoulli mixing property) of all such systems, i.e. the verification of the Boltzmann-Sinai ergodic hypothesis.

Extended Thermodynamics: a Theory of Symmetric Hyperbolic Field Equations

NASA Astrophysics Data System (ADS)

Müller, Ingo

2008-12-01

Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear first order differential equations. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation provide an explicit example for extended thermodynamics. The theory proves its usefulness and practicality in the successful treatment of light scattering in rarefied gases. This presentation is based upon the book [1] of which the author of this paper is a co-author. For more details about the motivation and exploitation of the basic principles the interested reader is referred to that reference. It would seem that extended thermodynamics is worthy of the attention of mathematicians. It may offer them a non-trivial field of study concerning hyperbolic equations, if ever they get tired of the Burgers equation. Physicists may prefer to appreciate the success of extended thermodynamics in light scattering and to work on the open problems concerning the modification of the Navier-Stokes-Fourier theory in rarefied gases as predicted by extended thermodynamics of 13, 14, and more moments.

Parabolic discounting of monetary rewards by physical effort.

PubMed

Hartmann, Matthias N; Hager, Oliver M; Tobler, Philippe N; Kaiser, Stefan

2013-11-01

When humans and other animals make decisions in their natural environments prospective rewards have to be weighed against costs. It is well established that increasing costs lead to devaluation or discounting of reward. While our knowledge about discount functions for time and probability costs is quite advanced, little is known about how physical effort discounts reward. In the present study we compared three different models in a binary choice task in which human participants had to squeeze a handgrip to earn monetary rewards: a linear, a hyperbolic, and a parabolic model. On the group as well as the individual level, the concave parabolic model explained most variance of the choice data, thus contrasting with the typical hyperbolic discounting of reward value by delay. Research on effort discounting is not only important to basic science but also holds the potential to quantify aberrant motivational states in neuropsychiatric disorders. Copyright © 2013 Elsevier B.V. All rights reserved.

Absorbing boundary conditions for second-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Jiang, Hong; Wong, Yau Shu

1989-01-01

A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.

Discretizing singular point sources in hyperbolic wave propagation problems

DOE PAGES

Petersson, N. Anders; O'Reilly, Ossian; Sjogreen, Bjorn; ...

2016-06-01

Here, we develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite difference schemes. By studying the Fourier series expansions of the source discretization and the finite difference operator, we derive sufficient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in Fourier space can be satisfied through moment conditions on the source discretization, and we develop smoothness conditions for satisfying the remaining accuracy conditions. The resulting source discretization has compact support in physical space, and is spread over as many grid points as themore » number of moment and smoothness conditions. In numerical experiments we demonstrate high order of accuracy in the numerical solution of the 1-D advection equation (both in the interior and near a boundary), the 3-D elastic wave equation, and the 3-D linearized Euler equations.« less

An hp-adaptivity and error estimation for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Bey, Kim S.

1995-01-01

This paper presents an hp-adaptive discontinuous Galerkin method for linear hyperbolic conservation laws. A priori and a posteriori error estimates are derived in mesh-dependent norms which reflect the dependence of the approximate solution on the element size (h) and the degree (p) of the local polynomial approximation. The a posteriori error estimate, based on the element residual method, provides bounds on the actual global error in the approximate solution. The adaptive strategy is designed to deliver an approximate solution with the specified level of error in three steps. The a posteriori estimate is used to assess the accuracy of a given approximate solution and the a priori estimate is used to predict the mesh refinements and polynomial enrichment needed to deliver the desired solution. Numerical examples demonstrate the reliability of the a posteriori error estimates and the effectiveness of the hp-adaptive strategy.

Ion Trap Quantum Computing

DTIC Science & Technology

2011-12-01

quantum computer architecture schemes, but there are several problems that will be discussed later. 15 IV. ION TRAPS Wolfgang Paul was the first...famous physics experiment [62]. Wolfgang Paul demonstrated a similar apparatus during his Nobel Prize speech [63]. This device is hyperbolic-parabolic...Although it does not apply to linear traps, it is useful to understand the interaction between the Coulomb force and the repulsive quantum-mechanical Pauli

Application of the Lienard-Wiechert solution to a lightning return stroke model

NASA Technical Reports Server (NTRS)

Meneghini, R.

1983-01-01

The electric and magnetic fields associated with the lightning return stroke are expressed as a convolution of the current waveform shape and the fields generated by a moving charge of amplitude one (i.e., the Lienard-Wiechert solution for a unit charge). The representation can be used to compute the fields produced by a current waveform of non-uniform velocity that propagates along a filament of arbitrary, but finite, curvature. To study numerically the effects of linear charge acceleration and channel curvature two simple channel models are used: the linear and the hyperbolic.

Application of the Lienard-Wiechert solution to a lightning return stroke model

NASA Technical Reports Server (NTRS)

Meneghini, R.

1984-01-01

The electric and magnetic fields associated with the lightning return stroke are expressed as a convolution of the current waveform shape and the fields generated by a moving charge of amplitude one (i.e., the Lienard-Wiechert solution for a unit charge). The representation can be used to compute the fields produced by a current waveform of non-uniform velocity that propagates along a filament of arbitrary, but finite, curvature. To study numerically the effects of linear charge acceleration and channel curvature two simple channel models are used: the linear and the hyperbolic.

Stability and error estimation for Component Adaptive Grid methods

NASA Technical Reports Server (NTRS)

Oliger, Joseph; Zhu, Xiaolei

1994-01-01

Component adaptive grid (CAG) methods for solving hyperbolic partial differential equations (PDE's) are discussed in this paper. Applying recent stability results for a class of numerical methods on uniform grids. The convergence of these methods for linear problems on component adaptive grids is established here. Furthermore, the computational error can be estimated on CAG's using the stability results. Using these estimates, the error can be controlled on CAG's. Thus, the solution can be computed efficiently on CAG's within a given error tolerance. Computational results for time dependent linear problems in one and two space dimensions are presented.

High order filtering methods for approximating hyperbolic systems of conservation laws

NASA Technical Reports Server (NTRS)

Lafon, F.; Osher, S.

1991-01-01

The essentially nonoscillatory (ENO) schemes, while potentially useful in the computation of discontinuous solutions of hyperbolic conservation-law systems, are computationally costly relative to simple central-difference methods. A filtering technique is presented which employs central differencing of arbitrarily high-order accuracy except where a local test detects the presence of spurious oscillations and calls upon the full ENO apparatus to remove them. A factor-of-three speedup is thus obtained over the full-ENO method for a wide range of problems, with high-order accuracy in regions of smooth flow.

Fully-Implicit Reconstructed Discontinuous Galerkin Method for Stiff Multiphysics Problems

NASA Astrophysics Data System (ADS)

Nourgaliev, Robert

2015-11-01

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method's capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing. We focus on the method's accuracy (in both space and time), as well as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, and funded by the LDRD at LLNL under project tracking code 13-SI-002.

Quantum Field Theory on Spacetimes with a Compactly Generated Cauchy Horizon

NASA Astrophysics Data System (ADS)

Kay, Bernard S.; Radzikowski, Marek J.; Wald, Robert M.

1997-02-01

We prove two theorems which concern difficulties in the formulation of the quantum theory of a linear scalar field on a spacetime, (M,g_{ab}), with a compactly generated Cauchy horizon. These theorems demonstrate the breakdown of the theory at certain base points of the Cauchy horizon, which are defined as 'past terminal accumulation points' of the horizon generators. Thus, the theorems may be interpreted as giving support to Hawking's 'Chronology Protection Conjecture', according to which the laws of physics prevent one from manufacturing a 'time machine'. Specifically, we prove: Theorem 1. There is no extension to (M,g_{ab}) of the usual field algebra on the initial globally hyperbolic region which satisfies the condition of F-locality at any base point. In other words, any extension of the field algebra must, in any globally hyperbolic neighbourhood of any base point, differ from the algebra one would define on that neighbourhood according to the rules for globally hyperbolic spacetimes. Theorem 2. The two-point distribution for any Hadamard state defined on the initial globally hyperbolic region must (when extended to a distributional bisolution of the covariant Klein-Gordon equation on the full spacetime) be singular at every base point x in the sense that the difference between this two point distribution and a local Hadamard distribution cannot be given by a bounded function in any neighbourhood (in M 2 M) of (x,x). In consequence of Theorem 2, quantities such as the renormalized expectation value of J2 or of the stress-energy tensor are necessarily ill-defined or singular at any base point. The proof of these theorems relies on the 'Propagation of Singularities' theorems of Duistermaat and Hörmander.

Modeling of ultrashort pulsed laser irradiation in the cornea based on parabolic and hyperbolic heat equations using electrical analogy

NASA Astrophysics Data System (ADS)

Gheitaghy, A. M.; Takabi, B.; Alizadeh, M.

2014-03-01

Hyperbolic and parabolic heat equations are formulated to study a nonperfused homogeneous transparent cornea irradiated by high power and ultrashort pulsed laser in the Laser Thermo Keratoplasty (LTK) surgery. Energy absorption inside the cornea is modeled using the Beer-Lambert law that is incorporated as an exponentially decaying heat source. The hyperbolic and parabolic bioheat models of the tissue were solved by exploiting the mathematical analogy between thermal and electrical systems, by using robust circuit simulation program called Hspice to get the solutions of simultaneous RLC and RC transmission line networks. This method can be used to rapidly calculate the temperature in laser-irradiated tissue at time and space domain. It is found that internal energy gained from the irradiated field results in a rapid rise of temperature in the cornea surface during the early heating period, while the hyperbolic wave model predicts a higher temperature rise than the classical heat diffusion model. In addition, this paper investigates and examines the effect of some critical parameters such as relaxation time, convection coefficient, radiation, tear evaporation and variable thermal conductivity of cornea. Accordingly, it is found that a better accordance between hyperbolic and parabolic models will be achieved by time.

A Systematic Methodology for Constructing High-Order Energy-Stable WENO Schemes

NASA Technical Reports Server (NTRS)

Yamaleev, Nail K.; Carpenter, Mark H.

2008-01-01

A third-order Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference scheme developed by Yamaleev and Carpenter (AIAA 2008-2876, 2008) was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables \\energy stable" modifications for existing WENO schemes of any order. The technique is demonstrated by developing a one-parameter family of fifth-order upwind-biased ESWENO schemes; ESWENO schemes up to eighth order are presented in the appendix. New weight functions are also developed that provide (1) formal consistency, (2) much faster convergence for smooth solutions with an arbitrary number of vanishing derivatives, and (3) improved resolution near strong discontinuities.

A Taylor weak-statement algorithm for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Baker, A. J.; Kim, J. W.

1987-01-01

Finite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak-statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and nonlinear test problems permit direct quantitative performance comparisons.

A Systematic Methodology for Constructing High-Order Energy Stable WENO Schemes

NASA Technical Reports Server (NTRS)

Yamaleev, Nail K.; Carpenter, Mark H.

2009-01-01

A third-order Energy Stable Weighted Essentially Non{Oscillatory (ESWENO) finite difference scheme developed by Yamaleev and Carpenter [1] was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables "energy stable" modifications for existing WENO schemes of any order. The technique is demonstrated by developing a one-parameter family of fifth-order upwind-biased ESWENO schemes; ESWENO schemes up to eighth order are presented in the appendix. New weight functions are also developed that provide (1) formal consistency, (2) much faster convergence for smooth solutions with an arbitrary number of vanishing derivatives, and (3) improved resolution near strong discontinuities.

Evolution of Advection Upstream Splitting Method Schemes

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

2010-01-01

This paper focuses on the evolution of advection upstream splitting method(AUSM) schemes. The main ingredients that have led to the development of modern computational fluid dynamics (CFD) methods have been reviewed, thus the ideas behind AUSM. First and foremost is the concept of upwinding. Second, the use of Riemann problem in constructing the numerical flux in the finite-volume setting. Third, the necessity of including all physical processes, as characterised by the linear (convection) and nonlinear (acoustic) fields. Fourth, the realisation of separating the flux into convection and pressure fluxes. The rest of this review briefly outlines the technical evolution of AUSM and more details can be found in the cited references. Keywords: Computational fluid dynamics methods, hyperbolic systems, advection upstream splitting method, conservation laws, upwinding, CFD

A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms

PubMed Central

2014-01-01

Systems of hyperbolic partial differential equations with source terms (balance laws) arise in many applications where it is important to compute accurate time-dependent solutions modeling small perturbations of equilibrium solutions in which the source terms balance the hyperbolic part. The f-wave version of the wave-propagation algorithm is one approach, but requires the use of a particular averaged value of the source terms at each cell interface in order to be “well balanced” and exactly maintain steady states. A general approach to choosing this average is developed using the theory of path conservative methods. A scalar advection equation with a decay or growth term is introduced as a model problem for numerical experiments. PMID:24563581

High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids

NASA Astrophysics Data System (ADS)

Dumbser, Michael; Peshkov, Ilya; Romenski, Evgeniy; Zanotti, Olindo

2016-06-01

This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell-Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic-parabolic Navier-Stokes-Fourier theory is established for the first time via a formal asymptotic analysis in the stiff relaxation limit. From a numerical point of view, the governing partial differential equations are very challenging, since they form a large nonlinear hyperbolic PDE system that includes stiff source terms and non-conservative products. We apply the successful family of one-step ADER-WENO finite volume (FV) and ADER discontinuous Galerkin (DG) finite element schemes to the HPR model in the stiff relaxation limit, and compare the numerical results with exact or numerical reference solutions obtained for the Euler and Navier-Stokes equations. Numerical convergence results are also provided. To show the universality of the HPR model, the paper is rounded-off with an application to wave propagation in elastic solids, for which one only needs to switch off the strain relaxation source term in the governing PDE system. We provide various examples showing that for the purpose of flow visualization, the distortion tensor A seems to be particularly useful.

Discontinuous Galerkin Methods for NonLinear Differential Systems

NASA Technical Reports Server (NTRS)

Barth, Timothy; Mansour, Nagi (Technical Monitor)

2001-01-01

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.

Well-posedness of the Cauchy problem for models of large amplitude internal waves

NASA Astrophysics Data System (ADS)

Guyenne, Philippe; Lannes, David; Saut, Jean-Claude

2010-02-01

We consider in this paper the 'shallow-water/shallow-water' asymptotic model obtained in Choi and Camassa (1999 J. Fluid Mech. 396 1-36), Craig et al (2005 Commun. Pure. Appl. Math. 58 1587-641) (one-dimensional interface) and Bona et al (2008 J. Math. Pures Appl. 89 538-66) (two-dimensional interface) from the two-layer system with rigid lid, for the description of large amplitude internal waves at the interface of two layers of immiscible fluids of different densities. For one-dimensional interfaces, this system is of hyperbolic type and its local well-posedness does not raise serious difficulties, although other issues (blow-up, loss of hyperbolicity, etc) turn out to be delicate. For two-dimensional interfaces, the system is nonlocal. Nevertheless, we prove that it conserves some properties of 'hyperbolic type' and show that the associated Cauchy problem is locally well posed in suitable Sobolev classes provided some natural restrictions are imposed on the data. These results are illustrated by numerical simulations with emphasis on the formation of shock waves.

Transforming wealth: using the inverse hyperbolic sine (IHS) and splines to predict youth's math achievement.

PubMed

Friedline, Terri; Masa, Rainier D; Chowa, Gina A N

2015-01-01

The natural log and categorical transformations commonly applied to wealth for meeting the statistical assumptions of research may not always be appropriate for adjusting for skewness given wealth's unique properties. Finding and applying appropriate transformations is becoming increasingly important as researchers consider wealth as a predictor of well-being. We present an alternative transformation-the inverse hyperbolic sine (IHS)-for simultaneously dealing with skewness and accounting for wealth's unique properties. Using the relationship between household wealth and youth's math achievement as an example, we apply the IHS transformation to wealth data from US and Ghanaian households. We also explore non-linearity and accumulation thresholds by combining IHS transformed wealth with splines. IHS transformed wealth relates to youth's math achievement similarly when compared to categorical and natural log transformations, indicating that it is a viable alternative to other transformations commonly used in research. Non-linear relationships and accumulation thresholds emerge that predict youth's math achievement when splines are incorporated. In US households, accumulating debt relates to decreases in math achievement whereas accumulating assets relates to increases in math achievement. In Ghanaian households, accumulating assets between the 25th and 50th percentiles relates to increases in youth's math achievement. Copyright © 2014 Elsevier Inc. All rights reserved.

Variational Lagrangian data assimilation in open channel networks

NASA Astrophysics Data System (ADS)

Wu, Qingfang; Tinka, Andrew; Weekly, Kevin; Beard, Jonathan; Bayen, Alexandre M.

2015-04-01

This article presents a data assimilation method in a tidal system, where data from both Lagrangian drifters and Eulerian flow sensors were fused to estimate water velocity. The system is modeled by first-order, hyperbolic partial differential equations subject to periodic forcing. The estimation problem can then be formulated as the minimization of the difference between the observed variables and model outputs, and eventually provide the velocity and water stage of the hydrodynamic system. The governing equations are linearized and discretized using an implicit discretization scheme, resulting in linear equality constraints in the optimization program. Thus, the flow estimation can be formed as an optimization problem and efficiently solved. The effectiveness of the proposed method was substantiated by a large-scale field experiment in the Sacramento-San Joaquin River Delta in California. A fleet of 100 sensors developed at the University of California, Berkeley, were deployed in Walnut Grove, CA, to collect a set of Lagrangian data, a time series of positions as the sensors moved through the water. Measurements were also taken from Eulerian sensors in the region, provided by the United States Geological Survey. It is shown that the proposed method can effectively integrate Lagrangian and Eulerian measurement data, resulting in a suited estimation of the flow variables within the hydraulic system.

A New Time-Space Accurate Scheme for Hyperbolic Problems. 1; Quasi-Explicit Case

NASA Technical Reports Server (NTRS)

Sidilkover, David

1998-01-01

This paper presents a new discretization scheme for hyperbolic systems of conservations laws. It satisfies the TVD property and relies on the new high-resolution mechanism which is compatible with the genuinely multidimensional approach proposed recently. This work can be regarded as a first step towards extending the genuinely multidimensional approach to unsteady problems. Discontinuity capturing capabilities and accuracy of the scheme are verified by a set of numerical tests.

Determination of Extensional Rheological Properties by Hyperbolic Contraction Flow

NASA Astrophysics Data System (ADS)

Stading, Mats

2008-07-01

Extensional rheologyy is important for diverse applications such as processing of viscoelastic fluids, mouthfeel of semi-solid foods, cell mitosis and baking, and is also a useful tool for testing the applicability of constitutive equations. Despite the documented influence of extensional rheological properties, it is seldom measured due to experimental difficulties. There are only commercial equipments available for low-viscosity fluids by Capillary Breakup and for polymer melts by Meissner-type winding of ribbons around cylinders. Both methods have limited applicability for medium-viscosity fluids such as foods and other biological systems. Contraction flows are extensively studied and a new test method has been developed based on contraction flow through a hyperbolic nozzle. The method is suitable for medium-viscosity fluids and has been validated by comparison to results from Filament Stretching and Capillary Breakup. The hyperbolic contraction flow method has been used to characterize food and medical systems, distinguish between different products having equal shear behavior, quantify ropy mouth feel and to predict foaming behavior of biopolymers.

On the hyperbolic nature of the equations of alluvial river hydraulics and the equivalence of stable and energy dissipating shocks

NASA Astrophysics Data System (ADS)

Zanraea, D. D. L.; Needham, D. J.

The depth-averaged hydraulic equations augmented with a suitable bed-load sediment transport function form a closed system which governs the one-dimensional flow in an alluvial river or channel. In this paper, it is shown that this system is hyperbolic and yields three families of shock-wave solutions. These are determined to be temporally stable in restricted regions of the (H, F0)-plane, via the Lax shock inequalities. Further, it is demonstrated that this criterion is equivalent to the energy dissipation criterion developed by Needham and Hey (1991).

Performance and limitations of p-version finite element method for problems containing singularities

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

Wong, K.K.; Surana, K.S.

1996-10-01

In this paper, the authors investigate the performance of p-version Least Squares Finite Element Formulation (LSFEF) for a hyperbolic system of equations describing a one-dimensional radial flow of an upper-convected Maxwell fluid. This problem has r{sup 2} singularity in stress and r{sup {minus}1} singularity in velocity at r = 0. By carefully controlling the inner radius r{sub j}, Deborah number DE and Reynolds number Re, this problem can be used to simulate the following four classes of problems: (a) smooth linear problems, (b) smooth non-linear problems, (c) singular linear problems and (d) singular non-linear problems. They demonstrate that in casesmore » (a) and (b) the p-version method, in particular p-version LSFEF is meritorious. However, for cases (c) and (d) p-version LSFEF, even with extreme mesh refinement and very high p-levels, either produces wrong solutions, or results in the failure of the iterative solution procedure. Even though in the numerical studies they have considered p-version LSFEF for the radial flow of the upper-convected Maxwell fluid, the findings and conclusions are equally valid for other smooth and singular problems as well, regardless of the formulation strategy chosen and element approximation functions employed.« less

Nonlinear sigma models with compact hyperbolic target spaces

NASA Astrophysics Data System (ADS)

Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; Stoica, Bogdan; Stokes, James

2016-06-01

We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model [1, 2]. Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.

Nonlinear sigma models with compact hyperbolic target spaces

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

Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.

We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model [1, 2]. Unlike in themore » O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. In conclusion, the diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.« less

Nonlinear sigma models with compact hyperbolic target spaces

DOE PAGES

Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; ...

2016-06-23

We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model [1, 2]. Unlike in themore » O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. In conclusion, the diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.« less

Optical nonlinearities in plasmonic metamaterials (Conference Presentation)

NASA Astrophysics Data System (ADS)

Zayats, Anatoly V.

2016-04-01

Metals exhibit strong and fast nonlinearities making metallic, plasmonic, structures very promising for ultrafast all-optical applications at low light intensities. Combining metallic nanostructures in metamaterials provides additional functionalities via prospect of precise engineering of spectral response and dispersion. From this point of view, hyperbolic metamaterials, in particular those based on plasmonic nanorod arrays, provide wealth of exciting possibilities in nonlinear optics offering designed linear and nonlinear properties, polarization control, spontaneous emission control and many others. Experiments and modeling have already demonstrated very strong Kerr-nonlinear response and its ultrafast recovery due to the nonlocal nature of the plasmonic mode of the metamaterial, so that small changes in the permittivity of the metallic component under the excitation modify the nonlocal response that in turn leads to strong changes of the metamaterial transmission. In this talk, we will discuss experimental studies and numerical modeling of second- and third-order nonlinear optical processes in hyperbolic metamaterials based on metallic nanorods and other plasmonic systems where coupling between the resonances plays important role in defining nonlinear response. Second-harmonic generation and ultrafast Kerr-type nonlinearity originating from metallic component of the metamaterial will be considered, including nonlinear magneto-optical effects. Nonlinear optical response of stand-alone as well as integrated metamaterial components will be presented. Some of the examples to be discussed include nonlinear polarization control, nonlinear metamaterial integrated in silicon photonic circuitry and second-harmonic generation, including magneto-optical effects.

New approach of a traditional analysis for predicting near-exit jet liquid instabilities

NASA Astrophysics Data System (ADS)

Jaramillo, Guillermo; Collicott, Steven

2015-11-01

Traditional linear instability theory for round liquid jets requires an exit-plane velocity profile be assumed so as to derive the characteristic growth rates and wavelengths of instabilities. This requires solving an eigenvalue problem for the Rayleigh Equation. In this new approach, a hyperbolic tangent velocity profile is assumed at the exit-plane of a round jet and a comparison is made with a hyperbolic secant profile. Temporal and Spatial Stability Analysis (TSA and SSA respectively) are the employed analytical tools to compare results of predicted most-unstable wavelengths from the given analytical velocity profiles and from previous experimental work. The local relevance of the velocity profile in the near-exit region of a liquid jet and the validity of an inviscid formulation through the Rayleigh equation are discussed as well. A comparison of numerical accuracy is made between two different mathematical approaches for the hyperbolic tangent profile with and without the Ricatti transformation. Reynolds number based on the momentum thickness of the boundary layer at the exit plane non-dimensionalizes the problem and, the Re range, based on measurements by Portillo in 2011, is 185 to 600. Wavelength measurements are taken from Portillo's experiment. School of Mechanical Engineering at Universidad del Valle, supported by a grant from Fulbright and Colciencias. Ph.D. student at the School of Aeronautics and Astronautics Purdue University.

Hyperbolic and semi-hyperbolic surface codes for quantum storage

NASA Astrophysics Data System (ADS)

Breuckmann, Nikolas P.; Vuillot, Christophe; Campbell, Earl; Krishna, Anirudh; Terhal, Barbara M.

2017-09-01

We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of 1.3 % for the \\{4,5\\}-hyperbolic surface code in a phenomenological noise model (as compared with 2.9 % for the toric code). In this code family, parity checks are of weight 4 and 5, while each qubit participates in four different parity checks. We introduce a family of semi-hyperbolic codes that interpolate between the toric code and the \\{4,5\\}-hyperbolic surface code in terms of encoding rate and threshold. We show how these hyperbolic codes outperform the toric code in terms of qubit overhead for a target logical error probability. We show how Dehn twists and lattice code surgery can be used to read and write individual qubits to this quantum storage medium.

Dynamical control of a quantum Kapitza pendulum in a spin-1 BEC

NASA Astrophysics Data System (ADS)

Hoang, Thai; Gerving, Corey; Land, Ben; Anquez, Martin; Hamley, Chris; Chapman, Michael

2013-05-01

We demonstrate dynamic stabilization of an unstable strongly interacting quantum many-body system by periodic manipulation of the phase of the collective states. The experiment employs a spin-1 atomic Bose condensate that has spin dynamics analogous to a non-rigid pendulum in the mean-field limit. The condensate spin is initialized to an unstable (hyperbolic) fixed point of the phase space, where subsequent free evolution gives rise to spin-nematic squeezing and quantum spin mixing. To stabilize the system, periodic microwave pulses are applied that manipulate the spin-nematic fluctuations and limit their growth. The range of pulse periods and phase shifts with which the condensate can be stabilized is measured and compares well with a linear stability analysis of the problem. C.D. Hamley, et al., ``Spin-Nematic Squeezed Vacuum in a Quantum Gas,'' Nature Physics 8, 305-308 (2012).

Well-balanced high-order solver for blood flow in networks of vessels with variable properties.

PubMed

Müller, Lucas O; Toro, Eleuterio F

2013-12-01

We present a well-balanced, high-order non-linear numerical scheme for solving a hyperbolic system that models one-dimensional flow in blood vessels with variable mechanical and geometrical properties along their length. Using a suitable set of test problems with exact solution, we rigorously assess the performance of the scheme. In particular, we assess the well-balanced property and the effective order of accuracy through an empirical convergence rate study. Schemes of up to fifth order of accuracy in both space and time are implemented and assessed. The numerical methodology is then extended to realistic networks of elastic vessels and is validated against published state-of-the-art numerical solutions and experimental measurements. It is envisaged that the present scheme will constitute the building block for a closed, global model for the human circulation system involving arteries, veins, capillaries and cerebrospinal fluid. Copyright © 2013 John Wiley & Sons, Ltd.

Dynamics and control of high area-to-mass ratio spacecraft and its application to geomagnetic exploration

NASA Astrophysics Data System (ADS)

Luo, Tong; Xu, Ming; Colombo, Camilla

2018-04-01

This paper studies the dynamics and control of a spacecraft, whose area-to-mass ratio is increased by deploying a reflective orientable surface such as a solar sail or a solar panel. The dynamical system describing the motion of a non-zero attitude angle high area-to-mass ratio spacecraft under the effects of the Earth's oblateness and solar radiation pressure admits the existence of equilibrium points, whose number and the eccentricity values depend on the semi-major axis, the area-to-mass ratio and the attitude angle of the spacecraft together. When two out of three parameters are fixed, five different dynamical topologies successively occur through varying the third parameter. Two of these five topologies are critical cases characterized by the appearance of the bifurcation phenomena. A conventional Hamiltonian structure-preserving (HSP) controller and an improved HSP controller are both constructed to stabilize the hyperbolic equilibrium point. Through the use of a conventional HSP controller, a bounded trajectory around the hyperbolic equilibrium point is obtained, while an improved HSP controller allows the spacecraft to easily transfer to the hyperbolic equilibrium point and to follow varying equilibrium points. A bifurcation control using topologies and changes of behavior areas can also stabilize a spacecraft near a hyperbolic equilibrium point. Natural trajectories around stable equilibrium point and these stabilized trajectories around hyperbolic equilibrium point can all be applied to geomagnetic exploration.

International Conference on Hyperbolic Problems (2nd). Theory, Numerical Methods and Applications, 14-18 March 1988

DTIC Science & Technology

1988-01-01

of this abstract got a spontaneous development of a transverse wave-strucure in a shock-oriented coordinate system without per- turbing the global ...We develop a formal asymptotic theory for hyperbolic conservation laws with large amplitude, rapidly varying initial data [1]. For small times, the...HUnefelderstr. 1-S, D-2800 Bremen 1 Today the most accurate and cost effective industrial codes used for aircraft design are based on full potential equations

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Goldberg, M.; Tadmor, E.

1985-01-01

New convenient stability criteria are provided in this paper for a large class of finite difference approximations to initial-boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter plane x or = 0, t or = 0. Using the new criteria, stability is easily established for numerous combinations of well known basic schemes and boundary conditins, thus generalizing many special cases studied in recent literature.

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Goldberg, M.; Tadmor, E.

1983-01-01

New convenient stability criteria are provided in this paper for a large class of finite difference approximations to initial-boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter plane x or = 0, t or = 0. Using the new criteria, stability is easily established for numerous combinations of well known basic schemes and boundary conditions, thus generalizing many special cases studied in recent literature.

A LAGRANGIAN GAUSS-NEWTON-KRYLOV SOLVER FOR MASS- AND INTENSITY-PRESERVING DIFFEOMORPHIC IMAGE REGISTRATION.

PubMed

Mang, Andreas; Ruthotto, Lars

2017-01-01

We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic PDE needs to be found such that the distance between the final state of the system (the transformed/transported template image) and the observation (the reference image) is minimized. Our solver supports both stationary and non-stationary (i.e., transient or time-dependent) velocity fields. As transformation models, we consider both the transport equation (assuming intensities are preserved during the deformation) and the continuity equation (assuming mass-preservation). We consider the reduced form of the optimal control problem and solve the resulting unconstrained optimization problem using a discretize-then-optimize approach. A key contribution is the elimination of the PDE constraint using a Lagrangian hyperbolic PDE solver. Lagrangian methods rely on the concept of characteristic curves. We approximate these curves using a fourth-order Runge-Kutta method. We also present an efficient algorithm for computing the derivatives of the final state of the system with respect to the velocity field. This allows us to use fast Gauss-Newton based methods. We present quickly converging iterative linear solvers using spectral preconditioners that render the overall optimization efficient and scalable. Our method is embedded into the image registration framework FAIR and, thus, supports the most commonly used similarity measures and regularization functionals. We demonstrate the potential of our new approach using several synthetic and real world test problems with up to 14.7 million degrees of freedom.

Tailoring High Order Time Discretizations for Use with Spatial Discretizations of Hyperbolic PDEs

DTIC Science & Technology

2015-05-19

Duration of Grant Sigal Gottlieb, Professor of Mathematics, UMass Dartmouth. Daniel Higgs , Graduate Student, UMass Dartmouth. Zachary Grant, Undergraduate...Grant, and D. Higgs , “Optimal Explicit Strong Stability Preserving Runge– Kutta Methods with High Linear Order and optimal Nonlinear Order.” Accepted...for publica- tion in Mathematics of Computation. Available on Arxiv at http://arxiv.org/abs/1403. 6519 4. C. Bresten, S. Gottlieb, Z. Grant, D. Higgs

Seeking Space Aliens and the Strong Approximation Property: A (disjoint) Study in Dust Plumes on Planetary Satellites and Nonsymmetric Algebraic Multigrid

NASA Astrophysics Data System (ADS)

Southworth, Benjamin Scott

PART I: One of the most fascinating questions to humans has long been whether life exists outside of our planet. To our knowledge, water is a fundamental building block of life, which makes liquid water on other bodies in the universe a topic of great interest. In fact, there are large bodies of water right here in our solar system, underneath the icy crust of moons around Saturn and Jupiter. The NASA-ESA Cassini Mission spent two decades studying the Saturnian system. One of the many exciting discoveries was a "plume" on the south pole of Enceladus, emitting hundreds of kg/s of water vapor and frozen water-ice particles from Enceladus' subsurface ocean. It has since been determined that Enceladus likely has a global liquid water ocean separating its rocky core from icy surface, with conditions that are relatively favorable to support life. The plume is of particular interest because it gives direct access to ocean particles from space, by flying through the plume. Recently, evidence has been found for similar geological activity occurring on Jupiter's moon Europa, long considered one of the most likely candidate bodies to support life in our solar system. Here, a model for plume-particle dynamics is developed based on studies of the Enceladus plume and data from the Cassini Cosmic Dust Analyzer. A C++, OpenMP/MPI parallel software package is then built to run large scale simulations of dust plumes on planetary satellites. In the case of Enceladus, data from simulations and the Cassini mission provide insight into the structure of emissions on the surface, the total mass production of the plume, and the distribution of particles being emitted. Each of these are fundamental to understanding the plume and, for Europa and Enceladus, simulation data provide important results for the planning of future missions to these icy moons. In particular, this work has contributed to the Europa Clipper mission and proposed Enceladus Life Finder. PART II: Solving large, sparse linear systems arises often in the modeling of biological and physical phenomenon, data analysis through graphs and networks, and other scientific applications. This work focuses primarily on linear systems resulting from the discretization of partial differential equations (PDEs). Because solving linear systems is the bottleneck of many large simulation codes, there is a rich field of research in developing "fast" solvers, with the ultimate goal being a method that solves an n x n linear system in O(n) operations. One of the most effective classes of solvers is algebraic multigrid (AMG), which is a multilevel iterative method based on projecting the problem into progressively smaller spaces, and scales like O(n) or O(nlog n) for certain classes of problems. The field of AMG is well-developed for symmetric positive definite matrices, and is typically most effective on linear systems resulting from the discretization of scalar elliptic PDEs, such as the heat equation. Systems of PDEs can add additional difficulties, but the underlying linear algebraic theory is consistent and, in many cases, an elliptic system of PDEs can be handled well by AMG with appropriate modifications of the solver. Solving general, nonsymmetric linear systems remains the wild west of AMG (and other fast solvers), lacking significant results in convergence theory as well as robust methods. Here, we develop new theoretical motivation and practical variations of AMG to solve nonsymmetric linear systems, often resulting from the discretization of hyperbolic PDEs. In particular, multilevel convergence of AMG for nonsymmetric systems is proven for the first time. A new nonsymmetric AMG solver is also developed based on an approximate ideal restriction, referred to as AIR, which is able to solve advection-dominated, hyperbolic-type problems that are outside the scope of existing AMG solvers and other fast iterative methods. AIR demonstrates scalable convergence on unstructured meshes, in multiple dimensions, and with high-order finite elements, expanding the applicability of AMG to a new class of problems.

