results obtained by the application of two different methods for the calculation of optimal coplanar orbital maneuvers with time limit

NASA Astrophysics Data System (ADS)

Rocco, Emr; Prado, Afbap; Souza, Mlos

In this work, the problem of bi-impulsive orbital transfers between coplanar elliptical orbits with minimum fuel consumption but with a time limit for this transfer is studied. As a first method, the equations presented by Lawden (1993) were used. Those equations furnishes the optimal transfer orbit with fixed time for this transfer, between two elliptical coplanar orbits considering fixed terminal points. The method was adapted to cases with free terminal points and those equations was solved to develop a software for orbital maneuvers. As a second method, the equations presented by Eckel and Vinh (1984) were used, those equations provide the transfer orbit between non-coplanar elliptical orbits with minimum fuel and fixed time transfer, or minimum time transfer for a prescribed fuel consumption, considering free terminal points. But in this work only the problem with fixed time transfer was considered, the case of minimum time for a prescribed fuel consumption was already studied in Rocco et al. (2000). Then, the method was modified to consider cases of coplanar orbital transfer, and develop a software for orbital maneuvers. Therefore, two software that solve the same problem using different methods were developed. The first method, presented by Lawden, uses the primer vector theory. The second method, presented by Eckel and Vinh, uses the ordinary theory of maxima and minima. So, to test the methods we choose the same terminal orbits and the same time as input. We could verify that we didn't obtain exactly the same result. In this work, that is an extension of Rocco et al. (2002), these differences in the results are explored with objective of determining the reason of the occurrence of these differences and which modifications should be done to eliminate them.

Renormalization group procedure for potential -g/r2

NASA Astrophysics Data System (ADS)

Dawid, S. M.; Gonsior, R.; Kwapisz, J.; Serafin, K.; Tobolski, M.; Głazek, S. D.

2018-02-01

Schrödinger equation with potential - g /r2 exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at r = 0. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of g.

Existence and uniqueness theorems for impulsive fractional differential equations with the two-point and integral boundary conditions.

PubMed

Mardanov, M J; Mahmudov, N I; Sharifov, Y A

2014-01-01

We study a boundary value problem for the system of nonlinear impulsive fractional differential equations of order α (0 < α ≤ 1) involving the two-point and integral boundary conditions. Some new results on existence and uniqueness of a solution are established by using fixed point theorems. Some illustrative examples are also presented. We extend previous results even in the integer case α = 1.

Mixed quantum/classical theory of rotationally and vibrationally inelastic scattering in space-fixed and body-fixed reference frames

NASA Astrophysics Data System (ADS)

Semenov, Alexander; Babikov, Dmitri

2013-11-01

We formulated the mixed quantum/classical theory for rotationally and vibrationally inelastic scattering process in the diatomic molecule + atom system. Two versions of theory are presented, first in the space-fixed and second in the body-fixed reference frame. First version is easy to derive and the resultant equations of motion are transparent, but the state-to-state transition matrix is complex-valued and dense. Such calculations may be computationally demanding for heavier molecules and/or higher temperatures, when the number of accessible channels becomes large. In contrast, the second version of theory requires some tedious derivations and the final equations of motion are rather complicated (not particularly intuitive). However, the state-to-state transitions are driven by real-valued sparse matrixes of much smaller size. Thus, this formulation is the method of choice from the computational point of view, while the space-fixed formulation can serve as a test of the body-fixed equations of motion, and the code. Rigorous numerical tests were carried out for a model system to ensure that all equations, matrixes, and computer codes in both formulations are correct.

Cyclic public goods games: Compensated coexistence among mutual cheaters stabilized by optimized penalty taxation

NASA Astrophysics Data System (ADS)

Griffin, Christopher; Belmonte, Andrew

2017-05-01

We study the problem of stabilized coexistence in a three-species public goods game in which each species simultaneously contributes to one public good while freeloading off another public good ("cheating"). The proportional population growth is governed by an appropriately modified replicator equation, depending on the returns from the public goods and the cost. We show that the replicator dynamic has at most one interior unstable fixed point and that the population becomes dominated by a single species. We then show that by applying an externally imposed penalty, or "tax" on success can stabilize the interior fixed point, allowing for the symbiotic coexistence of all species. We show that the interior fixed point is the point of globally minimal total population growth in both the taxed and untaxed cases. We then formulate an optimal taxation problem and show that it admits a quasilinearization, resulting in novel necessary conditions for the optimal control. In particular, the optimal control problem governing the tax rate must solve a certain second-order ordinary differential equation.

Cyclic public goods games: Compensated coexistence among mutual cheaters stabilized by optimized penalty taxation.

PubMed

Griffin, Christopher; Belmonte, Andrew

2017-05-01

We study the problem of stabilized coexistence in a three-species public goods game in which each species simultaneously contributes to one public good while freeloading off another public good ("cheating"). The proportional population growth is governed by an appropriately modified replicator equation, depending on the returns from the public goods and the cost. We show that the replicator dynamic has at most one interior unstable fixed point and that the population becomes dominated by a single species. We then show that by applying an externally imposed penalty, or "tax" on success can stabilize the interior fixed point, allowing for the symbiotic coexistence of all species. We show that the interior fixed point is the point of globally minimal total population growth in both the taxed and untaxed cases. We then formulate an optimal taxation problem and show that it admits a quasilinearization, resulting in novel necessary conditions for the optimal control. In particular, the optimal control problem governing the tax rate must solve a certain second-order ordinary differential equation.

Time-dependent spectral renormalization method

NASA Astrophysics Data System (ADS)

Cole, Justin T.; Musslimani, Ziad H.

2017-11-01

The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

SHORT COMMUNICATION: Correlation between the Resistance Ratios of Platinum Resistance Thermometers at the Melting Point of Gallium and the Triple Point of Mercury

NASA Astrophysics Data System (ADS)

Singh, Y. P.; Maas, H.; Edler, F.; Zaidi, Z. H.

1994-01-01

A set of resistance ratios (W) for platinum resistance thermometers was obtained at the triple point of Hg and the melting point of Ga in order to study their relationship. It was found that using measured values for one of the fixed points, a linear equation will predict the value of the other. These measurements also indicate that the fixed points of Hg and of Ga are inconsistent by about 1,5 mK in the sense that either the melting point of Ga or the triple point of Hg was assigned too high a value on the ITS-90.

Interacting charges and the classical electron radius

NASA Astrophysics Data System (ADS)

De Luca, Roberto; Di Mauro, Marco; Faella, Orazio; Naddeo, Adele

2018-03-01

The equation of the motion of a point charge q repelled by a fixed point-like charge Q is derived and studied. In solving this problem useful concepts in classical and relativistic kinematics, in Newtonian mechanics and in non-linear ordinary differential equations are revised. The validity of the approximations is discussed from the physical point of view. In particular the classical electron radius emerges naturally from the requirement that the initial distance is large enough for the non-relativistic approximation to be valid. The relevance of this topic for undergraduate physics teaching is pointed out.

Multiple positive solutions for a class of integral inclusions

NASA Astrophysics Data System (ADS)

Hong, Shihuang

2008-04-01

This paper deals with sufficient conditions for the existence of at least two positive solutions for a class of integral inclusions arising in the traffic theory. To show our main results, we apply a norm-type expansion and compression fixed point theorem for multivalued map due to Agarwal and O'Regan [A note on the existence of multiple fixed points for multivalued maps with applications, J. Differential Equation 160 (2000) 389-403].

Advection of nematic liquid crystals by chaotic flow

NASA Astrophysics Data System (ADS)

O'Náraigh, Lennon

2017-04-01

Consideration is given to the effects of inhomogeneous shear flow (both regular and chaotic) on nematic liquid crystals in a planar geometry. The Landau-de Gennes equation coupled to an externally prescribed flow field is the basis for the study: this is solved numerically in a periodic spatial domain. The focus is on a limiting case where the advection is passive, such that variations in the liquid-crystal properties do not feed back into the equation for the fluid velocity. The main tool for analyzing the results (both with and without flow) is the identification of the fixed points of the dynamical equations without flow, which are relevant (to varying degrees) when flow is introduced. The fixed points are classified as stable/unstable and further as either uniaxial or biaxial. Various models of passive shear flow are investigated. When tumbling is present, the flow is shown to have a strong effect on the liquid-crystal morphology; however, the main focus herein is on the case without tumbling. Accordingly, the main result of the work is that only the biaxial fixed point survives as a solution of the Q-tensor dynamics under the imposition of a general flow field. This is because the Q-tensor experiences not only transport due to advection but also co-rotation relative to the local vorticity field. A second result is that all families of fixed points survive for certain specific velocity fields, which we classify. We single out for close study those velocity fields for which the influence of co-rotation effectively vanishes along the Lagrangian trajectories of the imposed velocity field. In this scenario, the system exhibits coarsening arrest, whereby the liquid-crystal domains are "frozen in" to the flow structures, and the growth in their size is thus limited.

Analogies between the torque-free motion of a rigid body about a fixed point and light propagation in anisotropic media

NASA Astrophysics Data System (ADS)

Bellver-Cebreros, Consuelo; Rodriguez-Danta, Marcelo

2009-03-01

An apparently unnoticed analogy between the torque-free motion of a rotating rigid body about a fixed point and the propagation of light in anisotropic media is stated. First, a new plane construction for visualizing this torque-free motion is proposed. This method uses an intrinsic representation alternative to angular momentum and independent of the modulus of angular velocity ω. The equivalence between this plane construction and the well-known Poinsot's three-dimensional graphical procedure is also shown. From this equivalence, analogies have been found between the general plane wave equation (relation of dispersion) in anisotropic media and basic equations of torque-free motion of a rigid body about a fixed point. These analogies allow reciprocal transfer of results between optics and mechanics and, as an example, reinterpretation of the internal conical refraction phenomenon in biaxial media is carried out. This paper is intended as an interdisciplinary application of analogies for students and teachers in the context of intermediate physics courses at university level.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Boundary-induced pattern formation from uniform temporal oscillation

NASA Astrophysics Data System (ADS)

Kohsokabe, Takahiro; Kaneko, Kunihiko

2018-04-01

Pattern dynamics triggered by fixing a boundary is investigated. By considering a reaction-diffusion equation that has a unique spatially uniform and limit cycle attractor under a periodic or Neumann boundary condition, and then by choosing a fixed boundary condition, we found three novel phases depending on the ratio of diffusion constants of activator to inhibitor: transformation of temporally periodic oscillation into a spatially periodic fixed pattern, travelling wave emitted from the boundary, and aperiodic spatiotemporal dynamics. The transformation into a fixed, periodic pattern is analyzed by crossing of local nullclines at each spatial point, shifted by diffusion terms, as is analyzed by using recursive equations, to obtain the spatial pattern as an attractor. The generality of the boundary-induced pattern formation as well as its relevance to biological morphogenesis is discussed.

Floquet stability analysis of the longitudinal dynamics of two hovering model insects

PubMed Central

Wu, Jiang Hao; Sun, Mao

2012-01-01

Because of the periodically varying aerodynamic and inertial forces of the flapping wings, a hovering or constant-speed flying insect is a cyclically forcing system, and, generally, the flight is not in a fixed-point equilibrium, but in a cyclic-motion equilibrium. Current stability theory of insect flight is based on the averaged model and treats the flight as a fixed-point equilibrium. In the present study, we treated the flight as a cyclic-motion equilibrium and used the Floquet theory to analyse the longitudinal stability of insect flight. Two hovering model insects were considered—a dronefly and a hawkmoth. The former had relatively high wingbeat frequency and small wing-mass to body-mass ratio, and hence very small amplitude of body oscillation; while the latter had relatively low wingbeat frequency and large wing-mass to body-mass ratio, and hence relatively large amplitude of body oscillation. For comparison, analysis using the averaged-model theory (fixed-point stability analysis) was also made. Results of both the cyclic-motion stability analysis and the fixed-point stability analysis were tested by numerical simulation using complete equations of motion coupled with the Navier–Stokes equations. The Floquet theory (cyclic-motion stability analysis) agreed well with the simulation for both the model dronefly and the model hawkmoth; but the averaged-model theory gave good results only for the dronefly. Thus, for an insect with relatively large body oscillation at wingbeat frequency, cyclic-motion stability analysis is required, and for their control analysis, the existing well-developed control theories for systems of fixed-point equilibrium are no longer applicable and new methods that take the cyclic variation of the flight dynamics into account are needed. PMID:22491980

The use of solution adaptive grids in solving partial differential equations

NASA Technical Reports Server (NTRS)

Anderson, D. A.; Rai, M. M.

1982-01-01

The grid point distribution used in solving a partial differential equation using a numerical method has a substantial influence on the quality of the solution. An adaptive grid which adjusts as the solution changes provides the best results when the number of grid points available for use during the calculation is fixed. Basic concepts used in generating and applying adaptive grids are reviewed in this paper, and examples illustrating applications of these concepts are presented.

The stability of quadratic-reciprocal functional equation

NASA Astrophysics Data System (ADS)

Song, Aimin; Song, Minwei

2018-04-01

A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.

Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays

PubMed Central

2012-01-01

A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential equations with two fixed time lags is mainly studied for its dependency on varying connection strength between populations. Equilibria are identified, and using linear stability analysis, all transitions are determined under which both trivial and non-trivial fixed points lose stability. Periodic solutions arising at some of these bifurcations are numerically studied with a two-parameter bifurcation analysis. PMID:22655859

Some estimation formulae for continuous time-invariant linear systems

NASA Technical Reports Server (NTRS)

Bierman, G. J.; Sidhu, G. S.

1975-01-01

In this brief paper we examine a Riccati equation decomposition due to Reid and Lainiotis and apply the result to the continuous time-invariant linear filtering problem. Exploitation of the time-invariant structure leads to integration-free covariance recursions which are of use in covariance analyses and in filter implementations. A super-linearly convergent iterative solution to the algebraic Riccati equation (ARE) is developed. The resulting algorithm, arranged in a square-root form, is thought to be numerically stable and competitive with other ARE solution methods. Certain covariance relations that are relevant to the fixed-point and fixed-lag smoothing problems are also discussed.

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries.

PubMed

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-15

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 - 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

A Newton–Krylov method with an approximate analytical Jacobian for implicit solution of Navier–Stokes equations on staggered overset-curvilinear grids with immersed boundaries

PubMed Central

Asgharzadeh, Hafez; Borazjani, Iman

2016-01-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 – 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80–90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future. PMID:28042172

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries

NASA Astrophysics Data System (ADS)

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for non-linear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form a preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42-74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal and full Jacobian, respectivley, when the stretching factor was increased. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

Fixing the fixed-point system—Applying Dynamic Renormalization Group to systems with long-range interactions

NASA Astrophysics Data System (ADS)

Katzav, Eytan

2013-04-01

In this paper, a mode of using the Dynamic Renormalization Group (DRG) method is suggested in order to cope with inconsistent results obtained when applying it to a continuous family of one-dimensional nonlocal models. The key observation is that the correct fixed-point dynamical system has to be identified during the analysis in order to account for all the relevant terms that are generated under renormalization. This is well established for static problems, however poorly implemented in dynamical ones. An application of this approach to a nonlocal extension of the Kardar-Parisi-Zhang equation resolves certain problems in one-dimension. Namely, obviously problematic predictions are eliminated and the existing exact analytic results are recovered.

The Existence of the Solution to One Kind of Algebraic Riccati Equation

NASA Astrophysics Data System (ADS)

Liu, Jianming

2018-03-01

The matrix equation ATX + XA + XRX + Q = O is called algebraic Riccati equation, which is very important in the fields of automatic control and other engineering applications. Many researchers have studied the solutions to various algebraic Riccati equations and most of them mainly applied the matrix methods, while few used the functional analysis theories. This paper mainly studies the existence of the solution to the following kind of algebraic Riccati equation from the functional view point: ATX + XA + XRX ‑λX + Q = O Here, X, A, R, Q ∈ n×n , Q is a symmetric matrix, and R is a positive or negative semi-definite matrix, λ is arbitrary constants. This paper uses functional approach such as fixed point theorem and contraction mapping thinking so as to provide two sufficient conditions for the solvability about this kind of Riccati equation and to arrive at some relevant conclusions.

Entropic Approach to Brownian Movement.

ERIC Educational Resources Information Center

Neumann, Richard M.

1980-01-01

A diffusional driving force, called the radial force, which is responsible for the increase with time of the scalar separation between a fixed point and a particle undergoing three-dimensional Brownian motion, is derived using Boltzmann's equation. (Author/HM)

Motions about a fixed point by hypergeometric functions: new non-complex analytical solutions and integration of the herpolhode

NASA Astrophysics Data System (ADS)

Mingari Scarpello, Giovanni; Ritelli, Daniele

2018-06-01

The present study highlights the dynamics of a body moving about a fixed point and provides analytical closed form solutions. Firstly, for the symmetrical heavy body, that is the Lagrange-Poisson case, we compute the second (precession, ψ ) and third (spin, φ) Euler angles in explicit and real form by means of multiple hypergeometric (Lauricella) functions. Secondly, releasing the weight assumption but adding the complication of the asymmetry, by means of elliptic integrals of third kind, we provide the precession angle ψ completing the treatment of the Euler-Poinsot case. Thirdly, by integrating the relevant differential equation, we reach the finite polar equation of a special motion trajectory named the herpolhode. Finally, we keep the symmetry of the first problem, but without weight, and take into account a viscous dissipation. The use of motion first integrals—adopted for the first two problems—is no longer practicable in this situation; therefore, the Euler equations, faced directly, are driving to particular occurrences of Bessel functions of order - 1/2.

Dynamical System Analysis of Reynolds Stress Closure Equations

NASA Technical Reports Server (NTRS)

Girimaji, Sharath S.

1997-01-01

In this paper, we establish the causality between the model coefficients in the standard pressure-strain correlation model and the predicted equilibrium states for homogeneous turbulence. We accomplish this by performing a comprehensive fixed point analysis of the modeled Reynolds stress and dissipation rate equations. The results from this analysis will be very useful for developing improved pressure-strain correlation models to yield observed equilibrium behavior.

General purpose nonlinear system solver based on Newton-Krylov method.

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

2013-12-01

KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].

Dynamic renormalization-group analysis of the d+1 dimensional Kuramoto-Sivashinsky equation with both conservative and nonconservative noises

NASA Astrophysics Data System (ADS)

Zhang, L.; Tang, G.; Xun, Z.; Han, K.; Chen, H.; Hu, B.

2008-05-01

The long-wavelength properties of the (d + 1)-dimensional Kuramoto-Sivashinsky (KS) equation with both conservative and nonconservative noises are investigated by use of the dynamic renormalization-group (DRG) theory. The dynamic exponent z and roughness exponent α are calculated for substrate dimensions d = 1 and d = 2, respectively. In the case of d = 1, we arrive at the critical exponents z = 1.5 and α = 0.5 , which are consistent with the results obtained by Ueno et al. in the discussion of the same noisy KS equation in 1+1 dimensions [Phys. Rev. E 71, 046138 (2005)] and are believed to be identical with the dynamic scaling of the Kardar-Parisi-Zhang (KPZ) in 1+1 dimensions. In the case of d = 2, we find a fixed point with the dynamic exponents z = 2.866 and α = -0.866 , which show that, as in the 1 + 1 dimensions situation, the existence of the conservative noise in 2 + 1 or higher dimensional KS equation can also lead to new fixed points with different dynamic scaling exponents. In addition, since a higher order approximation is adopted, our calculations in this paper have improved the results obtained previously by Cuerno and Lauritsen [Phys. Rev. E 52, 4853 (1995)] in the DRG analysis of the noisy KS equation, where the conservative noise is not taken into account.

Fractional populations in sex-linked inheritance

NASA Astrophysics Data System (ADS)

Pyo Lee, Seung; Chung, Myung-Hoon; Koo Kim, Chul; Nahm, Kyun

2001-03-01

We study the fractional populations in chromosome inherited diseases. The governing equations for the fractional populations are found and solved in the presence of mutation and selection. The physical fixed points obtained are used to discuss the cases of color blindness and hemophilia.

Dynamics of f(R) gravity models and asymmetry of time

NASA Astrophysics Data System (ADS)

Verma, Murli Manohar; Yadav, Bal Krishna

We solve the field equations of modified gravity for f(R) model in metric formalism. Further, we obtain the fixed points of the dynamical system in phase-space analysis of f(R) models, both with and without the effects of radiation. The stability of these points is studied against the perturbations in a smooth spatial background by applying the conditions on the eigenvalues of the matrix obtained in the linearized first-order differential equations. Following this, these fixed points are used for analyzing the dynamics of the system during the radiation, matter and acceleration-dominated phases of the universe. Certain linear and quadratic forms of f(R) are determined from the geometrical and physical considerations and the behavior of the scale factor is found for those forms. Further, we also determine the Hubble parameter H(t), the Ricci scalar R and the scale factor a(t) for these cosmic phases. We show the emergence of an asymmetry of time from the dynamics of the scalar field exclusively owing to the f(R) gravity in the Einstein frame that may lead to an arrow of time at a classical level.

On power series representing solutions of the one-dimensional time-independent Schrödinger equation

NASA Astrophysics Data System (ADS)

Trotsenko, N. P.

2017-06-01

For the equation χ″( x) = u( x)χ( x) with infinitely smooth u( x), the general solution χ( x) is found in the form of a power series. The coefficients of the series are expressed via all derivatives u ( m)( y) of the function u( x) at a fixed point y. Examples of solutions for particular functions u( x) are considered.

Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect.

PubMed

Ma, Jinpeng; Sun, Yong; Yuan, Xiaoming; Kurths, Jürgen; Zhan, Meng

2016-01-01

Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.

Functional renormalization group for the U (1 )-T56 tensorial group field theory with closure constraint

NASA Astrophysics Data System (ADS)

Lahoche, Vincent; Ousmane Samary, Dine

2017-02-01

This paper is focused on the functional renormalization group applied to the T56 tensor model on the Abelian group U (1 ) with closure constraint. For the first time, we derive the flow equations for the couplings and mass parameters in a suitable truncation around the marginal interactions with respect to the perturbative power counting. For the second time, we study the behavior around the Gaussian fixed point, and show that the theory is nonasymptotically free. Finally, we discuss the UV completion of the theory. We show the existence of several nontrivial fixed points, study the behavior of the renormalization group flow around them, and point out evidence in favor of an asymptotically safe theory.

Nonalgebraic integrability of one reversible dynamical system of the Cremona type

NASA Astrophysics Data System (ADS)

Rerikh, K. V.

1998-05-01

A reversible dynamical system (RDS) and a system of nonlinear functional equations, defined by a certain rational quadratic Cremona mapping and arising from the static model of the dispersion approach in the theory of strong interactions [the Chew-Low-type equations with crossing-symmetry matrix A(l,1)], are considered. This RDS is split into one- and two-dimensional ones. An explicit Cremona transformation that completely determines the exact solution of the two-dimensional system is found. This solution depends on an odd function satisfying a nonlinear autonomous three-point functional equation. Nonalgebraic integrability of RDS under consideration is proved using the method of Poincaré normal forms and the Siegel theorem on biholomorphic linearization of a mapping at a nonresonant fixed point.

Applications of laser ranging and VLBI observations for selenodetic control

NASA Technical Reports Server (NTRS)

Fajemirokun, F. A.

1971-01-01

The observation equations necessary to utilize lunar laser ranging and very long baseline interferometry measurements were developed for the establishment of a primary control network on the moon. The network consists of coordinates of moon points in the selenodetic Cartesian coordinate system, which is fixed to the lunar body, oriented along the three principal axes of inertia of the moon, and centered at the lunar center of mass. The observation equations derived are based on a general model in which the unknown parameters included: the selenodetic Cartesian coordinates, the geocentric coordinates of earth stations, parameters of the orientation of the selenodetic coordinate system with respect to a fixed celestial system, the parameters of the orientation of the average terrestrial coordinate system with respect to a fixed celestial coordinate system, and the geocentric coordinates of the center of mass of the moon, given by a lunar ephemeris.

A solution to coupled Dyson-Schwinger equations for gluons and ghosts in Landau gauge.

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

von Smekal, L.; Alkofer, R.; Hauck, A.

1998-07-20

A truncation scheme for the Dyson-Schwinger equations of QCD in Landau gauge is presented which implements the Slavnov-Taylor identities for the 3-point vertex functions. Neglecting contributions from 4-point correlations such as the 4-gluon vertex function and irreducible scattering kernels, a closed system of equations for the propagators is obtained. For the pure gauge theory without quarks this system of equations for the propagators of gluons and ghosts is solved in an approximation which allows for an analytic discussion of its solutions in the infrared: The gluon propagator is shown to vanish for small spacelike momenta whereas the ghost propagator ismore » found to be infrared enhanced. The running coupling of the non-perturbative subtraction scheme approaches an infrared stable fixed point at a critical value of the coupling alpha c of approx. 9.5. The gluon propagator is shown to have no Lehmann representation. The results for the propagators obtained here compare favorably with recent lattice calculations.« less

Global Classical Solutions for MHD System

NASA Astrophysics Data System (ADS)

Casella, E.; Secchi, P.; Trebeschi, P.

In this paper we study the equations of magneto-hydrodynamics for a 2D incompressible ideal fluid in the exterior domain and in the half-plane. We prove the existence of a global classical solution in Hölder spaces, by applying Shauder fixed point theorem.

Pilot Comparison of Radiance Temperature Scale Realization Between NIMT and NMIJ

NASA Astrophysics Data System (ADS)

Keawprasert, T.; Yamada, Y.; Ishii, J.

2015-03-01

A pilot comparison of radiance temperature scale realizations between the National Institute of Metrology Thailand (NIMT) and the National Metrology Institute of Japan (NMIJ) was conducted. At the two national metrology institutes (NMIs), a 900 nm radiation thermometer, used as the transfer artifact, was calibrated by a means of a multiple fixed-point method using the fixed-point blackbody of Zn, Al, Ag, and Cu points, and by means of relative spectral responsivity measurements according to the International Temperature Scale of 1990 (ITS-90) definition. The Sakuma-Hattori equation is used for interpolating the radiance temperature scale between the four fixed points and also for extrapolating the ITS-90 temperature scale to 2000 C. This paper compares the calibration results in terms of fixed-point measurements, relative spectral responsivity, and finally the radiance temperature scale. Good agreement for the fixed-point measurements was found in case a correction for the change of the internal temperature of the artifact was applied using the temperature coefficient measured at the NMIJ. For the realized radiance temperature range from 400 C to 1100 C, the resulting scale differences between the two NMIs are well within the combined scale comparison uncertainty of 0.12 C (). The resulting spectral responsivity measured at the NIMT has a comparable curve to that measured at the NMIJ especially in the out-of-band region, yielding a ITS-90 scale difference within 1.0 C from the Cu point to 2000 C, whereas the realization comparison uncertainty of NIMT and NMIJ combined is 1.2 C () at 2000 C.

Multiple positive solutions to a coupled systems of nonlinear fractional differential equations.