Homogeneous and Non-Homogeneous Boundary Value Problems for First Order Linear Hyperbolic Systems Arising in Fluid Mechanics. Part II.

DTIC Science & Technology

1982-03-01

use indifferently the notations du and dtu . We begin with the uniqueness result: Proposition 3.1. Let f e LI(I;X), U0 e X and let u e L1 (I;X) be a...multiplying both sides of the last equation (scalarly in Xt) by u one gets ( dtu (itt), u (it))t+ ((L+B)u (1)(t), u ()(t))t " (f() (t),u (t)) t. On the other...lIX), u 0 e X and u e L1 CI;y) n AC(IX) such that u -w on I x R!-, dtu (i) + (L+B)u f ()(A) () (1) 1 MA U (0) -O U ( u0 in X, f + f in L (IPX) and u

Improvements to the construction of binary black hole initial data

NASA Astrophysics Data System (ADS)

Ossokine, Serguei; Foucart, Francois; Pfeiffer, Harald P.; Boyle, Michael; Szilágyi, Béla

2015-12-01

Construction of binary black hole initial data is a prerequisite for numerical evolutions of binary black holes. This paper reports improvements to the binary black hole initial data solver in the spectral Einstein code, to allow robust construction of initial data for mass-ratio above 10:1, and for dimensionless black hole spins above 0.9, while improving efficiency for lower mass-ratios and spins. We implement a more flexible domain decomposition, adaptive mesh refinement and an updated method for choosing free parameters. We also introduce a new method to control and eliminate residual linear momentum in initial data for precessing systems, and demonstrate that it eliminates gravitational mode mixing during the evolution. Finally, the new code is applied to construct initial data for hyperbolic scattering and for binaries with very small separation.

Total Variation Diminishing (TVD) schemes of uniform accuracy

NASA Technical Reports Server (NTRS)

Hartwich, PETER-M.; Hsu, Chung-Hao; Liu, C. H.

1988-01-01

Explicit second-order accurate finite-difference schemes for the approximation of hyperbolic conservation laws are presented. These schemes are nonlinear even for the constant coefficient case. They are based on first-order upwind schemes. Their accuracy is enhanced by locally replacing the first-order one-sided differences with either second-order one-sided differences or central differences or a blend thereof. The appropriate local difference stencils are selected such that they give TVD schemes of uniform second-order accuracy in the scalar, or linear systems, case. Like conventional TVD schemes, the new schemes avoid a Gibbs phenomenon at discontinuities of the solution, but they do not switch back to first-order accuracy, in the sense of truncation error, at extrema of the solution. The performance of the new schemes is demonstrated in several numerical tests.

Scalar-fluid interacting dark energy: Cosmological dynamics beyond the exponential potential

NASA Astrophysics Data System (ADS)

Dutta, Jibitesh; Khyllep, Wompherdeiki; Tamanini, Nicola

2017-01-01

We extend the dynamical systems analysis of scalar-fluid interacting dark energy models performed in C. G. Boehmer et al., Phys. Rev. D 91, 123002 (2015), 10.1103/PhysRevD.91.123002 by considering scalar field potentials beyond the exponential type. The properties and stability of critical points are examined using a combination of linear analysis, computational methods and advanced mathematical techniques, such as center manifold theory. We show that the interesting results obtained with an exponential potential can generally be recovered also for more complicated scalar field potentials. In particular, employing power law and hyperbolic potentials as examples, we find late time accelerated attractors, transitions from dark matter to dark energy domination with specific distinguishing features, and accelerated scaling solutions capable of solving the cosmic coincidence problem.

A numerical spectral approach to solve the dislocation density transport equation

NASA Astrophysics Data System (ADS)

Djaka, K. S.; Taupin, V.; Berbenni, S.; Fressengeas, C.

2015-09-01

A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme.

Contracting singular horseshoe

NASA Astrophysics Data System (ADS)

Morales, C. A.; San Martín, B.

2017-11-01

We suggest a notion of hyperbolicity adapted to the geometric Rovella attractor (Robinson 2012 An Introduction to Dynamical Systems—Continuous and Discrete (Pure and Applied Undergraduate Texts vol 19) 2nd edn (Providence, RI: American Mathematical Society)) . More precisely, we call a partially hyperbolic set asymptotically sectional-hyperbolic if its singularities are hyperbolic and if its central subbundle is asymptotically sectional expanding outside the stable manifolds of the singularities. We prove that there are highly chaotic flows with Rovella-like singularities exhibiting this kind of hyperbolicity. We shall call them contracting singular horseshoes.

On a Non-Reflecting Boundary Condition for Hyperbolic Conservation Laws

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2003-01-01

A non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented. The technique is based on the hyperbolicity of the Euler equation system and the first principle of plane (simple) wave propagation. The NRBC is simple and effective, provided the numerical scheme maintains locally a C(sup 1) continuous solution at the boundary. Several numerical examples in ID, 2D and 3D space are illustrated to demonstrate its robustness in practical computations.

On a Non-Reflecting Boundary Condition for Hyperbolic Conservation Laws

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2003-01-01

A non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented. The technique is based on the first principle of non-reflecting, plane wave propagation and the hyperbolicity of the Euler equation system. The NRBC is simple and effective, provided the numerical scheme maintains locally a C(sup 1) continuous solution at the boundary. Several numerical examples in 1D, 2D, and 3D space are illustrated to demonstrate its robustness in practical computations.

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Goldberg, M.; Tadmor, E.

1986-01-01

The purpose of this paper is to achieve more versatile, convenient stability criteria for a wide class of finite-difference approximations to initial boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter-plane x greater than or equal to 0, t greater than or equal to 0. With these criteria, stability is easily established for a large number of examples, thus incorporating and generalizing many of the cases studied in recent literature.

Preliminary Results on the Gravitational Slingshot Effect and the Population of Hyperbolic Meteoroids at Earth

NASA Technical Reports Server (NTRS)

Wiegert, P. A.

2011-01-01

Interstellar meteoroids, solid particles arriving from outside our Solar System, are not easily distinguished from local meteoroids. A velocity above the escape velocity of the Sun is often used as an indicator of a possible interstellar origin. We demonstrate that the gravitational slingshot effect, resulting from the passage of local meteoroid near a planet, can produce hyperbolic meteoroids at the Earth s orbit with excess velocities comparable to those expected of interstellar meteoroids.

Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes

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

Montecinos, Gino I.; Müller, Lucas O.; Toro, Eleuterio F.

2014-06-01

The applicability of ADER finite volume methods to solve hyperbolic balance laws with stiff source terms in the context of well-balanced and non-conservative schemes is extended to solve a one-dimensional blood flow model for viscoelastic vessels, reformulated as a hyperbolic system, via a relaxation time. A criterion for selecting relaxation times is found and an empirical convergence rate assessment is carried out to support this result. The proposed methodology is validated by applying it to a network of viscoelastic vessels for which experimental and numerical results are available. The agreement between the results obtained in the present paper and thosemore » available in the literature is satisfactory. Key features of the present formulation and numerical methodologies, such as accuracy, efficiency and robustness, are fully discussed in the paper.« less

Numerical methods for systems of conservation laws of mixed type using flux splitting

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1990-01-01

The essentially non-oscillatory (ENO) finite difference scheme is applied to systems of conservation laws of mixed hyperbolic-elliptic type. A flux splitting, with the corresponding Jacobi matrices having real and positive/negative eigenvalues, is used. The hyperbolic ENO operator is applied separately. The scheme is numerically tested on the van der Waals equation in fluid dynamics. Convergence was observed with good resolution to weak solutions for various Riemann problems, which are then numerically checked to be admissible as the viscosity-capillarity limits. The interesting phenomena of the shrinking of elliptic regions if they are present in the initial conditions were also observed.

The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations

NASA Technical Reports Server (NTRS)

Chakravarthy, S. R.; Anderson, D. A.; Salas, M. D.

1980-01-01

The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented. This new method is based on the mathematical theory of characteristics. The development of the method from characteristic theory is presented. Boundary point calculation procedures consistent with the SCM method used at interior points are explained. The split coefficient matrices that define the method for steady supersonic and unsteady inviscid flows are given for several examples. The SCM method is used to compute several flow fields to demonstrate its accuracy and versatility. The similarities and differences between the SCM method and the lambda-scheme are discussed.

A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

PubMed

Biala, T A; Jator, S N

2015-01-01

In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

Weak form of Stokes-Dirac structures and geometric discretization of port-Hamiltonian systems

NASA Astrophysics Data System (ADS)

Kotyczka, Paul; Maschke, Bernhard; Lefèvre, Laurent

2018-05-01

We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete power variables. (iii) With a consistent approximation of the Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models. By the degrees of freedom in the power-preserving maps, the resulting family of structure-preserving schemes allows for trade-offs between centered approximations and upwinding. We illustrate the method on the example of Whitney finite elements on a 2D simplicial triangulation and compare the eigenvalue approximation in 1D with a related approach.

Demonstrator of atmospheric reentry system with hyperbolic velocity—DASH

NASA Astrophysics Data System (ADS)

Morita, Yasuhiro; Kawaguchi, Jun'ichiro; Inatani, Yoshifumi; Abe, Takashi

2003-01-01

Among a wide variety of challenging projects planned for the coming decade is the MUSES-C mission designed by the ISAS of Japan. Despite huge amount of data collected by the previous interplanetary spacecraft and probes, the origin and evolution of the solar system still remains unveiled due to their limited information. Thus, our concern has been directed toward a sample return to carry sample from an asteroid back to the earth, which will contribute to better understanding of the system. One of the keys to success is considered the reentry technology with hyperbolic velocity, which has not been demonstrated yet. With this as background, the demonstrator of atmospheric reentry system with hyperbolic velocity, DASH, has been given a commitment to demonstrate the high-speed reentry technology, which will be launched in summer of next year by Japan's H-IIA rocket in a piggyback configuration. The spaceship, composed of a reentry capsule and its carrier, will be injected into a geostationary transfer orbit (GTO) and after several revolutions it will deorbit by burn of a solid propellant deorbit motor. The capsule, identical to that of the sample return mission, can experience the targeted level of thermal environment even from the GTO by tracing a specially designed reentry trajectory.

Multigrid Methods for Fully Implicit Oil Reservoir Simulation

NASA Technical Reports Server (NTRS)

Molenaar, J.

1996-01-01

In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

The art and science of hyperbolic tessellations.

PubMed

Van Dusen, B; Taylor, R P

2013-04-01

The visual impact of hyperbolic tessellations has captured artists' imaginations ever since M.C. Escher generated his Circle Limit series in the 1950s. The scaling properties generated by hyperbolic geometry are different to the fractal scaling properties found in nature's scenery. Consequently, prevalent interpretations of Escher's art emphasize the lack of connection with nature's patterns. However, a recent collaboration between the two authors proposed that Escher's motivation for using hyperbolic geometry was as a method to deliberately distort nature's rules. Inspired by this hypothesis, this year's cover artist, Ben Van Dusen, embeds natural fractals such as trees, clouds and lightning into a hyperbolic scaling grid. The resulting interplay of visual structure at multiple size scales suggests that hybridizations of fractal and hyperbolic geometries provide a rich compositional tool for artists.

Attractors in complex networks

NASA Astrophysics Data System (ADS)

Rodrigues, Alexandre A. P.

2017-10-01

In the framework of the generalized Lotka-Volterra model, solutions representing multispecies sequential competition can be predictable with high probability. In this paper, we show that it occurs because the corresponding "heteroclinic channel" forms part of an attractor. We prove that, generically, in an attracting heteroclinic network involving a finite number of hyperbolic and non-resonant saddle-equilibria whose linearization has only real eigenvalues, the connections corresponding to the most positive expanding eigenvalues form part of an attractor (observable in numerical simulations).

Attractors in complex networks.

PubMed

Rodrigues, Alexandre A P

2017-10-01

In the framework of the generalized Lotka-Volterra model, solutions representing multispecies sequential competition can be predictable with high probability. In this paper, we show that it occurs because the corresponding "heteroclinic channel" forms part of an attractor. We prove that, generically, in an attracting heteroclinic network involving a finite number of hyperbolic and non-resonant saddle-equilibria whose linearization has only real eigenvalues, the connections corresponding to the most positive expanding eigenvalues form part of an attractor (observable in numerical simulations).

Recent Developments and Open Problems in the Mathematical Theory of Viscoelasticity.

DTIC Science & Technology

1984-11-01

integral terms . At each step of the iteration, we have to solve a linear parabolic equation with time-dependent coefficients. In Sobolevskii’s... parabolic Volterra integro- differential equation, SIAN J. Math. Anal. 13 (1982), ’ ~81-105. :-- 12. Heard, M. L., A class of hyperbolic Volterra ...then puts an n + 1 on the highest derivatives (the "principal terms " in the equation) and an n on lower order derivatives. Two things must then be

Fourth order difference methods for hyperbolic IBVP's

NASA Technical Reports Server (NTRS)

Gustafsson, Bertil; Olsson, Pelle

1994-01-01

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.

Focal surfaces of hyperbolic cylinders

NASA Astrophysics Data System (ADS)

Georgiev, Georgi Hristov; Pavlov, Milen Dimov

2017-12-01

Cylindrical surfaces have many applications in geometric modeling, architecture and other branches of engineering. In this paper, we describe two cylindrical surfaces associated to a given hyperbolic cylinder. The first one is a focal surface which is determined by reciprocal principle curvature of the hyperbolic cylinder. The second one is a generalized focal surface obtained by reciprocal mean curvature of the same hyperbolic cylinder. In particular, we show that each of these surfaces admits three different parametric representations. As consequence, it is proved that the focal and generalized focal surfaces of the hyperbolic cylinder are rational surfaces. An illustrative example is included.

Hyperbolic Rendezvous at Mars: Risk Assessments and Mitigation Strategies

NASA Technical Reports Server (NTRS)

Jedrey, Ricky; Landau, Damon; Whitley, Ryan

2015-01-01

Given the current interest in the use of flyby trajectories for human Mars exploration, a key requirement is the capability to execute hyperbolic rendezvous. Hyperbolic rendezvous is used to transport crew from a Mars centered orbit, to a transiting Earth bound habitat that does a flyby. Representative cases are taken from future potential missions of this type, and a thorough sensitivity analysis of the hyperbolic rendezvous phase is performed. This includes early engine cutoff, missed burn times, and burn misalignment. A finite burn engine model is applied that assumes the hyperbolic rendezvous phase is done with at least two burns.

Global Resolution of the Physical Vacuum Singularity for Three-Dimensional Isentropic Inviscid Flows with Damping in Spherically Symmetric Motions

NASA Astrophysics Data System (ADS)

Zeng, Huihui

2017-10-01

For the gas-vacuum interface problem with physical singularity and the sound speed being {C^{{1}/{2}}}-Hölder continuous near vacuum boundaries of the isentropic compressible Euler equations with damping, the global existence of smooth solutions and the convergence to Barenblatt self-similar solutions of the corresponding porous media equation are proved in this paper for spherically symmetric motions in three dimensions; this is done by overcoming the analytical difficulties caused by the coordinate's singularity near the center of symmetry, and the physical vacuum singularity to which standard methods of symmetric hyperbolic systems do not apply. Various weights are identified to resolve the singularity near the vacuum boundary and the center of symmetry globally in time. The results obtained here contribute to the theory of global solutions to vacuum boundary problems of compressible inviscid fluids, for which the currently available results are mainly for the local-in-time well-posedness theory, and also to the theory of global smooth solutions of dissipative hyperbolic systems which fail to be strictly hyperbolic.

Trivial dynamics in discrete-time systems: carrying simplex and translation arcs

NASA Astrophysics Data System (ADS)

Niu, Lei; Ruiz-Herrera, Alfonso

2018-06-01

In this paper we show that the dynamical behavior in (first octant) of the classical Kolmogorov systems of competitive type admitting a carrying simplex can be sometimes determined completely by the number of fixed points on the boundary and the local behavior around them. Roughly speaking, T has trivial dynamics (i.e. the omega limit set of any orbit is a connected set contained in the set of fixed points) provided T has exactly four hyperbolic nontrivial fixed points in with local attractors on the carrying simplex and local repellers on the carrying simplex; and there exists a unique hyperbolic fixed point in Int. Our results are applied to some classical models including the Leslie–Gower models, Atkinson-Allen systems and Ricker maps.

An autonomous dynamical system captures all LCSs in three-dimensional unsteady flows.

PubMed

Oettinger, David; Haller, George

2016-10-01

Lagrangian coherent structures (LCSs) are material surfaces that shape the finite-time tracer patterns in flows with arbitrary time dependence. Depending on their deformation properties, elliptic and hyperbolic LCSs have been identified from different variational principles, solving different equations. Here we observe that, in three dimensions, initial positions of all variational LCSs are invariant manifolds of the same autonomous dynamical system, generated by the intermediate eigenvector field, ξ 2 (x 0 ), of the Cauchy-Green strain tensor. This ξ 2 -system allows for the detection of LCSs in any unsteady flow by classical methods, such as Poincaré maps, developed for autonomous dynamical systems. As examples, we consider both steady and time-aperiodic flows, and use their dual ξ 2 -system to uncover both hyperbolic and elliptic LCSs from a single computation.

Statistical Properties of Lorenz-like Flows, Recent Developments and Perspectives

NASA Astrophysics Data System (ADS)

Araujo, Vitor; Galatolo, Stefano; Pacifico, Maria José

We comment on the mathematical results about the statistical behavior of Lorenz equations and its attractor, and more generally on the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer-assisted proof together with an extension of the hyperbolic theory developed to encompass attractors robustly containing equilibria. We present some of the main results on the statistical behavior of such systems. We show that for attractors of three-dimensional flows, robust chaotic behavior is equivalent to the existence of certain hyperbolic structures, known as singular-hyperbolicity. These structures, in turn, are associated with the existence of physical measures: in low dimensions, robust chaotic behavior for flows ensures the existence of a physical measure. We then give more details on recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors: (1) there exists an invariant foliation whose leaves are forward contracted by the flow (and further properties which are useful to understand the statistical properties of the dynamics); (2) there exists a positive Lyapunov exponent at every orbit; (3) there is a unique physical measure whose support is the whole attractor and which is the equilibrium state with respect to the center-unstable Jacobian; (4) this measure is exact dimensional; (5) the induced measure on a suitable family of cross-sections has exponential decay of correlations for Lipschitz observables with respect to a suitable Poincaré return time map; (6) the hitting time associated to Lorenz-like attractors satisfy a logarithm law; (7) the geometric Lorenz flow satisfies the Almost Sure Invariance Principle (ASIP) and the Central Limit Theorem (CLT); (8) the rate of decay of large deviations for the volume measure on the ergodic basin of a geometric Lorenz attractor is exponential; (9) a class of geometric Lorenz flows exhibits robust exponential decay of correlations; (10) all geometric Lorenz flows are rapidly mixing and their time-1 map satisfies both ASIP and CLT.

Very Efficient High-order Hyperbolic Schemes for Time-dependent Advection Diffusion Problems: Third-, Fourth-, and Sixth-order

DTIC Science & Technology

2014-07-07

boundary condition (x ¼ 7p =2; j ¼ 2p; U ¼ 1; m ¼ 1) on N ¼ 10 uniform nodes (Dt ¼ 0:01.) Table 10 Unsteady linear advection–diffusion problem with periodic...500 3rd 55 2 4th 55 2 6th 55 2 1000 3rd 116 2 4th 116 2 6th 116 2 Table 11 Unsteady linear advection–diffusion problem with oscillatory BC (x ¼ 7p =2; a...dependent problem with oscillatory BC (x ¼ 7p =2; a ¼ 1.) using the third-order RD-GT scheme with the BDF3 time discretization. Number of nodes Dt (BDF3

Linear and nonlinear stability of periodic orbits in annular billiards.

PubMed

Dettmann, Carl P; Fain, Vitaly

2017-04-01

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.

Linear and nonlinear stability of periodic orbits in annular billiards

NASA Astrophysics Data System (ADS)

Dettmann, Carl P.; Fain, Vitaly

2017-04-01

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.

Extremal black holes, Stueckelberg scalars and phase transitions

NASA Astrophysics Data System (ADS)

Marrani, Alessio; Miskovic, Olivera; Leon, Paula Quezada

2018-02-01

We calculate the entropy of a static extremal black hole in 4D gravity, non-linearly coupled to a massive Stueckelberg scalar. We find that the scalar field does not allow the black hole to be magnetically charged. We also show that the system can exhibit a phase transition due to electric charge variations. For spherical and hyperbolic horizons, the critical point exists only in presence of a cosmological constant, and if the scalar is massive and non-linearly coupled to electromagnetic field. On one side of the critical point, two extremal solutions coexist: Reissner-Nordström (A)dS black hole and the charged hairy (A)dS black hole, while on the other side of the critical point the black hole does not have hair. A near-critical analysis reveals that the hairy black hole has larger entropy, thus giving rise to a zero temperature phase transition. This is characterized by a discontinuous second derivative of the entropy with respect to the electric charge at the critical point. The results obtained here are analytical and based on the entropy function formalism and the second law of thermodynamics.

Probability Weighting Functions Derived from Hyperbolic Time Discounting: Psychophysical Models and Their Individual Level Testing.

PubMed

Takemura, Kazuhisa; Murakami, Hajime

2016-01-01

A probability weighting function (w(p)) is considered to be a nonlinear function of probability (p) in behavioral decision theory. This study proposes a psychophysical model of probability weighting functions derived from a hyperbolic time discounting model and a geometric distribution. The aim of the study is to show probability weighting functions from the point of view of waiting time for a decision maker. Since the expected value of a geometrically distributed random variable X is 1/p, we formulized the probability weighting function of the expected value model for hyperbolic time discounting as w(p) = (1 - k log p)(-1). Moreover, the probability weighting function is derived from Loewenstein and Prelec's (1992) generalized hyperbolic time discounting model. The latter model is proved to be equivalent to the hyperbolic-logarithmic weighting function considered by Prelec (1998) and Luce (2001). In this study, we derive a model from the generalized hyperbolic time discounting model assuming Fechner's (1860) psychophysical law of time and a geometric distribution of trials. In addition, we develop median models of hyperbolic time discounting and generalized hyperbolic time discounting. To illustrate the fitness of each model, a psychological experiment was conducted to assess the probability weighting and value functions at the level of the individual participant. The participants were 50 university students. The results of individual analysis indicated that the expected value model of generalized hyperbolic discounting fitted better than previous probability weighting decision-making models. The theoretical implications of this finding are discussed.

Central Configurations of the Curved N-Body Problem

NASA Astrophysics Data System (ADS)

Diacu, Florin; Stoica, Cristina; Zhu, Shuqiang

2018-06-01

We consider the N-body problem of celestial mechanics in spaces of nonzero constant curvature. Using the concept of effective potential, we define the moment of inertia for systems moving on spheres and hyperbolic spheres and show that we can recover the classical definition in the Euclidean case. After proving some criteria for the existence of relative equilibria, we find a natural way to define the concept of central configuration in curved spaces using the moment of inertia and show that our definition is formally similar to the one that governs the classical problem. We prove that, for any given point masses on spheres and hyperbolic spheres, central configurations always exist. We end with results concerning the number of central configurations that lie on the same geodesic, thus extending the celebrated theorem of Moulton to hyperbolic spheres and pointing out that it has no straightforward generalization to spheres, where the count gets complicated even for two bodies.

Gummel Symmetry Test on charge based drain current expression using modified first-order hyperbolic velocity-field expression

NASA Astrophysics Data System (ADS)

Singh, Kirmender; Bhattacharyya, A. B.

2017-03-01

Gummel Symmetry Test (GST) has been a benchmark industry standard for MOSFET models and is considered as one of important tests by the modeling community. BSIM4 MOSFET model fails to pass GST as the drain current equation is not symmetrical because drain and source potentials are not referenced to bulk. BSIM6 MOSFET model overcomes this limitation by taking all terminal biases with reference to bulk and using proper velocity saturation (v -E) model. The drain current equation in BSIM6 is charge based and continuous in all regions of operation. It, however, adopts a complicated method to compute source and drain charges. In this work we propose to use conventional charge based method formulated by Enz for obtaining simpler analytical drain current expression that passes GST. For this purpose we adopt two steps: (i) In the first step we use a modified first-order hyperbolic v -E model with adjustable coefficients which is integrable, simple and accurate, and (ii) In the second we use a multiplying factor in the modified first-order hyperbolic v -E expression to obtain correct monotonic asymptotic behavior around the origin of lateral electric field. This factor is of empirical form, which is a function of drain voltage (vd) and source voltage (vs) . After considering both the above steps we obtain drain current expression whose accuracy is similar to that obtained from second-order hyperbolic v -E model. In modified first-order hyperbolic v -E expression if vd and vs is replaced by smoothing functions for the effective drain voltage (vdeff) and effective source voltage (vseff), it will as well take care of discontinuity between linear to saturation regions of operation. The condition of symmetry is shown to be satisfied by drain current and its higher order derivatives, as both of them are odd functions and their even order derivatives smoothly pass through the origin. In strong inversion region and technology node of 22 nm the GST is shown to pass till sixth-order derivative and for weak inversion it is shown till fifth-order derivative. In the expression of drain current major short channel phenomena like vertical field mobility reduction, velocity saturation and velocity overshoot have been taken into consideration.

On the local well-posedness of Lovelock and Horndeski theories

NASA Astrophysics Data System (ADS)

Papallo, Giuseppe; Reall, Harvey S.

2017-08-01

We investigate local well-posedness of the initial value problem for Lovelock and Horndeski theories of gravity. A necessary condition for local well-posedness is strong hyperbolicity of the equations of motion. Even weak hyperbolicity can fail for strong fields so we restrict to weak fields. The Einstein equation is known to be strongly hyperbolic in harmonic gauge so we study Lovelock theories in harmonic gauge. We show that the equation of motion is always weakly hyperbolic for weak fields but, in a generic weak-field background, it is not strongly hyperbolic. For Horndeski theories, we prove that, for weak fields, the equation of motion is always weakly hyperbolic in any generalized harmonic gauge. For some Horndeski theories there exists a generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a weak-field background. This includes "k-essence" like theories. However, for more general Horndeski theories, there is no generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a generic weak-field background. Our results show that the standard method used to establish local well-posedness of the Einstein equation does not extend to Lovelock or general Horndeski theories. This raises the possibility that these theories may not admit a well-posed initial value problem even for weak fields.

Accuracy limitations of range-range (spherical) multilateration systems.

DOT National Transportation Integrated Search

1973-10-11

This report presents a novel procedure for determining the accuracy of range-range (or spherical) multilateration systems. The procedure is a generalization of one previously described for hyperbolic multilateration systems. A central result is a dem...

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Kutler, Paul (Technical Monitor)

1998-01-01

Several stabilized demoralization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin demoralization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS, and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobean linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Discrete maximum principle theory will be presented for general finite volume approximations on unstructured meshes. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc, will. be addressed as needed.

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Barth, Timothy; Chancellor, Marisa K. (Technical Monitor)

1997-01-01

Several stabilized discretization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin discretization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobian linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. These variants have been implemented in the "ELF" library for which example calculations will be shown. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Some prevalent limiting strategies will be reviewed. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc. will be addressed as needed.

Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations

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

Nordström, Jan, E-mail: jan.nordstrom@liu.se; Wahlsten, Markus, E-mail: markus.wahlsten@liu.se

We consider a hyperbolic system with uncertainty in the boundary and initial data. Our aim is to show that different boundary conditions give different convergence rates of the variance of the solution. This means that we can with the same knowledge of data get a more or less accurate description of the uncertainty in the solution. A variety of boundary conditions are compared and both analytical and numerical estimates of the variance of the solution are presented. As an application, we study the effect of this technique on Maxwell's equations as well as on a subsonic outflow boundary for themore » Euler equations.« less

The properties of Q-deformed hyperbolic and trigonometric functions in quantum deformation

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

Deta, U. A., E-mail: utamaalan@yahoo.co.id, E-mail: utamadeta@unesa.ac.id; Suparmi

2015-09-30

Quantum deformation has been studied due to its relation with applications in nuclear physics, conformal field theory, and statistical-quantum theory. The q-deformation of hyperbolic function was introduced by Arai. The application of q-deformed functions has been widely used in quantum mechanics. The properties of this two kinds of system explained in this paper including their derivative. The graph of q-deformed functions presented using Matlab. The special case is given for modified Poschl-Teller plus q-deformed Scarf II trigonometry potentials.

General relativistic hydrodynamics with Adaptive-Mesh Refinement (AMR) and modeling of accretion disks

NASA Astrophysics Data System (ADS)

Donmez, Orhan

We present a general procedure to solve the General Relativistic Hydrodynamical (GRH) equations with Adaptive-Mesh Refinement (AMR) and model of an accretion disk around a black hole. To do this, the GRH equations are written in a conservative form to exploit their hyperbolic character. The numerical solutions of the general relativistic hydrodynamic equations is done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. We use Marquina fluxes with MUSCL left and right states to solve GRH equations. First, we carry out different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations to verify the second order convergence of the code in 1D, 2 D and 3D. Second, we solve the GRH equations and use the general relativistic test problems to compare the numerical solutions with analytic ones. In order to this, we couple the flux part of general relativistic hydrodynamic equation with a source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time. The test problems examined include shock tubes, geodesic flows, and circular motion of particle around the black hole. Finally, we apply this code to the accretion disk problems around the black hole using the Schwarzschild metric at the background of the computational domain. We find spiral shocks on the accretion disk. They are observationally expected results. We also examine the star-disk interaction near a massive black hole. We find that when stars are grounded down or a hole is punched on the accretion disk, they create shock waves which destroy the accretion disk.

The High-Resolution Wave-Propagation Method Applied to Meso- and Micro-Scale Flows

NASA Technical Reports Server (NTRS)

Ahmad, Nashat N.; Proctor, Fred H.

2012-01-01

The high-resolution wave-propagation method for computing the nonhydrostatic atmospheric flows on meso- and micro-scales is described. The design and implementation of the Riemann solver used for computing the Godunov fluxes is discussed in detail. The method uses a flux-based wave decomposition in which the flux differences are written directly as the linear combination of the right eigenvectors of the hyperbolic system. The two advantages of the technique are: 1) the need for an explicit definition of the Roe matrix is eliminated and, 2) the inclusion of source term due to gravity does not result in discretization errors. The resulting flow solver is conservative and able to resolve regions of large gradients without introducing dispersion errors. The methodology is validated against exact analytical solutions and benchmark cases for non-hydrostatic atmospheric flows.

A symmetric bipolar nebula around MWC 922.

PubMed

Tuthill, P G; Lloyd, J P

2007-04-13

We report regular and symmetric structure around dust-enshrouded Be star MWC 922 obtained with infrared imaging. Biconical lobes that appear nearly square in aspect, forming this "Red Square" nebula, are crossed by a series of rungs that terminate in bright knots or "vortices," and an equatorial dark band crossing the core delimits twin hyperbolic arcs. The intricate yet cleanly constructed forms that comprise the skeleton of the object argue for minimal perturbation from global turbulent or chaotic effects. We also report the presence of a linear comb structure, which may arise from optically projected shadows of a periodic feature in the inner regions, such as corrugations in the rim of a circumstellar disk. The sequence of nested polar rings draws comparison with the triple-ring system seen around the only naked-eye supernova in recent history: SN1987A.

Magnetic hyperbolic optical metamaterials

DOE PAGES

Kruk, Sergey S.; Wong, Zi Jing; Pshenay-Severin, Ekaterina; ...