PubMed

Shah, Kamal; Khan, Rahmat Ali

2016-01-01

In this article, we study existence, uniqueness and nonexistence of positive solution to a highly nonlinear coupled system of fractional order differential equations. Necessary and sufficient conditions for the existence and uniqueness of positive solution are developed by using Perov's fixed point theorem for the considered problem. Further, we also established sufficient conditions for existence of multiplicity results for positive solutions. Also, we developed some conditions under which the considered coupled system of fractional order differential equations has no positive solution. Appropriate examples are also provided which demonstrate our results.

Existence of a coupled system of fractional differential equations

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

Ibrahim, Rabha W.; Siri, Zailan

2015-10-22

We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator.

On an application of Tikhonov's fixed point theorem to a nonlocal Cahn-Hilliard type system modeling phase separation

NASA Astrophysics Data System (ADS)

Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen

2016-06-01

This paper investigates a nonlocal version of a model for phase separation on an atomic lattice that was introduced by P. Podio-Guidugli (2006) [36]. The model consists of an initial-boundary value problem for a nonlinearly coupled system of two partial differential equations governing the evolution of an order parameter ρ and the chemical potential μ. Singular contributions to the local free energy in the form of logarithmic or double-obstacle potentials are admitted. In contrast to the local model, which was studied by P. Podio-Guidugli and the present authors in a series of recent publications, in the nonlocal case the equation governing the evolution of the order parameter contains in place of the Laplacian a nonlocal expression that originates from nonlocal contributions to the free energy and accounts for possible long-range interactions between the atoms. It is shown that just as in the local case the model equations are well posed, where the technique of proving existence is entirely different: it is based on an application of Tikhonov's fixed point theorem in a rather unusual separable and reflexive Banach space.

A Fixed Point Theorem in Weak Topology for Successively Recurrent System of Set-Valued Mapping Equations and Its Applications

NASA Astrophysics Data System (ADS)

Horiuchi, Kazuo

Let us introduce n (≥ 2) mappings fi(i = 1, …, n ≡ 0) defined on reflexive real Banach spaces Xi-1 and let fi : Xi-1 → Yi be completely continuous on bounded convex closed subsets X_{i-1}^{(0)} \\\\subset X_{i-1}. Moreover, let us introduce n set-valued mappings F_i : X_{i-1} \\\\times Y_i \\\\to {\\\\cal F}_c(X_i) (the family of all non-empty compact subsets of Xi), (i=1, …, n ≡ 0). Here, we have a fixed point theorem in weak topology on the successively recurrent system of set-valued mapping equations: xi ∈ Fi(xi-1, fi(xi-1)), (i=1, …, n ≡ 0). This theorem can be applied immediately to analysis of the availability of system of circular networks of channels undergone by uncertain fluctuations and to evaluation of the tolerability of behaviors of those systems.

Cumulants, free cumulants and half-shuffles

PubMed Central

Ebrahimi-Fard, Kurusch; Patras, Frédéric

2015-01-01

Free cumulants were introduced as the proper analogue of classical cumulants in the theory of free probability. There is a mix of similarities and differences, when one considers the two families of cumulants. Whereas the combinatorics of classical cumulants is well expressed in terms of set partitions, that of free cumulants is described and often introduced in terms of non-crossing set partitions. The formal series approach to classical and free cumulants also largely differs. The purpose of this study is to put forward a different approach to these phenomena. Namely, we show that cumulants, whether classical or free, can be understood in terms of the algebra and combinatorics underlying commutative as well as non-commutative (half-)shuffles and (half-) unshuffles. As a corollary, cumulants and free cumulants can be characterized through linear fixed point equations. We study the exponential solutions of these linear fixed point equations, which display well the commutative, respectively non-commutative, character of classical and free cumulants. PMID:27547078

Applying the Manning equation to determine the critical distance in non-point source pollution using remotely sensed data and cartographic modelling

NASA Astrophysics Data System (ADS)

de Oliveira, Lília M.; Santos, Nádia A. P.; Maillard, Philippe

2013-10-01

Non-point source pollution (NPSP) is perhaps the leading cause of water quality problems and one of the most challenging environmental issues given the difficulty of modeling and controlling it. In this article, we applied the Manning equation, a hydraulic concept, to improve models of non-point source pollution and determine its influence as a function of slope - land cover roughness for runoff to reach the stream. In our study the equation is somewhat taken out of its usual context to be applies to the flow of an entire watershed. Here a digital elevation model (DEM) from the SRTM satellite was used to compute the slope and data from the RapidEye satellite constellation was used to produce a land cover map later transformed into a roughness surface. The methodology is applied to a 1433 km2 watershed in Southeast Brazil mostly covered by forest, pasture, urban and wetlands. The model was used to create slope buffer of varying width in which the proportions of land cover and roughness coefficient were obtained. Next we correlated these data, through regression, with four water quality parameters measured in situ: nitrate, phosphorous, faecal coliform and turbidity. We compare our results with the ones obtained by fixed buffer. It was found that slope buffer outperformed fixed buffer with higher coefficients of determination up to 15%.

Dynamics of Two Point Vortices in an External Compressible Shear Flow

NASA Astrophysics Data System (ADS)

Vetchanin, Evgeny V.; Mamaev, Ivan S.

2017-12-01

This paper is concerned with a system of equations that describes the motion of two point vortices in a flow possessing constant uniform vorticity and perturbed by an acoustic wave. The system is shown to have both regular and chaotic regimes of motion. In addition, simple and chaotic attractors are found in the system. Attention is given to bifurcations of fixed points of a Poincaré map which lead to the appearance of these regimes. It is shown that, in the case where the total vortex strength changes, the "reversible pitch-fork" bifurcation is a typical scenario of emergence of asymptotically stable fixed and periodic points. As a result of this bifurcation, a saddle point, a stable and an unstable point of the same period emerge from an elliptic point of some period. By constructing and analyzing charts of dynamical regimes and bifurcation diagrams we show that a cascade of period-doubling bifurcations is a typical scenario of transition to chaos in the system under consideration.

An Improved Model of Nonuniform Coleochaete Cell Division.

PubMed

Wang, Yuandi; Cong, Jinyu

2016-08-01

Cell division is a key biological process in which cells divide forming new daughter cells. In the present study, we investigate continuously how a Coleochaete cell divides by introducing a modified differential equation model in parametric equation form. We discuss both the influence of "dead" cells and the effects of various end-points on the formation of the new cells' boundaries. We find that the boundary condition on the free end-point is different from that on the fixed end-point; the former has a direction perpendicular to the surface. It is also shown that the outer boundaries of new cells are arc-shaped. The numerical experiments and theoretical analyses for this model to construct the outer boundary are given.

Impact of topology in foliated quantum Einstein gravity.

PubMed

Houthoff, W B; Kurov, A; Saueressig, F

2017-01-01

We use a functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation of gravity to study the scale dependence of Newton's coupling and the cosmological constant on a background spacetime with topology [Formula: see text]. The resulting beta functions possess a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism. The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme. The phase diagrams show that this fixed point is connected to a classical regime through a crossover. In addition the flow may exhibit a regime of "gravitational instability", modifying the theory in the deep infrared. Our work complements earlier studies of the gravitational renormalization group flow on a background topology [Formula: see text] (Biemans et al. Phys Rev D 95:086013, 2017, Biemans et al. arXiv:1702.06539, 2017) and establishes that the flow is essentially independent of the background topology.

Non-minimally coupled quintessence dark energy model with a cubic galileon term: a dynamical system analysis

NASA Astrophysics Data System (ADS)

Bhattacharya, Somnath; Mukherjee, Pradip; Roy, Amit Singha; Saha, Anirban

2018-03-01

We consider a scalar field which is generally non-minimally coupled to gravity and has a characteristic cubic Galilean-like term and a generic self-interaction, as a candidate of a Dark Energy model. The system is dynamically analyzed and novel fixed points with perturbative stability are demonstrated. Evolution of the system is numerically studied near a novel fixed point which owes its existence to the Galileon character of the model. It turns out that demanding the stability of this novel fixed point puts a strong restriction on the allowed non-minimal coupling and the choice of the self-interaction. The evolution of the equation of state parameter is studied, which shows that our model predicts an accelerated universe throughout and the phantom limit is only approached closely but never crossed. Our result thus extends the findings of Coley, Dynamical systems and cosmology. Kluwer Academic Publishers, Boston (2013) for more general NMC than linear and quadratic couplings.

New stability conditions for mixed linear Levin-Nohel integro-differential equations

NASA Astrophysics Data System (ADS)

Dung, Nguyen Tien

2013-08-01

For the mixed Levin-Nohel integro-differential equation, we obtain new necessary and sufficient conditions of asymptotic stability. These results improve those obtained by Becker and Burton ["Stability, fixed points and inverse of delays," Proc. - R. Soc. Edinburgh, Sect. A 136, 245-275 (2006)], 10.1017/S0308210500004546 and Jin and Luo ["Stability of an integro-differential equation," Comput. Math. Appl. 57(7), 1080-1088 (2009)], 10.1016/j.camwa.2009.01.006 when b(t) = 0 and supplement the 3/2-stability theorem when a(t, s) = 0. In addition, the case of the equations with several delays is discussed as well.

On homogeneous second order linear general quantum difference equations.

PubMed

Faried, Nashat; Shehata, Enas M; El Zafarani, Rasha M

2017-01-01

In this paper, we prove the existence and uniqueness of solutions of the β -Cauchy problem of second order β -difference equations [Formula: see text] [Formula: see text], in a neighborhood of the unique fixed point [Formula: see text] of the strictly increasing continuous function β , defined on an interval [Formula: see text]. These equations are based on the general quantum difference operator [Formula: see text], which is defined by [Formula: see text], [Formula: see text]. We also construct a fundamental set of solutions for the second order linear homogeneous β -difference equations when the coefficients are constants and study the different cases of the roots of their characteristic equations. Finally, we drive the Euler-Cauchy β -difference equation.

TOPICAL REVIEW: Nonlinear aspects of the renormalization group flows of Dyson's hierarchical model

NASA Astrophysics Data System (ADS)

Meurice, Y.

2007-06-01

We review recent results concerning the renormalization group (RG) transformation of Dyson's hierarchical model (HM). This model can be seen as an approximation of a scalar field theory on a lattice. We introduce the HM and show that its large group of symmetry simplifies drastically the blockspinning procedure. Several equivalent forms of the recursion formula are presented with unified notations. Rigourous and numerical results concerning the recursion formula are summarized. It is pointed out that the recursion formula of the HM is inequivalent to both Wilson's approximate recursion formula and Polchinski's equation in the local potential approximation (despite the very small difference with the exponents of the latter). We draw a comparison between the RG of the HM and functional RG equations in the local potential approximation. The construction of the linear and nonlinear scaling variables is discussed in an operational way. We describe the calculation of non-universal critical amplitudes in terms of the scaling variables of two fixed points. This question appears as a problem of interpolation between these fixed points. Universal amplitude ratios are calculated. We discuss the large-N limit and the complex singularities of the critical potential calculable in this limit. The interpolation between the HM and more conventional lattice models is presented as a symmetry breaking problem. We briefly introduce models with an approximate supersymmetry. One important goal of this review is to present a configuration space counterpart, suitable for lattice formulations, of functional RG equations formulated in momentum space (often called exact RG equations and abbreviated ERGE).

Constructive methods of invariant manifolds for kinetic problems

NASA Astrophysics Data System (ADS)

Gorban, Alexander N.; Karlin, Iliya V.; Zinovyev, Andrei Yu.

2004-06-01

The concept of the slow invariant manifold is recognized as the central idea underpinning a transition from micro to macro and model reduction in kinetic theories. We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades. The physical problem of reduced description is studied in the most general form as a problem of constructing the slow invariant manifold. The invariance conditions are formulated as the differential equation for a manifold immersed in the phase space ( the invariance equation). The equation of motion for immersed manifolds is obtained ( the film extension of the dynamics). Invariant manifolds are fixed points for this equation, and slow invariant manifolds are Lyapunov stable fixed points, thus slowness is presented as stability. A collection of methods to derive analytically and to compute numerically the slow invariant manifolds is presented. Among them, iteration methods based on incomplete linearization, relaxation method and the method of invariant grids are developed. The systematic use of thermodynamics structures and of the quasi-chemical representation allow to construct approximations which are in concordance with physical restrictions. The following examples of applications are presented: nonperturbative deviation of physically consistent hydrodynamics from the Boltzmann equation and from the reversible dynamics, for Knudsen numbers Kn∼1; construction of the moment equations for nonequilibrium media and their dynamical correction (instead of extension of list of variables) to gain more accuracy in description of highly nonequilibrium flows; determination of molecules dimension (as diameters of equivalent hard spheres) from experimental viscosity data; model reduction in chemical kinetics; derivation and numerical implementation of constitutive equations for polymeric fluids; the limits of macroscopic description for polymer molecules, etc.

Existence and discrete approximation for optimization problems governed by fractional differential equations

NASA Astrophysics Data System (ADS)

Bai, Yunru; Baleanu, Dumitru; Wu, Guo-Cheng

2018-06-01

We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Carathe ´odory solution is proved by using Weierstrass existence theorem, fixed point theorem and Filippov implicit function lemma etc. Then a numerical approximation algorithm is introduced, and a convergence theorem is established. Finally, a nonlinear programming problem constrained by the fractional differential equation is illustrated and the results verify the validity of the algorithm.

Permitted and forbidden sets in symmetric threshold-linear networks.