2016-04-13

Strongly anisotropic media where the principal components of electric permittivity or magnetic permeability tensors have opposite signs are termed as hyperbolic media. Such media support propagating electromagnetic waves with extremely large wave vectors exhibiting unique optical properties. However, in all artificial and natural optical materials studied to date, the hyperbolic dispersion originates solely from the electric response. This then restricts material functionality to one polarization of light and inhibits free-space impedance matching. Such restrictions can be overcome in media having components of opposite signs for both electric and magnetic tensors. Here we present the experimental demonstration of the magnetic hyperbolicmore » dispersion in three-dimensional metamaterials. We also measure metamaterial isofrequency contours and reveal the topological phase transition between the elliptic and hyperbolic dispersion. In the hyperbolic regime, we demonstrate the strong enhancement of thermal emission, which becomes directional, coherent and polarized. These findings show the possibilities for realizing efficient impedance-matched hyperbolic media for unpolarized light.« less

Fabrication of ф 160 mm convex hyperbolic mirror for remote sensing instrument

NASA Astrophysics Data System (ADS)

Kuo, Ching-Hsiang; Yu, Zong-Ru; Ho, Cheng-Fang; Hsu, Wei-Yao; Chen, Fong-Zhi

2012-10-01

In this study, efficient polishing processes with inspection procedures for a large convex hyperbolic mirror of Cassegrain optical system are presented. The polishing process combines the techniques of conventional lapping and CNC polishing. We apply the conventional spherical lapping process to quickly remove the sub-surface damage (SSD) layer caused by grinding process and to get the accurate radius of best-fit sphere (BFS) of aspheric surface with fine surface texture simultaneously. Thus the removed material for aspherization process can be minimized and the polishing time for SSD removal can also be reduced substantially. The inspection procedure was carried out by using phase shift interferometer with CGH and stitching technique. To acquire the real surface form error of each sub aperture, the wavefront errors of the reference flat and CGH flat due to gravity effect of the vertical setup are calibrated in advance. Subsequently, we stitch 10 calibrated sub-aperture surface form errors to establish the whole irregularity of the mirror in 160 mm diameter for correction polishing. The final result of the In this study, efficient polishing processes with inspection procedures for a large convex hyperbolic mirror of Cassegrain optical system are presented. The polishing process combines the techniques of conventional lapping and CNC polishing. We apply the conventional spherical lapping process to quickly remove the sub-surface damage (SSD) layer caused by grinding process and to get the accurate radius of best-fit sphere (BFS) of aspheric surface with fine surface texture simultaneously. Thus the removed material for aspherization process can be minimized and the polishing time for SSD removal can also be reduced substantially. The inspection procedure was carried out by using phase shift interferometer with CGH and stitching technique. To acquire the real surface form error of each sub aperture, the wavefront errors of the reference flat and CGH flat due to gravity effect of the vertical setup are calibrated in advance. Subsequently, we stitch 10 calibrated sub-aperture surface form errors to establish the whole irregularity of the mirror in 160 mm diameter for correction polishing. The final result of the Fabrication of ф160 mm Convex Hyperbolic Mirror for Remote Sensing Instrument160 mm convex hyperbolic mirror is 0.15 μm PV and 17.9 nm RMS.160 mm convex hyperbolic mirror is 0.15 μm PV and 17.9 nm RMS.

The growth rate of vertex-transitive planar graphs

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

Babai, L.

1997-06-01

A graph is vertex-transitive if all of its vertices axe equivalent under automorphisms. Confirming a conjecture of Jon Kleinberg and Eva Tardos, we prove the following trichotomy theorem concerning locally finite vertex-transitive planar graphs: the rate of growth of a graph with these properties is either linear or quadratic or exponential. The same result holds more generally for locally finite, almost vertex-transitive planar graphs (the automorphism group has a finite number of orbits). The proof uses the elements of hyperbolic plane geometry.

Optimal strategies for the control of autonomous vehicles in data assimilation

NASA Astrophysics Data System (ADS)

McDougall, D.; Moore, R. O.

2017-08-01

We propose a method to compute optimal control paths for autonomous vehicles deployed for the purpose of inferring a velocity field. In addition to being advected by the flow, the vehicles are able to effect a fixed relative speed with arbitrary control over direction. It is this direction that is used as the basis for the locally optimal control algorithm presented here, with objective formed from the variance trace of the expected posterior distribution. We present results for linear flows near hyperbolic fixed points.

The Hype over Hyperbolic Browsers.

ERIC Educational Resources Information Center

Allen, Maryellen Mott

2002-01-01

Considers complaints about the usability in the human-computer interaction aspect of information retrieval and discusses information visualization, the Online Library of Information Visualization Environments, hyperbolic information structure, subject searching, real-world applications, relational databases and hyperbolic trees, and the future of…

Adaptive aperture for Geiger mode avalanche photodiode flash ladar systems.

PubMed

Wang, Liang; Han, Shaokun; Xia, Wenze; Lei, Jieyu

2018-02-01

Although the Geiger-mode avalanche photodiode (GM-APD) flash ladar system offers the advantages of high sensitivity and simple construction, its detection performance is influenced not only by the incoming signal-to-noise ratio but also by the absolute number of noise photons. In this paper, we deduce a hyperbolic approximation to estimate the noise-photon number from the false-firing percentage in a GM-APD flash ladar system under dark conditions. By using this hyperbolic approximation function, we introduce a method to adapt the aperture to reduce the number of incoming background-noise photons. Finally, the simulation results show that the adaptive-aperture method decreases the false probability in all cases, increases the detection probability provided that the signal exceeds the noise, and decreases the average ranging error per frame.

Adaptive aperture for Geiger mode avalanche photodiode flash ladar systems

NASA Astrophysics Data System (ADS)

Wang, Liang; Han, Shaokun; Xia, Wenze; Lei, Jieyu

2018-02-01

Although the Geiger-mode avalanche photodiode (GM-APD) flash ladar system offers the advantages of high sensitivity and simple construction, its detection performance is influenced not only by the incoming signal-to-noise ratio but also by the absolute number of noise photons. In this paper, we deduce a hyperbolic approximation to estimate the noise-photon number from the false-firing percentage in a GM-APD flash ladar system under dark conditions. By using this hyperbolic approximation function, we introduce a method to adapt the aperture to reduce the number of incoming background-noise photons. Finally, the simulation results show that the adaptive-aperture method decreases the false probability in all cases, increases the detection probability provided that the signal exceeds the noise, and decreases the average ranging error per frame.

Point coordinates extraction from localized hyperbolic reflections in GPR data

NASA Astrophysics Data System (ADS)

Ristić, Aleksandar; Bugarinović, Željko; Vrtunski, Milan; Govedarica, Miro

2017-09-01

In this paper, we propose an automated detection algorithm for the localization of apexes and points on the prongs of hyperbolic reflection incurred as a result of GPR scanning technology. The objects of interest encompass cylindrical underground utilities that have a distinctive form of hyperbolic reflection in radargram. Algorithm involves application of trained neural network to analyze radargram in the form of raster image, resulting with extracted segments of interest that contain hyperbolic reflections. This significantly reduces the amount of data for further analysis. Extracted segments represent the zone for localization of apices. This is followed by extraction of points on prongs of hyperbolic reflections which is carried out until stopping criterion is satisfied, regardless the borders of segment of interest. In final step a classification of false hyperbolic reflections caused by the constructive interference and their removal is done. The algorithm is implemented in MATLAB environment. There are several advantages of the proposed algorithm. It can successfully recognize true hyperbolic reflections in radargram images and extracts coordinates, with very low rate of false detections and without prior knowledge about the number of hyperbolic reflections or buried utilities. It can be applied to radargrams containing single and multiple hyperbolic reflections, intersected, distorted, as well as incomplete (asymmetric) hyperbolic reflections, all in the presence of higher level of noise. Special feature of algorithm is developed procedure for analysis and removal of false hyperbolic reflections generated by the constructive interference from reflectors associated with the utilities. Algorithm was tested on a number of synthetic and radargram acquired in the field survey. To illustrate the performances of the proposed algorithm, we present the characteristics of the algorithm through five representative radargrams obtained in real conditions. In these examples we present different acquisition scenarios by varying the number of buried objects, their disposition, size, and level of noise. Example with highest complexity was tested also as a synthetic radargram generated by gprMax. Processing time in examples with one or two hyperbolic reflections is from 0.1 to 0.3 s, while for the most complex examples it is from 2.2 to 4.9 s. In general, the obtained experimental results show that the proposed algorithm exhibits promising performances both in terms of utility detection and processing speed of the algorithm.

On the hyperbolicity and stability of 3+1 formulations of metric f( R) gravity

NASA Astrophysics Data System (ADS)

Mongwane, Bishop

2016-11-01

3+1 formulations of the Einstein field equations have become an invaluable tool in Numerical relativity, having been used successfully in modeling spacetimes of black hole collisions, stellar collapse and other complex systems. It is plausible that similar considerations could prove fruitful for modified gravity theories. In this article, we pursue from a numerical relativistic viewpoint the 3+1 formulation of metric f( R) gravity as it arises from the fourth order equations of motion, without invoking the dynamical equivalence with Brans-Dicke theories. We present the resulting system of evolution and constraint equations for a generic function f( R), subject to the usual viability conditions. We confirm that the time propagation of the f( R) Hamiltonian and Momentum constraints take the same Mathematical form as in general relativity, irrespective of the f( R) model. We further recast the 3+1 system in a form akin to the BSSNOK formulation of numerical relativity. Without assuming any specific model, we show that the ADM version of f( R) is weakly hyperbolic and is plagued by similar zero speed modes as in the general relativity case. On the other hand the BSSNOK version is strongly hyperbolic and hence a promising formulation for numerical simulations in metric f( R) theories.

Quantum integrable systems from conformal blocks

NASA Astrophysics Data System (ADS)

Chen, Heng-Yu; Qualls, Joshua D.

2017-05-01

In this note, we extend the striking connections between quantum integrable systems and conformal blocks recently found in [M. Isachenkov and V. Schomerus, Phys. Rev. Lett. 117, 071602 (2016), 10.1103/PhysRevLett.117.071602] in several directions. First, we explicitly demonstrate that the action of the quartic conformal Casimir operator on general d-dimensional scalar conformal blocks can be expressed in terms of certain combinations of commuting integrals of motions of the two particle hyperbolic BC2 Calogero-Sutherland system. The permutation and reflection properties of the underlying Dunkl operators play crucial roles in establishing such a connection. Next, we show that the scalar superconformal blocks in superconformal field theories (SCFTs) with four and eight supercharges and suitable chirality constraints can also be identified with the eigenfunctions of the same Calogero-Sutherland system; this demonstrates the universality of such a connection. Finally, we observe that the so-called "seed" conformal blocks for constructing four point functions for operators with arbitrary space-time spins in four-dimensional CFTs can also be linearly expanded in terms of Calogero-Sutherland eigenfunctions.

Wavelets and Affine Distributions: A Time-Frequency Perspective

DTIC Science & Technology

2005-01-07

Ville Distribution ( WVD ) • Prominent member of the AC: the WVD • Properties of the WVD : – Covariant to TF scaling and time shift (of course) – Covariant...QTFRs • Wigner - Ville distribution and affine smoothing • Doppler tolerance and hyperbolic impulses • Hyperbolic TF localization and Bertrand P0...satisfy hyperbolic TF localization property: • Not satisfied by WVD ! 25 – 49 –WAMA-04 Cargèse, France The Bertrand P0 distribution • The hyperbolic

Thermal emitter comprising near-zero permittivity materials

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

Luk, Ting S.; Campione, Salvatore; Sinclair, Michael B.

A novel thermal source comprising a semiconductor hyperbolic metamaterial provides control of the emission spectrum and the angular emission pattern. These properties arise because of epsilon-near-zero conditions in the semiconductor hyperbolic metamaterial. In particular, the thermal emission is dominated by the epsilon-near-zero effect in the doped quantum wells composing the semiconductor hyperbolic metamaterial. Furthermore, different properties are observed for s and p polarizations, following the characteristics of the strong anisotropy of hyperbolic metamaterials.

On the identification of continuous vibrating systems modelled by hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Udwadia, F. E.; Garba, J. A.

1983-01-01

This paper deals with the identification of spatially varying parameters in systems of finite spatial extent which can be described by second order hyperbolic differential equations. Two questions have been addressed. The first deals with 'partial identification' and inquires into the possibility of retrieving all the eigenvalues of the system from response data obtained at one location x-asterisk epsilon (0, 1). The second deals with the identification of the distributed coefficients rho(x), a(x) and b(x). Sufficient conditions for unique identification of all the eigenvalues of the system are obtained, and conditions under which the coefficients can be uniquely identified using suitable response data obtained at one point in the spatial domain are determined. Application of the results and their usefulness is demonstrated in the identification of the properties of tall building structural systems subjected to dynamic load environments.

Jacobian-free approximate solvers for hyperbolic systems: Application to relativistic magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Castro, Manuel J.; Gallardo, José M.; Marquina, Antonio

2017-10-01

We present recent advances in PVM (Polynomial Viscosity Matrix) methods based on internal approximations to the absolute value function, and compare them with Chebyshev-based PVM solvers. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Another important feature of the proposed methods is that they are suitable to be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems for which the Jacobians involve complex expressions, e.g., the relativistic magnetohydrodynamics (RMHD) equations. On the other hand, the proposed Jacobian-free solvers have also been extended to the case of approximate DOT (Dumbser-Osher-Toro) methods, which can be regarded as simple and efficient approximations to the classical Osher-Solomon method, sharing most of it interesting features and being applicable to general hyperbolic systems. To test the properties of our schemes a number of numerical experiments involving the RMHD equations are presented, both in one and two dimensions. The obtained results are in good agreement with those found in the literature and show that our schemes are robust and accurate, running stable under a satisfactory time step restriction. It is worth emphasizing that, although this work focuses on RMHD, the proposed schemes are suitable to be applied to general hyperbolic systems.

Deep-Ultraviolet Hyperbolic Metacavity Laser.

PubMed

Shen, Kun-Ching; Ku, Chen-Ta; Hsieh, Chiieh; Kuo, Hao-Chung; Cheng, Yuh-Jen; Tsai, Din Ping

2018-05-01

Given the high demand for miniaturized optoelectronic circuits, plasmonic devices with the capability of generating coherent radiation at deep subwavelength scales have attracted great interest for diverse applications such as nanoantennas, single photon sources, and nanosensors. However, the design of such lasing devices remains a challenging issue because of the long structure requirements for producing strong radiation feedback. Here, a plasmonic laser made by using a nanoscale hyperbolic metamaterial cube, called hyperbolic metacavity, on a multiple quantum-well (MQW), deep-ultraviolet emitter is presented. The specifically designed metacavity merges plasmon resonant modes within the cube and provides a unique resonant radiation feedback to the MQW. This unique plasmon field allows the dipoles of the MQW with various orientations into radiative emission, achieving enhancement of spontaneous emission rate by a factor of 33 and of quantum efficiency by a factor of 2.5, which is beneficial for coherent laser action. The hyperbolic metacavity laser shows a clear clamping of spontaneous emission above the threshold, which demonstrates a near complete radiation coupling of the MQW with the metacavity. This approach shown here can greatly simplify the requirements of plasmonic nanolaser with a long plasmonic structure, and the metacavity effect can be extended to many other material systems. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Embedding recurrent neural networks into predator-prey models.

PubMed

Moreau, Yves; Louiès, Stephane; Vandewalle, Joos; Brenig, Leon

1999-03-01

We study changes of coordinates that allow the embedding of ordinary differential equations describing continuous-time recurrent neural networks into differential equations describing predator-prey models-also called Lotka-Volterra systems. We transform the equations for the neural network first into quasi-monomial form (Brenig, L. (1988). Complete factorization and analytic solutions of generalized Lotka-Volterra equations. Physics Letters A, 133(7-8), 378-382), where we express the vector field of the dynamical system as a linear combination of products of powers of the variables. In practice, this transformation is possible only if the activation function is the hyperbolic tangent or the logistic sigmoid. From this quasi-monomial form, we can directly transform the system further into Lotka-Volterra equations. The resulting Lotka-Volterra system is of higher dimension than the original system, but the behavior of its first variables is equivalent to the behavior of the original neural network. We expect that this transformation will permit the application of existing techniques for the analysis of Lotka-Volterra systems to recurrent neural networks. Furthermore, our results show that Lotka-Volterra systems are universal approximators of dynamical systems, just as are continuous-time neural networks.

Klein bottle logophysics: a unified principle for non-linear systems, cosmology, geophysics, biology, biomechanics and perception

NASA Astrophysics Data System (ADS)

Lucio Rapoport, Diego

2013-04-01

We present a unified principle for science that surmounts dualism, in terms of torsion fields and the non-orientable surfaces, notably the Klein Bottle and its logic, the Möbius strip and the projective plane. We apply it to the complex numbers and cosmology, to non-linear systems integrating the issue of hyperbolic divergences with the change of orientability, to the biomechanics of vision and the mammal heart, to the morphogenesis of crustal shapes on Earth in connection to the wavefronts of gravitation, elasticity and electromagnetism, to pattern recognition of artificial images and visual recognition, to neurology and the topographic maps of the sensorium, to perception, in particular of music. We develop it in terms of the fundamental 2:1 resonance inherent to the Möbius strip and the Klein Bottle, the minimal surfaces representation of the wavefronts, and the non-dual Klein Bottle logic inherent to pattern recognition, to the harmonic functions and vector fields that lay at the basis of geophysics and physics at large. We discuss the relation between the topographic maps of the sensorium, and the issue of turning inside-out of the visual world as a general principle for cognition, topological chemistry, cell biology and biological morphogenesis in particular in embryology

Parabolic replicator dynamics and the principle of minimum Tsallis information gain

PubMed Central

2013-01-01

Background Non-linear, parabolic (sub-exponential) and hyperbolic (super-exponential) models of prebiological evolution of molecular replicators have been proposed and extensively studied. The parabolic models appear to be the most realistic approximations of real-life replicator systems due primarily to product inhibition. Unlike the more traditional exponential models, the distribution of individual frequencies in an evolving parabolic population is not described by the Maximum Entropy (MaxEnt) Principle in its traditional form, whereby the distribution with the maximum Shannon entropy is chosen among all the distributions that are possible under the given constraints. We sought to identify a more general form of the MaxEnt principle that would be applicable to parabolic growth. Results We consider a model of a population that reproduces according to the parabolic growth law and show that the frequencies of individuals in the population minimize the Tsallis relative entropy (non-additive information gain) at each time moment. Next, we consider a model of a parabolically growing population that maintains a constant total size and provide an “implicit” solution for this system. We show that in this case, the frequencies of the individuals in the population also minimize the Tsallis information gain at each moment of the ‘internal time” of the population. Conclusions The results of this analysis show that the general MaxEnt principle is the underlying law for the evolution of a broad class of replicator systems including not only exponential but also parabolic and hyperbolic systems. The choice of the appropriate entropy (information) function depends on the growth dynamics of a particular class of systems. The Tsallis entropy is non-additive for independent subsystems, i.e. the information on the subsystems is insufficient to describe the system as a whole. In the context of prebiotic evolution, this “non-reductionist” nature of parabolic replicator systems might reflect the importance of group selection and competition between ensembles of cooperating replicators. Reviewers This article was reviewed by Viswanadham Sridhara (nominated by Claus Wilke), Puushottam Dixit (nominated by Sergei Maslov), and Nick Grishin. For the complete reviews, see the Reviewers’ Reports section. PMID:23937956

Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation

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

Ruban, V. P., E-mail: ruban@itp.ac.ru

2015-05-15

The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of roguemore » wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.« less

Infrared hyperbolic metasurface based on nanostructured van der Waals materials

NASA Astrophysics Data System (ADS)

Li, Peining; Dolado, Irene; Alfaro-Mozaz, Francisco Javier; Casanova, Fèlix; Hueso, Luis E.; Liu, Song; Edgar, James H.; Nikitin, Alexey Y.; Vélez, Saül; Hillenbrand, Rainer

2018-02-01

Metasurfaces with strongly anisotropic optical properties can support deep subwavelength-scale confined electromagnetic waves (polaritons), which promise opportunities for controlling light in photonic and optoelectronic applications. We developed a mid-infrared hyperbolic metasurface by nanostructuring a thin layer of hexagonal boron nitride that supports deep subwavelength-scale phonon polaritons that propagate with in-plane hyperbolic dispersion. By applying an infrared nanoimaging technique, we visualize the concave (anomalous) wavefronts of a diverging polariton beam, which represent a landmark feature of hyperbolic polaritons. The results illustrate how near-field microscopy can be applied to reveal the exotic wavefronts of polaritons in anisotropic materials and demonstrate that nanostructured van der Waals materials can form a highly variable and compact platform for hyperbolic infrared metasurface devices and circuits.

On the Behavior of Eisenstein Series Through Elliptic Degeneration

NASA Astrophysics Data System (ADS)

Garbin, D.; Pippich, A.-M. V.

2009-12-01

Let Γ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane {mathbb{H}}, and let {M = Γbackslash mathbb{H}} be the associated finite volume hyperbolic Riemann surface. If γ is a primitive parabolic, hyperbolic, resp. elliptic element of Γ, there is an associated parabolic, hyperbolic, resp. elliptic Eisenstein series. In this article, we study the limiting behavior of these Eisenstein series on an elliptically degenerating family of finite volume hyperbolic Riemann surfaces. In particular, we prove the following result. The elliptic Eisenstein series associated to a degenerating elliptic element converges up to a factor to the parabolic Eisenstein series associated to the parabolic element which fixes the newly developed cusp on the limit surface.

Hyperbolic metamaterials: new physics behind a classical problem.

PubMed

Drachev, Vladimir P; Podolskiy, Viktor A; Kildishev, Alexander V

2013-06-17

Hyperbolic materials enable numerous surprising applications that include far-field subwavelength imaging, nanolithography, and emission engineering. The wavevector of a plane wave in these media follows the surface of a hyperboloid in contrast to an ellipsoid for conventional anisotropic dielectric. The consequences of hyperbolic dispersion were first studied in the 50's pertaining to the problems of electromagnetic wave propagation in the Earth's ionosphere and in the stratified artificial materials of transmission lines. Recent years have brought explosive growth in optics and photonics of hyperbolic media based on metamaterials across the optical spectrum. Here we summarize earlier theories in the Clemmow's prescription for transformation of the electromagnetic field in hyperbolic media and provide a review of recent developments in this active research area.

Guidance of Nonlinear Nonminimum-Phase Dynamic Systems

NASA Technical Reports Server (NTRS)

Devasia, Santosh

1997-01-01

The first two years research work has advanced the inversion-based guidance theory for: (1) systems with non-hyperbolic internal dynamics; (2) systems with parameter jumps; (3) systems where a redesign of the output trajectory is desired; and (4) the generation of recovery guidance maneuvers.

Polyhedra and packings from hyperbolic honeycombs.

PubMed

Pedersen, Martin Cramer; Hyde, Stephen T

2018-06-20

We derive more than 80 embeddings of 2D hyperbolic honeycombs in Euclidean 3 space, forming 3-periodic infinite polyhedra with cubic symmetry. All embeddings are "minimally frustrated," formed by removing just enough isometries of the (regular, but unphysical) 2D hyperbolic honeycombs [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] to allow embeddings in Euclidean 3 space. Nearly all of these triangulated "simplicial polyhedra" have symmetrically identical vertices, and most are chiral. The most symmetric examples include 10 infinite "deltahedra," with equilateral triangular faces, 6 of which were previously unknown and some of which can be described as packings of Platonic deltahedra. We describe also related cubic crystalline packings of equal hyperbolic discs in 3 space that are frustrated analogues of optimally dense hyperbolic disc packings. The 10-coordinated packings are the least "loosened" Euclidean embeddings, although frustration swells all of the hyperbolic disc packings to give less dense arrays than the flat penny-packing even though their unfrustrated analogues in [Formula: see text] are denser.

Boundary causality versus hyperbolicity for spherical black holes in Gauss-Bonnet gravity

NASA Astrophysics Data System (ADS)

Andrade, Tomás; Cáceres, Elena; Keeler, Cynthia

2017-07-01

We explore the constraints boundary causality places on the allowable Gauss-Bonnet gravitational couplings in asymptotically AdS spaces, specifically considering spherical black hole solutions. We additionally consider the hyperbolicity properties of these solutions, positing that hyperbolicity-violating solutions are sick solutions whose causality properties provide no information about the theory they reside in. For both signs of the Gauss-Bonnet coupling, spherical black holes violate boundary causality at smaller absolute values of the coupling than planar black holes do. For negative coupling, as we tune the Gauss-Bonnet coupling away from zero, both spherical and planar black holes violate hyperbolicity before they violate boundary causality. For positive coupling, the only hyperbolicity-respecting spherical black holes which violate boundary causality do not do so appreciably far from the planar bound. Consequently, eliminating hyperbolicity-violating solutions means the bound on Gauss-Bonnet couplings from the boundary causality of spherical black holes is no tighter than that from planar black holes.

Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces

NASA Astrophysics Data System (ADS)

Cammarota, V.; Orsingher, E.

2008-12-01

A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincaré half-plane and Poincaré disk) is examined. Each particle can split into two particles only once at Poisson spaced times and deviates orthogonally when splitted. At time t, after N( t) Poisson events, there are N( t)+1 particles moving along different geodesic lines. We are able to obtain the exact expression of the mean hyperbolic distance of the center of mass of the cloud of particles. We derive such mean hyperbolic distance from two different and independent ways and we study the behavior of the relevant expression as t increases and for different values of the parameters c (hyperbolic velocity of motion) and λ (rate of reproduction). The mean hyperbolic distance of each moving particle is also examined and a useful representation, as the distance of a randomly stopped particle moving over the main geodesic line, is presented.

Super-Coulombic atom–atom interactions in hyperbolic media

PubMed Central

Cortes, Cristian L.; Jacob, Zubin

2017-01-01

Dipole–dipole interactions, which govern phenomena such as cooperative Lamb shifts, superradiant decay rates, Van der Waals forces and resonance energy transfer rates, are conventionally limited to the Coulombic near-field. Here we reveal a class of real-photon and virtual-photon long-range quantum electrodynamic interactions that have a singularity in media with hyperbolic dispersion. The singularity in the dipole–dipole coupling, referred to as a super-Coulombic interaction, is a result of an effective interaction distance that goes to zero in the ideal limit irrespective of the physical distance. We investigate the entire landscape of atom–atom interactions in hyperbolic media confirming the giant long-range enhancement. We also propose multiple experimental platforms to verify our predicted effect with phonon–polaritonic hexagonal boron nitride, plasmonic super-lattices and hyperbolic meta-surfaces as well. Our work paves the way for the control of cold atoms above hyperbolic meta-surfaces and the study of many-body physics with hyperbolic media. PMID:28120826

Super-Coulombic atom-atom interactions in hyperbolic media

NASA Astrophysics Data System (ADS)

Cortes, Cristian L.; Jacob, Zubin

2017-01-01

Dipole-dipole interactions, which govern phenomena such as cooperative Lamb shifts, superradiant decay rates, Van der Waals forces and resonance energy transfer rates, are conventionally limited to the Coulombic near-field. Here we reveal a class of real-photon and virtual-photon long-range quantum electrodynamic interactions that have a singularity in media with hyperbolic dispersion. The singularity in the dipole-dipole coupling, referred to as a super-Coulombic interaction, is a result of an effective interaction distance that goes to zero in the ideal limit irrespective of the physical distance. We investigate the entire landscape of atom-atom interactions in hyperbolic media confirming the giant long-range enhancement. We also propose multiple experimental platforms to verify our predicted effect with phonon-polaritonic hexagonal boron nitride, plasmonic super-lattices and hyperbolic meta-surfaces as well. Our work paves the way for the control of cold atoms above hyperbolic meta-surfaces and the study of many-body physics with hyperbolic media.

Code Samples Used for Complexity and Control

NASA Astrophysics Data System (ADS)

Ivancevic, Vladimir G.; Reid, Darryn J.

2015-11-01

The following sections are included: * MathematicaⓇ Code * Generic Chaotic Simulator * Vector Differential Operators * NLS Explorer * 2C++ Code * C++ Lambda Functions for Real Calculus * Accelerometer Data Processor * Simple Predictor-Corrector Integrator * Solving the BVP with the Shooting Method * Linear Hyperbolic PDE Solver * Linear Elliptic PDE Solver * Method of Lines for a Set of the NLS Equations * C# Code * Iterative Equation Solver * Simulated Annealing: A Function Minimum * Simple Nonlinear Dynamics * Nonlinear Pendulum Simulator * Lagrangian Dynamics Simulator * Complex-Valued Crowd Attractor Dynamics * Freeform Fortran Code * Lorenz Attractor Simulator * Complex Lorenz Attractor * Simple SGE Soliton * Complex Signal Presentation * Gaussian Wave Packet * Hermitian Matrices * Euclidean L2-Norm * Vector/Matrix Operations * Plain C-Code: Levenberg-Marquardt Optimizer * Free Basic Code: 2D Crowd Dynamics with 3000 Agents

Stability analysis of spectral methods for hyperbolic initial-boundary value systems

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Lustman, L.; Tadmor, E.

1986-01-01

A constant coefficient hyperbolic system in one space variable, with zero initial data is discussed. Dissipative boundary conditions are imposed at the two points x = + or - 1. This problem is discretized by a spectral approximation in space. Sufficient conditions under which the spectral numerical solution is stable are demonstrated - moreover, these conditions have to be checked only for scalar equations. The stability theorems take the form of explicit bounds for the norm of the solution in terms of the boundary data. The dependence of these bounds on N, the number of points in the domain (or equivalently the degree of the polynomials involved), is investigated for a class of standard spectral methods, including Chebyshev and Legendre collocations.

Transition from complete synchronization to spatio-temporal chaos in coupled chaotic systems with nonhyperbolic and hyperbolic attractors

NASA Astrophysics Data System (ADS)

Rybalova, Elena; Semenova, Nadezhda; Strelkova, Galina; Anishchenko, Vadim

2017-06-01

We study the transition from coherence (complete synchronization) to incoherence (spatio-temporal chaos) in ensembles of nonlocally coupled chaotic maps with nonhyperbolic and hyperbolic attractors. As basic models of a partial element we use the Henon map and the Lozi map. We show that the transition to incoherence in a ring of coupled Henon maps occurs through the appearance of phase and amplitude chimera states. An ensemble of coupled Lozi maps demonstrates the coherence-incoherence transition via solitary states and no chimera states are observed in this case.

A Few New 2+1-Dimensional Nonlinear Dynamics and the Representation of Riemann Curvature Tensors

NASA Astrophysics Data System (ADS)

Wang, Yan; Zhang, Yufeng; Zhang, Xiangzhi

2016-09-01

We first introduced a linear stationary equation with a quadratic operator in ∂x and ∂y, then a linear evolution equation is given by N-order polynomials of eigenfunctions. As applications, by taking N=2, we derived a (2+1)-dimensional generalized linear heat equation with two constant parameters associative with a symmetric space. When taking N=3, a pair of generalized Kadomtsev-Petviashvili equations with the same eigenvalues with the case of N=2 are generated. Similarly, a second-order flow associative with a homogeneous space is derived from the integrability condition of the two linear equations, which is a (2+1)-dimensional hyperbolic equation. When N=3, the third second flow associative with the homogeneous space is generated, which is a pair of new generalized Kadomtsev-Petviashvili equations. Finally, as an application of a Hermitian symmetric space, we established a pair of spectral problems to obtain a new (2+1)-dimensional generalized Schrödinger equation, which is expressed by the Riemann curvature tensors.

Evolution of inviscid Kelvin-Helmholtz instability from a piecewise linear shear layer

NASA Astrophysics Data System (ADS)

Guha, Anirban; Rahmani, Mona; Lawrence, Gregory

2012-11-01

Here we study the evolution of 2D, inviscid Kelvin-Helmholtz instability (KH) ensuing from a piecewise linear shear layer. Although KH pertaining to smooth shear layers (eg. Hyperbolic tangent profile) has been thorough investigated in the past, very little is known about KH resulting from sharp shear layers. Pozrikidis and Higdon (1985) have shown that piecewise shear layer evolves into elliptical vortex patches. This non-linear state is dramatically different from the well known spiral-billow structure of KH. In fact, there is a little acknowledgement that elliptical vortex patches can represent non-linear KH. In this work, we show how such patches evolve through the interaction of vorticity waves. Our work is based on two types of computational methods (i) Contour Dynamics: a boundary-element method which tracks the evolution of the contour of a vortex patch using Lagrangian marker points, and (ii) Direct Numerical Simulation (DNS): an Eulerian pseudo-spectral method heavily used in studying hydrodynamic instability and turbulence.

Numerical Simulations of Free Surface Magnetohydrodynamic Flows

NASA Astrophysics Data System (ADS)

Samulyak, Roman; Glimm, James; Oh, Wonho; Prykarpatskyy, Yarema

2003-11-01

We have developed a numerical algorithm and performed simulations of magnetohydrodynamic (MHD) free surface flows. The corresponding system of MHD equations is a system of strongly coupled hyperbolic and parabolic/elliptic equations in moving and geometrically complex domains. The hyperbolic system is solved using the front tracking technique for the free fluid interface. Parallel algorithms for solving elliptic and parabolic equations are based on a finite element discretization on moving grids dynamically conforming to fluid interfaces. The method has been implemented as an MHD extension of the FronTier code. The code has been applied for modeling the behavior of lithium and mercury jets in magnetic fields, laser ablation plumes, and the Richtmyer-Meshkov instability of a liquid mercury jet interacting with a high energy proton pulse in a strong magnetic field. Such an instability occurs in the target for the Muon Collider.

Efficient embedding of complex networks to hyperbolic space via their Laplacian

PubMed Central

Alanis-Lobato, Gregorio; Mier, Pablo; Andrade-Navarro, Miguel A.

2016-01-01

The different factors involved in the growth process of complex networks imprint valuable information in their observable topologies. How to exploit this information to accurately predict structural network changes is the subject of active research. A recent model of network growth sustains that the emergence of properties common to most complex systems is the result of certain trade-offs between node birth-time and similarity. This model has a geometric interpretation in hyperbolic space, where distances between nodes abstract this optimisation process. Current methods for network hyperbolic embedding search for node coordinates that maximise the likelihood that the network was produced by the afore-mentioned model. Here, a different strategy is followed in the form of the Laplacian-based Network Embedding, a simple yet accurate, efficient and data driven manifold learning approach, which allows for the quick geometric analysis of big networks. Comparisons against existing embedding and prediction techniques highlight its applicability to network evolution and link prediction. PMID:27445157

Efficient embedding of complex networks to hyperbolic space via their Laplacian

NASA Astrophysics Data System (ADS)

Alanis-Lobato, Gregorio; Mier, Pablo; Andrade-Navarro, Miguel A.

2016-07-01

The different factors involved in the growth process of complex networks imprint valuable information in their observable topologies. How to exploit this information to accurately predict structural network changes is the subject of active research. A recent model of network growth sustains that the emergence of properties common to most complex systems is the result of certain trade-offs between node birth-time and similarity. This model has a geometric interpretation in hyperbolic space, where distances between nodes abstract this optimisation process. Current methods for network hyperbolic embedding search for node coordinates that maximise the likelihood that the network was produced by the afore-mentioned model. Here, a different strategy is followed in the form of the Laplacian-based Network Embedding, a simple yet accurate, efficient and data driven manifold learning approach, which allows for the quick geometric analysis of big networks. Comparisons against existing embedding and prediction techniques highlight its applicability to network evolution and link prediction.