PubMed

Hahnloser, Richard H R; Seung, H Sebastian; Slotine, Jean-Jacques

2003-03-01

The richness and complexity of recurrent cortical circuits is an inexhaustible source of inspiration for thinking about high-level biological computation. In past theoretical studies, constraints on the synaptic connection patterns of threshold-linear networks were found that guaranteed bounded network dynamics, convergence to attractive fixed points, and multistability, all fundamental aspects of cortical information processing. However, these conditions were only sufficient, and it remained unclear which were the minimal (necessary) conditions for convergence and multistability. We show that symmetric threshold-linear networks converge to a set of attractive fixed points if and only if the network matrix is copositive. Furthermore, the set of attractive fixed points is nonconnected (the network is multiattractive) if and only if the network matrix is not positive semidefinite. There are permitted sets of neurons that can be coactive at a stable steady state and forbidden sets that cannot. Permitted sets are clustered in the sense that subsets of permitted sets are permitted and supersets of forbidden sets are forbidden. By viewing permitted sets as memories stored in the synaptic connections, we provide a formulation of long-term memory that is more general than the traditional perspective of fixed-point attractor networks. There is a close correspondence between threshold-linear networks and networks defined by the generalized Lotka-Volterra equations.

Asymmetric simple exclusion process with position-dependent hopping rates: Phase diagram from boundary-layer analysis.

PubMed

Mukherji, Sutapa

2018-03-01

In this paper, we study a one-dimensional totally asymmetric simple exclusion process with position-dependent hopping rates. Under open boundary conditions, this system exhibits boundary-induced phase transitions in the steady state. Similarly to totally asymmetric simple exclusion processes with uniform hopping, the phase diagram consists of low-density, high-density, and maximal-current phases. In various phases, the shape of the average particle density profile across the lattice including its boundary-layer parts changes significantly. Using the tools of boundary-layer analysis, we obtain explicit solutions for the density profile in different phases. A detailed analysis of these solutions under different boundary conditions helps us obtain the equations for various phase boundaries. Next, we show how the shape of the entire density profile including the location of the boundary layers can be predicted from the fixed points of the differential equation describing the boundary layers. We discuss this in detail through several examples of density profiles in various phases. The maximal-current phase appears to be an especially interesting phase where the boundary layer flows to a bifurcation point on the fixed-point diagram.

Asymmetric simple exclusion process with position-dependent hopping rates: Phase diagram from boundary-layer analysis

NASA Astrophysics Data System (ADS)

Mukherji, Sutapa

2018-03-01

In this paper, we study a one-dimensional totally asymmetric simple exclusion process with position-dependent hopping rates. Under open boundary conditions, this system exhibits boundary-induced phase transitions in the steady state. Similarly to totally asymmetric simple exclusion processes with uniform hopping, the phase diagram consists of low-density, high-density, and maximal-current phases. In various phases, the shape of the average particle density profile across the lattice including its boundary-layer parts changes significantly. Using the tools of boundary-layer analysis, we obtain explicit solutions for the density profile in different phases. A detailed analysis of these solutions under different boundary conditions helps us obtain the equations for various phase boundaries. Next, we show how the shape of the entire density profile including the location of the boundary layers can be predicted from the fixed points of the differential equation describing the boundary layers. We discuss this in detail through several examples of density profiles in various phases. The maximal-current phase appears to be an especially interesting phase where the boundary layer flows to a bifurcation point on the fixed-point diagram.

A solution to coupled Dyson{endash}Schwinger equations for gluons and ghosts in Landau gauge

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

von Smekal, L.; Hauck, A.; Alkofer, R.

1998-07-01

A truncation scheme for the Dyson{endash}Schwinger equations of QCD in Landau gauge is presented which implements the Slavnov{endash}Taylor identities for the 3-point vertex functions. Neglecting contributions from 4-point correlations such as the 4-gluon vertex function and irreducible scattering kernels, a closed system of equations for the propagators is obtained. For the pure gauge theory without quarks this system of equations for the propagators of gluons and ghosts is solved in an approximation which allows for an analytic discussion of its solutions in the infrared: The gluon propagator is shown to vanish for small spacelike momenta whereas the ghost propagator ismore » found to be infrared enhanced. The running coupling of the non-perturbative subtraction scheme approaches an infrared stable fixed point at a critical value of the coupling, {alpha}{sub c}{approx_equal}9.5. The gluon propagator is shown to have no Lehmann representation. The results for the propagators obtained here compare favorably with recent lattice calculations. {copyright} 1998 Academic Press, Inc.« less

A new method for true and spurious eigensolutions of arbitrary cavities using the combined Helmholtz exterior integral equation formulation method.

PubMed

Chen, I L; Chen, J T; Kuo, S R; Liang, M T

2001-03-01

Integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems (radiation and scattering). It was recently found that the real-part boundary element method (BEM) for the interior problem results in spurious eigensolutions if the singular (UT) or the hypersingular (LM) equation is used alone. The real-part BEM results in spurious solutions for interior problems in a similar way that the singular integral equation (UT method) results in fictitious solutions for the exterior problem. To solve this problem, a Combined Helmholtz Exterior integral Equation Formulation method (CHEEF) is proposed. Based on the CHEEF method, the spurious solutions can be filtered out if additional constraints from the exterior points are chosen carefully. Finally, two examples for the eigensolutions of circular and rectangular cavities are considered. The optimum numbers and proper positions for selecting the points in the exterior domain are analytically studied. Also, numerical experiments were designed to verify the analytical results. It is worth pointing out that the nodal line of radiation mode of a circle can be rotated due to symmetry, while the nodal line of the rectangular is on a fixed position.

Time Reparametrization Group and the Long Time Behavior in Quantum Glassy Systems

NASA Astrophysics Data System (ADS)

Kennett, Malcolm P.; Chamon, Claudio

2001-02-01

We study the long time dynamics of a quantum version of the Sherrington-Kirkpatrick model. Time reparametrizations of the dynamical equations have a parallel with renormalization group transformations; in this language the long time behavior of this model is controlled by a reparametrization group ( RpG) fixed point of the classical dynamics. The irrelevance of quantum terms in the dynamical equations in the aging regime explains the classical nature of the out of equilibrium fluctuation-dissipation relation.

Shift-connected SIMD array architectures for digital optical computing systems, with algorithms for numerical transforms and partial differential equations

NASA Astrophysics Data System (ADS)

Drabik, Timothy J.; Lee, Sing H.

1986-11-01

The intrinsic parallelism characteristics of easily realizable optical SIMD arrays prompt their present consideration in the implementation of highly structured algorithms for the numerical solution of multidimensional partial differential equations and the computation of fast numerical transforms. Attention is given to a system, comprising several spatial light modulators (SLMs), an optical read/write memory, and a functional block, which performs simple, space-invariant shifts on images with sufficient flexibility to implement the fastest known methods for partial differential equations as well as a wide variety of numerical transforms in two or more dimensions. Either fixed or floating-point arithmetic may be used. A performance projection of more than 1 billion floating point operations/sec using SLMs with 1000 x 1000-resolution and operating at 1-MHz frame rates is made.

Aerodynamics Via Acoustics: Application of Acoustic Formulas for Aerodynamic Calculations

NASA Technical Reports Server (NTRS)

Farassat, F.; Myers, M. K.

1986-01-01

Prediction of aerodynamic loads on bodies in arbitrary motion is considered from an acoustic point of view, i.e., in a frame of reference fixed in the undisturbed medium. An inhomogeneous wave equation which governs the disturbance pressure is constructed and solved formally using generalized function theory. When the observer is located on the moving body surface there results a singular linear integral equation for surface pressure. Two different methods for obtaining such equations are discussed. Both steady and unsteady aerodynamic calculations are considered. Two examples are presented, the more important being an application to propeller aerodynamics. Of particular interest for numerical applications is the analytical behavior of the kernel functions in the various integral equations.

Non-algebraic integrability of the Chew-Low reversible dynamical system of the Cremona type and the relation with the 7th Hilbert problem (non-resonant case)

NASA Astrophysics Data System (ADS)

Rerikh, K. V.

A smooth reversible dynamical system (SRDS) and a system of nonlinear functional equations, defined by a certain rational quadratic Cremona mapping and arising from the static model of the dispersion approach in the theory of strong interactions (the Chew-Low equations for p- wave πN- scattering) are considered. This SRDS is splitted into 1- and 2-dimensional ones. An explicit Cremona transformation that completely determines the exact solution of the two-dimensional system is found. This solution depends on an odd function satisfying a nonlinear autonomous 3-point functional equation. Non-algebraic integrability of SRDS under consideration is proved using the method of Poincaré normal forms and the Siegel theorem on biholomorphic linearization of a mapping at a non-resonant fixed point. The proof is based on the classical Feldman-Baker theorem on linear forms of logarithms of algebraic numbers, which, in turn, relies upon solving the 7th Hilbert problem by A.I. Gel'fond and T. Schneider and new powerful methods of A. Baker in the theory of transcendental numbers. The general theorem, following from the Feldman-Baker theorem, on applicability of the Siegel theorem to the set of the eigenvalues λ ɛ Cn of a mapping at a non-resonant fixed point which belong to the algebraic number field A is formulated and proved. The main results are presented in Theorems 1-3, 5, 7, 8 and Remarks 3, 7.

Determination of point of incidence for the case of reflection or refraction at spherical surface knowing two points lying on the ray.

PubMed

Mikš, Antonín; Novák, Pavel

2017-09-01

The paper is focused on the problem of determination of the point of incidence of a light ray for the case of reflection or refraction at the spherical optical surface, assuming that two fixed points in space that the sought light ray should go through are given. The requirement is that one of these points lies on the incident ray and the other point on the reflected/refracted ray. Although at first glance it seems to be a simple problem, it will be shown that it has no simple analytical solution. The basic idea of the solution is given, and it is shown that the problem leads to a nonlinear equation in one variable. The roots of the resulting nonlinear equation can be found by numerical methods of mathematical optimization. The proposed methods were implemented in MATLAB, and the proper function of these algorithms was verified on several examples.

Reference-point-independent dynamics of molecular liquids and glasses in the tensorial formalism

NASA Astrophysics Data System (ADS)

Schilling, Rolf

2002-05-01

We apply the tensorial formalism to the dynamics of molecular liquids and glasses. This formalism separates the degrees of freedom into translational and orientational ones. Using the Mori-Zwanzig projection formalism, the equations of motion for the tensorial density correlators Slmn,l'm'n'(q-->,t) are derived. For this we show how to choose the slow variables such that the resulting Mori-Zwanzig equations are covariant under a change of the reference point of the body fixed frame. We also prove that the memory kernels obtained from mode-coupling theory (MCT) including all approximations preserve the covariance. This covariance makes, e.g., the glass transition point, the two universal scaling laws and particularly the corresponding exponents independent on the reference point and on the mass and moments of inertia, i.e., they only depend on the properties of the potential energy landscape. Finally, we show that the corresponding MCT questions for linear molecules can be obtained from those for arbitrary molecules and that they differ from earlier equations that are not covariant.

Inflation with a massive vector field nonminimally coupled to gravity

NASA Astrophysics Data System (ADS)

Páramos, J.

2018-01-01

The possibility that inflation is driven by a massive vector field with SO(3) global symmetry nonminimally coupled to gravity is presented. Through an appropriate Ansatz for the vector field, the behaviour of the equations of motion is studied through the ensuing dynamical system, focusing on the characterisation of the ensuing fixed points.

Wavefronts for a global reaction-diffusion population model with infinite distributed delay

NASA Astrophysics Data System (ADS)

Weng, Peixuan; Xu, Zhiting

2008-09-01

We consider a global reaction-diffusion population model with infinite distributed delay which includes models of Nicholson's blowflies and hematopoiesis derived by Gurney, Mackey and Glass, respectively. The existence of monotone wavefronts is derived by using the abstract settings of functional differential equations and Schauder fixed point theory.

Using an internal coordinate Gaussian basis and a space-fixed Cartesian coordinate kinetic energy operator to compute a vibrational spectrum with rectangular collocation.

PubMed

Manzhos, Sergei; Carrington, Tucker

2016-12-14

We demonstrate that it is possible to use basis functions that depend on curvilinear internal coordinates to compute vibrational energy levels without deriving a kinetic energy operator (KEO) and without numerically computing coefficients of a KEO. This is done by using a space-fixed KEO and computing KEO matrix elements numerically. Whenever one has an excellent basis, more accurate solutions to the Schrödinger equation can be obtained by computing the KEO, potential, and overlap matrix elements numerically. Using a Gaussian basis and bond coordinates, we compute vibrational energy levels of formaldehyde. We show, for the first time, that it is possible with a Gaussian basis to solve a six-dimensional vibrational Schrödinger equation. For the zero-point energy (ZPE) and the lowest 50 vibrational transitions of H 2 CO, we obtain a mean absolute error of less than 1 cm -1 ; with 200 000 collocation points and 40 000 basis functions, most errors are less than 0.4 cm -1 .

Using an internal coordinate Gaussian basis and a space-fixed Cartesian coordinate kinetic energy operator to compute a vibrational spectrum with rectangular collocation

NASA Astrophysics Data System (ADS)

Manzhos, Sergei; Carrington, Tucker

2016-12-01

We demonstrate that it is possible to use basis functions that depend on curvilinear internal coordinates to compute vibrational energy levels without deriving a kinetic energy operator (KEO) and without numerically computing coefficients of a KEO. This is done by using a space-fixed KEO and computing KEO matrix elements numerically. Whenever one has an excellent basis, more accurate solutions to the Schrödinger equation can be obtained by computing the KEO, potential, and overlap matrix elements numerically. Using a Gaussian basis and bond coordinates, we compute vibrational energy levels of formaldehyde. We show, for the first time, that it is possible with a Gaussian basis to solve a six-dimensional vibrational Schrödinger equation. For the zero-point energy (ZPE) and the lowest 50 vibrational transitions of H2CO, we obtain a mean absolute error of less than 1 cm-1; with 200 000 collocation points and 40 000 basis functions, most errors are less than 0.4 cm-1.

Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic Chaos

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1996-01-01

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.

Implicit integration methods for dislocation dynamics

DOE PAGES

Gardner, D. J.; Woodward, C. S.; Reynolds, D. R.; ...

2015-01-20

In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events, and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. Here, this paper investigates the viability of high order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge-Kutta time integrators are explored as a waymore » of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newton's method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newton's method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.« less

An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem

DOE PAGES

Goldberg, Daniel N.; Narayanan, Sri Hari Krishna; Hascoet, Laurent; ...

2016-05-20

We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixed-point iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson (1994) for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enablingmore » larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. Finally, the methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a hybrid shallow ice/shallow shelf approximation to the Stokes equations.« less

Asymptotic analysis of quasilinear parabolic-hyperbolic equations describing the large longitudinal motion of a light viscoelastic bar with a heavy attachment

NASA Astrophysics Data System (ADS)

Yip, Shui Cheung

We study the longitudinal motion of a nonlinearly viscoelastic bar with one end fixed and the other end attached to a heavy tip mass. This problem is a precise continuum mechanical analog of the basic discrete mechanical problem of the motion of a mass point on a (massless) spring. This motion is governed by an initial-boundary-value problem for a class of third-order quasilinear parabolic-hyperbolic partial differential equations subject to a nonstandard boundary condition, which is the equation of motion of the tip mass. The ratio of the mass of the bar to that of the tip mass is taken to be a small parameter varepsilon. We prove that this problem has a unique regular solution that admits a valid asymptotic expansion, including an initial-layer expansion, in powers of varepsilon for varepsilon near 0. The fundamental constitutive hypothesis that the tension be a uniformly monotone function of the strain rate plays a critical role in a delicate proof that each term of the initial layer expansion decays exponentially in time. These results depend on new decay estimates for the solution of quasilinear parabolic equations. The constitutive hypothesis that the viscosity become large where the bar nears total compression leads to important uniform bounds for the strain and the strain rate. Higher-order energy estimates support the proof by the Schauder Fixed-Point Theorem of the existence of solutions having a level of regularity appropriate for the asymptotics.

Stability analysis in tachyonic potential chameleon cosmology

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

Farajollahi, H.; Salehi, A.; Tayebi, F.

2011-05-01

We study general properties of attractors for tachyonic potential chameleon scalar-field model which possess cosmological scaling solutions. An analytic formulation is given to obtain fixed points with a discussion on their stability. The model predicts a dynamical equation of state parameter with phantom crossing behavior for an accelerating universe. We constrain the parameters of the model by best fitting with the recent data-sets from supernovae and simulated data points for redshift drift experiment generated by Monte Carlo simulations.

Multicritical points of the O(N) scalar theory in 2 < d < 4 for large N

NASA Astrophysics Data System (ADS)

Katsis, A.; Tetradis, N.

2018-05-01

We solve analytically the renormalization-group equation for the potential of the O (N)-symmetric scalar theory in the large-N limit and in dimensions 2 < d < 4, in order to look for nonperturbative fixed points that were found numerically in a recent study. We find new real solutions with singularities in the higher derivatives of the potential at its minimum, and complex solutions with branch cuts along the negative real axis.

An overview of longitudinal data analysis methods for neurological research.

PubMed

Locascio, Joseph J; Atri, Alireza

2011-01-01

The purpose of this article is to provide a concise, broad and readily accessible overview of longitudinal data analysis methods, aimed to be a practical guide for clinical investigators in neurology. In general, we advise that older, traditional methods, including (1) simple regression of the dependent variable on a time measure, (2) analyzing a single summary subject level number that indexes changes for each subject and (3) a general linear model approach with a fixed-subject effect, should be reserved for quick, simple or preliminary analyses. We advocate the general use of mixed-random and fixed-effect regression models for analyses of most longitudinal clinical studies. Under restrictive situations or to provide validation, we recommend: (1) repeated-measure analysis of covariance (ANCOVA), (2) ANCOVA for two time points, (3) generalized estimating equations and (4) latent growth curve/structural equation models.

Numerical optimization using flow equations.

PubMed

Punk, Matthias

2014-12-01

We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.

Numerical optimization using flow equations

NASA Astrophysics Data System (ADS)

Punk, Matthias

2014-12-01

We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.

Fingering in a channel and tripolar Loewner evolutions.

PubMed

Durán, Miguel A; Vasconcelos, Giovani L

2011-11-01

A class of Laplacian growth models in the channel geometry is studied using the formalism of tripolar Loewner evolutions, in which three points, namely, the channel corners and the point at infinity, are kept fixed. Initially, the problem of fingered growth, where growth takes place only at the tips of slitlike fingers, is revisited and a class of exact solutions of the corresponding Loewner equation is presented for the case of stationary driving functions. A model for interface growth is then formulated in terms of a generalized tripolar Loewner equation and several examples are presented. It is shown that the growing interface evolves into a steadily moving finger and that tip competition arises for nonsymmetric initial configurations with multiple tips.

Fingering in a channel and tripolar Loewner evolutions

NASA Astrophysics Data System (ADS)

Durán, Miguel A.; Vasconcelos, Giovani L.

2011-11-01

A class of Laplacian growth models in the channel geometry is studied using the formalism of tripolar Loewner evolutions, in which three points, namely, the channel corners and the point at infinity, are kept fixed. Initially, the problem of fingered growth, where growth takes place only at the tips of slitlike fingers, is revisited and a class of exact solutions of the corresponding Loewner equation is presented for the case of stationary driving functions. A model for interface growth is then formulated in terms of a generalized tripolar Loewner equation and several examples are presented. It is shown that the growing interface evolves into a steadily moving finger and that tip competition arises for nonsymmetric initial configurations with multiple tips.

Existence, uniqueness, and stability of stochastic neutral functional differential equations of Sobolev-type

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

Yang, Xuetao; Zhu, Quanxin, E-mail: zqx22@126.com

2015-12-15

In this paper, we are mainly concerned with a class of stochastic neutral functional differential equations of Sobolev-type with Poisson jumps. Under two different sets of conditions, we establish the existence of the mild solution by applying the Leray-Schauder alternative theory and the Sadakovskii’s fixed point theorem, respectively. Furthermore, we use the Bihari’s inequality to prove the Osgood type uniqueness. Also, the mean square exponential stability is investigated by applying the Gronwall inequality. Finally, two examples are given to illustrate the theory results.

Numerical solution of second order ODE directly by two point block backward differentiation formula

NASA Astrophysics Data System (ADS)

Zainuddin, Nooraini; Ibrahim, Zarina Bibi; Othman, Khairil Iskandar; Suleiman, Mohamed; Jamaludin, Noraini

2015-12-01

Direct Two Point Block Backward Differentiation Formula, (BBDF2) for solving second order ordinary differential equations (ODEs) will be presented throughout this paper. The method is derived by differentiating the interpolating polynomial using three back values. In BBDF2, two approximate solutions are produced simultaneously at each step of integration. The method derived is implemented by using fixed step size and the numerical results that follow demonstrate the advantage of the direct method as compared to the reduction method.

Synthesis of a controller for stabilizing the motion of a rigid body about a fixed point

NASA Astrophysics Data System (ADS)

Zabolotnov, Yu. M.; Lobanov, A. A.

2017-05-01

A method for the approximate design of an optimal controller for stabilizing the motion of a rigid body about a fixed point is considered. It is assumed that rigid body motion is nearly the motion in the classical Lagrange case. The method is based on the common use of the Bellman dynamic programming principle and the averagingmethod. The latter is used to solve theHamilton-Jacobi-Bellman equation approximately, which permits synthesizing the controller. The proposed method for controller design can be used in many problems close to the problem of motion of the Lagrange top (the motion of a rigid body in the atmosphere, the motion of a rigid body fastened to a cable in deployment of the orbital cable system, etc.).

Robustness of predator-prey models for confinement regime transitions in fusion plasmas

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

Zhu, H.; Chapman, S. C.; Department of Mathematics and Statistics, University of Tromso

2013-04-15

Energy transport and confinement in tokamak fusion plasmas is usually determined by the coupled nonlinear interactions of small-scale drift turbulence and larger scale coherent nonlinear structures, such as zonal flows, together with free energy sources such as temperature gradients. Zero-dimensional models, designed to embody plausible physical narratives for these interactions, can help to identify the origin of enhanced energy confinement and of transitions between confinement regimes. A prime zero-dimensional paradigm is predator-prey or Lotka-Volterra. Here, we extend a successful three-variable (temperature gradient; microturbulence level; one class of coherent structure) model in this genre [M. A. Malkov and P. H. Diamond,more » Phys. Plasmas 16, 012504 (2009)], by adding a fourth variable representing a second class of coherent structure. This requires a fourth coupled nonlinear ordinary differential equation. We investigate the degree of invariance of the phenomenology generated by the model of Malkov and Diamond, given this additional physics. We study and compare the long-time behaviour of the three-equation and four-equation systems, their evolution towards the final state, and their attractive fixed points and limit cycles. We explore the sensitivity of paths to attractors. It is found that, for example, an attractive fixed point of the three-equation system can become a limit cycle of the four-equation system. Addressing these questions which we together refer to as 'robustness' for convenience is particularly important for models which, as here, generate sharp transitions in the values of system variables which may replicate some key features of confinement transitions. Our results help to establish the robustness of the zero-dimensional model approach to capturing observed confinement phenomenology in tokamak fusion plasmas.« less

Scaling fixed-field alternating gradient accelerators with a small orbit excursion.

PubMed

Machida, Shinji

2009-10-16

A novel scaling type of fixed-field alternating gradient (FFAG) accelerator is proposed that solves the major problems of conventional scaling and nonscaling types. This scaling FFAG accelerator can achieve a much smaller orbit excursion by taking a larger field index k. A triplet focusing structure makes it possible to set the operating point in the second stability region of Hill's equation with a reasonable sensitivity to various errors. The orbit excursion is about 5 times smaller than in a conventional scaling FFAG accelerator and the beam size growth due to typical errors is at most 10%.

An Overview of Longitudinal Data Analysis Methods for Neurological Research

PubMed Central

Locascio, Joseph J.; Atri, Alireza

2011-01-01

The purpose of this article is to provide a concise, broad and readily accessible overview of longitudinal data analysis methods, aimed to be a practical guide for clinical investigators in neurology. In general, we advise that older, traditional methods, including (1) simple regression of the dependent variable on a time measure, (2) analyzing a single summary subject level number that indexes changes for each subject and (3) a general linear model approach with a fixed-subject effect, should be reserved for quick, simple or preliminary analyses. We advocate the general use of mixed-random and fixed-effect regression models for analyses of most longitudinal clinical studies. Under restrictive situations or to provide validation, we recommend: (1) repeated-measure analysis of covariance (ANCOVA), (2) ANCOVA for two time points, (3) generalized estimating equations and (4) latent growth curve/structural equation models. PMID:22203825

Signs and stability in higher-derivative gravity

NASA Astrophysics Data System (ADS)

Narain, Gaurav

2018-02-01

Perturbatively renormalizable higher-derivative gravity in four space-time dimensions with arbitrary signs of couplings has been considered. Systematic analysis of the action with arbitrary signs of couplings in Lorentzian flat space-time for no-tachyons, fixes the signs. Feynman + i𝜖 prescription for these signs further grants necessary convergence in path-integral, suppressing the field modes with large action. This also leads to a sensible wick rotation where quantum computation can be performed. Running couplings for these sign of parameters make the massive tensor ghost innocuous leading to a stable and ghost-free renormalizable theory in four space-time dimensions. The theory has a transition point arising from renormalization group (RG) equations, where the coefficient of R2 diverges without affecting the perturbative quantum field theory (QFT). Redefining this coefficient gives a better handle over the theory around the transition point. The flow equations push the flow of parameters across the transition point. The flow beyond the transition point is analyzed using the one-loop RG equations which shows that the regime beyond the transition point has unphysical properties: there are tachyons, the path-integral loses positive definiteness, Newton’s constant G becomes negative and large, and perturbative parameters become large. These shortcomings indicate a lack of completeness beyond the transition point and need of a nonperturbative treatment of the theory beyond the transition point.

A complex fermionic tensor model in d dimensions

NASA Astrophysics Data System (ADS)

Prakash, Shiroman; Sinha, Ritam

2018-02-01

In this note, we study a melonic tensor model in d dimensions based on three-index Dirac fermions with a four-fermion interaction. Summing the melonic diagrams at strong coupling allows one to define a formal large- N saddle point in arbitrary d and calculate the spectrum of scalar bilinear singlet operators. For d = 2 - ɛ the theory is an infrared fixed point, which we find has a purely real spectrum that we determine numerically for arbitrary d < 2, and analytically as a power series in ɛ. The theory appears to be weakly interacting when ɛ is small, suggesting that fermionic tensor models in 1-dimension can be studied in an ɛ expansion. For d > 2, the spectrum can still be calculated using the saddle point equations, which may define a formal large- N ultraviolet fixed point analogous to the Gross-Neveu model in d > 2. For 2 < d < 6, we find that the spectrum contains at least one complex scalar eigenvalue (similar to the complex eigenvalue present in the bosonic tensor model recently studied by Giombi, Klebanov and Tarnopolsky) which indicates that the theory is unstable. We also find that the fixed point is weakly-interacting when d = 6 (or more generally d = 4 n + 2) and has a real spectrum for 6 < d < 6 .14 which we present as a power series in ɛ in 6 + ɛ dimensions.

Improved belief propagation algorithm finds many Bethe states in the random-field Ising model on random graphs

NASA Astrophysics Data System (ADS)

Perugini, G.; Ricci-Tersenghi, F.

2018-01-01

We first present an empirical study of the Belief Propagation (BP) algorithm, when run on the random field Ising model defined on random regular graphs in the zero temperature limit. We introduce the notion of extremal solutions for the BP equations, and we use them to fix a fraction of spins in their ground state configuration. At the phase transition point the fraction of unconstrained spins percolates and their number diverges with the system size. This in turn makes the associated optimization problem highly non trivial in the critical region. Using the bounds on the BP messages provided by the extremal solutions we design a new and very easy to implement BP scheme which is able to output a large number of stable fixed points. On one hand this new algorithm is able to provide the minimum energy configuration with high probability in a competitive time. On the other hand we found that the number of fixed points of the BP algorithm grows with the system size in the critical region. This unexpected feature poses new relevant questions about the physics of this class of models.

Computing eigenfunctions and eigenvalues of boundary-value problems with the orthogonal spectral renormalization method

NASA Astrophysics Data System (ADS)

Cartarius, Holger; Musslimani, Ziad H.; Schwarz, Lukas; Wunner, Günter

2018-03-01

The spectral renormalization method was introduced in 2005 as an effective way to compute ground states of nonlinear Schrödinger and Gross-Pitaevskii type equations. In this paper, we introduce an orthogonal spectral renormalization (OSR) method to compute ground and excited states (and their respective eigenvalues) of linear and nonlinear eigenvalue problems. The implementation of the algorithm follows four simple steps: (i) reformulate the underlying eigenvalue problem as a fixed-point equation, (ii) introduce a renormalization factor that controls the convergence properties of the iteration, (iii) perform a Gram-Schmidt orthogonalization process in order to prevent the iteration from converging to an unwanted mode, and (iv) compute the solution sought using a fixed-point iteration. The advantages of the OSR scheme over other known methods (such as Newton's and self-consistency) are (i) it allows the flexibility to choose large varieties of initial guesses without diverging, (ii) it is easy to implement especially at higher dimensions, and (iii) it can easily handle problems with complex and random potentials. The OSR method is implemented on benchmark Hermitian linear and nonlinear eigenvalue problems as well as linear and nonlinear non-Hermitian PT -symmetric models.

Higgs boson self-coupling from two-loop analysis

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

Alhendi, H. A.; National Center for Mathematics and Physics, KACST P. O. Box 6086, Riyadh 11442; Barakat, T.

2010-09-01

The scale invariant of the effective potential of the standard model at two loop is used as a boundary condition under the assumption that the two-loop effective potential approximates the full effective potential. This condition leads with the help of the renormalization-group functions of the model at two loop to an algebraic equation of the scalar self-coupling with coefficients that depend on the gauge and the top quark couplings. It admits only two real positive solutions. One of them, in the absence of the gauge and top quark couplings, corresponds to the nonperturbative ultraviolet fixed point of the scalar renormalization-groupmore » function and the other corresponds to the perturbative infrared fixed point. The dependence of the scalar coupling on the top quark and the strong couplings at two-loop radiative corrections is analyzed.« less

Dynamical analysis of continuous higher-order hopfield networks for combinatorial optimization.

PubMed

Atencia, Miguel; Joya, Gonzalo; Sandoval, Francisco

2005-08-01

In this letter, the ability of higher-order Hopfield networks to solve combinatorial optimization problems is assessed by means of a rigorous analysis of their properties. The stability of the continuous network is almost completely clarified: (1) hyperbolic interior equilibria, which are unfeasible, are unstable; (2) the state cannot escape from the unitary hypercube; and (3) a Lyapunov function exists. Numerical methods used to implement the continuous equation on a computer should be designed with the aim of preserving these favorable properties. The case of nonhyperbolic fixed points, which occur when the Hessian of the target function is the null matrix, requires further study. We prove that these nonhyperbolic interior fixed points are unstable in networks with three neurons and order two. The conjecture that interior equilibria are unstable in the general case is left open.

Existence of solutions of a two-dimensional boundary value problem for a system of nonlinear equations arising in growing cell populations.

PubMed

Jeribi, Aref; Krichen, Bilel; Mefteh, Bilel

2013-01-01

In the paper [A. Ben Amar, A. Jeribi, and B. Krichen, Fixed point theorems for block operator matrix and an application to a structured problem under boundary conditions of Rotenberg's model type, to appear in Math. Slovaca. (2014)], the existence of solutions of the two-dimensional boundary value problem (1) and (2) was discussed in the product Banach space L(p)×L(p) for p∈(1, ∞). Due to the lack of compactness on L1 spaces, the analysis did not cover the case p=1. The purpose of this work is to extend the results of Ben Amar et al. to the case p=1 by establishing new variants of fixed-point theorems for a 2×2 operator matrix, involving weakly compact operators.

The Simple Map for a Single-null Divertor Tokamak: How to Find the Last Good Surface

NASA Astrophysics Data System (ADS)

Phan, Huong; Ali, Halima; Punjabi, Alkesh

2000-10-01

The Simple Map^1 is a representation of the magnetic field inside a single-null divertor tokamak. It is given by the equations: X_n+1=X_n kYn (1-Y_n), Y_n+1= Y_n+kX_n+1. These equations mimic the motion of the magnetic field lines in a single-null divertor tokamak. The fixed stable point is (0,0) and the unstable fixed oint is (0,1). k is fixed at 0.60. In our work, the starting values of Y in the map is kept in the interval of 0 to 1, and the starting value of X is 0. Using the successive bifurcation method, we first run these equations for 10^6 iterations to find the approximate value of Y when chaos occurs. We examine the neighborhood of this Y value to find the exact value of Y for the last good surface. We call this value Y_lgs. We find Y_lgs to be 0.997135768 for k=0.60 and X=0. This work is supported by US DOE OFES. Ms. Huong Phan is a HU CFRT Summer Fusion High School Workshop Scholar from Andrew P. Hill High School in California. She is supported by NASA SHARP Plus Program. 1. Punjabi A, Verma A and Boozer A, Phys Rev Lett 69 3322 (1992) and J Plasma Phys 52 91 (1994)

Continuation of probability density functions using a generalized Lyapunov approach

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

Baars, S., E-mail: s.baars@rug.nl; Viebahn, J.P., E-mail: viebahn@cwi.nl; Mulder, T.E., E-mail: t.e.mulder@uu.nl

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.

Ordinary Differential Equation Models for Adoptive Immunotherapy.

PubMed

Talkington, Anne; Dantoin, Claudia; Durrett, Rick

2018-05-01

Modified T cells that have been engineered to recognize the CD19 surface marker have recently been shown to be very successful at treating acute lymphocytic leukemias. Here, we explore four previous approaches that have used ordinary differential equations to model this type of therapy, compare their properties, and modify the models to address their deficiencies. Although the four models treat the workings of the immune system in slightly different ways, they all predict that adoptive immunotherapy can be successful to move a patient from the large tumor fixed point to an equilibrium with little or no tumor.

Augmenting the one-shot framework by additional constraints

DOE PAGES

Bosse, Torsten

2016-05-12

The (multistep) one-shot method for design optimization problems has been successfully implemented for various applications. To this end, a slowly convergent primal fixed-point iteration of the state equation is augmented by an adjoint iteration and a corresponding preconditioned design update. In this paper we present a modification of the method that allows for additional equality constraints besides the usual state equation. Finally, a retardation analysis and the local convergence of the method in terms of necessary and sufficient conditions are given, which depend on key characteristics of the underlying problem and the quality of the utilized preconditioner.

Augmenting the one-shot framework by additional constraints

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

Bosse, Torsten

The (multistep) one-shot method for design optimization problems has been successfully implemented for various applications. To this end, a slowly convergent primal fixed-point iteration of the state equation is augmented by an adjoint iteration and a corresponding preconditioned design update. In this paper we present a modification of the method that allows for additional equality constraints besides the usual state equation. Finally, a retardation analysis and the local convergence of the method in terms of necessary and sufficient conditions are given, which depend on key characteristics of the underlying problem and the quality of the utilized preconditioner.

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

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

Compatibility check of measured aircraft responses using kinematic equations and extended Kalman filter

NASA Technical Reports Server (NTRS)

Klein, V.; Schiess, J. R.

1977-01-01

An extended Kalman filter smoother and a fixed point smoother were used for estimation of the state variables in the six degree of freedom kinematic equations relating measured aircraft responses and for estimation of unknown constant bias and scale factor errors in measured data. The computing algorithm includes an analysis of residuals which can improve the filter performance and provide estimates of measurement noise characteristics for some aircraft output variables. The technique developed was demonstrated using simulated and real flight test data. Improved accuracy of measured data was obtained when the data were corrected for estimated bias errors.

An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations

PubMed Central

Özkum, Gülcan

2013-01-01

We develop a high-order fixed point type method to approximate a multiple root. By using three functional evaluations per full cycle, a new class of fourth-order methods for this purpose is suggested and established. The methods from the class require the knowledge of the multiplicity. We also present a method in the absence of multiplicity for nonlinear equations. In order to attest the efficiency of the obtained methods, we employ numerical comparisons alongside obtaining basins of attraction to compare them in the complex plane according to their convergence speed and chaotic behavior. PMID:24453914

Maximum likelihood clustering with dependent feature trees

NASA Technical Reports Server (NTRS)

Chittineni, C. B. (Principal Investigator)

1981-01-01

The decomposition of mixture density of the data into its normal component densities is considered. The densities are approximated with first order dependent feature trees using criteria of mutual information and distance measures. Expressions are presented for the criteria when the densities are Gaussian. By defining different typs of nodes in a general dependent feature tree, maximum likelihood equations are developed for the estimation of parameters using fixed point iterations. The field structure of the data is also taken into account in developing maximum likelihood equations. Experimental results from the processing of remotely sensed multispectral scanner imagery data are included.

A spline-based non-linear diffeomorphism for multimodal prostate registration.

PubMed

Mitra, Jhimli; Kato, Zoltan; Martí, Robert; Oliver, Arnau; Lladó, Xavier; Sidibé, Désiré; Ghose, Soumya; Vilanova, Joan C; Comet, Josep; Meriaudeau, Fabrice

2012-08-01

This paper presents a novel method for non-rigid registration of transrectal ultrasound and magnetic resonance prostate images based on a non-linear regularized framework of point correspondences obtained from a statistical measure of shape-contexts. The segmented prostate shapes are represented by shape-contexts and the Bhattacharyya distance between the shape representations is used to find the point correspondences between the 2D fixed and moving images. The registration method involves parametric estimation of the non-linear diffeomorphism between the multimodal images and has its basis in solving a set of non-linear equations of thin-plate splines. The solution is obtained as the least-squares solution of an over-determined system of non-linear equations constructed by integrating a set of non-linear functions over the fixed and moving images. However, this may not result in clinically acceptable transformations of the anatomical targets. Therefore, the regularized bending energy of the thin-plate splines along with the localization error of established correspondences should be included in the system of equations. The registration accuracies of the proposed method are evaluated in 20 pairs of prostate mid-gland ultrasound and magnetic resonance images. The results obtained in terms of Dice similarity coefficient show an average of 0.980±0.004, average 95% Hausdorff distance of 1.63±0.48 mm and mean target registration and target localization errors of 1.60±1.17 mm and 0.15±0.12 mm respectively. Copyright © 2012 Elsevier B.V. All rights reserved.

On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind

NASA Astrophysics Data System (ADS)

Voytishek, Anton V.; Shipilov, Nikolay M.

2017-11-01

In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.

A viable dark fluid model

NASA Astrophysics Data System (ADS)

Elkhateeb, Esraa

2018-01-01

We consider a cosmological model based on a generalization of the equation of state proposed by Nojiri and Odintsov (2004) and Štefančić (2005, 2006). We argue that this model works as a dark fluid model which can interpolate between dust equation of state and the dark energy equation of state. We show how the asymptotic behavior of the equation of state constrained the parameters of the model. The causality condition for the model is also studied to constrain the parameters and the fixed points are tested to determine different solution classes. Observations of Hubble diagram of SNe Ia supernovae are used to further constrain the model. We present an exact solution of the model and calculate the luminosity distance and the energy density evolution. We also calculate the deceleration parameter to test the state of the universe expansion.

Effects of aircraft and flight parameters on energy-efficient profile descents in time-based metered traffic

NASA Technical Reports Server (NTRS)

Dejarnette, F. R.

1984-01-01

Concepts to save fuel while preserving airport capacity by combining time based metering with profile descent procedures were developed. A computer algorithm is developed to provide the flight crew with the information needed to fly from an entry fix to a metering fix and arrive there at a predetermined time, altitude, and airspeed. The flight from the metering fix to an aim point near the airport was calculated. The flight path is divided into several descent and deceleration segments. Descents are performed at constant Mach numbers or calibrated airspeed, whereas decelerations occur at constant altitude. The time and distance associated with each segment are calculated from point mass equations of motion for a clean configuration with idle thrust. Wind and nonstandard atmospheric properties have a large effect on the flight path. It is found that uncertainty in the descent Mach number has a large effect on the predicted flight time. Of the possible combinations of Mach number and calibrated airspeed for a descent, only small changes were observed in the fuel consumed.

The Mean Curvature of the Influence Surface of Wave Equation With Sources on a Moving Surface

NASA Technical Reports Server (NTRS)

Farassat, F.; Farris, Mark

1999-01-01

The mean curvature of the influence surface of the space-time point (x, t) appears in linear supersonic propeller noise theory and in the Kirchhoff formula for a supersonic surface. Both these problems are governed by the linear wave equation with sources on a moving surface. The influence surface is also called the Sigma - surface in the aeroacoustic literature. This surface is the locus, in a frame fixed to the quiescent medium, of all the points of a radiating surface f(x, t) = 0 whose acoustic signals arrive simultaneously to an observer at position x and at the time t. Mathematically, the Sigma- surface is produced by the intersection of the characteristic conoid of the space-time point (x, t) and the moving surface. In this paper, we derive the expression for the local mean curvature of the Sigma - space of the space-time point for a moving rigid or deformable surface f(x, t) = 0. This expression is a complicated function of the geometric and kinematic parameters of the surface f(x, t) = 0. Using the results of this paper, the solution of the governing wave equation of high speed propeller noise radiation as well as the Kirchhoff formula for a supersonic surface can be written as very compact analytic expression.