Use of selection indices to model the functional response of predators

USGS Publications Warehouse

Joly, D.O.; Patterson, B.R.

2003-01-01

The functional response of a predator to changing prey density is an important determinant of stability of predatora??prey systems. We show how Manly's selection indices can be used to distinguish between hyperbolic and sigmoidal models of a predator functional response to primary prey density in the presence of alternative prey. Specifically, an inverse relationship between prey density and preference for that prey results in a hyperbolic functional response while a positive relationship can yield either a hyperbolic or sigmoidal functional response, depending on the form and relative magnitudes of the density-dependent preference model, attack rate, and handling time. As an example, we examine wolf (Canis lupus) functional response to moose (Alces alces) density in the presence of caribou (Rangifer tarandus). The use of selection indices to evaluate the form of the functional response has significant advantages over previous attempts to fit Holling's functional response curves to killing-rate data directly, including increased sensitivity, use of relatively easily collected data, and consideration of other explanatory factors (e.g., weather, seasons, productivity).

Lift of noninvariant solutions of heavenly equations from three to four dimensions and new ultra-hyperbolic metrics

NASA Astrophysics Data System (ADS)

Malykh, A. A.; Nutku, Y.; Sheftel, M. B.

2007-08-01

We demonstrate that partner symmetries provide a lift of noninvariant solutions of the three-dimensional Boyer-Finley equation to noninvariant solutions of the four-dimensional hyperbolic complex Monge-Ampère equation. The lift is applied to noninvariant solutions of the Boyer-Finley equation, obtained earlier by the method of group foliation, to yield noninvariant solutions of the hyperbolic complex Monge-Ampère equation. Using these solutions we construct new Ricci-flat ultra-hyperbolic metrics with non-zero curvature tensor that have no Killing vectors.

Construction of energy-stable projection-based reduced order models

DOE PAGES

Kalashnikova, Irina; Barone, Matthew F.; Arunajatesan, Srinivasan; ...

2014-12-15

Our paper aims to unify and extend several approaches for building stable projection-based reduced order models (ROMs) using the energy method and the concept of “energy-stability”. Attention is focused on linear time-invariant (LTI) systems. First, an approach for building energy stable Galerkin ROMs for linear hyperbolic or incompletely parabolic systems of partial differential equations (PDEs) using continuous projection is proposed. The key idea is to apply to the system a transformation induced by the Lyapunov function for the system, and to build the ROM in the transformed variables. The result of this procedure will be a ROM that is energy-stablemore » for any choice of reduced basis. It is shown that, for many PDE systems, the desired transformation is induced by a special inner product, termed the “symmetry inner product”. Next, attention is turned to building energy-stable ROMs via discrete projection. A discrete counterpart of the continuous symmetry inner product, termed the “Lyapunov inner product”, is derived. Moreover, it is shown that the Lyapunov inner product can be computed in a black-box fashion for a stable LTI system ari sing from the discretization of a system of PDEs in space. Projection in this inner product guarantees a ROM that is energy-stable, again for any choice of reduced basis. Connections between the Lyapunov inner product and the inner product induced by the balanced truncation algorithm are made. We also made comparisons between the symmetry inner product and the Lyapunov inner product. Performance of ROMs constructed using these inner products is evaluated on several benchmark test cases.« less

On Stable Wall Boundary Conditions for the Hermite Discretization of the Linearised Boltzmann Equation

NASA Astrophysics Data System (ADS)

Sarna, Neeraj; Torrilhon, Manuel

2018-01-01

We define certain criteria, using the characteristic decomposition of the boundary conditions and energy estimates, which a set of stable boundary conditions for a linear initial boundary value problem, involving a symmetric hyperbolic system, must satisfy. We first use these stability criteria to show the instability of the Maxwell boundary conditions proposed by Grad (Commun Pure Appl Math 2(4):331-407, 1949). We then recognise a special block structure of the moment equations which arises due to the recursion relations and the orthogonality of the Hermite polynomials; the block structure will help us in formulating stable boundary conditions for an arbitrary order Hermite discretization of the Boltzmann equation. The formulation of stable boundary conditions relies upon an Onsager matrix which will be constructed such that the newly proposed boundary conditions stay close to the Maxwell boundary conditions at least in the lower order moments.

Boundary Closures for Fourth-order Energy Stable Weighted Essentially Non-Oscillatory Finite Difference Schemes

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.; Yamaleev, Nail K.; Frankel, Steven H.

2009-01-01

A general strategy exists for constructing Energy Stable Weighted Essentially Non Oscillatory (ESWENO) finite difference schemes up to eighth-order on periodic domains. These ESWENO schemes satisfy an energy norm stability proof for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, boundary closures are developed for the fourth-order ESWENO scheme that maintain wherever possible the WENO stencil biasing properties, while satisfying the summation-by-parts (SBP) operator convention, thereby ensuring stability in an L2 norm. Second-order, and third-order boundary closures are developed that achieve stability in diagonal and block norms, respectively. The global accuracy for the second-order closures is three, and for the third-order closures is four. A novel set of non-uniform flux interpolation points is necessary near the boundaries to simultaneously achieve 1) accuracy, 2) the SBP convention, and 3) WENO stencil biasing mechanics.

Arnold diffusion for smooth convex systems of two and a half degrees of freedom

NASA Astrophysics Data System (ADS)

Kaloshin, V.; Zhang, K.

2015-08-01

In the present note we announce a proof of a strong form of Arnold diffusion for smooth convex Hamiltonian systems. Let { T}2 be a 2-dimensional torus and B2 be the unit ball around the origin in { R}2 . Fix ρ > 0. Our main result says that for a ‘generic’ time-periodic perturbation of an integrable system of two degrees of freedom H_0(p)+\\varepsilon H_1(θ,p,t),\\quad θ\\in { T}^2, p\\in B^2, t\\in { T}={ R}/{ Z} , with a strictly convex H0, there exists a ρ-dense orbit (θε, pε, t)(t) in { T}2 × B2 × { T} , namely, a ρ-neighborhood of the orbit contains { T}2 × B2 × { T} . Our proof is a combination of geometric and variational methods. The fundamental elements of the construction are the usage of crumpled normally hyperbolic invariant cylinders from [9], flower and simple normally hyperbolic invariant manifolds from [36] as well as their kissing property at a strong double resonance. This allows us to build a ‘connected’ net of three-dimensional normally hyperbolic invariant manifolds. To construct diffusing orbits along this net we employ a version of the Mather variational method [41] equipped with weak KAM theory [28], proposed by Bernard in [7].

Assessing the relative bioavailability of DOC in regional groundwater systems

USGS Publications Warehouse

Chapelle, Francis H.; Bradley, Paul M.; Journey, Celeste A.; McMahon, Peter B.

2013-01-01

It has been hypothesized that the degree to which a hyperbolic relationship exists between concentrations of dissolved organic carbon (DOC) and dissolved oxygen (DO) in groundwater may indicate the relative bioavailability of DOC. This hypothesis was examined for 73 different regional aquifers of the United States using 7745 analyses of groundwater compiled by the National Water Assessment (NAWQA) program of the U.S. Geological Survey. The relative reaction quotient (RRQ), a measure of the curvature of DOC concentrations plotted versus DO concentrations and regressed to a decaying hyperbolic equation, was used to assess the relative bioavailability of DOC. For the basalt aquifer of Oahu, Hawaii, RRQ values were low (0.0013 mM−2), reflecting a nearly random relationship between DOC and DO concentrations. In contrast, on the island of Maui, treated sewage effluent injected into a portion of the basalt aquifer resulted in pronounced hyperbolic DOC-DO behavior and a higher RRQ (142 mM−2). RRQ values for the 73 aquifers correlated positively with mean concentrations of ammonia, dissolved iron, and manganese, and correlated negatively with mean pH. This indicates that greater RRQ values are associated with greater concentrations of the final products of microbial reduction reactions. RRQ values and DOC concentrations were negatively correlated with the thickness of the unsaturated zone (UNST) and depth to the top of the screened interval. Finally, RRQ values were positively correlated with mean annual precipitation (MAP), and the highest observed RRQ values were associated with aquifers receiving MAP rates ranging between 900 and 1300 mm/year. These results are uniformly consistent with the hypothesis that the hyperbolic behavior of DOC-DO plots, as quantified by the RRQ metric, can be an indicator of relative DOC bioavailability in groundwater systems.

"That's Really Clever!" Ironic Hyperbole Understanding in Children

ERIC Educational Resources Information Center

Aguert, Marc; Le Vallois, Coralie; Martel, Karine; Laval, Virginie

2018-01-01

Hyperbole supports irony comprehension in adults by heightening the contrast between what is said and the actual situation. Because young children do not perceive the communication situation as a whole, but rather give precedence to either the utterance or the context, we predicted that hyperbole would reduce irony comprehension in six-year-olds…

Human red blood cell behavior under homogeneous extensional flow in a hyperbolic-shaped microchannel.

PubMed

Yaginuma, T; Oliveira, M S N; Lima, R; Ishikawa, T; Yamaguchi, T

2013-01-01

It is well known that certain pathological conditions result in a decrease of red blood cells (RBCs) deformability and subsequently can significantly alter the blood flow in microcirculation, which may block capillaries and cause ischemia in the tissues. Microfluidic systems able to obtain reliable quantitative measurements of RBC deformability hold the key to understand and diagnose RBC related diseases. In this work, a microfluidic system composed of a microchannel with a hyperbolic-shaped contraction followed by a sudden expansion is presented. We provide a detailed quantitative description of the degree of deformation of human RBCs under a controlled homogeneous extensional flow field. We measured the deformation index (DI) as well as the velocity of the RBCs travelling along the centerline of the channel for four different flow rates and analyze the impact of the particle Reynolds number. The results show that human RBC deformation tends to reach a plateau value in the region of constant extensional rate, the value of which depends on the extension rate. Additionally, we observe that the presence of a sudden expansion downstream of the hyperbolic contraction modifies the spatial distribution of cells and substantially increases the cell free layer (CFL) downstream of the expansion plane similarly to what is seen in other expansion flows. Beyond a certain value of flow rate, there is only a weak effect of inlet flow rates on the enhancement of the downstream CFL. These in vitro experiments show the potential of using microfluidic systems with hyperbolic-shaped microchannels both for the separation of the RBCs from plasma and to assess changes in RBC deformability in physiological and pathological situations for clinical purposes. However, the selection of the geometry and the identification of the most suitable region to evaluate the changes on the RBC deformability under extensional flows are crucial if microfluidics is to be used as an in vitro clinical methodology to detect circulatory diseases.

Human red blood cell behavior under homogeneous extensional flow in a hyperbolic-shaped microchannel

PubMed Central

Yaginuma, T.; Oliveira, M. S. N.; Lima, R.; Ishikawa, T.; Yamaguchi, T.

2013-01-01

It is well known that certain pathological conditions result in a decrease of red blood cells (RBCs) deformability and subsequently can significantly alter the blood flow in microcirculation, which may block capillaries and cause ischemia in the tissues. Microfluidic systems able to obtain reliable quantitative measurements of RBC deformability hold the key to understand and diagnose RBC related diseases. In this work, a microfluidic system composed of a microchannel with a hyperbolic-shaped contraction followed by a sudden expansion is presented. We provide a detailed quantitative description of the degree of deformation of human RBCs under a controlled homogeneous extensional flow field. We measured the deformation index (DI) as well as the velocity of the RBCs travelling along the centerline of the channel for four different flow rates and analyze the impact of the particle Reynolds number. The results show that human RBC deformation tends to reach a plateau value in the region of constant extensional rate, the value of which depends on the extension rate. Additionally, we observe that the presence of a sudden expansion downstream of the hyperbolic contraction modifies the spatial distribution of cells and substantially increases the cell free layer (CFL) downstream of the expansion plane similarly to what is seen in other expansion flows. Beyond a certain value of flow rate, there is only a weak effect of inlet flow rates on the enhancement of the downstream CFL. These in vitro experiments show the potential of using microfluidic systems with hyperbolic-shaped microchannels both for the separation of the RBCs from plasma and to assess changes in RBC deformability in physiological and pathological situations for clinical purposes. However, the selection of the geometry and the identification of the most suitable region to evaluate the changes on the RBC deformability under extensional flows are crucial if microfluidics is to be used as an in vitro clinical methodology to detect circulatory diseases. PMID:24404073

On Compressible Vortex Sheets

NASA Astrophysics Data System (ADS)

Secchi, Paolo

2005-05-01

We introduce the main known results of the theory of incompressible and compressible vortex sheets. Moreover, we present recent results obtained by the author with J. F. Coulombel about supersonic compressible vortex sheets in two space dimensions. The problem is a nonlinear free boundary hyperbolic problem with two difficulties: the free boundary is characteristic and the Lopatinski condition holds only in a weak sense, yielding losses of derivatives. Under a supersonic condition that precludes violent instabilities, we prove an energy estimate for the boundary value problem obtained by linearization around an unsteady piecewise solution.

Anosov C-systems and random number generators

NASA Astrophysics Data System (ADS)

Savvidy, G. K.

2016-08-01

We further develop our previous proposal to use hyperbolic Anosov C-systems to generate pseudorandom numbers and to use them for efficient Monte Carlo calculations in high energy particle physics. All trajectories of hyperbolic dynamical systems are exponentially unstable, and C-systems therefore have mixing of all orders, a countable Lebesgue spectrum, and a positive Kolmogorov entropy. These exceptional ergodic properties follow from the C-condition introduced by Anosov. This condition defines a rich class of dynamical systems forming an open set in the space of all dynamical systems. An important property of C-systems is that they have a countable set of everywhere dense periodic trajectories and their density increases exponentially with entropy. Of special interest are the C-systems defined on higher-dimensional tori. Such C-systems are excellent candidates for generating pseudorandom numbers that can be used in Monte Carlo calculations. An efficient algorithm was recently constructed that allows generating long C-system trajectories very rapidly. These trajectories have good statistical properties and can be used for calculations in quantum chromodynamics and in high energy particle physics.

Causal dissipation for the relativistic dynamics of ideal gases

NASA Astrophysics Data System (ADS)

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

Stability of an abstract system of coupled hyperbolic and parabolic equations

NASA Astrophysics Data System (ADS)

Hao, Jianghao; Liu, Zhuangyi

2013-08-01

In this paper, we provide a complete stability analysis for an abstract system of coupled hyperbolic and parabolic equations = -Au + γ A^{α} θ, quad θ_t = -γ A^{α}u_t - kA^{β}θ, u(0) = u_0, quad u_t(0) = v_0, quad θ(0) = θ_0 where A is a self-adjoint, positive definite operator on a Hilbert space H. For {(α,β) in [0,1] × [0,1]} , the region of exponential stability had been identified in Ammar-Khodja et al. (ESAIM Control Optim Calc Var 4:577-593,1999). Our contribution is to show that the rest of the region can be classified as region of polynomial stability and region of instability. Moreover, we obtain the optimality of the order of polynomial stability.

Causal dissipation for the relativistic dynamics of ideal gases

PubMed Central

2017-01-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier–Stokes equations. PMID:28588397

Causal dissipation for the relativistic dynamics of ideal gases.

PubMed

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

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

Dumbser, Michael, E-mail: michael.dumbser@unitn.it; Balsara, Dinshaw S., E-mail: dbalsara@nd.edu

In this paper a new, simple and universal formulation of the HLLEM Riemann solver (RS) is proposed that works for general conservative and non-conservative systems of hyperbolic equations. For non-conservative PDE, a path-conservative formulation of the HLLEM RS is presented for the first time in this paper. The HLLEM Riemann solver is built on top of a novel and very robust path-conservative HLL method. It thus naturally inherits the positivity properties and the entropy enforcement of the underlying HLL scheme. However, with just the slight additional cost of evaluating eigenvectors and eigenvalues of intermediate characteristic fields, we can represent linearlymore » degenerate intermediate waves with a minimum of smearing. For conservative systems, our paper provides the easiest and most seamless path for taking a pre-existing HLL RS and quickly and effortlessly converting it to a RS that provides improved results, comparable with those of an HLLC, HLLD, Osher or Roe-type RS. This is done with minimal additional computational complexity, making our variant of the HLLEM RS also a very fast RS that can accurately represent linearly degenerate discontinuities. Our present HLLEM RS also transparently extends these advantages to non-conservative systems. For shallow water-type systems, the resulting method is proven to be well-balanced. Several test problems are presented for shallow water-type equations and two-phase flow models, as well as for gas dynamics with real equation of state, magnetohydrodynamics (MHD & RMHD), and nonlinear elasticity. Since our new formulation accommodates multiple intermediate waves and has a broader applicability than the original HLLEM method, it could alternatively be called the HLLI Riemann solver, where the “I” stands for the intermediate characteristic fields that can be accounted for. -- Highlights: •New simple and general path-conservative formulation of the HLLEM Riemann solver. •Application to general conservative and non-conservative hyperbolic systems. •Inclusion of sub-structure and resolution of intermediate characteristic fields. •Well-balanced for single- and two-layer shallow water equations and multi-phase flows. •Euler equations with real equation of state, MHD equations, nonlinear elasticity.« less

Delay, Probability, and Social Discounting in a Public Goods Game

ERIC Educational Resources Information Center

Jones, Bryan A.; Rachlin, Howard

2009-01-01

A human social discount function measures the value to a person of a reward to another person at a given social distance. Just as delay discounting is a hyperbolic function of delay, and probability discounting is a hyperbolic function of odds-against, social discounting is a hyperbolic function of social distance. Experiment 1 obtained individual…

Conservation laws with coinciding smooth solutions but different conserved variables

NASA Astrophysics Data System (ADS)

Colombo, Rinaldo M.; Guerra, Graziano

2018-04-01

Consider two hyperbolic systems of conservation laws in one space dimension with the same eigenvalues and (right) eigenvectors. We prove that solutions to Cauchy problems with the same initial data differ at third order in the total variation of the initial datum. As a first application, relying on the classical Glimm-Lax result (Glimm and Lax in Decay of solutions of systems of nonlinear hyperbolic conservation laws. Memoirs of the American Mathematical Society, No. 101. American Mathematical Society, Providence, 1970), we obtain estimates improving those in Saint-Raymond (Arch Ration Mech Anal 155(3):171-199, 2000) on the distance between solutions to the isentropic and non-isentropic inviscid compressible Euler equations, under general equations of state. Further applications are to the general scalar case, where rather precise estimates are obtained, to an approximation by Di Perna of the p-system and to a traffic model.

Near-perfect broadband absorption from hyperbolic metamaterial nanoparticles

NASA Astrophysics Data System (ADS)

Riley, Conor T.; Smalley, Joseph S. T.; Brodie, Jeffrey R. J.; Fainman, Yeshaiahu; Sirbuly, Donald J.; Liu, Zhaowei

2017-02-01

Broadband absorbers are essential components of many light detection, energy harvesting, and camouflage schemes. Current designs are either bulky or use planar films that cause problems in cracking and delamination during flexing or heating. In addition, transferring planar materials to flexible, thin, or low-cost substrates poses a significant challenge. On the other hand, particle-based materials are highly flexible and can be transferred and assembled onto a more desirable substrate but have not shown high performance as an absorber in a standalone system. Here, we introduce a class of particle absorbers called transferable hyperbolic metamaterial particles (THMMP) that display selective, omnidirectional, tunable, broadband absorption when closely packed. This is demonstrated with vertically aligned hyperbolic nanotube (HNT) arrays composed of alternating layers of aluminum-doped zinc oxide and zinc oxide. The broadband absorption measures >87% from 1,200 nm to over 2,200 nm with a maximum absorption of 98.1% at 1,550 nm and remains large for high angles. Furthermore, we show the advantages of particle-based absorbers by transferring the HNTs to a polymer substrate that shows excellent mechanical flexibility and visible transparency while maintaining near-perfect absorption in the telecommunications region. In addition, other material systems and geometries are proposed for a wider range of applications.

ParaExp Using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations

NASA Astrophysics Data System (ADS)

Merkel, M.; Niyonzima, I.; Schöps, S.

2017-12-01

Recently, ParaExp was proposed for the time integration of linear hyperbolic problems. It splits the time interval of interest into subintervals and computes the solution on each subinterval in parallel. The overall solution is decomposed into a particular solution defined on each subinterval with zero initial conditions and a homogeneous solution propagated by the matrix exponential applied to the initial conditions. The efficiency of the method depends on fast approximations of this matrix exponential based on recent results from numerical linear algebra. This paper deals with the application of ParaExp in combination with Leapfrog to electromagnetic wave problems in time domain. Numerical tests are carried out for a simple toy problem and a realistic spiral inductor model discretized by the Finite Integration Technique.

Grammatical complexity for two-dimensional maps

NASA Astrophysics Data System (ADS)

Hagiwara, Ryouichi; Shudo, Akira

2004-11-01

We calculate the grammatical complexity of the symbol sequences generated from the Hénon map and the Lozi map using the recently developed methods to construct the pruning front. When the map is hyperbolic, the language of symbol sequences is regular in the sense of the Chomsky hierarchy and the corresponding grammatical complexity takes finite values. It is found that the complexity exhibits a self-similar structure as a function of the system parameter, and the similarity of the pruning fronts is discussed as an origin of such self-similarity. For non-hyperbolic cases, it is observed that the complexity monotonically increases as we increase the resolution of the pruning front.

Hyperbolic spoof plasmonic metasurfaces

DOE PAGES

Yang, Yihao; Jing, Liqiao; Shen, Lian; ...

2017-08-25

Hyperbolic metasurfaces have recently emerged as a new research frontier because of the unprecedented capabilities to manipulate surface plasmon polaritons (SPPs) and many potential applications. But, thus far, the existence of hyperbolic metasurfaces has neither been observed nor predicted at low frequencies because noble metals cannot support SPPs at longer wavelengths. Here, we propose and experimentally demonstrate spoof plasmonic metasurfaces with a hyperbolic dispersion, where the spoof SPPs propagate on complementary H-shaped, perfectly conducting surfaces at low frequencies. Therefore, non-divergent diffractions, negative refraction and dispersion-dependent spin-momentum locking are observed as the spoof SPPs travel over the hyperbolic spoof plasmonic metasurfacesmore » (HSPMs). The HSPMs provide fundamental new platforms to explore the propagation and spin of spoof SPPs. They show great capabilities for designing advanced surface wave devices such as spatial multiplexers, focusing and imaging devices, planar hyperlenses, and dispersion-dependent directional couplers, at both microwave and terahertz frequencies.« less

Lamb Shift in the Near Field of Hyperbolic Metamaterial Half Space

NASA Astrophysics Data System (ADS)

Deng, Nai Jing; Yu, Kin Wah

2013-03-01

Hyperbolic metamaterials give a large magnification of the density of states in a specific frequency ranges, and has motivated various applications in emission lifetime reduction, strong absorption, and extraordinary black body radiation, etc. The boost of vacuum energy, which is proportional to the density of states, is expected in hyperbolic metamaterial. We have studied the Lamb shift in vacuum-hyperbolic-metamterial half spaces and shown the non-trivial role of vacuum energy. In our calculation, the easy-fabricated multilayer structure is employed to generate a hyperbolic dispersion relation. The spectrum of hydrogen atoms is calculated with a perturbation method after quantizing the half spaces with a complete mode expansion. It appears that the shift of spectrum is mainly contributed by the terahertz response of materials, which has been well described and predicted in both theories and experiments. Work supported by the General Research Fund of the Hong Kong SAR Government

Direction-aware Slope Limiter for 3D Cubic Grids with Adaptive Mesh Refinement

DOE PAGES

Velechovsky, Jan; Francois, Marianne M.; Masser, Thomas

2018-06-07

In the context of finite volume methods for hyperbolic systems of conservation laws, slope limiters are an effective way to suppress creation of unphysical local extrema and/or oscillations near discontinuities. We investigate properties of these limiters as applied to piecewise linear reconstructions of conservative fluid quantities in three-dimensional simulations. In particular, we are interested in linear reconstructions on Cartesian adaptively refined meshes, where a reconstructed fluid quantity at a face center depends on more than a single gradient component of the quantity. We design a new slope limiter, which combines the robustness of a minmod limiter with the accuracy ofmore » a van Leer limiter. The limiter is called Direction-Aware Limiter (DAL), because the combination is based on a principal flow direction. In particular, DAL is useful in situations where the Barth–Jespersen limiter for general meshes fails to maintain global linear functions, such as on cubic computational meshes with stencils including only faceneighboring cells. Here, we verify the new slope limiter on a suite of standard hydrodynamic test problems on Cartesian adaptively refined meshes. Lastly, we demonstrate reduced mesh imprinting; for radially symmetric problems such as the Sedov blast wave or the Noh implosion test cases, the results with DAL show better preservation of radial symmetry compared to the other standard methods on Cartesian meshes.« less

Direction-aware Slope Limiter for 3D Cubic Grids with Adaptive Mesh Refinement

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

Velechovsky, Jan; Francois, Marianne M.; Masser, Thomas

In the context of finite volume methods for hyperbolic systems of conservation laws, slope limiters are an effective way to suppress creation of unphysical local extrema and/or oscillations near discontinuities. We investigate properties of these limiters as applied to piecewise linear reconstructions of conservative fluid quantities in three-dimensional simulations. In particular, we are interested in linear reconstructions on Cartesian adaptively refined meshes, where a reconstructed fluid quantity at a face center depends on more than a single gradient component of the quantity. We design a new slope limiter, which combines the robustness of a minmod limiter with the accuracy ofmore » a van Leer limiter. The limiter is called Direction-Aware Limiter (DAL), because the combination is based on a principal flow direction. In particular, DAL is useful in situations where the Barth–Jespersen limiter for general meshes fails to maintain global linear functions, such as on cubic computational meshes with stencils including only faceneighboring cells. Here, we verify the new slope limiter on a suite of standard hydrodynamic test problems on Cartesian adaptively refined meshes. Lastly, we demonstrate reduced mesh imprinting; for radially symmetric problems such as the Sedov blast wave or the Noh implosion test cases, the results with DAL show better preservation of radial symmetry compared to the other standard methods on Cartesian meshes.« less

Curvature and temperature of complex networks.

PubMed

Krioukov, Dmitri; Papadopoulos, Fragkiskos; Vahdat, Amin; Boguñá, Marián

2009-09-01

We show that heterogeneous degree distributions in observed scale-free topologies of complex networks can emerge as a consequence of the exponential expansion of hidden hyperbolic space. Fermi-Dirac statistics provides a physical interpretation of hyperbolic distances as energies of links. The hidden space curvature affects the heterogeneity of the degree distribution, while clustering is a function of temperature. We embed the internet into the hyperbolic plane and find a remarkable congruency between the embedding and our hyperbolic model. Besides proving our model realistic, this embedding may be used for routing with only local information, which holds significant promise for improving the performance of internet routing.

Smoothing-based compressed state Kalman filter for joint state-parameter estimation: Applications in reservoir characterization and CO2 storage monitoring

NASA Astrophysics Data System (ADS)

Li, Y. J.; Kokkinaki, Amalia; Darve, Eric F.; Kitanidis, Peter K.

2017-08-01

The operation of most engineered hydrogeological systems relies on simulating physical processes using numerical models with uncertain parameters and initial conditions. Predictions by such uncertain models can be greatly improved by Kalman-filter techniques that sequentially assimilate monitoring data. Each assimilation constitutes a nonlinear optimization, which is solved by linearizing an objective function about the model prediction and applying a linear correction to this prediction. However, if model parameters and initial conditions are uncertain, the optimization problem becomes strongly nonlinear and a linear correction may yield unphysical results. In this paper, we investigate the utility of one-step ahead smoothing, a variant of the traditional filtering process, to eliminate nonphysical results and reduce estimation artifacts caused by nonlinearities. We present the smoothing-based compressed state Kalman filter (sCSKF), an algorithm that combines one step ahead smoothing, in which current observations are used to correct the state and parameters one step back in time, with a nonensemble covariance compression scheme, that reduces the computational cost by efficiently exploring the high-dimensional state and parameter space. Numerical experiments show that when model parameters are uncertain and the states exhibit hyperbolic behavior with sharp fronts, as in CO2 storage applications, one-step ahead smoothing reduces overshooting errors and, by design, gives physically consistent state and parameter estimates. We compared sCSKF with commonly used data assimilation methods and showed that for the same computational cost, combining one step ahead smoothing and nonensemble compression is advantageous for real-time characterization and monitoring of large-scale hydrogeological systems with sharp moving fronts.

A zonally symmetric model for the monsoon-Hadley circulation with stochastic convective forcing

NASA Astrophysics Data System (ADS)

De La Chevrotière, Michèle; Khouider, Boualem

2017-02-01

Idealized models of reduced complexity are important tools to understand key processes underlying a complex system. In climate science in particular, they are important for helping the community improve our ability to predict the effect of climate change on the earth system. Climate models are large computer codes based on the discretization of the fluid dynamics equations on grids of horizontal resolution in the order of 100 km, whereas unresolved processes are handled by subgrid models. For instance, simple models are routinely used to help understand the interactions between small-scale processes due to atmospheric moist convection and large-scale circulation patterns. Here, a zonally symmetric model for the monsoon circulation is presented and solved numerically. The model is based on the Galerkin projection of the primitive equations of atmospheric synoptic dynamics onto the first modes of vertical structure to represent free tropospheric circulation and is coupled to a bulk atmospheric boundary layer (ABL) model. The model carries bulk equations for water vapor in both the free troposphere and the ABL, while the processes of convection and precipitation are represented through a stochastic model for clouds. The model equations are coupled through advective nonlinearities, and the resulting system is not conservative and not necessarily hyperbolic. This makes the design of a numerical method for the solution of this system particularly difficult. Here, we develop a numerical scheme based on the operator time-splitting strategy, which decomposes the system into three pieces: a conservative part and two purely advective parts, each of which is solved iteratively using an appropriate method. The conservative system is solved via a central scheme, which does not require hyperbolicity since it avoids the Riemann problem by design. One of the advective parts is a hyperbolic diagonal matrix, which is easily handled by classical methods for hyperbolic equations, while the other advective part is a nilpotent matrix, which is solved via the method of lines. Validation tests using a synthetic exact solution are presented, and formal second-order convergence under grid refinement is demonstrated. Moreover, the model is tested under realistic monsoon conditions, and the ability of the model to simulate key features of the monsoon circulation is illustrated in two distinct parameter regimes.

Reduction and relative equilibria for the two-body problem on spaces of constant curvature

NASA Astrophysics Data System (ADS)

Borisov, A. V.; García-Naranjo, L. C.; Mamaev, I. S.; Montaldi, J.

2018-06-01

We consider the two-body problem on surfaces of constant nonzero curvature and classify the relative equilibria and their stability. On the hyperbolic plane, for each q>0 we show there are two relative equilibria where the masses are separated by a distance q. One of these is geometrically of elliptic type and the other of hyperbolic type. The hyperbolic ones are always unstable, while the elliptic ones are stable when sufficiently close, but unstable when far apart. On the sphere of positive curvature, if the masses are different, there is a unique relative equilibrium (RE) for every angular separation except π /2. When the angle is acute, the RE is elliptic, and when it is obtuse the RE can be either elliptic or linearly unstable. We show using a KAM argument that the acute ones are almost always nonlinearly stable. If the masses are equal, there are two families of relative equilibria: one where the masses are at equal angles with the axis of rotation (`isosceles RE') and the other when the two masses subtend a right angle at the centre of the sphere. The isosceles RE are elliptic if the angle subtended by the particles is acute and is unstable if it is obtuse. At π /2, the two families meet and a pitchfork bifurcation takes place. Right-angled RE are elliptic away from the bifurcation point. In each of the two geometric settings, we use a global reduction to eliminate the group of symmetries and analyse the resulting reduced equations which live on a five-dimensional phase space and possess one Casimir function.

Critical load: a novel approach to determining a sustainable intensity during resistance exercise.

PubMed

Arakelian, Vivian M; Mendes, Renata G; Trimer, Renata; Rossi Caruso, Flavia C; de Sousa, Nuno M; Borges, Vanessa C; do Valle Gomes Gatto, Camila; Baldissera, Vilmar; Arena, Ross; Borghi-Silva, Audrey

2017-05-01

A hyperbolic function as well as a linear relationship between power output and time to exhaustion (Tlim) has been consistently observed during dynamic non-resistive exercises. However, little is known about its concept to resistance exercises (RE), which could be defined as critical load (CL). This study aimed to verify the existence of CL during dynamic RE and to verify the number of workbouts necessary to determine the optimal modeling to achieve it. Fifteen healthy men (23±2.5 yrs) completed 1 repetition maximum test (1RM) on a leg press and 3 (60%, 75% and 90% of 1RM) or 4 (+ 30% of 1RM) workbouts protocols to obtain the CL by hyperbolic and linear regression models between Tlim and load performed. Blood lactate and leg fatigue were also measured. CL was obtained during RE and 3 workbouts protocol estimate it at 53% while 4 tests at 38% of 1 RM. However, based on coefficients of determination, 3 protocols provided a better fit than the 4-parameter model, respectively (R2>0.95 vs. >0.77). Moreover, all intensities increased blood lactate and leg fatigue, however, when corrected by Tlim, were significantly lower at CL. It was possible to determinate CL during dynamic lower limbs RE and that 3 exhaustive workbouts can be used to better estimate the CL, constituting a new concept of determining this threshold during dynamic RE and reducing the physically demanding nature of the protocol. These findings may have important applications for functional performance evaluation and prescription of RE programs.

Bifurcations and chaos in convection taking non-Fourier heat-flux

NASA Astrophysics Data System (ADS)

Layek, G. C.; Pati, N. C.

2017-11-01

In this Letter, we report the influences of thermal time-lag on the onset of convection, its bifurcations and chaos of a horizontal layer of Boussinesq fluid heated underneath taking non-Fourier Cattaneo-Christov hyperbolic model for heat propagation. A five-dimensional nonlinear system is obtained for a low-order Galerkin expansion, and it reduces to Lorenz system for Cattaneo number tending to zero. The linear stability agreed with existing results that depend on Cattaneo number C. It also gives a threshold Cattaneo number, CT, above which only oscillatory solutions can persist. The oscillatory solutions branch terminates at the subcritical steady branch with a heteroclinic loop connecting a pair of saddle points for subcritical steady-state solutions. For subcritical onset of convection two stable solutions coexist, that is, hysteresis phenomenon occurs at this stage. The steady solution undergoes a Hopf bifurcation and is of subcritical type for small value of C, while it becomes supercritical for moderate Cattaneo number. The system goes through period-doubling/noisy period-doubling transition to chaos depending on the control parameters. There after the system exhibits Shil'nikov chaos via homoclinic explosion. The complexity of spiral strange attractor is analyzed using fractal dimension and return map.

Relations between nonlinear Riccati equations and other equations in fundamental physics

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2014-10-01

Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract "quantizations" such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown.

Developing a reversible rapid coordinate transformation model for the cylindrical projection

NASA Astrophysics Data System (ADS)

Ye, Si-jing; Yan, Tai-lai; Yue, Yan-li; Lin, Wei-yan; Li, Lin; Yao, Xiao-chuang; Mu, Qin-yun; Li, Yong-qin; Zhu, De-hai

2016-04-01

Numerical models are widely used for coordinate transformations. However, in most numerical models, polynomials are generated to approximate "true" geographic coordinates or plane coordinates, and one polynomial is hard to make simultaneously appropriate for both forward and inverse transformations. As there is a transformation rule between geographic coordinates and plane coordinates, how accurate and efficient is the calculation of the coordinate transformation if we construct polynomials to approximate the transformation rule instead of "true" coordinates? In addition, is it preferable to compare models using such polynomials with traditional numerical models with even higher exponents? Focusing on cylindrical projection, this paper reports on a grid-based rapid numerical transformation model - a linear rule approximation model (LRA-model) that constructs linear polynomials to approximate the transformation rule and uses a graticule to alleviate error propagation. Our experiments on cylindrical projection transformation between the WGS 84 Geographic Coordinate System (EPSG 4326) and the WGS 84 UTM ZONE 50N Plane Coordinate System (EPSG 32650) with simulated data demonstrate that the LRA-model exhibits high efficiency, high accuracy, and high stability; is simple and easy to use for both forward and inverse transformations; and can be applied to the transformation of a large amount of data with a requirement of high calculation efficiency. Furthermore, the LRA-model exhibits advantages in terms of calculation efficiency, accuracy and stability for coordinate transformations, compared to the widely used hyperbolic transformation model.

Tsien's method for generating non-Keplerian trajectories. Part 2: The question of thrust to orbit a sphere and the restricted three-body problem

NASA Technical Reports Server (NTRS)

Murad, P. A.

1993-01-01

Tsien's method is extended to treat the orbital motion of a body undergoing accelerations and decelerations. A generalized solution is discussed for the generalized case where a body undergoes azimuthal and radial thrust and the problem is further simplified for azimuthal thrust alone. Judicious selection of thrust could generate either an elliptic or hyperbolic trajectory. This is unexpected especially when the body has only enough energy for a lower state trajectory. The methodology is extended treating the problem of vehicle thrust for orbiting a sphere and vehicle thrust within the classical restricted three-body problem. Results for the latter situation can produce hyperbolic trajectories through eigen value decomposition. Since eigen values for no-thrust can be imaginary, thrust can generate real eigen values to describe hyperbolic trajectories. Keplerian dynamics appears to represent but a small subset of a much larger non-Keplerian domain especially when thrust effects are considered. The need for high thrust long duration space-based propulsion systems for changing a trajectory's canonical form is clearly demonstrated.

Lagrangian transport near perturbed periodic lines in three-dimensional unsteady flows

NASA Astrophysics Data System (ADS)

Speetjens, Michel

2015-11-01

Periodic lines formed by continuous strings of periodic points are key organizing entities in the Lagrangian flow topology of certain three-dimensional (3D) time-periodic flows. Such lines generically consist of elliptic and/or hyperbolic points and thus give rise to 3D flow topologies made up of families of concentric closed trajectories embedded in chaotic regions. Weak perturbation destroys the periodic lines and causes said trajectories to coalesce into families of concentric tubes. However, emergence of isolated periodic points near the disintegrating periodic lines and/or partitioning of the original lines into elliptic and hyperbolic segments interrupt the tube formation. This yields incomplete tubes that interact with the (chaotic) environment through their open ends, resulting in intricate and essentially 3D flow topologies These phenomena have been observed in various realistic flows yet the underlying mechanisms are to date only partially understood. This study deepens insight into the (perturbed) Lagrangian dynamics of these flows by way of a linearized representation of the equations of motion near the periodic lines. Predictions on the basis of this investigation are in full (qualitative) agreement with observed behavior in the actual flows

Euler and Navier-Stokes equations on the hyperbolic plane.

PubMed

Khesin, Boris; Misiolek, Gerard

2012-11-06

We show that nonuniqueness of the Leray-Hopf solutions of the Navier-Stokes equation on the hyperbolic plane (2) observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on (n) whenever n ≥ 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting.

The Arabic Hyperbolic Pattern "Fa??al" in Two Recent Translations of the Qur'an

ERIC Educational Resources Information Center

El-Zawawy, Amr M.

2014-01-01

The present study addresses the problem of rendering the ?? ?? 'fa??al' hyperbolic pattern into English in two recent translations of the Qur'an. Due to the variety of Qur'an translations and the large amount of hyperbolic forms of Arabic verbs recorded in the Qur'an, only two translations of the Qur'an are consulted and analyzed: these two…

Critiquing Neoliberalism in Australian Universities

ERIC Educational Resources Information Center

Rea, Jeannie

2016-01-01

While students chanting "No cuts, No fees, No corporate universities" may be dismissed as youthful hyperbole by some, it is not as superficial a characterisation of the state of our public university system as it seems.

An iterative Riemann solver for systems of hyperbolic conservation law s, with application to hyperelastic solid mechanics

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

Miller, Gregory H.

2003-08-06

In this paper we present a general iterative method for the solution of the Riemann problem for hyperbolic systems of PDEs. The method is based on the multiple shooting method for free boundary value problems. We demonstrate the method by solving one-dimensional Riemann problems for hyperelastic solid mechanics. Even for conditions representative of routine laboratory conditions and military ballistics, dramatic differences are seen between the exact and approximate Riemann solution. The greatest discrepancy arises from misallocation of energy between compressional and thermal modes by the approximate solver, resulting in nonphysical entropy and temperature estimates. Several pathological conditions arise in commonmore » practice, and modifications to the method to handle these are discussed. These include points where genuine nonlinearity is lost, degeneracies, and eigenvector deficiencies that occur upon melting.« less

Computation of Quasiperiodic Normally Hyperbolic Invariant Tori: Rigorous Results

NASA Astrophysics Data System (ADS)

Canadell, Marta; Haro, Àlex

2017-12-01

The development of efficient methods for detecting quasiperiodic oscillations and computing the corresponding invariant tori is a subject of great importance in dynamical systems and their applications in science and engineering. In this paper, we prove the convergence of a new Newton-like method for computing quasiperiodic normally hyperbolic invariant tori carrying quasiperiodic motion in smooth families of real-analytic dynamical systems. The main result is stated as an a posteriori KAM-like theorem that allows controlling the inner dynamics on the torus with appropriate detuning parameters, in order to obtain a prescribed quasiperiodic motion. The Newton-like method leads to several fast and efficient computational algorithms, which are discussed and tested in a companion paper (Canadell and Haro in J Nonlinear Sci, 2017. doi: 10.1007/s00332-017-9388-z), in which new mechanisms of breakdown are presented.

Some remarks on the topology of hyperbolic actions of Rn on n-manifolds

NASA Astrophysics Data System (ADS)

Bouloc, Damien

2017-11-01

This paper contains some results on the topology of a nondegenerate action of Rn on a compact connected n-manifold M when the action is totally hyperbolic (i.e. its toric degree is zero). We study the R-action generated by a fixed vector of Rn, that provides some results on the number of hyperbolic domains and the number of fixed points of the action. We study with more details the case of the 2-sphere, in particular we investigate some combinatorial properties of the associated 4-valent graph embedded in S2. We also construct hyperbolic actions in dimension 3, on the sphere S3 and on the projective space RP3.

Fundamental Theorems of Algebra for the Perplexes

ERIC Educational Resources Information Center

Poodiak, Robert; LeClair, Kevin

2009-01-01

The fundamental theorem of algebra for the complex numbers states that a polynomial of degree n has n roots, counting multiplicity. This paper explores the "perplex number system" (also called the "hyperbolic number system" and the "spacetime number system") In this system (which has extra roots of +1 besides the usual [plus or minus]1 of the…

Hyperbolic polaritons in nanoparticles

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Rubio, Angel; Guinea, Francisco; Basov, Dimitri; Fogler, Michael

2015-03-01

Hyperbolic optical materials (HM) are characterized by permittivity tensor that has both positive and negative principal values. Collective electromagnetic modes (polaritons) of HM have novel properties promising for various applications including subdiffractional imaging and on-chip optical communication. Hyperbolic response is actively investigated in the context of metamaterials, anisotropic polar insulators, and layered superconductors. We study polaritons in spheroidal HM nanoparticles using Hamiltonian optics. The field equations are mapped to classical dynamics of fictitious particles (wave packets) of an indefinite Hamiltonian. This dynamics is quantized using the Einstein-Brillouin-Keller quantization rule. The eigenmodes are classified as either bulk or surface according to whether their transverse momenta are real or imaginary. To model how such hyperbolic polaritons can be probed by near-field experiments, we compute the field distribution induced inside and outside the spheroid by an external point dipole. At certain magic frequencies the field shows striking geometric patterns whose origin is traced to the classical periodic orbits. The theory is applied to natural hyperbolic materials hexagonal boron nitride and superconducting LaSrCuO.

Partial stabilisation of non-homogeneous bilinear systems

NASA Astrophysics Data System (ADS)

Hamidi, Z.; Ouzahra, M.

2018-06-01

In this work, we study in a Hilbert state space, the partial stabilisation of non-homogeneous bilinear systems using a bounded control. Necessary and sufficient conditions for weak and strong stabilisation are formulated in term of approximate observability like assumptions. Applications to parabolic and hyperbolic equations are presented.

Application of a new multiphase multicomponent volcanic conduit model with magma degassing and crystallization to Stromboli volcano.

NASA Astrophysics Data System (ADS)

La Spina, Giuseppe; Burton, Mike; de'Michieli Vitturi, Mattia

2014-05-01

Volcanoes exhibit a wide range of eruption styles, from relatively slow effusive eruptions, generating lava flows and lava domes, to explosive eruptions, in which very large volumes of fragmented magma and volcanic gas are ejected high into the atmosphere. During an eruption, much information regarding the magma ascent dynamics can be gathered: melt and exsolved gas composition, crystal content, mass flow rate and ballistic velocities, to name just a few. Due to the lack of direct observations of the conduit itself, mathematical models for magma ascent provide invaluable tools for a better comprehension of the system. The complexity of the multiphase multicomponent gas-magma-solid system is reflected in the corresponding mathematical model; a set of non-linear hyperbolic partial differential and constitutive equations, which describe the physical system, has to be formulated and solved. The standard approach to derive governing equations for two-phase flow is based on averaging procedures, which leads to a system of governing equations in the form of mass, momentum and energy balance laws for each phase coupled with algebraic and differential source terms which represent phase interactions. For this work, we used the model presented by de' Michieli Vitturi et al. (EGU General Assembly Conference Abstracts, 2013), where a different approach based on the theory of thermodynamically compatible systems has been adopted to write the governing multiphase equations for two-phase compressible flow (with two velocities and two pressures) in the form of a conservative hyperbolic system of partial differential equations, coupled with non-differential source terms. Here, in order to better describe the multicomponent nature of the system, we extended the model adding several transport equations to the system for different crystal components and different gas species, and implementing appropriate equations of state. The constitutive equations of the model are chosen to reproduce both effusive and explosive eruptive activities at Stromboli volcano. Three different crystal components (olivine, pyroxene and feldspar) and two different gas species (water and carbon dioxide) are taken into account. The equilibrium profiles of crystallization as function of pressure, temperature and water content are modeled using the numerical codes AlphaMELTS and DAKOTA. The equilibrium of dissolved gas content, instead, is obtained using a non-linear fitting of data computed using VolatileCALC. With these data, we simulate numerically the lava effusion that occurred at Stromboli between 27 February and 2 April 2007, and find good agreement with the observed data (vesicularity, exsolved gas composition, crystal content and mass flow rate) at the vent. We find that the model is highly sensitive to input magma temperature, going from effusive to explosive eruption with temperature changes by just 20 °C. We thoroughly investigated through a sensitivity analysis the control of the temperature of magma chamber and of the radius of the conduit on the mass flow rate, obtaining also a set of admissible temperatures and conduit radii that produce results in agreement with the real observations.

Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces

NASA Astrophysics Data System (ADS)

de Lima, Levi Lopes; Girão, Frederico

2015-03-01

We establish versions of the positive mass and Penrose inequalities for a class of asymptotically hyperbolic hypersurfaces. In particular, under the usual dominant energy condition, we prove in all dimensions an optimal Penrose inequality for certain graphs in hyperbolic space whose boundary has constant mean curvature . This settles, for this class of manifolds, an inequality first conjectured by Wang (J Differ Geom 57(2):273-299, 2001).

Euler and Navier–Stokes equations on the hyperbolic plane

PubMed Central

Khesin, Boris; Misiołek, Gerard

2012-01-01

We show that nonuniqueness of the Leray–Hopf solutions of the Navier–Stokes equation on the hyperbolic plane ℍ2 observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on ℍn whenever n ≥ 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting. PMID:23091015

The hyperbolic step potential: Anti-bound states, SUSY partners and Wigner time delays

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

Gadella, M.; Kuru, Ş.; Negro, J., E-mail: jnegro@fta.uva.es

We study the scattering produced by a one dimensional hyperbolic step potential, which is exactly solvable and shows an unusual interest because of its asymmetric character. The analytic continuation of the scattering matrix in the momentum representation has a branch cut and an infinite number of simple poles on the negative imaginary axis which are related with the so called anti-bound states. This model does not show resonances. Using the wave functions of the anti-bound states, we obtain supersymmetric (SUSY) partners which are the series of Rosen–Morse II potentials. We have computed the Wigner reflection and transmission time delays formore » the hyperbolic step and such SUSY partners. Our results show that the more bound states a partner Hamiltonian has the smaller is the time delay. We also have evaluated time delays for the hyperbolic step potential in the classical case and have obtained striking similitudes with the quantum case. - Highlights: • The scattering matrix of hyperbolic step potential is studied. • The scattering matrix has a branch cut and an infinite number of poles. • The poles are associated to anti-bound states. • Susy partners using antibound states are computed. • Wigner time delays for the hyperbolic step and partner potentials are compared.« less

A model and numerical method for compressible flows with capillary effects

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

Schmidmayer, Kevin, E-mail: kevin.schmidmayer@univ-amu.fr; Petitpas, Fabien, E-mail: fabien.petitpas@univ-amu.fr; Daniel, Eric, E-mail: eric.daniel@univ-amu.fr

2017-04-01

A new model for interface problems with capillary effects in compressible fluids is presented together with a specific numerical method to treat capillary flows and pressure waves propagation. This new multiphase model is in agreement with physical principles of conservation and respects the second law of thermodynamics. A new numerical method is also proposed where the global system of equations is split into several submodels. Each submodel is hyperbolic or weakly hyperbolic and can be solved with an adequate numerical method. This method is tested and validated thanks to comparisons with analytical solutions (Laplace law) and with experimental results onmore » droplet breakup induced by a shock wave.« less

Spectral approach to homogenization of hyperbolic equations with periodic coefficients

NASA Astrophysics Data System (ADS)

Dorodnyi, M. A.; Suslina, T. A.

2018-06-01

In L2 (Rd ;Cn), we consider selfadjoint strongly elliptic second order differential operators Aε with periodic coefficients depending on x / ε, ε > 0. We study the behavior of the operators cos ⁡ (Aε1/2 τ) and Aε-1/2 sin ⁡ (Aε1/2 τ), τ ∈ R, for small ε. Approximations for these operators in the (Hs →L2)-operator norm with a suitable s are obtained. The results are used to study the behavior of the solution vε of the Cauchy problem for the hyperbolic equation ∂τ2 vε = -Aεvε + F. General results are applied to the acoustics equation and the system of elasticity theory.

Spatiotemporal optical pulse transformation by a resonant diffraction grating

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

Golovastikov, N. V.; Bykov, D. A., E-mail: bykovd@gmail.com; Doskolovich, L. L., E-mail: leonid@smr.ru

The diffraction of a spatiotemporal optical pulse by a resonant diffraction grating is considered. The pulse diffraction is described in terms of the signal (the spatiotemporal incident pulse envelope) passage through a linear system. An analytic approximation in the form of a rational function of two variables corresponding to the angular and spatial frequencies has been obtained for the transfer function of the system. A hyperbolic partial differential equation describing the general form of the incident pulse envelope transformation upon diffraction by a resonant diffraction grating has been derived from the transfer function. A solution of this equation has beenmore » obtained for the case of normal incidence of a pulse with a central frequency lying near the guided-mode resonance of a diffraction structure. The presented results of numerical simulations of pulse diffraction by a resonant grating show profound changes in the pulse envelope shape that closely correspond to the proposed theoretical description. The results of the paper can be applied in creating new devices for optical pulse shape transformation, in optical information processing problems, and analog optical computations.« less

Exact representation of the asymptotic drift speed and diffusion matrix for a class of velocity-jump processes

NASA Astrophysics Data System (ADS)

Mascia, Corrado

2016-01-01

This paper examines a class of linear hyperbolic systems which generalizes the Goldstein-Kac model to an arbitrary finite number of speeds vi with transition rates μij. Under the basic assumptions that the transition matrix is symmetric and irreducible, and the differences vi -vj generate all the space, the system exhibits a large-time behavior described by a parabolic advection-diffusion equation. The main contribution is to determine explicit formulas for the asymptotic drift speed and diffusion matrix in term of the kinetic parameters vi and μij, establishing a complete connection between microscopic and macroscopic coefficients. It is shown that the drift speed is the arithmetic mean of the velocities vi. The diffusion matrix has a more complicate representation, based on the graph with vertices the velocities vi and arcs weighted by the transition rates μij. The approach is based on an exhaustive analysis of the dispersion relation and on the application of a variant of the Kirchoff's matrix tree Theorem from graph theory.

Collisions with meteoroid streams as one possible mechanism for the formation of hyperbolic cometary orbits

NASA Astrophysics Data System (ADS)

Guliyev, Ayyub; Nabiyev, Shaig

2017-07-01

This paper presents the results of a statistical analysis of the dynamic parameters of 300 comets that have osculating hyperbolic orbits. It is shown that such comets differ from other comets by their large perihelion distances and by a predominance of retrograde motion. It is shown that the values of i, the inclination of the hyperbolic comets, are in comparative excess over the interval 90-120°. The dominance by q, the perihelion distance, renders it difficult to suggest that the excess hyperbolic velocity of these comets can be the result of physical processes that take place in their nuclei. Aspects of the following working hypothesis, that the hyperbolic excess of parameter e might be formed after comets pass through meteoroid streams, are also studied. To evaluate this hypothesis, the distribution of the orbits of hyperbolic comets relative to the plane of motion of 112 established meteoroid streams are analyzed. The number (N) of orbit nodes for hyperbolic comets with respect to the plane of each stream at various distances is calculated. To determine the degree of redundancy of N, a special computing algorithm was applied that provided the expected value nav as well as the standard deviation σ for the number of cometary nodes at the plane of each stream. A comparative analysis of the N and nav values that take σ into account suggests an excess in 40 stream cases. This implies that the passage of comets through meteoroid streams can lead to an acceleration of the comets' heliocentric velocity.

Topics in spectral methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1985-01-01

After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

Powerless fluxes and forces, and change of scale in irreversible thermodynamics

NASA Astrophysics Data System (ADS)

Ostoja-Starzewski, M.; Zubelewicz, A.

2011-08-01

We show that the dissipation function of linear processes in continuum thermomechanics may be treated as the average of the statistically fluctuating dissipation rate on either coarse or small spatial scales. The first case involves thermodynamic orthogonality due to Ziegler, while the second one involves powerless forces in a general solution of the Clausius-Duhem inequality according to Poincaré and Edelen. This formulation is demonstrated using the example of parabolic versus hyperbolic heat conduction. The existence of macroscopic powerless heat fluxes is traced here to the hidden dissipative processes at lower temporal and spatial scales.

Numerical simulations of compressible mixing layers

NASA Technical Reports Server (NTRS)

Normand, Xavier

1990-01-01

Direct numerical simulations of two-dimensional temporally growing compressible mixing layers are presented. The Kelvin-Helmholtz instability is initially excited by a white-noise perturbation superimposed onto a hyperbolic tangent meanflow profile. The linear regime is studied at low resolution in the case of two flows of equal temperatures, for convective Mach numbers from 0.1 to 1 and for different values of the Reynolds number. At higher resolution, the complete evolution of a two-eddy mixing layer between two flows of different temperatures is simulated at moderate Reynolds number. Similarities and differences between flows of equal convective Mach numbers are discussed.

On some approaches to model reversible magnetization processes

NASA Astrophysics Data System (ADS)

Chwastek, K.; Baghel, A. P. S.; Sai Ram, B.; Borowik, B.; Daniel, L.; Kulkarni, S. V.

2018-04-01

This paper focuses on the problem of how reversible magnetization processes are taken into account in contemporary descriptions of hysteresis curves. For comparison, three versions of the phenomenological T(x) model based on hyperbolic tangent mapping are considered. Two of them are based on summing the output of the hysteresis operator with a linear or nonlinear mapping. The third description is inspired by the concept of the product Preisach model. Total susceptibility is modulated with a magnetization-dependent function. The models are verified using measurement data for grain-oriented electrical steel. The proposed third description represents minor loops most accurately.

Storage and retrieval of time-entangled soliton trains in a three-level atom system coupled to an optical cavity

NASA Astrophysics Data System (ADS)

Welakuh, Davis D. M.; Dikandé, Alain M.

2017-11-01

The storage and subsequent retrieval of coherent pulse trains in the quantum memory (i.e. cavity-dark state) of three-level Λ atoms, are considered for an optical medium in which adiabatic photon transfer occurs under the condition of quantum impedance matching. The underlying mechanism is based on intracavity Electromagnetically-Induced Transparency, by which properties of a cavity filled with three-level Λ-type atoms are manipulated by an external control field. Under the impedance matching condition, we derive analytic expressions that suggest a complete transfer of an input field into the cavity-dark state by varying the mixing angle in a specific way, and its subsequent retrieval at a desired time. We illustrate the scheme by demonstrating the complete transfer and retrieval of a Gaussian, a single hyperbolic-secant and a periodic train of time-entangled hyperbolic-secant input photon pulses in the atom-cavity system. For the time-entangled hyperbolic-secant input field, a total controllability of the periodic evolution of the dark state population is made possible by changing the Rabi frequency of the classical driving field, thus allowing to alternately store and retrieve high-intensity photons from the optically dense Electromagnetically-Induced transparent medium. Such multiplexed photon states, which are expected to allow sharing quantum information among many users, are currently of very high demand for applications in long-distance and multiplexed quantum communication.

2×2 systems of conservation laws with L data

NASA Astrophysics Data System (ADS)

Bianchini, Stefano; Colombo, Rinaldo M.; Monti, Francesca

Consider a hyperbolic system of conservation laws with genuinely nonlinear characteristic fields. We extend the classical Glimm-Lax (1970) result [13, Theorem 5.1] proving the existence of solutions for L initial datum, relaxing the assumptions taken therein on the geometry of the shock-rarefaction curves.

Tunable VO2/Au Hyperbolic Metamaterial

DTIC Science & Technology

2016-02-12

phenomenon having a potential of advancing the control of light-matter interaction . Metamaterials are engineered composite materials containing sub...ellipsoids15 – the phenomenon known as hyperbolic dispersion. Hyperbolic metamaterials can propagate light waves with very large wave vectors and have a...incidence angles equal to 15°, 45° and 65°. The spectra measured at 45o are depicted in Fig. 6(a). The wavy pattern in the spectra is due to the parasitic

Concave utility, transaction costs, and risk in measuring discounting of delayed rewards.

PubMed

Kirby, Kris N; Santiesteban, Mariana

2003-01-01

Research has consistently found that the decline in the present values of delayed rewards as delay increases is better fit by hyperbolic than by exponential delay-discounting functions. However, concave utility, transaction costs, and risk each could produce hyperbolic-looking data, even when the underlying discounting function is exponential. In Experiments 1 (N = 45) and 2 (N = 103), participants placed bids indicating their present values of real future monetary rewards in computer-based 2nd-price auctions. Both experiments suggest that utility is not sufficiently concave to account for the superior fit of hyperbolic functions. Experiment 2 provided no evidence that the effects of transaction costs and risk are large enough to account for the superior fit of hyperbolic functions.

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

Dumbser, Michael, E-mail: michael.dumbser@unitn.it; Peshkov, Ilya, E-mail: peshkov@math.nsc.ru; Romenski, Evgeniy, E-mail: evrom@math.nsc.ru

Highlights: • High order schemes for a unified first order hyperbolic formulation of continuum mechanics. • The mathematical model applies simultaneously to fluid mechanics and solid mechanics. • Viscous fluids are treated in the frame of hyper-elasticity as generalized visco-plastic solids. • Formal asymptotic analysis reveals the connection with the Navier–Stokes equations. • The distortion tensor A in the model appears to be well-suited for flow visualization. - Abstract: This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. Inmore » that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell–Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic–parabolic Navier–Stokes–Fourier theory is established for the first time via a formal asymptotic analysis in the stiff relaxation limit. From a numerical point of view, the governing partial differential equations are very challenging, since they form a large nonlinear hyperbolic PDE system that includes stiff source terms and non-conservative products. We apply the successful family of one-step ADER–WENO finite volume (FV) and ADER discontinuous Galerkin (DG) finite element schemes to the HPR model in the stiff relaxation limit, and compare the numerical results with exact or numerical reference solutions obtained for the Euler and Navier–Stokes equations. Numerical convergence results are also provided. To show the universality of the HPR model, the paper is rounded-off with an application to wave propagation in elastic solids, for which one only needs to switch off the strain relaxation source term in the governing PDE system. We provide various examples showing that for the purpose of flow visualization, the distortion tensor A seems to be particularly useful.« less

The Riemann problem for the relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation

NASA Astrophysics Data System (ADS)

Shao, Zhiqiang

2018-04-01

The relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation is studied. The Riemann problem is solved constructively. The delta shock wave arises in the Riemann solutions, provided that the initial data satisfy some certain conditions, although the system is strictly hyperbolic and the first and third characteristic fields are genuinely nonlinear, while the second one is linearly degenerate. There are five kinds of Riemann solutions, in which four only consist of a shock wave and a centered rarefaction wave or two shock waves or two centered rarefaction waves, and a contact discontinuity between the constant states (precisely speaking, the solutions consist in general of three waves), and the other involves delta shocks on which both the rest mass density and the proper energy density simultaneously contain the Dirac delta function. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. The formation mechanism, generalized Rankine-Hugoniot relation and entropy condition are clarified for this type of delta shock wave. Under the generalized Rankine-Hugoniot relation and entropy condition, we establish the existence and uniqueness of solutions involving delta shocks for the Riemann problem.

Third-harmonic generation in tunable nonlinear hyperbolic metamaterial

NASA Astrophysics Data System (ADS)

Wicharn, Surawut; Buranasiri, Prathan

2018-03-01

In this research, a third-harmonic generation (THG) in a tunable nonlinear hyperbolic metamaterial (TNHM) has been investigated numerically. The TNHM is consisted of periodically arranging of multilayered graphene layers system for controlled optical properties purpose, and ordinary nonlinear dielectric layer. The possibility of TNHM permittivity dispersion controlled by number of graphene layers and external bias voltage to graphene layers was satisfied, then the structure has created the nearly perfect phase-matching scheme based on epsilon-near-zero (ENZ) behavior of the nonlinear medium. Finally, the optimal designed TNHM structure with sufficient bias voltage have given the forwardand backward-direction TH pulses, which the backward-forward TH intensity ratio is closely unity. The THG conversion efficiencies have been maximized after increasing the pumping level to 800 MW/cm2 . From this study, the optimal designed TNHM can be applied as a bi-directional nonlinear frequency converters in nanophotonic systems.

String Theory: exact solutions, marginal deformations and hyperbolic spaces

NASA Astrophysics Data System (ADS)

Orlando, Domenico

2006-10-01

This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is given by Wess-Zumino-Witten models, describing string propagation in a group manifold or, equivalently, a class of conformal field theories with current algebras. We study the moduli space of such models by using truly marginal deformations. Particular emphasis is placed on asymmetric deformations that, together with the CFT description, enjoy a very nice spacetime interpretation in terms of the underlying Lie algebra. Then we take a slight detour so to deal with off-shell systems. Using a renormalization-group approach we describe the relaxation towards the symmetrical equilibrium situation. In he final chapter we consider backgrounds with Ramond-Ramond field and in particular we analyze direct products of constant-curvature spaces and find solutions with hyperbolic spaces.

A numerical algorithm for MHD of free surface flows at low magnetic Reynolds numbers

NASA Astrophysics Data System (ADS)

Samulyak, Roman; Du, Jian; Glimm, James; Xu, Zhiliang

2007-10-01

We have developed a numerical algorithm and computational software for the study of magnetohydrodynamics (MHD) of free surface flows at low magnetic Reynolds numbers. The governing system of equations is a coupled hyperbolic-elliptic system in moving and geometrically complex domains. The numerical algorithm employs the method of front tracking and the Riemann problem for material interfaces, second order Godunov-type hyperbolic solvers, and the embedded boundary method for the elliptic problem in complex domains. The numerical algorithm has been implemented as an MHD extension of FronTier, a hydrodynamic code with free interface support. The code is applicable for numerical simulations of free surface flows of conductive liquids or weakly ionized plasmas. The code has been validated through the comparison of numerical simulations of a liquid metal jet in a non-uniform magnetic field with experiments and theory. Simulations of the Muon Collider/Neutrino Factory target have also been discussed.

Central Limit Theorems for the Shrinking Target Problem

NASA Astrophysics Data System (ADS)

Haydn, Nicolai; Nicol, Matthew; Vaienti, Sandro; Zhang, Licheng

2013-12-01

Suppose B i := B( p, r i ) are nested balls of radius r i about a point p in a dynamical system ( T, X, μ). The question of whether T i x∈ B i infinitely often (i.o.) for μ a.e. x is often called the shrinking target problem. In many dynamical settings it has been shown that if diverges then there is a quantitative rate of entry and for μ a.e. x∈ X. This is a self-norming type of strong law of large numbers. We establish self-norming central limit theorems (CLT) of the form (in distribution) for a variety of hyperbolic and non-uniformly hyperbolic dynamical systems, the normalization constants are . Dynamical systems to which our results apply include smooth expanding maps of the interval, Rychlik type maps, Gibbs-Markov maps, rational maps and, in higher dimensions, piecewise expanding maps. For such central limit theorems the main difficulty is to prove that the non-stationary variance has a limit in probability.

The curious case of large-N expansions on a (pseudo)sphere

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

Polyakov, Alexander M.; Saleem, Zain H.; Stokes, James

We elucidate the large-N dynamics of one-dimensional sigma models with spherical and hyperbolic target spaces and find a duality between the Lagrange multiplier and the angular momentum. In the hyperbolic model we propose a new class of operators based on the irreducible representations of hyperbolic space. We also uncover unexpected zero modes which lead to the double scaling of the 1/N expansion and explore these modes using Gelfand-Dikiy equations.

The curious case of large-N expansions on a (pseudo)sphere

DOE PAGES

Polyakov, Alexander M.; Saleem, Zain H.; Stokes, James

2015-02-03

We elucidate the large-N dynamics of one-dimensional sigma models with spherical and hyperbolic target spaces and find a duality between the Lagrange multiplier and the angular momentum. In the hyperbolic model we propose a new class of operators based on the irreducible representations of hyperbolic space. We also uncover unexpected zero modes which lead to the double scaling of the 1/N expansion and explore these modes using Gelfand-Dikiy equations.

New Techniques in Time-Frequency Analysis: Adaptive Band, Ultra-Wide Band and Multi-Rate Signal Processing

DTIC Science & Technology

2016-03-02

Nyquist tiles and sampling groups in Euclidean geometry, and discussed the extension of these concepts to hyperbolic and spherical geometry and...hyperbolic or spherical spaces. We look to develop a structure for the tiling of frequency spaces in both Euclidean and non-Euclidean domains. In particular...we establish Nyquist tiles and sampling groups in Euclidean geometry, and discuss the extension of these concepts to hyperbolic and spherical geometry

Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow

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

Smith, L. D., E-mail: lachlan.smith@monash.edu; CSIRO Mineral Resources, Clayton, Victoria 3800; Rudman, M.

2016-05-15

Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points also play an important role. These points represent a bifurcation in local stability and Lagrangian topology. In this study, we consider the ramifications of the two types of degenerate periodic points that occur in a model 3D fluid flow. (1) Period-tripling bifurcations occur when the local rotation angle associated with elliptic points is reversed, creating a reversalmore » in the orientation of associated Lagrangian structures. Even though a single unstable point is created, the bifurcation in local stability has a large influence on local transport and the global arrangement of manifolds as the unstable degenerate point has three stable and three unstable directions, similar to hyperbolic points, and occurs at the intersection of three hyperbolic periodic lines. The presence of period-tripling bifurcation points indicates regions of both chaos and confinement, with the extent of each depending on the nature of the associated manifold intersections. (2) The second type of bifurcation occurs when periodic lines become tangent to local or global invariant surfaces. This bifurcation creates both saddle–centre bifurcations which can create both chaotic and stable regions, and period-doubling bifurcations which are a common route to chaos in 2D systems. We provide conditions for the occurrence of these tangent bifurcations in 3D conservative systems, as well as constraints on the possible types of tangent bifurcation that can occur based on topological considerations.« less

z -classes of isometries of the hyperbolic space

NASA Astrophysics Data System (ADS)

Gongopadhyay, Krishnendu; Kulkarni, Ravi S.