Chaos control in delayed phase space constructed by the Takens embedding theory

NASA Astrophysics Data System (ADS)

Hajiloo, R.; Salarieh, H.; Alasty, A.

2018-01-01

In this paper, the problem of chaos control in discrete-time chaotic systems with unknown governing equations and limited measurable states is investigated. Using the time-series of only one measurable state, an algorithm is proposed to stabilize unstable fixed points. The approach consists of three steps: first, using Takens embedding theory, a delayed phase space preserving the topological characteristics of the unknown system is reconstructed. Second, a dynamic model is identified by recursive least squares method to estimate the time-series data in the delayed phase space. Finally, based on the reconstructed model, an appropriate linear delayed feedback controller is obtained for stabilizing unstable fixed points of the system. Controller gains are computed using a systematic approach. The effectiveness of the proposed algorithm is examined by applying it to the generalized hyperchaotic Henon system, prey-predator population map, and the discrete-time Lorenz system.

On iterative algorithms for quantitative photoacoustic tomography in the radiative transport regime

NASA Astrophysics Data System (ADS)

Wang, Chao; Zhou, Tie

2017-11-01

In this paper, we present a numerical reconstruction method for quantitative photoacoustic tomography (QPAT), based on the radiative transfer equation (RTE), which models light propagation more accurately than diffusion approximation (DA). We investigate the reconstruction of absorption coefficient and scattering coefficient of biological tissues. An improved fixed-point iterative method to retrieve the absorption coefficient, given the scattering coefficient, is proposed for its cheap computational cost; the convergence of this method is also proved. The Barzilai-Borwein (BB) method is applied to retrieve two coefficients simultaneously. Since the reconstruction of optical coefficients involves the solutions of original and adjoint RTEs in the framework of optimization, an efficient solver with high accuracy is developed from Gao and Zhao (2009 Transp. Theory Stat. Phys. 38 149-92). Simulation experiments illustrate that the improved fixed-point iterative method and the BB method are competitive methods for QPAT in the relevant cases.

Time-dependent real space RG on the spin-1/2 XXZ chain

NASA Astrophysics Data System (ADS)

Mason, Peter; Zagoskin, Alexandre; Betouras, Joseph

In order to measure the spread of information in a system of interacting fermions with nearest-neighbour couplings and strong bond disorder, one could utilise a dynamical real space renormalisation group (RG) approach on the spin-1/2 XXZ chain. Under such a procedure, a many-body localised state is established as an infinite randomness fixed point and the entropy scales with time as log(log(t)). One interesting further question that results from such a study is the case when the Hamiltonian explicitly depends on time. Here we answer this question by considering a dynamical renormalisation group treatment on the strongly disordered random spin-1/2 XXZ chain where the couplings are time-dependent and chosen to reflect a (slow) evolution of the governing Hamiltonian. Under the condition that the renormalisation process occurs at fixed time, a set of coupled second order, nonlinear PDE's can be written down in terms of the random distributions of the bonds and fields. Solution of these flow equations at the relevant critical fixed points leads us to establish the dynamics of the flow as we sweep through the quantum critical point of the Hamiltonian. We will present these critical flows as well as discussing the issues of duality, entropy and many-body localisation.

Apparent Transition Behavior of Widely-Used Turbulence Models

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.

2006-01-01

The Spalart-Allmaras and the Menter SST kappa-omega turbulence models are shown to have the undesirable characteristic that, for fully turbulent computations, a transition region can occur whose extent varies with grid density. Extremely fine two-dimensional grids over the front portion of an airfoil are used to demonstrate the effect. As the grid density is increased, the laminar region near the nose becomes larger. In the Spalart-Allmaras model this behavior is due to convergence to a laminar-behavior fixed point that occurs in practice when freestream turbulence is below some threshold. It is the result of a feature purposefully added to the original model in conjunction with a special trip function. This degenerate fixed point can also cause nonuniqueness regarding where transition initiates on a given grid. Consistent fully turbulent results can easily be achieved by either using a higher freestream turbulence level or by making a simple change to one of the model constants. Two-equation kappa-omega models, including the SST model, exhibit strong sensitivity to numerical resolution near the area where turbulence initiates. Thus, inconsistent apparent transition behavior with grid refinement in this case does not appear to stem from the presence of a degenerate fixed point. Rather, it is a fundamental property of the kappa-omega model itself, and is not easily remedied.

Apparent Transition Behavior of Widely-Used Turbulence Models

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.

2007-01-01

The Spalart-Allmaras and the Menter SST k-omega turbulence models are shown to have the undesirable characteristic that, for fully turbulent computations, a transition region can occur whose extent varies with grid density. Extremely fine two-dimensional grids over the front portion of an airfoil are used to demonstrate the effect. As the grid density is increased, the laminar region near the nose becomes larger. In the Spalart-Allmaras model this behavior is due to convergence to a laminar-behavior fixed point that occurs in practice when freestream turbulence is below some threshold. It is the result of a feature purposefully added to the original model in conjunction with a special trip function. This degenerate fixed point can also cause non-uniqueness regarding where transition initiates on a given grid. Consistent fully turbulent results can easily be achieved by either using a higher freestream turbulence level or by making a simple change to one of the model constants. Two-equation k-omega models, including the SST model, exhibit strong sensitivity to numerical resolution near the area where turbulence initiates. Thus, inconsistent apparent transition behavior with grid refinement in this case does not appear to stem from the presence of a degenerate fixed point. Rather, it is a fundamental property of the k-omega model itself, and is not easily remedied.

Modeling and analysis of the effect of training on V O2 kinetics and anaerobic capacity.

PubMed

Stirling, J R; Zakynthinaki, M S; Billat, V

2008-07-01

In this paper, we present an application of a number of tools and concepts for modeling and analyzing raw, unaveraged, and unedited breath-by-breath oxygen uptake data. A method for calculating anaerobic capacity is used together with a model, in the form of a set of coupled nonlinear ordinary differential equations to make predictions of the VO(2) kinetics, the time to achieve a percentage of a certain constant oxygen demand, and the time limit to exhaustion at intensities other than those in which we have data. Speeded oxygen kinetics and increased time limit to exhaustion are also investigated using the eigenvalues of the fixed points of our model. We also use a way of analyzing the oxygen uptake kinetics using a plot of V O(2)(t) vs V O(2)(t) which allows one to observe both the fixed point solutions and also the presence of speeded oxygen kinetics following training. A method of plotting the eigenvalue versus oxygen demand is also used which allows one to observe where the maximum amplitude of the so-called slow component will be and also how training has changed the oxygen uptake kinetics by changing the strength of the attracting fixed point for a particular demand.

Dynamic contact problem with adhesion and damage between thermo-electro-elasto-viscoplastic bodies

NASA Astrophysics Data System (ADS)

Hadj ammar, Tedjani; Saïdi, Abdelkader; Azeb Ahmed, Abdelaziz

2017-05-01

We study of a dynamic contact problem between two thermo-electro-elasto-viscoplastic bodies with damage and adhesion. The contact is frictionless and is modeled with normal compliance condition. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of evolutionary variational inequalities, parabolic inequalities, differential equations, and fixed point theorem.

Products of composite operators in the exact renormalization group formalism

NASA Astrophysics Data System (ADS)

Pagani, C.; Sonoda, H.

2018-02-01

We discuss a general method of constructing the products of composite operators using the exact renormalization group formalism. Considering mainly the Wilson action at a generic fixed point of the renormalization group, we give an argument for the validity of short-distance expansions of operator products. We show how to compute the expansion coefficients by solving differential equations, and test our method with some simple examples.

Mean Field Games for Stochastic Growth with Relative Utility

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

Huang, Minyi, E-mail: mhuang@math.carleton.ca; Nguyen, Son Luu, E-mail: sonluu.nguyen@upr.edu

This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation errormore » estimate.« less

Control of sound radiation from a wavepacket over a curved surface

NASA Technical Reports Server (NTRS)

Maestrello, Lucio; El Hady, Nabil M.

1989-01-01

Active control of acoustic pressure in the far field resulting from the growth and decay of a wavepacket convecting in a boundary layer over a concave-convex surface is investigated numerically using direct computations of the Navier-Stokes equations. The resulting sound radiation is computed using linearized Euler equations with the pressure from the Navier-Stokes solution as a time-dependent boundary condition. The acoustic far field exhibits directivity type of behavior that points upstream to the flow direction. A fixed control algorithm is used where the attenuation signal is synthesized by a filter which actively adapt it to the amplitude-time response of the outgoing acoustic wave.

Study of the Bellman equation in a production model with unstable demand

NASA Astrophysics Data System (ADS)

Obrosova, N. K.; Shananin, A. A.

2014-09-01

A production model with allowance for a working capital deficit and a restricted maximum possible sales volume is proposed and analyzed. The study is motivated by the urgency of analyzing well-known problems of functioning low competitive macroeconomic structures. The original formulation of the task represents an infinite-horizon optimal control problem. As a result, the model is formalized in the form of a Bellman equation. It is proved that the corresponding Bellman operator is a contraction and has a unique fixed point in the chosen class of functions. A closed-form solution of the Bellman equation is found using the method of steps. The influence of the credit interest rate on the firm market value assessment is analyzed by applying the developed model.

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods. Ph.D. Thesis - Paris Univ.; [mathematical models of transonic flow using nonlinear equations

NASA Technical Reports Server (NTRS)

Periaux, J.

1979-01-01

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

Modulated amplitude waves in collisionally inhomogeneous Bose Einstein condensates

NASA Astrophysics Data System (ADS)

Porter, Mason A.; Kevrekidis, P. G.; Malomed, Boris A.; Frantzeskakis, D. J.

2007-05-01

We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length a subjected to a spatially periodic modulation, a=a(x)=a(x+L). This “collisionally inhomogeneous” BEC is described by a Gross-Pitaevskii (GP) equation whose nonlinearity coefficient is a periodic function of x. We transform this equation into a GP equation with a constant coefficient and an additional effective potential and study a class of extended wave solutions of the transformed equation. For weak underlying inhomogeneity, the effective potential takes a form resembling a superlattice, and the amplitude dynamics of the solutions of the constant-coefficient GP equation obey a nonlinear generalization of the Ince equation. In the small-amplitude limit, we use averaging to construct analytical solutions for modulated amplitude waves (MAWs), whose stability we subsequently examine using both numerical simulations of the original GP equation and fixed-point computations with the MAWs as numerically exact solutions. We show that “on-site” solutions, whose maxima correspond to maxima of a(x), are more robust and likely to be observed than their “off-site” counterparts.

Resurgent transseries & Dyson–Schwinger equations

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

Klaczynski, Lutz, E-mail: klacz@mathematik.hu-berlin.de

2016-09-15

We employ resurgent transseries as algebraic tools to investigate two self-consistent Dyson–Schwinger equations, one in Yukawa theory and one in quantum electrodynamics. After a brief but pedagogical review, we derive fixed point equations for the associated anomalous dimensions and insert a moderately generic log-free transseries ansatz to study the possible strictures imposed. While proceeding in various stages, we develop an algebraic method to keep track of the transseries’ coefficients. We explore what conditions must be violated in order to stay clear of fixed point theorems to eschew a unique solution, if so desired, as we explain. An interesting finding ismore » that the flow of data between the different sectors of the transseries shows a pattern typical of resurgence, i.e. the phenomenon that the perturbative sector of the transseries talks to the nonperturbative ones in a one-way fashion. However, our ansatz is not exotic enough as it leads to trivial solutions with vanishing nonperturbative sectors, even when logarithmic monomials are included. We see our result as a harbinger of what future work might reveal about the transseries representations of observables in fully renormalised four-dimensional quantum field theories and adduce a tentative yet to our mind weighty argument as to why one should not expect otherwise. This paper is considerably self-contained. Readers with little prior knowledge are let in on the basic reasons why perturbative series in quantum field theory eventually require an upgrade to transseries. Furthermore, in order to acquaint the reader with the language utilised extensively in this work, we also provide a concise mathematical introduction to grid-based transseries.« less

Turbulence and deterministic chaos. [computational fluid dynamics

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1992-01-01

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, largest Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low Reynolds number fully developed turbulence are compared. Several flows are noted: fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, only fully chaotic is classified as turbulent. Besides the sustained flows, a flow which decays as it becomes turbulent is examined. For the finest grid, 128(exp 3) points, the spatial resolution appears to be quite good. As a final note, the variation of the velocity derivatives skewness of a Navier-Stokes flow as the Reynolds number goes to zero is calculated numerically. The value of the skewness is shown to become small at low Reynolds numbers, in agreement with intuitive arguments that nonlinear terms should be negligible.

Transfers between libration-point orbits in the elliptic restricted problem

NASA Astrophysics Data System (ADS)

Hiday-Johnston, L. A.; Howell, K. C.