Let G be a group. Two elements x, y are said to be z -equivalent if their centralizers are conjugate in G . The class equation of G is the partition of G into conjugacy classes. Further decomposition of conjugacy classes into z -classes provides important information about the internal structure of the group; cf. J. Ramanujan Math. Soc. 22 (2007), 35-56, for the elaboration of this theme. Let I(H^n) denote the group of isometries of the hyperbolic n -space, and let I_o(H^n) be the identity component of I(H^n) . We show that the number of z -classes in I(H^n) is finite. We actually compute their number; cf. theorem 1.3. We interpret the finiteness of z -classes as accounting for the finiteness of ``dynamical types'' in I(H^n) . Along the way we also parametrize conjugacy classes. We mainly use the linear model of the hyperbolic space for this purpose. This description of parametrizing conjugacy classes appears to be new; cf. Academic Press, New York, 1974, 49-87 and Conformal geometry (Bonn, 1985/1986), 41-64, Aspects Math., E12, Vieweg, Braunschweig, 1988, for previous attempts. Ahlfors (Differential Geometry and Complex Analysis (Springer, 1985), 65-73) suggested the use of Clifford algebras to deal with higher dimensional hyperbolic geometry; cf. Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 15-27, Quasiconformal Mappings and Analysis (Springer, 1998), 109-139, Complex Variables Theory Appl. 15 (1990), 125-133, and Adv. Math. 101 (1993), 87-113. These works may be compared to the approach suggested in this paper. In dimensions 2 and 3 , by remarkable Lie-theoretic isomorphisms, I_o(H2) and I_o(H3) can be lifted to GL_o(2, R) , and GL(2, C) respectively. For orientation-reversing isometries there are some modifications of these liftings. Using these liftings, in the appendix A, we have introduced a single numerical invariant c(A) , to classify the elements of I(H2) and I(H3) , and explained the classical terminology. Using the ``Iwasawa decomposition'' of I_o(H^n) , it is possible to equip H^n with a group structure. In the appendix B, we visualize the stratification of the group H^n into its conjugacy and z -classes.

From Experiment to Theory: What Can We Learn from Growth Curves?

PubMed

Kareva, Irina; Karev, Georgy

2018-01-01

Finding an appropriate functional form to describe population growth based on key properties of a described system allows making justified predictions about future population development. This information can be of vital importance in all areas of research, ranging from cell growth to global demography. Here, we use this connection between theory and observation to pose the following question: what can we infer about intrinsic properties of a population (i.e., degree of heterogeneity, or dependence on external resources) based on which growth function best fits its growth dynamics? We investigate several nonstandard classes of multi-phase growth curves that capture different stages of population growth; these models include hyperbolic-exponential, exponential-linear, exponential-linear-saturation growth patterns. The constructed models account explicitly for the process of natural selection within inhomogeneous populations. Based on the underlying hypotheses for each of the models, we identify whether the population that it best fits by a particular curve is more likely to be homogeneous or heterogeneous, grow in a density-dependent or frequency-dependent manner, and whether it depends on external resources during any or all stages of its development. We apply these predictions to cancer cell growth and demographic data obtained from the literature. Our theory, if confirmed, can provide an additional biomarker and a predictive tool to complement experimental research.

Hyperbolic Prismatic Grid Generation and Solution of Euler Equations on Prismatic Grids

NASA Technical Reports Server (NTRS)

Pandya, S. A.; Chattot, JJ; Hafez, M. M.; Kutler, Paul (Technical Monitor)

1994-01-01

A hyperbolic grid generation method is used to generate prismatic grids and an approach using prismatic grids to solve the Euler equations is presented. The theory of the stability and feasibility of the hyperbolic grid generation method is presented. The hyperbolic grid generation method of Steger et al for structured grids is applied to a three dimensional triangularized surface definition to generate a grid that is unstructured on each successive layer. The grid, however, retains structure in the body-normal direction and has a computational cell shaped like a triangular prism. In order to take advantage of the structure in the normal direction, a finite-volume scheme that treats the unknowns along the normal direction implicitly is introduced and the flow over a sphere is simulated.

Progressive wave expansions and open boundary problems

NASA Technical Reports Server (NTRS)

Hagstrom, T.; Hariharan, S. I.

1995-01-01

In this paper we construct progressive wave expansions and asymptotic boundary conditions for wave-like equations in exterior domains, including applications to electromagnetics, compressible flows and aero-acoustics. The development of the conditions will be discussed in two parts. The first part will include derivations of asymptotic conditions based on the well-known progressive wave expansions for the two-dimensional wave equations. A key feature in the derivations is that the resulting family of boundary conditions involves a single derivative in the direction normal to the open boundary. These conditions are easy to implement and an application in electromagnetics will be presented. The second part of the paper will discuss the theory for hyperbolic systems in two dimensions. Here, the focus will be to obtain the expansions in a general way and to use them to derive a class of boundary conditions that involve only time derivatives or time and tangential derivatives. Maxwell's equations and the compressible Euler equations are used as examples. Simulations with the linearized Euler equations are presented to validate the theory.

Acoustically-driven surface and hyperbolic plasmon-phonon polaritons in graphene/h-BN heterostructures on piezoelectric substrates

NASA Astrophysics Data System (ADS)

Fandan, R.; Pedrós, J.; Schiefele, J.; Boscá, A.; Martínez, J.; Calle, F.

2018-05-01

Surface plasmon polaritons in graphene couple strongly to surface phonons in polar substrates leading to hybridized surface plasmon-phonon polaritons (SPPPs). We demonstrate that a surface acoustic wave (SAW) can be used to launch propagating SPPPs in graphene/h-BN heterostructures on a piezoelectric substrate like AlN, where the SAW-induced surface modulation acts as a dynamic diffraction grating. The efficiency of the light coupling is greatly enhanced by the introduction of the h-BN film as compared to the bare graphene/AlN system. The h-BN interlayer not only significantly changes the dispersion of the SPPPs but also enhances their lifetime. The strengthening of the SPPPs is shown to be related to both the higher carrier mobility induced in graphene and the coupling with h-BN and AlN surface phonons. In addition to surface phonons, hyperbolic phonons polaritons (HPPs) appear in the case of multilayer h-BN films leading to hybridized hyperbolic plasmon-phonon polaritons (HPPPs) that are also mediated by the SAW. These results pave the way for engineering SAW-based graphene/h-BN plasmonic devices and metamaterials covering the mid-IR to THz range.

O(2) Hopf bifurcation of viscous shock waves in a channel

NASA Astrophysics Data System (ADS)

Pogan, Alin; Yao, Jinghua; Zumbrun, Kevin

2015-07-01

Extending work of Texier and Zumbrun in the semilinear non-reflection symmetric case, we study O(2) transverse Hopf bifurcation, or "cellular instability", of viscous shock waves in a channel, for a class of quasilinear hyperbolic-parabolic systems including the equations of thermoviscoelasticity. The main difficulties are to (i) obtain Fréchet differentiability of the time- T solution operator by appropriate hyperbolic-parabolic energy estimates, and (ii) handle O(2) symmetry in the absence of either center manifold reduction (due to lack of spectral gap) or (due to nonstandard quasilinear hyperbolic-parabolic form) the requisite framework for treatment by spatial dynamics on the space of time-periodic functions, the two standard treatments for this problem. The latter issue is resolved by Lyapunov-Schmidt reduction of the time- T map, yielding a four-dimensional problem with O(2) plus approximate S1 symmetry, which we treat "by hand" using direct Implicit Function Theorem arguments. The former is treated by balancing information obtained in Lagrangian coordinates with that from associated constraints. Interestingly, this argument does not apply to gas dynamics or magnetohydrodynamics (MHD), due to the infinite-dimensional family of Lagrangian symmetries corresponding to invariance under arbitrary volume-preserving diffeomorphisms.

A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Fluid Flow

NASA Technical Reports Server (NTRS)

Xu, Kun

1999-01-01

A gas-kinetic method for the hyperbolic-elliptic equations is presented in this paper. In the mixed type system, the co-existence and the phase transition between liquid and gas are described by the van der Waals-type equation of state (EOS). Due to the unstable mechanism for a fluid in the elliptic region, interface between the liquid and gas can be kept sharp through the condensation and evaporation process to remove the "averaged" numerical fluid away from the elliptic region, and the interface thickness depends on the numerical diffusion and stiffness of the phase change. A few examples are presented in this paper for both phase transition and multifluid interface problems.

Discontinuous Galerkin method with Gaussian artificial viscosity on graphical processing units for nonlinear acoustics

NASA Astrophysics Data System (ADS)

Tripathi, Bharat B.; Marchiano, Régis; Baskar, Sambandam; Coulouvrat, François

2015-10-01

Propagation of acoustical shock waves in complex geometry is a topic of interest in the field of nonlinear acoustics. For instance, simulation of Buzz Saw Noice requires the treatment of shock waves generated by the turbofan through the engines of aeroplanes with complex geometries and wall liners. Nevertheless, from a numerical point of view it remains a challenge. The two main hurdles are to take into account the complex geometry of the domain and to deal with the spurious oscillations (Gibbs phenomenon) near the discontinuities. In this work, first we derive the conservative hyperbolic system of nonlinear acoustics (up to quadratic nonlinear terms) using the fundamental equations of fluid dynamics. Then, we propose to adapt the classical nodal discontinuous Galerkin method to develop a high fidelity solver for nonlinear acoustics. The discontinuous Galerkin method is a hybrid of finite element and finite volume method and is very versatile to handle complex geometry. In order to obtain better performance, the method is parallelized on Graphical Processing Units. Like other numerical methods, discontinuous Galerkin method suffers with the problem of Gibbs phenomenon near the shock, which is a numerical artifact. Among the various ways to manage these spurious oscillations, we choose the method of parabolic regularization. Although, the introduction of artificial viscosity into the system is a popular way of managing shocks, we propose a new approach of introducing smooth artificial viscosity locally in each element, wherever needed. Firstly, a shock sensor using the linear coefficients of the spectral solution is used to locate the position of the discontinuities. Then, a viscosity coefficient depending on the shock sensor is introduced into the hyperbolic system of equations, only in the elements near the shock. The viscosity is applied as a two-dimensional Gaussian patch with its shape parameters depending on the element dimensions, referred here as Element Centered Smooth Artificial Viscosity. Using this numerical solver, various numerical experiments are presented for one and two-dimensional test cases in homogeneous and quiescent medium. This work is funded by CEFIPRA (Indo-French Centre for the Promotion of Advance Research) and partially aided by EGIDE (Campus France).

Hyperbolic heat conduction problems involving non-Fourier effects - Numerical simulations via explicit Lax-Wendroff/Taylor-Galerkin finite element formulations

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; Namburu, Raju R.

1989-01-01

Numerical simulations are presented for hyperbolic heat-conduction problems that involve non-Fourier effects, using explicit, Lax-Wendroff/Taylor-Galerkin FEM formulations as the principal computational tool. Also employed are smoothing techniques which stabilize the numerical noise and accurately predict the propagating thermal disturbances. The accurate capture of propagating thermal disturbances at characteristic time-step values is achieved; numerical test cases are presented which validate the proposed hyperbolic heat-conduction problem concepts.

Dissipation models for central difference schemes

NASA Astrophysics Data System (ADS)

Eliasson, Peter

1992-12-01

In this paper different flux limiters are used to construct dissipation models. The flux limiters are usually of Total Variation Diminishing (TVD type and are applied to the characteristic variables for the hyperbolic Euler equations in one, two or three dimensions. A number of simplified dissipation models with a reduced number of limiters are considered to reduce the computational effort. The most simplified methods use only one limiter, the dissipation model by Jameson belongs to this class since the Jameson pressure switch is considered as a limiter, not TVD though. Other one-limiter models with TVD limiters are also investigated. Models in between the most simplified one-limiter models and the full model with limiters on all the different characteristics are considered where different dissipation models are applied to the linear and non-linear characteristcs. In this paper the theory by Yee is extended to a general explicit Runge-Kutta type of schemes.

Methods of Investigation of Equations that Describe Waves in Tubes with Elastic Walls and Application of the Theory of Reversible and Weak Dissipative Shocks

NASA Astrophysics Data System (ADS)

Bakholdin, Igor

2018-02-01

Various models of a tube with elastic walls are investigated: with controlled pressure, filled with incompressible fluid, filled with compressible gas. The non-linear theory of hyperelasticity is applied. The walls of a tube are described with complete membrane model. It is proposed to use linear model of plate in order to take the bending resistance of walls into account. The walls of the tube were treated previously as inviscid and incompressible. Compressibility of material of walls and viscosity of material, either gas or liquid are considered. Equations are solved numerically. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical scheme with approximation of time derivatives by Runge-Kutta method are used. A method of correction of numerical schemes by inclusion of terms with highorder derivatives is developed. Simplified hyperbolic equations are derived.

Targeted ENO schemes with tailored resolution property for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Fu, Lin; Hu, Xiangyu Y.; Adams, Nikolaus A.

2017-11-01

In this paper, we extend the range of targeted ENO (TENO) schemes (Fu et al. (2016) [18]) by proposing an eighth-order TENO8 scheme. A general formulation to construct the high-order undivided difference τK within the weighting strategy is proposed. With the underlying scale-separation strategy, sixth-order accuracy for τK in the smooth solution regions is designed for good performance and robustness. Furthermore, a unified framework to optimize independently the dispersion and dissipation properties of high-order finite-difference schemes is proposed. The new framework enables tailoring of dispersion and dissipation as function of wavenumber. The optimal linear scheme has minimum dispersion error and a dissipation error that satisfies a dispersion-dissipation relation. Employing the optimal linear scheme, a sixth-order TENO8-opt scheme is constructed. A set of benchmark cases involving strong discontinuities and broadband fluctuations is computed to demonstrate the high-resolution properties of the new schemes.

Hadamard States for the Linearized Yang-Mills Equation on Curved Spacetime

NASA Astrophysics Data System (ADS)

Gérard, C.; Wrochna, M.

2015-07-01

We construct Hadamard states for the Yang-Mills equation linearized around a smooth, space-compact background solution. We assume the spacetime is globally hyperbolic and its Cauchy surface is compact or equal . We first consider the case when the spacetime is ultra-static, but the background solution depends on time. By methods of pseudodifferential calculus we construct a parametrix for the associated vectorial Klein-Gordon equation. We then obtain Hadamard two-point functions in the gauge theory, acting on Cauchy data. A key role is played by classes of pseudodifferential operators that contain microlocal or spectral type low-energy cutoffs. The general problem is reduced to the ultra-static spacetime case using an extension of the deformation argument of Fulling, Narcowich and Wald. As an aside, we derive a correspondence between Hadamard states and parametrices for the Cauchy problem in ordinary quantum field theory.

Nonlocal modification and quantum optical generalization of effective-medium theory for metamaterials

NASA Astrophysics Data System (ADS)

Wubs, Martijn; Yan, Wei; Amooghorban, Ehsan; Mortensen, N. Asger

2013-09-01

A well-known challenge for fabricating metamaterials is to make unit cells significantly smaller than the operating wavelength of light, so one can be sure that effective-medium theories apply. But do they apply? Here we show that nonlocal response in the metal constituents of the metamaterial leads to modified effective parameters for strongly subwavelength unit cells. For infinite hyperbolic metamaterials, nonlocal response gives a very large finite upper bound to the optical density of states that otherwise would diverge. Moreover, for finite hyperbolic metamaterials we show that nonlocal response affects their operation as superlenses, and interestingly that sometimes nonlocal theory predicts the better imaging. Finally, we discuss how to describe metamaterials effectively in quantum optics. Media with loss or gain have associated quantum noise, and the question is whether the effective index is enough to describe this quantum noise effectively. We show that this is true for passive metamaterials, but not for metamaterials where loss is compensated by linear gain. For such loss-compensated metamaterials we present a quantum optical effective medium theory with an effective noise photon distribution as an additional parameter. Interestingly, we find that at the operating frequency, metamaterials with the same effective index but with different amounts of loss compensation can be told apart in quantum optics.

Self-stimulation in the rat: quantitative characteristics of the reward pathway.

PubMed

Gallistel, C R

1978-12-01

Quantitative characteristics of the neural pathway that carries the reinforcing signal in electrical self-stimulation of the brain were established by finding which combinations of stimulation parameters give the same performance in a runway. The reward for each run was a train of evenly spaced monophasic cathodal pulses from a monopolar electrode. With train duration and pulse frequency held constant, the required current was a hyperbolic function of pulse duration, with chronaxie c approximately 1.5 msec. With pulse duration held constant, the required strength of the train (the charge delivered per second) was a hyperbolic function of train duration, with chronaxie C approximately 500 msec. To a first approximation, the values of c and C were independent of the choice either of train duration and pulse frequency or of pulse duration, respectively. Hence, the current intensity required by any choice of train duration, pulse frequency, and pulse duration dependent on only two basic parameters, c and C, and one quantity, Qi, the required impulse charge. These may reflect, respectively, current integration by directly excited neurons; temporal integration of neural activity by synaptic processes in a neural network; and the peak of the impulse response of the network, assuming that the network has linear dynamics and that the reward depends on the peak of the output of the network.

Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material

PubMed Central

Dai, S.; Ma, Q.; Andersen, T.; Mcleod, A. S.; Fei, Z.; Liu, M. K.; Wagner, M.; Watanabe, K.; Taniguchi, T.; Thiemens, M.; Keilmann, F.; Jarillo-Herrero, P.; Fogler, M. M.; Basov, D. N.

2015-01-01

Uniaxial materials whose axial and tangential permittivities have opposite signs are referred to as indefinite or hyperbolic media. In such materials, light propagation is unusual leading to novel and often non-intuitive optical phenomena. Here we report infrared nano-imaging experiments demonstrating that crystals of hexagonal boron nitride, a natural mid-infrared hyperbolic material, can act as a ‘hyper-focusing lens' and as a multi-mode waveguide. The lensing is manifested by subdiffractional focusing of phonon–polaritons launched by metallic disks underneath the hexagonal boron nitride crystal. The waveguiding is revealed through the modal analysis of the periodic patterns observed around such launchers and near the sample edges. Our work opens new opportunities for anisotropic layered insulators in infrared nanophotonics complementing and potentially surpassing concurrent artificial hyperbolic materials with lower losses and higher optical localization. PMID:25902364

"That's really clever!" Ironic hyperbole understanding in children.

PubMed

Aguert, Marc; LE Vallois, Coralie; Martel, Karine; Laval, Virginie

2018-01-01

Hyperbole supports irony comprehension in adults by heightening the contrast between what is said and the actual situation. Because young children do not perceive the communication situation as a whole, but rather give precedence to either the utterance or the context, we predicted that hyperbole would reduce irony comprehension in six-year-olds (n = 40) by overemphasizing what was said. By contrast, ten-year-olds (n = 40) would benefit from hyperbole in the way that adults do, as they would perceive the utterance and context as a whole, highlighted by the speaker's ironic intent. Short animated cartoons featuring ironic criticisms were shown to participants. We assessed comprehension of the speaker's belief and speaker's intent. Results supported our predictions. The development of mentalization during school years and its impact on the development of irony comprehension is discussed.

Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar

2018-05-01

The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.

Theory of hyperbolic stratified nanostructures for surface-enhanced Raman scattering

NASA Astrophysics Data System (ADS)

Wong, Herman M. K.; Dezfouli, Mohsen Kamandar; Axelrod, Simon; Hughes, Stephen; Helmy, Amr S.

2017-11-01

We theoretically investigate the enhancement of surface enhanced Raman spectroscopy (SERS) using hyperbolic stratified nanostructures and compare to metal nanoresonators. The photon Green function of each nanostructure within its environment is first obtained from a semianalytical modal theory, which is used in a quantum optics formalism of the molecule-nanostructure interaction to model the SERS spectrum. An intuitive methodology is presented for calculating the single-molecule enhancement factor (SMEF), which is also able to predict known experimental SERS enhancement factors of a gold nanodimer. We elucidate the important figures-of-merit of the enhancement and explore these for different designs. We find that the use of hyperbolic stratified materials can enhance the photonic local density of states (LDOS) by close to two times in comparison to pure metal nanostructures, when both designed to work at the same operating wavelengths. However, the increased LDOS is accompanied by higher electric field concentration within the lossy hyperbolic material, which leads to increased quenching that serves to reduce the overall detected SERS enhancement in the far field. For nanoresonators with resonant localized surface plasmon wavelengths in the near-infrared, the SMEF for the hyperbolic stratified nanostructure is approximately one order of magnitude lower than the pure metal counterpart. Conversely, we show that by detecting the Raman signal using a near-field probe, hyperbolic materials can provide an improvement in SERS enhancement compared to using pure metal nanostructures when the probe is sufficiently close (<50 nm ) to the Raman active molecule at the plasmonic hotspot.

Practical Aspects of Stabilized FEM Discretizations of Nonlinear Conservation Law Systems with Convex Extension

NASA Technical Reports Server (NTRS)

Barth, Timothy; Saini, Subhash (Technical Monitor)

1999-01-01

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the Galerkin least-squares (GLS) and the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the POE system. Central to the development of the simplified GLS and DG methods is the Degenerative Scaling Theorem which characterizes right symmetrizes of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobean matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler, Navier-Stokes, and magnetohydrodynamic (MHD) equations. Linear and nonlinear energy stability is proven for the simplified GLS and DG methods. Spatial convergence properties of the simplified GLS and DO methods are numerical evaluated via the computation of Ringleb flow on a sequence of successively refined triangulations. Finally, we consider a posteriori error estimates for the GLS and DG demoralization assuming error functionals related to the integrated lift and drag of a body. Sample calculations in 20 are shown to validate the theory and implementation.

Does temporal discounting explain unhealthy behavior? A systematic review and reinforcement learning perspective

PubMed Central

Story, Giles W.; Vlaev, Ivo; Seymour, Ben; Darzi, Ara; Dolan, Raymond J.

2014-01-01

The tendency to make unhealthy choices is hypothesized to be related to an individual's temporal discount rate, the theoretical rate at which they devalue delayed rewards. Furthermore, a particular form of temporal discounting, hyperbolic discounting, has been proposed to explain why unhealthy behavior can occur despite healthy intentions. We examine these two hypotheses in turn. We first systematically review studies which investigate whether discount rates can predict unhealthy behavior. These studies reveal that high discount rates for money (and in some instances food or drug rewards) are associated with several unhealthy behaviors and markers of health status, establishing discounting as a promising predictive measure. We secondly examine whether intention-incongruent unhealthy actions are consistent with hyperbolic discounting. We conclude that intention-incongruent actions are often triggered by environmental cues or changes in motivational state, whose effects are not parameterized by hyperbolic discounting. We propose a framework for understanding these state-based effects in terms of the interplay of two distinct reinforcement learning mechanisms: a “model-based” (or goal-directed) system and a “model-free” (or habitual) system. Under this framework, while discounting of delayed health may contribute to the initiation of unhealthy behavior, with repetition, many unhealthy behaviors become habitual; if health goals then change, habitual behavior can still arise in response to environmental cues. We propose that the burgeoning development of computational models of these processes will permit further identification of health decision-making phenotypes. PMID:24659960

Does temporal discounting explain unhealthy behavior? A systematic review and reinforcement learning perspective.

PubMed

Story, Giles W; Vlaev, Ivo; Seymour, Ben; Darzi, Ara; Dolan, Raymond J

2014-01-01

The tendency to make unhealthy choices is hypothesized to be related to an individual's temporal discount rate, the theoretical rate at which they devalue delayed rewards. Furthermore, a particular form of temporal discounting, hyperbolic discounting, has been proposed to explain why unhealthy behavior can occur despite healthy intentions. We examine these two hypotheses in turn. We first systematically review studies which investigate whether discount rates can predict unhealthy behavior. These studies reveal that high discount rates for money (and in some instances food or drug rewards) are associated with several unhealthy behaviors and markers of health status, establishing discounting as a promising predictive measure. We secondly examine whether intention-incongruent unhealthy actions are consistent with hyperbolic discounting. We conclude that intention-incongruent actions are often triggered by environmental cues or changes in motivational state, whose effects are not parameterized by hyperbolic discounting. We propose a framework for understanding these state-based effects in terms of the interplay of two distinct reinforcement learning mechanisms: a "model-based" (or goal-directed) system and a "model-free" (or habitual) system. Under this framework, while discounting of delayed health may contribute to the initiation of unhealthy behavior, with repetition, many unhealthy behaviors become habitual; if health goals then change, habitual behavior can still arise in response to environmental cues. We propose that the burgeoning development of computational models of these processes will permit further identification of health decision-making phenotypes.

Particle orbits in two-dimensional equilibrium models for the magnetotail

NASA Technical Reports Server (NTRS)

Karimabadi, H.; Pritchett, P. L.; Coroniti, F. V.

1990-01-01

Assuming that there exist an equilibrium state for the magnetotail, particle orbits are investigated in two-dimensional kinetic equilibrium models for the magnetotail. Particle orbits in the equilibrium field are compared with those calculated earlier with one-dimensional models, where the main component of the magnetic field (Bx) was approximated as either a hyperbolic tangent or a linear function of z with the normal field (Bz) assumed to be a constant. It was found that the particle orbits calculated with the two types of models are significantly different, mainly due to the neglect of the variation of Bx with x in the one-dimensional fields.

Numerical Hydrodynamics in General Relativity.

PubMed

Font, José A

2000-01-01

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A representative sample of available numerical schemes is discussed and particular emphasis is paid to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of relevant astrophysical simulations in strong gravitational fields, including gravitational collapse, accretion onto black holes and evolution of neutron stars, is also presented. Supplementary material is available for this article at 10.12942/lrr-2000-2.

Multi-time-scale heat transfer modeling of turbid tissues exposed to short-pulsed irradiations.

PubMed

Kim, Kyunghan; Guo, Zhixiong

2007-05-01

A combined hyperbolic radiation and conduction heat transfer model is developed to simulate multi-time-scale heat transfer in turbid tissues exposed to short-pulsed irradiations. An initial temperature response of a tissue to an ultrashort pulse irradiation is analyzed by the volume-average method in combination with the transient discrete ordinates method for modeling the ultrafast radiation heat transfer. This response is found to reach pseudo steady state within 1 ns for the considered tissues. The single pulse result is then utilized to obtain the temperature response to pulse train irradiation at the microsecond/millisecond time scales. After that, the temperature field is predicted by the hyperbolic heat conduction model which is solved by the MacCormack's scheme with error terms correction. Finally, the hyperbolic conduction is compared with the traditional parabolic heat diffusion model. It is found that the maximum local temperatures are larger in the hyperbolic prediction than the parabolic prediction. In the modeled dermis tissue, a 7% non-dimensional temperature increase is found. After about 10 thermal relaxation times, thermal waves fade away and the predictions between the hyperbolic and parabolic models are consistent.

Improving the assessment of predator functional responses by considering alternate prey and predator interactions.

PubMed

Chan, K; Boutin, S; Hossie, T J; Krebs, C J; O'Donoghue, M; Murray, D L

2017-07-01

To improve understanding of the complex and variable patterns of predator foraging behavior in natural systems, it is critical to determine how density-dependent predation and predator hunting success are mediated by alternate prey or predator interference. Despite considerable theory and debate seeking to place predator-prey interactions in a more realistic context, few empirical studies have quantified the role of alternate prey or intraspecific interactions on predator-prey dynamics. We assessed functional responses of two similarly sized, sympatric carnivores, lynx (Lynx canadensis) and coyotes (Canis latrans), foraging on common primary (snowshoe hares; Lepus americanus) and alternate (red squirrels; Tamiasciurus hudsonicus) prey in a natural system. Lynx exhibited a hyperbolic prey-dependent response to changes in hare density, which is characteristic of predators relying primarily on a single prey species. In contrast, the lynx-squirrel response was found to be linear ratio dependent, or inversely dependent on hare density. The coyote-hare and coyote-squirrel interactions also were linear and influenced by predator density. We explain these novel results by apparent use of spatial and temporal refuges by prey, and the likelihood that predators commonly experience interference and lack of satiation when foraging. Our study provides empirical support from a natural predator-prey system that (1) predation rate may not be limited at high prey densities when prey are small or rarely captured; (2) interference competition may influence the predator functional response; and (3) predator interference has a variable role across different prey types. Ultimately, distinct functional responses of predators to different prey types illustrates the complexity associated with predator-prey interactions in natural systems and highlights the need to investigate predator behavior and predation rate in relation to the broader ecological community. © 2017 by the Ecological Society of America.

Generation of three-dimensional body-fitted grids by solving hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Steger, Joseph L.

1989-01-01

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, an extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Generation of three-dimensional body-fitted grids by solving hyperbolic and parabolic partial differential equations

NASA Technical Reports Server (NTRS)

Steger, Joseph L.

1989-01-01

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Motion Among Random Obstacles on a Hyperbolic Space

NASA Astrophysics Data System (ADS)

Orsingher, Enzo; Ricciuti, Costantino; Sisti, Francesco

2016-02-01

We consider the motion of a particle along the geodesic lines of the Poincaré half-plane. The particle is specularly reflected when it hits randomly-distributed obstacles that are assumed to be motionless. This is the hyperbolic version of the well-known Lorentz Process studied in the Euclidean context. We analyse the limit in which the density of the obstacles increases to infinity and the size of each obstacle vanishes: under a suitable scaling, we prove that our process converges to a Markovian process, namely a random flight on the hyperbolic manifold.

Exotica and the status of the strong cosmic censor conjecture in four dimensions

NASA Astrophysics Data System (ADS)

Etesi, Gábor

2017-12-01

An immense class of physical counterexamples to the four dimensional strong cosmic censor conjecture—in its usual broad formulation—is exhibited. More precisely, out of any closed and simply connected 4-manifold an open Ricci-flat Lorentzian 4-manifold is constructed which is not globally hyperbolic, and no perturbation of which, in any sense, can be globally hyperbolic. This very stable non-global-hyperbolicity is the consequence of our open spaces having a ‘creased end’—i.e. an end diffeomorphic to an exotic \

Louisiana Threads the Needle on ED Reform: Launching a Coherent Curriculum in a Local-Control State

ERIC Educational Resources Information Center

Pondiscio, Robert

2017-01-01

Officials of state education agencies are not known for hyperbole. Maintaining data systems, drafting rules and regulations, and monitoring compliance are not the stuff of breathless raves--especially in Louisiana, whose education system ranks near the bottom nationwide on measures of student achievement and high-school graduation rates. Yet in…

Private Schools and Parental Choice: Dubious Assumptions, Frail Claims, and Excessive Hyperbole. Occasional Paper.

ERIC Educational Resources Information Center

Corwin, Ronald G.

The preoccupation with choice between public and private schools offered under voucher programs obscures the greater problem of a lack of variety in the present educational system. If providing a greater variety of school structures and improving the educational system is the objective, competition between the public and private sectors will not…

A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities

NASA Astrophysics Data System (ADS)

Muscoloni, Alessandro; Vittorio Cannistraci, Carlo

2018-05-01

The investigation of the hidden metric space behind complex network topologies is a fervid topic in current network science and the hyperbolic space is one of the most studied, because it seems associated to the structural organization of many real complex systems. The popularity-similarity-optimization (PSO) model simulates how random geometric graphs grow in the hyperbolic space, generating realistic networks with clustering, small-worldness, scale-freeness and rich-clubness. However, it misses to reproduce an important feature of real complex networks, which is the community organization. The geometrical-preferential-attachment (GPA) model was recently developed in order to confer to the PSO also a soft community structure, which is obtained by forcing different angular regions of the hyperbolic disk to have a variable level of attractiveness. However, the number and size of the communities cannot be explicitly controlled in the GPA, which is a clear limitation for real applications. Here, we introduce the nonuniform PSO (nPSO) model. Differently from GPA, the nPSO generates synthetic networks in the hyperbolic space where heterogeneous angular node attractiveness is forced by sampling the angular coordinates from a tailored nonuniform probability distribution (for instance a mixture of Gaussians). The nPSO differs from GPA in other three aspects: it allows one to explicitly fix the number and size of communities; it allows one to tune their mixing property by means of the network temperature; it is efficient to generate networks with high clustering. Several tests on the detectability of the community structure in nPSO synthetic networks and wide investigations on their structural properties confirm that the nPSO is a valid and efficient model to generate realistic complex networks with communities.

Using periodic orbits to compute chaotic transport rates between resonance zones.

PubMed

Sattari, Sulimon; Mitchell, Kevin A

2017-11-01

Transport properties of chaotic systems are computable from data extracted from periodic orbits. Given a sufficient number of periodic orbits, the escape rate can be computed using the spectral determinant, a function that incorporates the eigenvalues and periods of periodic orbits. The escape rate computed from periodic orbits converges to the true value as more and more periodic orbits are included. Escape from a given region of phase space can be computed by considering only periodic orbits that lie within the region. An accurate symbolic dynamics along with a corresponding partitioning of phase space is useful for systematically obtaining all periodic orbits up to a given period, to ensure that no important periodic orbits are missing in the computation. Homotopic lobe dynamics (HLD) is an automated technique for computing accurate partitions and symbolic dynamics for maps using the topological forcing of intersections of stable and unstable manifolds of a few periodic anchor orbits. In this study, we apply the HLD technique to compute symbolic dynamics and periodic orbits, which are then used to find escape rates from different regions of phase space for the Hénon map. We focus on computing escape rates in parameter ranges spanning hyperbolic plateaus, which are parameter intervals where the dynamics is hyperbolic and the symbolic dynamics does not change. After the periodic orbits are computed for a single parameter value within a hyperbolic plateau, periodic orbit continuation is used to compute periodic orbits over an interval that spans the hyperbolic plateau. The escape rates computed from a few thousand periodic orbits agree with escape rates computed from Monte Carlo simulations requiring hundreds of billions of orbits.

A simple hyperbolic model for communication in parallel processing environments

NASA Technical Reports Server (NTRS)

Stoica, Ion; Sultan, Florin; Keyes, David

1994-01-01

We introduce a model for communication costs in parallel processing environments called the 'hyperbolic model,' which generalizes two-parameter dedicated-link models in an analytically simple way. Dedicated interprocessor links parameterized by a latency and a transfer rate that are independent of load are assumed by many existing communication models; such models are unrealistic for workstation networks. The communication system is modeled as a directed communication graph in which terminal nodes represent the application processes that initiate the sending and receiving of the information and in which internal nodes, called communication blocks (CBs), reflect the layered structure of the underlying communication architecture. The direction of graph edges specifies the flow of the information carried through messages. Each CB is characterized by a two-parameter hyperbolic function of the message size that represents the service time needed for processing the message. The parameters are evaluated in the limits of very large and very small messages. Rules are given for reducing a communication graph consisting of many to an equivalent two-parameter form, while maintaining an approximation for the service time that is exact in both large and small limits. The model is validated on a dedicated Ethernet network of workstations by experiments with communication subprograms arising in scientific applications, for which a tight fit of the model predictions with actual measurements of the communication and synchronization time between end processes is demonstrated. The model is then used to evaluate the performance of two simple parallel scientific applications from partial differential equations: domain decomposition and time-parallel multigrid. In an appropriate limit, we also show the compatibility of the hyperbolic model with the recently proposed LogP model.

The hyperbolic chemical bond: Fourier analysis of ground and first excited state potential energy curves of HX (X = H-Ne).

PubMed

Harrison, John A

2008-09-04

RHF/aug-cc-pVnZ, UHF/aug-cc-pVnZ, and QCISD/aug-cc-pVnZ, n = 2-5, potential energy curves of H2 X (1) summation g (+) are analyzed by Fourier transform methods after transformation to a new coordinate system via an inverse hyperbolic cosine coordinate mapping. The Fourier frequency domain spectra are interpreted in terms of underlying mathematical behavior giving rise to distinctive features. There is a clear difference between the underlying mathematical nature of the potential energy curves calculated at the HF and full-CI levels. The method is particularly suited to the analysis of potential energy curves obtained at the highest levels of theory because the Fourier spectra are observed to be of a compact nature, with the envelope of the Fourier frequency coefficients decaying in magnitude in an exponential manner. The finite number of Fourier coefficients required to describe the CI curves allows for an optimum sampling strategy to be developed, corresponding to that required for exponential and geometric convergence. The underlying random numerical noise due to the finite convergence criterion is also a clearly identifiable feature in the Fourier spectrum. The methodology is applied to the analysis of MRCI potential energy curves for the ground and first excited states of HX (X = H-Ne). All potential energy curves exhibit structure in the Fourier spectrum consistent with the existence of resonances. The compact nature of the Fourier spectra following the inverse hyperbolic cosine coordinate mapping is highly suggestive that there is some advantage in viewing the chemical bond as having an underlying hyperbolic nature.

SAHARA: A package of PC computer programs for estimating both log-hyperbolic grain-size parameters and standard moments

NASA Astrophysics Data System (ADS)

Christiansen, Christian; Hartmann, Daniel

This paper documents a package of menu-driven POLYPASCAL87 computer programs for handling grouped observations data from both sieving (increment data) and settling tube procedures (cumulative data). The package is designed deliberately for use on IBM-compatible personal computers. Two of the programs solve the numerical problem of determining the estimates of the four (main) parameters of the log-hyperbolic distribution and their derivatives. The package also contains a program for determining the mean, sorting, skewness. and kurtosis according to the standard moments. Moreover, the package contains procedures for smoothing and grouping of settling tube data. A graphic part of the package plots the data in a log-log plot together with the estimated log-hyperbolic curve. Along with the plot follows all estimated parameters. Another graphic option is a plot of the log-hyperbolic shape triangle with the (χ,ζ) position of the sample.

Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes.

PubMed

Kapitanova, Polina V; Ginzburg, Pavel; Rodríguez-Fortuño, Francisco J; Filonov, Dmitry S; Voroshilov, Pavel M; Belov, Pavel A; Poddubny, Alexander N; Kivshar, Yuri S; Wurtz, Gregory A; Zayats, Anatoly V

2014-01-01

The routing of light in a deep subwavelength regime enables a variety of important applications in photonics, quantum information technologies, imaging and biosensing. Here we describe and experimentally demonstrate the selective excitation of spatially confined, subwavelength electromagnetic modes in anisotropic metamaterials with hyperbolic dispersion. A localized, circularly polarized emitter placed at the boundary of a hyperbolic metamaterial is shown to excite extraordinary waves propagating in a prescribed direction controlled by the polarization handedness. Thus, a metamaterial slab acts as an extremely broadband, nearly ideal polarization beam splitter for circularly polarized light. We perform a proof of concept experiment with a uniaxial hyperbolic metamaterial at radio-frequencies revealing the directional routing effect and strong subwavelength λ/300 confinement. The proposed concept of metamaterial-based subwavelength interconnection and polarization-controlled signal routing is based on the photonic spin Hall effect and may serve as an ultimate platform for either conventional or quantum electromagnetic signal processing.

Realizing high-quality ultralarge momentum states and ultrafast topological transitions using semiconductor hyperbolic metamaterials

DOE PAGES

Campione, Salvatore; Liu, Sheng; Luk, Ting S.; ...

2015-08-05

We employ both the effective medium approximation (EMA) and Bloch theory to compare the dispersion properties of semiconductor hyperbolic metamaterials (SHMs) at mid-infrared frequencies and metallic hyperbolic metamaterials (MHMs) at visible frequencies. This analysis reveals the conditions under which the EMA can be safely applied for both MHMs and SHMs. We find that the combination of precise nanoscale layering and the longer infrared operating wavelengths puts the SHMs well within the effective medium limit and, in contrast to MHMs, allows for the attainment of very high photon momentum states. Additionally, SHMs allow for new phenomena such as ultrafast creation ofmore » the hyperbolic manifold through optical pumping. Furthermore, we examine the possibility of achieving ultrafast topological transitions through optical pumping which can photo-dope appropriately designed quantum wells on the femtosecond time scale.« less

Path integration on the hyperbolic plane with a magnetic field

NASA Astrophysics Data System (ADS)

Grosche, Christian

1990-08-01

In this paper I discuss the path integrals on three formulations of hyperbolic geometry, where a constant magnetic field B is included. These are: the pseudosphere Λ2, the Poincaré disc D, and the hyperbolic strip S. The corresponding path integrals can be reformulated in terms of the path integral for the modified Pöschl-Teller potential. The wave-functions and the energy spectrum for the discrete and continuous part of the spectrum are explicitly calculated in each case. First the results are compared for the limit B → 0 with previous calculations and second with the path integration on the Poincaré upper half-plane U. This work is a continuation of the path integral calculations for the free motion on the various formulations on the hyperbolic plane and for the case of constant magnetic field on the Poincaré upper half-plane U.

Hyperbolic metamaterial lens with hydrodynamic nonlocal response.

PubMed

Yan, Wei; Mortensen, N Asger; Wubs, Martijn

2013-06-17

We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves of the free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective material parameters analytically, and illustrate the noticeable nonlocal effects on the dispersion curves numerically. As an application, we find that the focusing characteristics of a HMM lens in the local-response approximation and in the hydrodynamic Drude model can differ considerably. In particular, the optimal frequency for imaging in the nonlocal theory is blueshifted with respect to that in the local theory. Thus, to detect whether nonlocal response is at work in a hyperbolic metamaterial, we propose to measure the near-field distribution of a hyperbolic metamaterial lens.

Cosmology in the laboratory: An analogy between hyperbolic metamaterials and the Milne universe

NASA Astrophysics Data System (ADS)

Figueiredo, David; Moraes, Fernando; Fumeron, Sébastien; Berche, Bertrand

2017-11-01

This article shows that the compactified Milne universe geometry, a toy model for the big crunch/big bang transition, can be realized in hyperbolic metamaterials, a new class of nanoengineered systems which have recently found its way as an experimental playground for cosmological ideas. On one side, Klein-Gordon particles, as well as tachyons, are used as probes of the Milne geometry. On the other side, the propagation of light in two versions of a liquid crystal-based metamaterial provides the analogy. It is shown that ray and wave optics in the metamaterial mimic, respectively, the classical trajectories and wave function propagation, of the Milne probes, leading to the exciting perspective of realizing experimental tests of particle tunneling through the cosmic singularity, for instance.

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. I - Nonstiff strongly dynamic problems

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

An implicit finite difference method of fourth order accuracy in space and time is introduced for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The basic form of the method is a two-level scheme which is unconditionally stable and nondissipative. The scheme uses only three mesh points at level t and three mesh points at level t + delta t. The dissipative version of the basic method given is conditionally stable under the CFL (Courant-Friedrichs-Lewy) condition. This version is particularly useful for the numerical solution of problems with strong but nonstiff dynamic features, where the CFL restriction is reasonable on accuracy grounds. Numerical results are provided to illustrate properties of the proposed method.

CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. II. GRAY RADIATION HYDRODYNAMICS

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

Zhang, W.; Almgren, A.; Bell, J.

We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem is solved explicitly with a high-order Godunovmore » scheme, whereas the parabolic part is solved implicitly with a first-order backward Euler method.« less

Broadband Enhancement of Spontaneous Emission in Two-Dimensional Semiconductors Using Photonic Hypercrystals.

PubMed

Galfsky, Tal; Sun, Zheng; Considine, Christopher R; Chou, Cheng-Tse; Ko, Wei-Chun; Lee, Yi-Hsien; Narimanov, Evgenii E; Menon, Vinod M

2016-08-10

The low quantum yield observed in two-dimensional semiconductors of transition metal dichalcogenides (TMDs) has motivated the quest for approaches that can enhance the light emission from these systems. Here, we demonstrate broadband enhancement of spontaneous emission and increase in Raman signature from archetype two-dimensional semiconductors: molybdenum disulfide (MoS2) and tungsten disulfide (WS2) by placing the monolayers in the near field of a photonic hypercrystal having hyperbolic dispersion. Hypercrystals are characterized by a large broadband photonic density of states due to hyperbolic dispersion while having enhanced light in/out coupling by a subwavelength photonic crystal lattice. This dual advantage is exploited here to enhance the light emission from the 2D TMDs and can be utilized for developing light emitters and solar cells using two-dimensional semiconductors.

Studying ventricular abnormalities in mild cognitive impairment with hyperbolic Ricci flow and tensor-based morphometry.

PubMed

Shi, Jie; Stonnington, Cynthia M; Thompson, Paul M; Chen, Kewei; Gutman, Boris; Reschke, Cole; Baxter, Leslie C; Reiman, Eric M; Caselli, Richard J; Wang, Yalin

2015-01-01

Mild Cognitive Impairment (MCI) is a transitional stage between normal aging and dementia and people with MCI are at high risk of progression to dementia. MCI is attracting increasing attention, as it offers an opportunity to target the disease process during an early symptomatic stage. Structural magnetic resonance imaging (MRI) measures have been the mainstay of Alzheimer's disease (AD) imaging research, however, ventricular morphometry analysis remains challenging because of its complicated topological structure. Here we describe a novel ventricular morphometry system based on the hyperbolic Ricci flow method and tensor-based morphometry (TBM) statistics. Unlike prior ventricular surface parameterization methods, hyperbolic conformal parameterization is angle-preserving and does not have any singularities. Our system generates a one-to-one diffeomorphic mapping between ventricular surfaces with consistent boundary matching conditions. The TBM statistics encode a great deal of surface deformation information that could be inaccessible or overlooked by other methods. We applied our system to the baseline MRI scans of a set of MCI subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI: 71 MCI converters vs. 62 MCI stable). Although the combined ventricular area and volume features did not differ between the two groups, our fine-grained surface analysis revealed significant differences in the ventricular regions close to the temporal lobe and posterior cingulate, structures that are affected early in AD. Significant correlations were also detected between ventricular morphometry, neuropsychological measures, and a previously described imaging index based on fluorodeoxyglucose positron emission tomography (FDG-PET) scans. This novel ventricular morphometry method may offer a new and more sensitive approach to study preclinical and early symptomatic stage AD. Copyright © 2014 Elsevier Inc. All rights reserved.

STUDYING VENTRICULAR ABNORMALITIES IN MILD COGNITIVE IMPAIRMENT WITH HYPERBOLIC RICCI FLOW AND TENSOR-BASED MORPHOMETRY

PubMed Central

Shi, Jie; Stonnington, Cynthia M.; Thompson, Paul M.; Chen, Kewei; Gutman, Boris; Reschke, Cole; Baxter, Leslie C.; Reiman, Eric M.; Caselli, Richard J.; Wang, Yalin

2014-01-01

Mild Cognitive Impairment (MCI) is a transitional stage between normal aging and dementia and people with MCI are at high risk of progression to dementia. MCI is attracting increasing attention, as it offers an opportunity to target the disease process during an early symptomatic stage. Structural magnetic resonance imaging (MRI) measures have been the mainstay of Alzheimer’s disease (AD) imaging research, however, ventricular morphometry analysis remains challenging because of its complicated topological structure. Here we describe a novel ventricular morphometry system based on the hyperbolic Ricci flow method and tensor-based morphometry (TBM) statistics. Unlike prior ventricular surface parameterization methods, hyperbolic conformal parameterization is angle-preserving and does not have any singularities. Our system generates a one-to-one diffeomorphic mapping between ventricular surfaces with consistent boundary matching conditions. The TBM statistics encode a great deal of surface deformation information that could be inaccessible or overlooked by other methods. We applied our system to the baseline MRI scans of a set of MCI subjects from the Alzheimer’s Disease Neuroimaging Initiative (ADNI: 71 MCI converters vs. 62 MCI stable). Although the combined ventricular area and volume features did not differ between the two groups, our fine-grained surface analysis revealed significant differences in the ventricular regions close to the temporal lobe and posterior cingulate, structures that are affected early in AD. Significant correlations were also detected between ventricular morphometry, neuropsychological measures, and a previously described imaging index based on fluorodeoxyglucose positron emission tomography (FDG-PET) scans. This novel ventricular morphometry method may offer a new and more sensitive approach to study preclinical and early symptomatic stage AD. PMID:25285374

The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul; Don, Wai-Sun

1993-01-01

The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: (1) impose the exact boundary condition only at the end of the complete RK cycle, (2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases, results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.

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

Chacon, Luis; Stanier, Adam John

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm ismore » shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.« less

Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two Dimensional Scalar Equation

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2002-01-01

The framework for constructing a high-order, conservative Spectral (Finite) Volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids. Each triangular grid cell forms a spectral volume (SV), and the SV is further subdivided into polygonal control volumes (CVs) to supported high-order data reconstructions. Cell-averaged solutions from these CVs are used to reconstruct a high order polynomial approximation in the SV. Each CV is then updated independently with a Godunov-type finite volume method and a high-order Runge-Kutta time integration scheme. A universal reconstruction is obtained by partitioning all SVs in a geometrically similar manner. The convergence of the SV method is shown to depend on how a SV is partitioned. A criterion based on the Lebesgue constant has been developed and used successfully to determine the quality of various partitions. Symmetric, stable, and convergent linear, quadratic, and cubic SVs have been obtained, and many different types of partitions have been evaluated. The SV method is tested for both linear and non-linear model problems with and without discontinuities.

Near-field heat transfer between graphene/hBN multilayers

NASA Astrophysics Data System (ADS)

Zhao, Bo; Guizal, Brahim; Zhang, Zhuomin M.; Fan, Shanhui; Antezza, Mauro

2017-06-01

We study the radiative heat transfer between multilayer structures made by a periodic repetition of a graphene sheet and a hexagonal boron nitride (hBN) slab. Surface plasmons in a monolayer graphene can couple with hyperbolic phonon polaritons in a single hBN film to form hybrid polaritons that can assist photon tunneling. For periodic multilayer graphene/hBN structures, the stacked metallic/dielectric array can give rise to a further effective hyperbolic behavior, in addition to the intrinsic natural hyperbolic behavior of hBN. The effective hyperbolicity can enable more hyperbolic polaritons that enhance the photon tunneling and hence the near-field heat transfer. However, the hybrid polaritons on the surface, i.e., surface plasmon-phonon polaritons, dominate the near-field heat transfer between multilayer structures when the topmost layer is graphene. The effective hyperbolic regions can be well predicted by the effective medium theory (EMT), thought EMT fails to capture the hybrid surface polaritons and results in a heat transfer rate much lower compared to the exact calculation. The chemical potential of the graphene sheets can be tuned through electrical gating and results in an additional modulation of the heat transfer. We found that the near-field heat transfer between multilayer structures does not increase monotonously with the number of layers in the stack, which provides a way to control the heat transfer rate by the number of graphene layers in the multilayer structure. The results may benefit the applications of near-field energy harvesting and radiative cooling based on hybrid polaritons in two-dimensional materials.

Plasmonic Lithography Utilizing Epsilon Near Zero Hyperbolic Metamaterial.

PubMed

Chen, Xi; Zhang, Cheng; Yang, Fan; Liang, Gaofeng; Li, Qiaochu; Guo, L Jay

2017-10-24

In this work, a special hyperbolic metamaterial (HMM) metamaterial is investigated for plasmonic lithography of period reduction patterns. It is a type II HMM (ϵ ∥ < 0 and ϵ ⊥ > 0) whose tangential component of the permittivity ϵ ∥ is close to zero. Due to the high anisotropy of the type II epsilon-near-zero (ENZ) HMM, only one plasmonic mode can propagate horizontally with low loss in a waveguide system with ENZ HMM as its core. This work takes the advantage of a type II ENZ HMM composed of aluminum/aluminum oxide films and the associated unusual mode to expose a photoresist layer in a specially designed lithography system. Periodic patterns with a half pitch of 58.3 nm were achieved due to the interference of third-order diffracted light of the grating. The lines were 1/6 of the mask with a period of 700 nm and ∼1/7 of the wavelength of the incident light. Moreover, the theoretical analyses performed are widely applicable to structures made of different materials such as silver as well as systems working at deep ultraviolet wavelengths including 193, 248, and 365 nm.

Adaptive iterative learning control of a class of nonlinear time-delay systems with unknown backlash-like hysteresis input and control direction.

PubMed

Wei, Jianming; Zhang, Youan; Sun, Meimei; Geng, Baoliang

2017-09-01

This paper presents an adaptive iterative learning control scheme for a class of nonlinear systems with unknown time-varying delays and control direction preceded by unknown nonlinear backlash-like hysteresis. Boundary layer function is introduced to construct an auxiliary error variable, which relaxes the identical initial condition assumption of iterative learning control. For the controller design, integral Lyapunov function candidate is used, which avoids the possible singularity problem by introducing hyperbolic tangent funciton. After compensating for uncertainties with time-varying delays by combining appropriate Lyapunov-Krasovskii function with Young's inequality, an adaptive iterative learning control scheme is designed through neural approximation technique and Nussbaum function method. On the basis of the hyperbolic tangent function's characteristics, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Inverse-Square Orbits: A Geometric Approach.

ERIC Educational Resources Information Center

Rainwater, James C.; Weinstock, Robert

1979-01-01

Presents a derivation of Kepler's first law of planetary motion from Newtonian principles. Analogus derivations of the hyperbolic and parabolic orbits of nonreturning comets and the hyperbolic orbit for a particle in a repulsive inverse-square field are also presented. (HM)

Use of hyperbolic partial differential equations to generate body fitted coordinates

NASA Technical Reports Server (NTRS)

Steger, J. L.; Sorenson, R. L.

1980-01-01

The hyperbolic scheme is used to efficiently generate smoothly varying grids with good step size control near the body. Although only two dimensional applications are presented, the basic concepts are shown to extend to three dimensions.

Modeling Global Spatial-Temporal Evolution of Society: Hyperbolic Growth and Historical Cycles

NASA Astrophysics Data System (ADS)

Kurkina, E. S.

2011-09-01

The global historical processes are under consideration; and laws of global evolution of the world community are studied. The world community is considered as a united complex self-developing and self-organizing system. It supposed that the main driving force of social-economical evolution was the positive feedback between the population size and the level of technological development, which was a cause of growth in blow-up regime both of population and of global economic indexes. The study is supported by the results of mathematical modeling founded on a nonlinear heat equation with a source. Every social-economical epoch characterizes by own specific spatial distributed structures. So the global dynamics of world community during the whole history is investigated throughout the prism of the developing of spatial-temporal structures. The model parameters have been chosen so that 1) total population follows stable hyperbolic growth, consistently with the demographic data; 2) the evolution of the World-System goes through 11 stages corresponding to the main historical epochs.

A class of high resolution explicit and implicit shock-capturing methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1989-01-01

An attempt is made to give a unified and generalized formulation of a class of high resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock wave computations. Included is a systematic review of the basic design principle of the various related numerical methods. Special emphasis is on the construction of the basis nonlinear, spatially second and third order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and the flux vector splitting approaches. Generalization of these methods to efficiently include equilibrium real gases and large systems of nonequilibrium flows are discussed. Some issues concerning the applicability of these methods that were designed for homogeneous hyperbolic conservation laws to problems containing stiff source terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for 1-, 2- and 3-dimensional gas dynamics problems.

Outer boundary as arrested history in general relativity

NASA Astrophysics Data System (ADS)

Lau, Stephen R.

2002-06-01

We present explicit outer boundary conditions for the canonical variables of general relativity. The conditions are associated with the causal evolution of a finite Cauchy domain, a so-called quasilocal boost, and they suggest a consistent scheme for modelling such an evolution numerically. The scheme involves a continuous boost in the spacetime orthogonal complement ⊥Tp(B) of the tangent space Tp(B) belonging to each point p on the system boundary B. We show how the boost rate may be computed numerically via equations similar to those appearing in canonical investigations of black-hole thermodynamics (although here holding at an outer two-surface rather than the bifurcate two-surface of a Killing horizon). We demonstrate the numerical scheme on a model example, the quasilocal boost of a spherical three-ball in Minkowski spacetime. Developing our general formalism with recent hyperbolic formulations of the Einstein equations in mind, we use Anderson and York's 'Einstein-Christoffel' hyperbolic system as the evolution equations for our numerical simulation of the model.

Optimal control of suspended sediment distribution model of Talaga lake

NASA Astrophysics Data System (ADS)

Ratianingsih, R.; Resnawati, Azim, Mardlijah, Widodo, B.

2017-08-01

Talaga Lake is one of several lakes in Central Sulawesi that potentially to be managed in multi purposes scheme because of its characteristic. The scheme is addressed not only due to the lake maintenance because of its sediment but also due to the Algae farming for its biodiesel fuel. This paper governs a suspended sediment distribution model of Talaga lake. The model is derived from the two dimensional hydrodynamic shallow water equations of the mass and momentum conservation law of sediment transport. An order reduction of the model gives six equations of hyperbolic systems of the depth, two dimension directional velocities and sediment concentration while the bed elevation as the second order of turbulent diffusion and dispersion are neglected. The system is discreted and linearized such that could be solved numerically by box-Keller method for some initial and boundary condition. The solutions shows that the downstream velocity is play a role in transversal direction of stream function flow. The downstream accumulated sediment indicate that the suspended sediment and its changing should be controlled by optimizing the downstream velocity and transversal suspended sediment changing due to the ideal algae growth need.

Probing low-energy hyperbolic polaritons in van der Waals crystals with an electron microscope.

PubMed

Govyadinov, Alexander A; Konečná, Andrea; Chuvilin, Andrey; Vélez, Saül; Dolado, Irene; Nikitin, Alexey Y; Lopatin, Sergei; Casanova, Fèlix; Hueso, Luis E; Aizpurua, Javier; Hillenbrand, Rainer

2017-07-21

Van der Waals materials exhibit intriguing structural, electronic, and photonic properties. Electron energy loss spectroscopy within scanning transmission electron microscopy allows for nanoscale mapping of such properties. However, its detection is typically limited to energy losses in the eV range-too large for probing low-energy excitations such as phonons or mid-infrared plasmons. Here, we adapt a conventional instrument to probe energy loss down to 100 meV, and map phononic states in hexagonal boron nitride, a representative van der Waals material. The boron nitride spectra depend on the flake thickness and on the distance of the electron beam to the flake edges. To explain these observations, we developed a classical response theory that describes the interaction of fast electrons with (anisotropic) van der Waals slabs, revealing that the electron energy loss is dominated by excitation of hyperbolic phonon polaritons, and not of bulk phonons as often reported. Thus, our work is of fundamental importance for interpreting future low-energy loss spectra of van der Waals materials.Here the authors adapt a STEM-EELS system to probe energy loss down to 100 meV, and apply it to map phononic states in hexagonal boron nitride, revealing that the electron loss is dominated by hyperbolic phonon polaritons.

Development of an anaesthetized-rat model of exercise hyperpnoea: an integrative model of respiratory control using an equilibrium diagram.

PubMed

Miyamoto, Tadayoshi; Manabe, Kou; Ueda, Shinya; Nakahara, Hidehiro

2018-05-01

What is the central question of this study? The lack of useful small-animal models for studying exercise hyperpnoea makes it difficult to investigate the underlying mechanisms of exercise-induced ventilatory abnormalities in various disease states. What is the main finding and its importance? We developed an anaesthetized-rat model for studying exercise hyperpnoea, using a respiratory equilibrium diagram for quantitative characterization of the respiratory chemoreflex feedback system. This experimental model will provide an opportunity to clarify the major determinant mechanisms of exercise hyperpnoea, and will be useful for understanding the mechanisms responsible for abnormal ventilatory responses to exercise in disease models. Exercise-induced ventilatory abnormalities in various disease states seem to arise from pathological changes of respiratory regulation. Although experimental studies in small animals are essential to investigate the pathophysiological basis of various disease models, the lack of an integrated framework for quantitatively characterizing respiratory regulation during exercise prevents us from resolving these problems. The purpose of this study was to develop an anaesthetized-rat model for studying exercise hyperpnoea for quantitative characterization of the respiratory chemoreflex feedback system. In 24 anaesthetized rats, we induced muscle contraction by stimulating bilateral distal sciatic nerves at low and high voltage to mimic exercise. We recorded breath-by-breath respiratory gas analysis data and cardiorespiratory responses while running two protocols to characterize the controller and plant of the respiratory chemoreflex. The controller was characterized by determining the linear relationship between end-tidal CO 2 pressure (P ETC O2) and minute ventilation (V̇E), and the plant by the hyperbolic relationship between V̇E and P ETC O2. During exercise, the controller curve shifted upward without change in controller gain, accompanying increased oxygen uptake. The hyperbolic plant curve shifted rightward and downward depending on exercise intensity as predicted by increased metabolism. Exercise intensity-dependent changes in operating points (V̇E and P ETC O2) were estimated by integrating the controller and plant curves in a respiratory equilibrium diagram. In conclusion, we developed an anaesthetized-rat model for studying exercise hyperpnoea, using systems analysis for quantitative characterization of the respiratory system. This novel experimental model will be useful for understanding the mechanisms responsible for abnormal ventilatory responses to exercise in disease models. © 2018 Morinomiya University of Medical Sciences. Experimental Physiology © 2018 The Physiological Society.

Novel Plasmonic and Hyberbolic Optical Materials for Control of Quantum Nanoemitters

DTIC Science & Technology

2016-12-08

properties, metal ion implantation techniques, and multi- physics modeling to produce hyperbolic quantum nanoemitters. 15. SUBJECT TERMS nanotechnology 16...techniques, and multi- physics modeling to produce hyperbolic quantum nanoemitters. During the course of this project we studied plasmonic

Explicit formulae for Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation C(2n, 3)

NASA Astrophysics Data System (ADS)

Ham, Ji-Young; Lee, Joongul

2017-03-01

We calculate the Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation C(2n, 3) using the Schläfli formula for the generalized Chern-Simons function on the family of C(2n, 3) cone-manifold structures. We present the concrete and explicit formula of them. We apply the general instructions of Hilden, Lozano, and Montesinos-Amilibia and extend the Ham and Lee's methods. As an application, we calculate the Chern-Simons invariants of cyclic coverings of the hyperbolic C(2n, 3) orbifolds.

Origin of hyperbolicity in brain-to-brain coordination networks

NASA Astrophysics Data System (ADS)

Tadić, Bosiljka; Andjelković, Miroslav; Šuvakov, Milovan

2018-02-01

Hyperbolicity or negative curvature of complex networks is the intrinsic geometric proximity of nodes in the graph metric space, which implies an improved network function. Here, we investigate hidden combinatorial geometries in brain-to-brain coordination networks arising through social communications. The networks originate from correlations among EEG signals previously recorded during spoken communications comprising of 14 individuals with 24 speaker-listener pairs. We find that the corresponding networks are delta-hyperbolic with delta_max=1 and the graph diameter D=3 in each brain. While the emergent hyperbolicity in the two-brain networks satisfies delta_max/D/2 < 1 and can be attributed to the topology of the subgraph formed around the cross-brains linking channels. We identify these subgraphs in each studied two-brain network and decompose their structure into simple geometric descriptors (triangles, tetrahedra and cliques of higher orders) that contribute to hyperbolicity. Considering topologies that exceed two separate brain networks as a measure of coordination synergy between the brains, we identify different neuronal correlation patterns ranging from weak coordination to super-brain structure. These topology features are in qualitative agreement with the listener’s self-reported ratings of own experience and quality of the speaker, suggesting that studies of the cross-brain connector networks can reveal new insight into the neural mechanisms underlying human social behavior.

Time discounting and smoking behavior: evidence from a panel survey(*).

PubMed

Kang, Myong-Il; Ikeda, Shinsuke

2014-12-01

By using a panel survey of Japanese adults, we show that smoking behavior is associated with personal time discounting and its biases, such as hyperbolic discounting and the sign effect, in the way that theory predicts: smoking depends positively on the discount rate and the degree of hyperbolic discounting and negatively on the presence of the sign effect. Positive effects of hyperbolic discounting on smoking are salient for naïve people, who are not aware of their self-control problem. By estimating smoking participation and smokers' cigarette consumption in Cragg's two-part model, we find that the two smoking decisions depend on different sets of time-discounting variables. Particularly, smoking participation is affected by being a naïve hyperbolic discounter, whereas the discount rate, the presence of the sign effect, and a hyperbolic discounting proxy constructed from procrastination behavior vis-à-vis doing homework assignments affect both types of decision making. The panel data enable us to analyze the over-time instability of elicited discount rates. The instability is shown to come from measurement errors, rather than preference shocks on time preference. Several evidences indicate that the detected associations between time preferences and smoking behavior are interpersonal one, rather than within-personal one. Copyright © 2013 John Wiley & Sons, Ltd.

Thermal Non-Equilibrium Flows in Three Space Dimensions

NASA Astrophysics Data System (ADS)

Zeng, Yanni

2016-01-01

We study the equations describing the motion of a thermal non-equilibrium gas in three space dimensions. It is a hyperbolic system of six equations with a relaxation term. The dissipation mechanism induced by the relaxation is weak in the sense that the Shizuta-Kawashima criterion is violated. This implies that a perturbation of a constant equilibrium state consists of two parts: one decays in time while the other stays. In fact, the entropy wave grows weakly along the particle path as the process is irreversible. We study thermal properties related to the well-posedness of the nonlinear system. We also obtain a detailed pointwise estimate on the Green's function for the Cauchy problem when the system is linearized around an equilibrium constant state. The Green's function provides a complete picture of the wave pattern, with an exact and explicit leading term. Comparing with existing results for one dimensional flows, our results reveal a new feature of three dimensional flows: not only does the entropy wave not decay, but the velocity also contains a non-decaying part, strongly coupled with its decaying one. The new feature is supported by the second order approximation via the Chapman-Enskog expansions, which are the Navier-Stokes equations with vanished shear viscosity and heat conductivity.

Classification of almost toric singularities of Lagrangian foliations

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

Izosimov, Anton M

2011-07-31

The topological classification is given of almost toric singularities of integrable Hamiltonian systems with a large number of degrees of freedom, that is, of nondegenerate singularities without hyperbolic components. A descriptive geometric model is constructed, which makes it possible to perform effective calculations. Bibliography: 10 titles.

DEVELOPMENT OF LOW-DIFFUSION FLUX-SPLITTING METHODS FOR DENSE GAS-SOLID FLOWS

EPA Science Inventory

The development of a class of low-diffusion upwinding methods for computing dense gas-solid flows is presented in this work. An artificial compressibility/low-Mach preconditioning strategy is developed for a hyperbolic two-phase flow equation system consisting of separate solids ...

Characterizing Surface Transport Barriers in the South China Sea

DTIC Science & Technology

2015-09-30

to a coral reef system flow, rigorously identifying hyperbolic and elliptic flow structures. 2 RESULTS The FTLE approach was found to be...included in real world applications (Allshouse et al. 2015). Figure 3: The impact of windage on a hypothetical tracer release event of Ningaloo Reef

Correlation Functions of σ Fields with Values in a Hyperbolic Space

NASA Astrophysics Data System (ADS)

Haba, Z.

It is shown that the functional integral for a σ field with values in the Poincare upper half-plane (and some other hyperbolic spaces) can be performed explicitly resulting in a conformal invariant noncanonical field theory in two dimensions.

On the Wave Equation with Hyperbolic Dynamical Boundary Conditions, Interior and Boundary Damping and Source

NASA Astrophysics Data System (ADS)

Vitillaro, Enzo

2017-03-01

The aim of this paper is to study the problem u_{tt}-Δ u+P(x,u_t)=f(x,u) quad & in (0,∞)×Ω, u=0 & on (0,∞)× Γ_0, u_{tt}+partial_ν u-Δ_Γ u+Q(x,u_t)=g(x,u)quad & on (0,∞)× Γ_1, u(0,x)=u_0(x),quad u_t(0,x)=u_1(x) & in overline Ω, where {Ω} is a open bounded subset of R^N with C 1 boundary ({N ≥ 2}), {Γ = partialΩ}, {(Γ0,Γ1)} is a measurable partition of {Γ}, {Δ_{Γ}} denotes the Laplace-Beltrami operator on {Γ}, {ν} is the outward normal to {Ω}, and the terms P and Q represent nonlinear damping terms, while f and g are nonlinear subcritical perturbations. In the paper a local Hadamard well-posedness result for initial data in the natural energy space associated to the problem is given. Moreover, when {Ω} is C 2 and {overline{Γ0} \\cap overline{Γ1} = emptyset}, the regularity of solutions is studied. Next a blow-up theorem is given when P and Q are linear and f and g are superlinear sources. Finally a dynamical system is generated when the source parts of f and g are at most linear at infinity, or they are dominated by the damping terms.

Formation mechanism of a basin of attraction for passive dynamic walking induced by intrinsic hyperbolicity

PubMed Central

Aoi, Shinya; Tsuchiya, Kazuo; Kokubu, Hiroshi

2016-01-01

Passive dynamic walking is a useful model for investigating the mechanical functions of the body that produce energy-efficient walking. The basin of attraction is very small and thin, and it has a fractal-like shape; this explains the difficulty in producing stable passive dynamic walking. The underlying mechanism that produces these geometric characteristics was not known. In this paper, we consider this from the viewpoint of dynamical systems theory, and we use the simplest walking model to clarify the mechanism that forms the basin of attraction for passive dynamic walking. We show that the intrinsic saddle-type hyperbolicity of the upright equilibrium point in the governing dynamics plays an important role in the geometrical characteristics of the basin of attraction; this contributes to our understanding of the stability mechanism of bipedal walking. PMID:27436971

Bianchi transformation between the real hyperbolic Monge-Ampère equation and the Born-Infeld equation

NASA Astrophysics Data System (ADS)

Mokhov, O. I.; Nutku, Y.

1994-10-01

By casting the Born-Infeld equation and the real hyperbolic Monge-Ampère equation into the form of equations of hydrodynamic type, we find that there exists an explicit transformation between them. This is Bianchi transformation.

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

Out-of-plane heat transfer in van der Waals stacks through electron-hyperbolic phonon coupling

NASA Astrophysics Data System (ADS)

Tielrooij, Klaas-Jan; Hesp, Niels C. H.; Principi, Alessandro; Lundeberg, Mark B.; Pogna, Eva A. A.; Banszerus, Luca; Mics, Zoltán; Massicotte, Mathieu; Schmidt, Peter; Davydovskaya, Diana; Purdie, David G.; Goykhman, Ilya; Soavi, Giancarlo; Lombardo, Antonio; Watanabe, Kenji; Taniguchi, Takashi; Bonn, Mischa; Turchinovich, Dmitry; Stampfer, Christoph; Ferrari, Andrea C.; Cerullo, Giulio; Polini, Marco; Koppens, Frank H. L.

2018-01-01

Van der Waals heterostructures have emerged as promising building blocks that offer access to new physics, novel device functionalities and superior electrical and optoelectronic properties1-7. Applications such as thermal management, photodetection, light emission, data communication, high-speed electronics and light harvesting8-16 require a thorough understanding of (nanoscale) heat flow. Here, using time-resolved photocurrent measurements, we identify an efficient out-of-plane energy transfer channel, where charge carriers in graphene couple to hyperbolic phonon polaritons17-19 in the encapsulating layered material. This hyperbolic cooling is particularly efficient, giving picosecond cooling times for hexagonal BN, where the high-momentum hyperbolic phonon polaritons enable efficient near-field energy transfer. We study this heat transfer mechanism using distinct control knobs to vary carrier density and lattice temperature, and find excellent agreement with theory without any adjustable parameters. These insights may lead to the ability to control heat flow in van der Waals heterostructures.

Terahertz radiation in graphene hyperbolic medium excited by an electric dipole.

PubMed

Feng, Xiaodong; Gong, Sen; Zhong, Renbin; Zhao, Tao; Hu, Min; Zhang, Chao; Liu, Shenggang

2018-03-01

In this Letter, the enhanced and directional radiation in a wide terahertz (THz) frequency range in a graphene hyperbolic medium excited by an electric dipole is presented. The numerical simulations and theoretical analyses indicate that the enhanced radiation comes from the strong surface plasmon couplings in the graphene hyperbolic medium, consisting of alternative graphene and dielectric substrate layers. The simulation results also show that the peak power flow of the enhanced THz radiation in the graphene hyperbolic medium is dramatically enhanced by more than 1 order of magnitude over that in a general medium within a certain distance from the dipole, and the electromagnetic fields are strongly concentrated in a narrow angle. Also, the radiation fields can be manipulated, and the fields' angular distributions can be tuned by adjusting the dielectric permittivity and thickness of the substrates, and the chemical potential of graphene. Accordingly, it provides a good opportunity for developing miniature, integratable, high-power-density, and tunable radiation sources in the THz band at room temperature.

Can rodents conceive hyperbolic spaces?

PubMed Central

Urdapilleta, Eugenio; Troiani, Francesca; Stella, Federico; Treves, Alessandro

2015-01-01

The grid cells discovered in the rodent medial entorhinal cortex have been proposed to provide a metric for Euclidean space, possibly even hardwired in the embryo. Yet, one class of models describing the formation of grid unit selectivity is entirely based on developmental self-organization, and as such it predicts that the metric it expresses should reflect the environment to which the animal has adapted. We show that, according to self-organizing models, if raised in a non-Euclidean hyperbolic cage rats should be able to form hyperbolic grids. For a given range of grid spacing relative to the radius of negative curvature of the hyperbolic surface, such grids are predicted to appear as multi-peaked firing maps, in which each peak has seven neighbours instead of the Euclidean six, a prediction that can be tested in experiments. We thus demonstrate that a useful universal neuronal metric, in the sense of a multi-scale ruler and compass that remain unaltered when changing environments, can be extended to other than the standard Euclidean plane. PMID:25948611

Uniformly high-order accurate non-oscillatory schemes, 1

NASA Technical Reports Server (NTRS)

Harten, A.; Osher, S.

1985-01-01

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws was begun. These schemes share many desirable properties with total variation diminishing schemes (TVD), but TVD schemes have at most first order accuracy, in the sense of truncation error, at extreme of the solution. A uniformly second order approximation was constucted, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

A refined analysis of composite laminates. [theory of statics and dynamics

NASA Technical Reports Server (NTRS)

Srinivas, S.

1973-01-01

The purpose of this paper is to develop a sufficiently accurate analysis, which is much simpler than exact three-dimensional analysis, for statics and dynamics of composite laminates. The governing differential equations and boundary conditions are derived by following a variational approach. The displacements are assumed piecewise linear across the thickness and the effects of transverse shear deformations and rotary inertia are included. A procedure for obtaining the general solution of the above governing differential equations in the form of hyperbolic-trigonometric series is given. The accuracy of the present theory is assessed by obtaining results for free vibrations and flexure of simply supported rectangular laminates and comparing them with results from exact three-dimensional analysis.

A numerical study of the axisymmetric Couette-Taylor problem using a fast high-resolution second-order central scheme

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

Kupferman, R.

The author presents a numerical study of the axisymmetric Couette-Taylor problem using a finite difference scheme. The scheme is based on a staggered version of a second-order central-differencing method combined with a discrete Hodge projection. The use of central-differencing operators obviates the need to trace the characteristic flow associated with the hyperbolic terms. The result is a simple and efficient scheme which is readily adaptable to other geometries and to more complicated flows. The scheme exhibits competitive performance in terms of accuracy, resolution, and robustness. The numerical results agree accurately with linear stability theory and with previous numerical studies.

Numerical solution of the unsteady Navier-Stokes equation

NASA Technical Reports Server (NTRS)

Osher, Stanley J.; Engquist, Bjoern

1985-01-01

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws are discussed. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first-order accuracy, in the sense of truncation error, at extrema of the solution. In this paper a uniformly second-order approximation is constructed, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Stability Analysis of Finite Difference Approximations to Hyperbolic Systems, and Problems in Applied and Computational Matrix Theory

DTIC Science & Technology

1988-07-08

Marcus and C. Baczynski), Computer Science Press, Rockville, Maryland, 1986. 3. An Introduction to Pascal and Precalculus , Computer Science Press...Science Press, Rockville, Maryland, 1986. 35. An Introduction to Pascal and Precalculus , Computer Science Press, Rockville, Maryland, 1986. 36

A method for the investigation of hyperbolic motions in the gravitational field of a spheroidal planet

NASA Astrophysics Data System (ADS)

Konks, V. Ia.

1981-05-01

Barrar's (1961) method for the analysis of the motion of a satellite of an oblate planet is extended to the case of hyperbolic motion. An analysis is presented of the motion of a material point in the gravitational field of a fixed center, combined with a gravitational dipole located at the point of inertia of a dynamically symmetric planet. Formulas are obtained for the hyperbolic motion of a spacecraft in the gravitational field of a spheroidal planet with an accuracy up to the second zonal harmonic of the expansion of its potential into a Legendre polynomial series in spherical coordinates.

Euclidean, Spherical, and Hyperbolic Shadows

ERIC Educational Resources Information Center

Hoban, Ryan

2013-01-01

Many classical problems in elementary calculus use Euclidean geometry. This article takes such a problem and solves it in hyperbolic and in spherical geometry instead. The solution requires only the ability to compute distances and intersections of points in these geometries. The dramatically different results we obtain illustrate the effect…

A global multiscale mathematical model for the human circulation with emphasis on the venous system.

PubMed

Müller, Lucas O; Toro, Eleuterio F

2014-07-01

We present a global, closed-loop, multiscale mathematical model for the human circulation including the arterial system, the venous system, the heart, the pulmonary circulation and the microcirculation. A distinctive feature of our model is the detailed description of the venous system, particularly for intracranial and extracranial veins. Medium to large vessels are described by one-dimensional hyperbolic systems while the rest of the components are described by zero-dimensional models represented by differential-algebraic equations. Robust, high-order accurate numerical methodology is implemented for solving the hyperbolic equations, which are adopted from a recent reformulation that includes variable material properties. Because of the large intersubject variability of the venous system, we perform a patient-specific characterization of major veins of the head and neck using MRI data. Computational results are carefully validated using published data for the arterial system and most regions of the venous system. For head and neck veins, validation is carried out through a detailed comparison of simulation results against patient-specific phase-contrast MRI flow quantification data. A merit of our model is its global, closed-loop character; the imposition of highly artificial boundary conditions is avoided. Applications in mind include a vast range of medical conditions. Of particular interest is the study of some neurodegenerative diseases, whose venous haemodynamic connection has recently been identified by medical researchers. Copyright © 2014 John Wiley & Sons, Ltd.

An almost symmetric Strang splitting scheme for nonlinear evolution equations.

PubMed

Einkemmer, Lukas; Ostermann, Alexander

2014-07-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.

Ideal flow theory for the double - shearing model as a basis for metal forming design

NASA Astrophysics Data System (ADS)

Alexandrov, S.; Trung, N. T.

2018-02-01

In the case of Tresca’ solids (i.e. solids obeying the Tresca yield criterion and its associated flow rule) ideal flows have been defined elsewhere as solenoidal smooth deformations in which an eigenvector field associated everywhere with the greatest principal stress (and strain rate) is fixed in the material. Under such conditions all material elements undergo paths of minimum plastic work, a condition which is often advantageous for metal forming processes. Therefore, the ideal flow theory is used as the basis of a procedure for the preliminary design of such processes. The present paper extends the theory of stationary planar ideal flow to pressure dependent materials obeying the double shearing model and the double slip and rotation model. It is shown that the original problem of plasticity reduces to a purely geometric problem. The corresponding system of equations is hyperbolic. The characteristic relations are integrated in elementary functions. In regions where one family of characteristics is straight, mapping between the principal lines and Cartesian coordinates is determined by linear ordinary differential equations. An illustrative example is provided.

An almost symmetric Strang splitting scheme for nonlinear evolution equations☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2014-01-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation. PMID:25844017

The effects of atmospheric [CO2] on carbon isotope fractionation and magnesium incorporation into biogenic marine calcite

NASA Technical Reports Server (NTRS)

Vieira, Veronica

1997-01-01

The influences of atmospheric carbon dioxide on the fractionation of carbon isotopes and the magnesium incorporation into biogenic marine calcite were investigated using samples of the calcareous alga Amphiroa and benthic foraminifer Sorites grown in the Biosphere 2 Ocean system under variable atmospheric CO2 concentrations (approximately 500 to 1200 ppm). Carbon isotope fractionation was studied in both the organic matter and the skeletal carbonate. Magnesium analysis was to be performed on the carbonate removed during decalcification. These data have not been collected due to technical problems. Carbon isotope data from Amphiroa yields a linear relation between [CO2] and Delta(sup 13)C(sub Corg)values suggesting that the fractionation of carbon isotopes during photosynthesis is positively correlated with atmospheric [CO2]. [CO2] and Delta(sup 13)C(sub Corg) values for Sorites produce a relation that is best described by a hyperbolic function where Delta(sup 13)C(sub Corg) values increase between 300 and 700 ppm and decrease from 700 to 1200 ppm. Further investigation of this relation and Sorites physiology is needed.

Gapped pulses for frequency-swept MRI

NASA Astrophysics Data System (ADS)

Idiyatullin, Djaudat; Corum, Curt; Moeller, Steen; Garwood, Michael

2008-08-01

A recently introduced method called SWIFT (SWeep Imaging with Fourier Transform) is a fundamentally different approach to MRI which is particularly well suited to imaging objects with extremely fast spin-spin relaxation rates. The method exploits a frequency-swept excitation pulse and virtually simultaneous signal acquisition in a time-shared mode. Correlation of the spin system response with the excitation pulse function is used to extract the signals of interest. With SWIFT, image quality is highly dependent on producing uniform and broadband spin excitation. These requirements are satisfied by using frequency-modulated pulses belonging to the hyperbolic secant family (HS n pulses). This article describes the experimental steps needed to properly implement HS n pulses in SWIFT. In addition, properties of HS n pulses in the rapid passage, linear region are investigated, followed by an analysis of the pulses after inserting the "gaps" needed for time-shared excitation and acquisition. Finally, compact expressions are presented to estimate the amplitude and flip angle of the HS n pulses, as well as the relative energy deposited by the SWIFT sequence.

Survey on the Performance of Source Localization Algorithms.

PubMed

Fresno, José Manuel; Robles, Guillermo; Martínez-Tarifa, Juan Manuel; Stewart, Brian G

2017-11-18

The localization of emitters using an array of sensors or antennas is a prevalent issue approached in several applications. There exist different techniques for source localization, which can be classified into multilateration, received signal strength (RSS) and proximity methods. The performance of multilateration techniques relies on measured time variables: the time of flight (ToF) of the emission from the emitter to the sensor, the time differences of arrival (TDoA) of the emission between sensors and the pseudo-time of flight (pToF) of the emission to the sensors. The multilateration algorithms presented and compared in this paper can be classified as iterative and non-iterative methods. Both standard least squares (SLS) and hyperbolic least squares (HLS) are iterative and based on the Newton-Raphson technique to solve the non-linear equation system. The metaheuristic technique particle swarm optimization (PSO) used for source localisation is also studied. This optimization technique estimates the source position as the optimum of an objective function based on HLS and is also iterative in nature. Three non-iterative algorithms, namely the hyperbolic positioning algorithms (HPA), the maximum likelihood estimator (MLE) and Bancroft algorithm, are also presented. A non-iterative combined algorithm, MLE-HLS, based on MLE and HLS, is further proposed in this paper. The performance of all algorithms is analysed and compared in terms of accuracy in the localization of the position of the emitter and in terms of computational time. The analysis is also undertaken with three different sensor layouts since the positions of the sensors affect the localization; several source positions are also evaluated to make the comparison more robust. The analysis is carried out using theoretical time differences, as well as including errors due to the effect of digital sampling of the time variables. It is shown that the most balanced algorithm, yielding better results than the other algorithms in terms of accuracy and short computational time, is the combined MLE-HLS algorithm.

Survey on the Performance of Source Localization Algorithms

PubMed Central

2017-01-01

The localization of emitters using an array of sensors or antennas is a prevalent issue approached in several applications. There exist different techniques for source localization, which can be classified into multilateration, received signal strength (RSS) and proximity methods. The performance of multilateration techniques relies on measured time variables: the time of flight (ToF) of the emission from the emitter to the sensor, the time differences of arrival (TDoA) of the emission between sensors and the pseudo-time of flight (pToF) of the emission to the sensors. The multilateration algorithms presented and compared in this paper can be classified as iterative and non-iterative methods. Both standard least squares (SLS) and hyperbolic least squares (HLS) are iterative and based on the Newton–Raphson technique to solve the non-linear equation system. The metaheuristic technique particle swarm optimization (PSO) used for source localisation is also studied. This optimization technique estimates the source position as the optimum of an objective function based on HLS and is also iterative in nature. Three non-iterative algorithms, namely the hyperbolic positioning algorithms (HPA), the maximum likelihood estimator (MLE) and Bancroft algorithm, are also presented. A non-iterative combined algorithm, MLE-HLS, based on MLE and HLS, is further proposed in this paper. The performance of all algorithms is analysed and compared in terms of accuracy in the localization of the position of the emitter and in terms of computational time. The analysis is also undertaken with three different sensor layouts since the positions of the sensors affect the localization; several source positions are also evaluated to make the comparison more robust. The analysis is carried out using theoretical time differences, as well as including errors due to the effect of digital sampling of the time variables. It is shown that the most balanced algorithm, yielding better results than the other algorithms in terms of accuracy and short computational time, is the combined MLE-HLS algorithm. PMID:29156565

Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity.

PubMed

Font, José A

2008-01-01

This article presents a comprehensive overview of numerical hydrodynamics and magneto-hydrodynamics (MHD) in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003), most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do) overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable, an effort has been made to focus on multidimensional studies, directing the interested reader to earlier versions of the review for discussions on one-dimensional works. Supplementary material is available for this article at 10.12942/lrr-2008-7.

On the global "two-sided" characteristic Cauchy problem for linear wave equations on manifolds

NASA Astrophysics Data System (ADS)

Lupo, Umberto

2018-04-01

The global characteristic Cauchy problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown that, if geometrically well-motivated restrictions are placed on the supports of the (smooth) initial datum and of the (smooth) inhomogeneous term, then there exists a continuous global solution which is smooth "on each side" of the initial value hypersurface. A uniqueness result in Sobolev regularity H^{1/2+ɛ }_{loc} is proved among solutions supported in the union of the causal past and future of the initial value hypersurface, and whose product with the indicator function of the causal future (resp. past) of the hypersurface is past compact (resp. future compact). An explicit representation formula for solutions is obtained, which prominently features an invariantly defined, densitised version of the null expansion of the hypersurface. Finally, applications to quantum field theory on curved spacetimes are briefly discussed.

A high order accurate finite element algorithm for high Reynolds number flow prediction

NASA Technical Reports Server (NTRS)

Baker, A. J.

1978-01-01

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

Mathematical model for determining the effects of intracytoplasmic inclusions on volume and density of microorganisms.

PubMed Central

Mas, J; Pedrós-Alió, C; Guerrero, R

1985-01-01

Procaryotic microorganisms accumulate several polymers in the form of intracellular inclusions as a strategy to increase survival in a changing environment. Such inclusions avoid osmotic pressure increases by tightly packaging certain macromolecules into the inclusion. In the present paper, a model describing changes in volume and density of the microbial cell as a function of the weight of the macromolecule forming the inclusion is derived from simple theoretical principles. The model is then tested by linear regression with experimental data from glycogen accumulation in Escherichia coli, poly-beta-hydroxybutyrate accumulation in Alcaligenes eutrophus, and sulfur accumulation in Chromatium spp. The model predicts a certain degree of hydration of the polymer in the inclusion and explains both the linear relationship between volume of the cell and weight of the polymer and the hyperbolic relationship between density of the cell and weight of the polymer. Other implications of the model are also discussed. PMID:3902798

Linearization of Positional Response Curve of a Fiber-optic Displacement Sensor

NASA Astrophysics Data System (ADS)

Babaev, O. G.; Matyunin, S. A.; Paranin, V. D.

2018-01-01

Currently, the creation of optical measuring instruments and sensors for measuring linear displacement is one of the most relevant problems in the area of instrumentation. Fiber-optic contactless sensors based on the magneto-optical effect are of special interest. They are essentially contactless, non-electrical and have a closed optical channel not subject to contamination. The main problem of this type of sensors is the non-linearity of their positional response curve due to the hyperbolic nature of the magnetic field intensity variation induced by moving the magnetic source mounted on the controlled object relative to the sensing element. This paper discusses an algorithmic method of linearizing the positional response curve of fiber-optic displacement sensors in any selected range of the displacements to be measured. The method is divided into two stages: 1 - definition of the calibration function, 2 - measurement and linearization of the positional response curve (including its temperature stabilization). The algorithm under consideration significantly reduces the number of points of the calibration function, which is essential for the calibration of temperature dependence, due to the use of the points that randomly deviate from the grid points with uniform spacing. Subsequent interpolation of the deviating points and piecewise linear-plane approximation of the calibration function reduces the microcontroller storage capacity for storing the calibration function and the time required to process the measurement results. The paper also presents experimental results of testing real samples of fiber-optic displacement sensors.

Conservative supra-characteristics method for splitting the hyperbolic systems of gasdynamics for real and perfect gases

NASA Technical Reports Server (NTRS)

Lombard, C. K.

1982-01-01

A conservative flux difference splitting is presented for the hyperbolic systems of gasdynamics. The stable robust method is suitable for wide application in a variety of schemes, explicit or implicit, iterative or direct, for marching in either time or space. The splitting is modeled on the local quasi one dimensional characteristics system for multi-dimensional flow similar to Chakravarthy's nonconservative split coefficient matrix method; but, as the result of maintaining global conservation, the method is able to capture sharp shocks correctly. The embedded characteristics formulation is cast in a primitive variable the volumetric internal energy (rather than the pressure) that is effective for treating real as well as perfect gases. Finally the relationship of the splitting to characteristics boundary conditions is discussed and the associated conservative matrix formulation for a computed blown wall boundary condition is developed as an example. The theoretical development employs and extends the notion of Roe of constructing stable upwind difference formulae by sending split simple one sided flux difference pieces to appropriate mesh sites. The developments are also believed to have the potential for aiding in the analysis of both existing and new conservative difference schemes.

Examining Changes in Radioxenon Isotope Activity Ratios during Subsurface Transport

NASA Astrophysics Data System (ADS)

Annewandter, Robert

2014-05-01

The Non-Proliferation Experiment (NPE) has demonstrated and modelled the usefulness of barometric pumping induced gas transport and subsequent soil gas sampling during On-Site inspections. Generally, gas transport has been widely studied with different numerical codes. However, gas transport of radioxenons and radioiodines in the post-detonation regime and their possible fractionation is still neglected in the open peer-reviewed literature. Atmospheric concentrations of the radioxenons Xe-135, Xe-133m, Xe-133 and Xe-131m can be used to discriminate between civilian releases (nuclear power plants or medical isotope facilities), and nuclear explosion sources. It is based on the multiple isotopic activity ratio method. Yet it is not clear whether subsurface migration of the radionuclides, with eventual release into the atmosphere, can affect the activity ratios due to fractionation. Fractionation can be caused by different mass diffusivities due to mass differences between the radionuclides. Cyclical changes in atmospheric pressure can drive subsurface gas transport. This barometric pumping phenomenon causes an oscillatoric flow in upward trending fractures or highly conductive faults which, combined with diffusion into the porous matrix, leads to a net transport of gaseous components - a so-called ratcheting effect. We use a general purpose reservoir simulator (Complex System Modelling Platform, CSMP++) which is recognized by the oil industry as leading in Discrete Fracture-Matrix (DFM) simulations. It has been applied in a range of fields such as deep geothermal systems, three-phase black oil simulations, fracture propagation in fractured, porous media, and Navier-Stokes pore-scale modelling among others. It is specifically designed to account for structurally complex geologic situation of fractured, porous media. Parabolic differential equations are solved by a continuous Galerkin finite-element method, hyperbolic differential equations by a complementary finite volume method. The parabolic and hyperbolic problem can be solved separately by operator-splitting. The resulting system of linear equations is solved by the algebraic multigrid library SAMG, developed at the Fraunhofer Institute for Algorithms and Scientific Computing, Germany. CSMP++ is developed at Montan University of Leoben, ETH Zuerich, Imperial College London and Heriot-Watt University in Edinburgh. This study examines barometric pumping-driven subsurface transport of Xe-135, Xe-133m, Xe-133, Xe-131m including I-131, I-133 and I-135 on arrival times and isotopic activity ratios. This work was funded by the CTBTO Research Award for Young Scientist and Engineers (2013).

Directional and monochromatic thermal emitter from epsilon-near-zero conditions in semiconductor hyperbolic metamaterials

DOE PAGES

Campione, Salvatore; Marquier, Francois; Hugonin, Jean -Paul; ...

2016-10-05

The development of novel thermal sources that control the emission spectrum and the angular emission pattern is of fundamental importance. In this paper, we investigate the thermal emission properties of semiconductor hyperbolic metamaterials (SHMs). Our structure does not require the use of any periodic corrugation to provide monochromatic and directional emission properties. We show that these properties arise because of epsilon-near-zero conditions in SHMs. The thermal emission is dominated by the epsilon-near-zero effect in the doped quantum wells composing the SHM. In conclusion, different properties are observed for s and p polarizations, following the characteristics of the strong anisotropy ofmore » hyperbolic metamaterials.« less

Directional and monochromatic thermal emitter from epsilon-near-zero conditions in semiconductor hyperbolic metamaterials

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

Campione, Salvatore; Marquier, Francois; Hugonin, Jean -Paul

The development of novel thermal sources that control the emission spectrum and the angular emission pattern is of fundamental importance. In this paper, we investigate the thermal emission properties of semiconductor hyperbolic metamaterials (SHMs). Our structure does not require the use of any periodic corrugation to provide monochromatic and directional emission properties. We show that these properties arise because of epsilon-near-zero conditions in SHMs. The thermal emission is dominated by the epsilon-near-zero effect in the doped quantum wells composing the SHM. In conclusion, different properties are observed for s and p polarizations, following the characteristics of the strong anisotropy ofmore » hyperbolic metamaterials.« less

Theoretical stability in coefficient inverse problems for general hyperbolic equations with numerical reconstruction

NASA Astrophysics Data System (ADS)

Yu, Jie; Liu, Yikan; Yamamoto, Masahiro

2018-04-01

In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic operators and an auxiliary Carleman estimate, we establish local Hölder stability with either partial boundary or interior measurements under certain geometrical conditions. For numerical reconstruction, we minimize a Tikhonov functional which penalizes the gradient of the unknown function. Based on the resulting variational equation, we design an iteration method which is updated by solving a Poisson equation at each step. One-dimensional prototype examples illustrate the numerical performance of the proposed iteration.

Near-field radiative heat transfer between graphene-covered hyperbolic metamaterials

NASA Astrophysics Data System (ADS)

Hong, Xiao-Juan; Li, Jian-Wen; Wang, Tong-Biao; Zhang, De-Jian; Liu, Wen-Xing; Liao, Qing-Hua; Yu, Tian-Bao; Liu, Nian-Hua

2018-04-01

We propose the use of graphene-covered silicon carbide (SiC) nanowire arrays (NWAs) for theoretical studies of near-field radiative heat transfer. The SiC NWAs exhibit a hyperbolic characteristic at an appropriately selected filling-volume fraction. The surface plasmon supported by graphene and the hyperbolic modes supported by SiC NWAs significantly affect radiative heat transfer. The heat-transfer coefficient (HTC) between the proposed structures is larger than that between SiC NWAs. We also find that the chemical potential of graphene plays an important role in modulating the HTC. The tunability of chemical potential through gate voltage enables flexible control of heat transfer using the graphene-covered SiC NWAs.

Extreme current fluctuations in lattice gases: Beyond nonequilibrium steady states

NASA Astrophysics Data System (ADS)

Meerson, Baruch; Sasorov, Pavel V.

2014-01-01

We use the macroscopic fluctuation theory (MFT) to study large current fluctuations in nonstationary diffusive lattice gases. We identify two universality classes of these fluctuations, which we call elliptic and hyperbolic. They emerge in the limit when the deterministic mass flux is small compared to the mass flux due to the shot noise. The two classes are determined by the sign of compressibility of effective fluid, obtained by mapping the MFT into an inviscid hydrodynamics. An example of the elliptic class is the symmetric simple exclusion process, where, for some initial conditions, we can solve the effective hydrodynamics exactly. This leads to a super-Gaussian extreme current statistics conjectured by Derrida and Gerschenfeld [J. Stat. Phys. 137, 978 (2009), 10.1007/s10955-009-9830-1] and yields the optimal path of the system. For models of the hyperbolic class, the deterministic mass flux cannot be neglected, leading to a different extreme current statistics.

Numerical simulation of idealized front motion in neutral and stratified atmosphere with a hyperbolic system of equations

NASA Astrophysics Data System (ADS)

Yudin, M. S.

2017-11-01

In the present paper, stratification effects on surface pressure in the propagation of an atmospheric gravity current (cold front) over flat terrain are estimated with a non-hydrostatic finite-difference model of atmospheric dynamics. Artificial compressibility is introduced into the model in order to make its equations hyperbolic. For comparison with available simulation data, the physical processes under study are assumed to be adiabatic. The influence of orography is also eliminated. The front surface is explicitly described by a special equation. A time filter is used to suppress the non-physical oscillations. The results of simulations of surface pressure under neutral and stable stratification are presented. Under stable stratification the front moves faster and shows an abrupt pressure jump at the point of observation. This fact is in accordance with observations and the present-day theory of atmospheric fronts.

No elliptic islands for the universal area-preserving map

NASA Astrophysics Data System (ADS)

Johnson, Tomas

2011-07-01

A renormalization approach has been used in Eckmann et al (1982) and Eckmann et al (1984) to prove the existence of a universal area-preserving map, a map with hyperbolic orbits of all binary periods. The existence of a horseshoe, with positive Hausdorff dimension, in its domain was demonstrated in Gaidashev and Johnson (2009a). In this paper the coexistence problem is studied, and a computer-aided proof is given that no elliptic islands with period less than 18 exist in the domain. It is also shown that less than 1.5% of the measure of the domain consists of elliptic islands. This is proven by showing that the measure of initial conditions that escape to infinity is at least 98.5% of the measure of the domain, and we conjecture that the escaping set has full measure. This is highly unexpected, since generically it is believed that for conservative systems hyperbolicity and ellipticity coexist.

"Coherence-incoherence" transition in ensembles of nonlocally coupled chaotic oscillators with nonhyperbolic and hyperbolic attractors

NASA Astrophysics Data System (ADS)

Semenova, Nadezhda I.; Rybalova, Elena V.; Strelkova, Galina I.; Anishchenko, Vadim S.

2017-03-01

We consider in detail similarities and differences of the "coherence-incoherence" transition in ensembles of nonlocally coupled chaotic discrete-time systems with nonhyperbolic and hyperbolic attractors. As basic models we employ the Hénon map and the Lozi map. We show that phase and amplitude chimera states appear in a ring of coupled Hénon maps, while no chimeras are observed in an ensemble of coupled Lozi maps. In the latter, the transition to spatio-temporal chaos occurs via solitary states. We present numerical results for the coupling function which describes the impact of neighboring oscillators on each partial element of an ensemble with nonlocal coupling. Varying the coupling strength we analyze the evolution of the coupling function and discuss in detail its role in the "coherence-incoherence" transition in the ensembles of Hénon and Lozi maps.

Nonlinear hyperbolic theory of thermal waves in metals

NASA Technical Reports Server (NTRS)

Wilhelm, H. E.; Choi, S. H.

1975-01-01

A closed-form solution for cylindrical thermal waves in metals is given based on the nonlinear hyperbolic system of energy-conservation and heat-flux relaxation equations. It is shown that heat released from a line source propagates radially outward with finite speed in the form of a thermal wave which exhibits a discontinuous wave front. Unique nonlinear thermal-wave solutions exist up to a critical amount of driving energy, i.e., for larger energy releases, the thermal flow becomes multivalued (occurrence of shock waves). By comparison, it is demonstrated that the parabolic thermal-wave theory gives, in general, a misleading picture of the profile and propagation of thermal waves and leads to physical (infinite speed of heat propagation) and mathematical (divergent energy integrals) difficulties. Attention is drawn to the importance of temporal heat-flux relaxation for the physical understanding of fast transient processes such as thermal waves and more general explosions and implosions.

Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties

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

Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Cari, C., E-mail: cari@staff.uns.ac.id; Pratiwi, B. N., E-mail: namakubetanurpratiwi@gmail.com

2016-02-08

The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy.more » The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.« less

Symmetry analysis for hyperbolic equilibria using a TB/dengue fever model

NASA Astrophysics Data System (ADS)

Massoukou, R. Y. M.'Pika; Govinder, K. S.

2016-08-01

We investigate the interplay between Lie symmetry analysis and dynamical systems analysis. As an example, we take a toy model describing the spread of TB and dengue fever. We first undertake a comprehensive dynamical systems analysis including a discussion about local stability. For those regions in which such analyzes cannot be translated to global behavior, we undertake a Lie symmetry analysis. It is shown that the Lie analysis can be useful in providing information for systems where the (local) dynamical systems analysis breaks down.

Technology requirements for a generic aerocapture system. [for atmospheric entry

NASA Technical Reports Server (NTRS)

Cruz, M. I.

1980-01-01

The technology requirements for the design of a generic aerocapture vehicle system are summarized. These spacecraft have the capability of completely eliminating fuel-costly retropropulsion for planetary orbit capture through a single aerodynamically controlled atmospheric braking pass from a hyperbolic trajectory into a near circular orbit. This generic system has application at both the inner and outer planets. Spacecraft design integration, navigation, communications, and aerothermal protection system design problems were assessed in the technology requirements study and are discussed in this paper.