1994-04-01

A strategy is formulated to design optimal time-fixed impulsive transfers between three-dimensional libration-point orbits in the vicinity of the interior L1 libration point of the Sun-Earth/Moon barycenter system. The adjoint equation in terms of rotating coordinates in the elliptic restricted three-body problem is shown to be of a distinctly different form from that obtained in the analysis of trajectories in the two-body problem. Also, the necessary conditions for a time-fixed two-impulse transfer to be optimal are stated in terms of the primer vector. Primer vector theory is then extended to nonoptimal impulsive trajectories in order to establish a criterion whereby the addition of an interior impulse reduces total fuel expenditure. The necessary conditions for the local optimality of a transfer containing additional impulses are satisfied by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses. Determination of location, orientation, and magnitude of each additional impulse is accomplished by the unconstrained minimization of the cost function using a multivariable search method. Results indicate that substantial savings in fuel can be achieved by the addition of interior impulsive maneuvers on transfers between libration-point orbits.

Existence and global attractivity of unique positive periodic solution for a model of hematopoiesis

NASA Astrophysics Data System (ADS)

Liu, Guirong; Yan, Jurang; Zhang, Fengqin

2007-10-01

In this paper, we consider the generalized model of hematopoiesis By using a fixed point theorem, some criteria are established for the existence of the unique positive [omega]-periodic solution of the above equation. In particular, we not only give the conclusion of convergence of xk to , where {xk} is a successive sequence, but also show that is a global attractor of all other positive solutions.

A micro-CMM with metrology frame for low uncertainty measurements

NASA Astrophysics Data System (ADS)

Brand, Uwe; Kirchhoff, Juergen

2005-12-01

A conventional bridge-type coordinate measuring machine (CMM) with an opto-tactile fibre probe for the measurement of microstructures has been equipped with a metrology frame in order to reduce its measurement uncertainty. The frame contains six laser interferometers for high-precision position and guiding deviation measurements, a Zerodur cuboid with three measuring surfaces for the laser interferometers to which the fibre probe is fixed, and an invar frame which supports the measuring objects and to which the reference mirrors of the interferometers are fixed. The orthogonality and flatness deviations of the Zerodur measuring surfaces have been measured and taken into account in the equation of motion of the probing sphere. As a first performance test, the flatness of an optical flat has been measured with the fibre probe. Measuring-depth-dependent and probing-force-dependent shifts of the probing position were observed. In order to reduce the scattering of the probing points, 77 measurements were averaged for one coordinate point to be measured. This has led to measuring times of several hours for one plane and strong thermal drifts of the measured probing points.

A simple parameter can switch between different weak-noise-induced phenomena in a simple neuron model

NASA Astrophysics Data System (ADS)

Yamakou, Marius E.; Jost, Jürgen

2017-10-01

In recent years, several, apparently quite different, weak-noise-induced resonance phenomena have been discovered. Here, we show that at least two of them, self-induced stochastic resonance (SISR) and inverse stochastic resonance (ISR), can be related by a simple parameter switch in one of the simplest models, the FitzHugh-Nagumo (FHN) neuron model. We consider a FHN model with a unique fixed point perturbed by synaptic noise. Depending on the stability of this fixed point and whether it is located to either the left or right of the fold point of the critical manifold, two distinct weak-noise-induced phenomena, either SISR or ISR, may emerge. SISR is more robust to parametric perturbations than ISR, and the coherent spike train generated by SISR is more robust than that generated deterministically. ISR also depends on the location of initial conditions and on the time-scale separation parameter of the model equation. Our results could also explain why real biological neurons having similar physiological features and synaptic inputs may encode very different information.

On global solutions of the random Hamilton-Jacobi equations and the KPZ problem

NASA Astrophysics Data System (ADS)

Bakhtin, Yuri; Khanin, Konstantin

2018-04-01

In this paper, we discuss possible qualitative approaches to the problem of KPZ universality. Throughout the paper, our point of view is based on the geometrical and dynamical properties of minimisers and shocks forming interlacing tree-like structures. We believe that the KPZ universality can be explained in terms of statistics of these structures evolving in time. The paper is focussed on the setting of the random Hamilton-Jacobi equations. We formulate several conjectures concerning global solutions and discuss how their properties are connected to the KPZ scalings in dimension 1  +  1. In the case of general viscous Hamilton-Jacobi equations with non-quadratic Hamiltonians, we define generalised directed polymers. We expect that their behaviour is similar to the behaviour of classical directed polymers, and present arguments in favour of this conjecture. We also define a new renormalisation transformation defined in purely geometrical terms and discuss conjectural properties of the corresponding fixed points. Most of our conjectures are widely open, and supported by only partial rigorous results for particular models.

A BRST gauge-fixing procedure for Yang Mills theory on sphere

NASA Astrophysics Data System (ADS)

Banerjee, Rabin; Deguchi, Shinichi

2006-01-01

A gauge-fixing procedure for the Yang-Mills theory on an n-dimensional sphere (or a hypersphere) is discussed in a systematic manner. We claim that Adler's gauge-fixing condition used in massless Euclidean QED on a hypersphere is not conventional because of the presence of an extra free index, and hence is unfavorable for the gauge-fixing procedure based on the BRST invariance principle (or simply BRST gauge-fixing procedure). Choosing a suitable gauge condition, which is proved to be equivalent to a generalization of Adler's condition, we apply the BRST gauge-fixing procedure to the Yang-Mills theory on a hypersphere to obtain consistent results. Field equations for the Yang-Mills field and associated fields are derived in manifestly O (n + 1) covariant or invariant forms. In the large radius limit, these equations reproduce the corresponding field equations defined on the n-dimensional flat space.

Topologically massive gravity and the AdS/CFT correspondence

NASA Astrophysics Data System (ADS)

Skenderis, Kostas; Taylor, Marika; van Rees, Balt C.

2009-09-01

We set up the AdS/CFT correspondence for topologically massive gravity (TMG) in three dimensions. The first step in this procedure is to determine the appropriate fall off conditions at infinity. These cannot be fixed a priori as they depend on the bulk theory under consideration and are derived by solving asymptotically the non-linear field equations. We discuss in detail the asymptotic structure of the field equations for TMG, showing that it contains leading and subleading logarithms, determine the map between bulk fields and CFT operators, obtain the appropriate counterterms needed for holographic renormalization and compute holographically one- and two-point functions at and away from the ``chiral point'' (μ = 1). The 2-point functions at the chiral point are those of a logarithmic CFT (LCFT) with cL = 0,cR = 3l/GN and b = -3l/GN, where b is a parameter characterizing different c = 0 LCFTs. The bulk correlators away from the chiral point (μ ≠ 1) smoothly limit to the LCFT ones as μ → 1. Away from the chiral point, the CFT contains a state of negative norm and the expectation value of the energy momentum tensor in that state is also negative, reflecting a corresponding bulk instability due to negative energy modes.

Power Laws, Scale Invariance and the Generalized Frobenius Series:

NASA Astrophysics Data System (ADS)

Visser, Matt; Yunes, Nicolas

We present a self-contained formalism for calculating the background solution, the linearized solutions and a class of generalized Frobenius-like solutions to a system of scale-invariant differential equations. We first cast the scale-invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background solutions. After linearizing about these fixed points, we find a second linearized solution, which provides a distinct collection of power laws characterizing the deviations from the fixed point. We prove that generically there will be a region surrounding the fixed point in which the complete general solution can be represented as a generalized Frobenius-like power series with exponents that are integer multiples of the exponents arising in the linearized problem. While discussions of the linearized system are common, and one can often find a discussion of power-series with integer exponents, power series with irrational (indeed complex) exponents are much rarer in the extant literature. The Frobenius-like series we encounter can be viewed as a variant of the rarely-discussed Liapunov expansion theorem (not to be confused with the more commonly encountered Liapunov functions and Liapunov exponents). As specific examples we apply these ideas to Newtonian and relativistic isothermal stars and construct two separate power series with the overlapping radius of convergence. The second of these power series solutions represents an expansion around "spatial infinity," and in realistic models it is this second power series that gives information about the stellar core, and the damped oscillations in core mass and core radius as the central pressure goes to infinity. The power-series solutions we obtain extend classical results; as exemplified for instance by the work of Lane, Emden, and Chandrasekhar in the Newtonian case, and that of Harrison, Thorne, Wakano, and Wheeler in the relativistic case. We also indicate how to extend these ideas to situations where fixed points may not exist — either due to "monotone" flow or due to the presence of limit cycles. Monotone flow generically leads to logarithmic deviations from scaling, while limit cycles generally lead to discrete self-similar solutions.

Analysis of the cable equation with non-local and non-singular kernel fractional derivative

NASA Astrophysics Data System (ADS)

Karaagac, Berat

2018-02-01

Recently a new concept of differentiation was introduced in the literature where the kernel was converted from non-local singular to non-local and non-singular. One of the great advantages of this new kernel is its ability to portray fading memory and also well defined memory of the system under investigation. In this paper the cable equation which is used to develop mathematical models of signal decay in submarine or underwater telegraphic cables will be analysed using the Atangana-Baleanu fractional derivative due to the ability of the new fractional derivative to describe non-local fading memory. The existence and uniqueness of the more generalized model is presented in detail via the fixed point theorem. A new numerical scheme is used to solve the new equation. In addition, stability, convergence and numerical simulations are presented.

Multidimensional fractional Schrödinger equation

NASA Astrophysics Data System (ADS)

Rodrigues, M. M.; Vieira, N.

2012-11-01

This work is intended to investigate the multi-dimensional space-time fractional Schrödinger equation of the form (CDt0+αu)(t,x) = iħ/2m(C∇βu)(t,x), with ħ the Planck's constant divided by 2π, m is the mass and u(t,x) is a wave function of the particle. Here (CDt0+α,C∇β are operators of the Caputo fractional derivatives, where α ∈]0,1] and β ∈]1,2]. The wave function is obtained using Laplace and Fourier transforms methods and a symbolic operational form of solutions in terms of the Mittag-Leffler functions is exhibited. It is presented an expression for the wave function and for the quantum mechanical probability density. Using Banach fixed point theorem, the existence and uniqueness of solutions is studied for this kind of fractional differential equations.

Multistep integration formulas for the numerical integration of the satellite problem

NASA Technical Reports Server (NTRS)

Lundberg, J. B.; Tapley, B. D.

1981-01-01

The use of two Class 2/fixed mesh/fixed order/multistep integration packages of the PECE type for the numerical integration of the second order, nonlinear, ordinary differential equation of the satellite orbit problem. These two methods are referred to as the general and the second sum formulations. The derivation of the basic equations which characterize each formulation and the role of the basic equations in the PECE algorithm are discussed. Possible starting procedures are examined which may be used to supply the initial set of values required by the fixed mesh/multistep integrators. The results of the general and second sum integrators are compared to the results of various fixed step and variable step integrators.

Separation of Undersampled Composite Signals Using the Dantzig Selector with Overcomplete Dictionaries

DTIC Science & Technology

2014-06-02

2011). [22] Li, Q., Micchelli, C., Shen, L., and Xu, Y. A proximity algorithm acelerated by Gauss - Seidel iterations for L1/TV denoising models. Inverse...system of equations and their relationship to the solution of Model (2) and present an algorithm with an iterative approach for finding these solutions...Using the fixed-point characterization above, the (k + 1)th iteration of the prox- imity operator algorithm to find the solution of the Dantzig

Geometric situation of points of division of regions of direct and return currency in channels with the presence of heating zone limited on the longitudinal coordinate

NASA Astrophysics Data System (ADS)

Gerasimov, A.; Kirpichnikov, A.; Sabirova, F.

2018-03-01

The analysis of energy balance equation for viscous laminar flow of fluid or gas in the cylindrical channel in the area (zone) of warm up bounded along the longitudinal coordinate is made. It was found that at laminar flow of fluid or gas in a round pipe, in each warm up area bounded along the longitudinal coordinate there are the areas of direct and reverse flows separated by a plane that is a locus of points where temperature is maximal for each fixed value of radial coordinate r.

Convergence Time towards Periodic Orbits in Discrete Dynamical Systems

PubMed Central

San Martín, Jesús; Porter, Mason A.

2014-01-01

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we use linearized equations to examine the evolution near that neighborhood. The underlying idea is that points of stable periodic orbit are associated with intervals. We state and prove a theorem that details what regions of phase space are mapped into these intervals (once they are known) and how many iterations are required to get there. We also construct algorithms that allow our theoretical results to be implemented successfully in practice. PMID:24736594

An hp symplectic pseudospectral method for nonlinear optimal control

NASA Astrophysics Data System (ADS)

Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong

2017-01-01

An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.

Self-focusing quantum states

NASA Astrophysics Data System (ADS)

Villanueva, Anthony Allan D.

2018-02-01

We discuss a class of solutions of the time-dependent Schrödinger equation such that the position uncertainty temporarily decreases. This self-focusing or contractive behavior is a consequence of the anti-correlation of the position and momentum observables. Since the associated position density satisfies a continuity equation, upon contraction the probability current at a given fixed point may flow in the opposite direction of the group velocity of the wave packet. For definiteness, we consider a free particle incident from the left of the origin, and establish a condition for the initial position-momentum correlation such that a negative probability current at the origin is possible. This implies a decrease in the particle's detection probability in the region x > 0, and we calculate how long this occurs. Analogous results are obtained for a particle subject to a uniform gravitational force if we consider the particle approaching the turning point. We show that position-momentum anti-correlation may cause a negative probability current at the turning point, leading to a temporary decrease in the particle's detection probability in the classically forbidden region.

Use of laterite for the removal of fluoride from contaminated drinking water.

PubMed

Sarkar, Mitali; Banerjee, Aparna; Pramanick, Partha Pratim; Sarkar, Asit R

2006-10-15

The effects of different operational variables on the mechanistic function of laterite in removal of fluoride have been investigated. Thermodynamic parameters such as free energy change, enthalpy, and entropy of the process, as well as the sorption isotherm, were evaluated. The extent of solute removal is determined by initial solute concentration, operational conditions, laterite dose, and solution pH. For a fixed set of experimental conditions, a model equation is developed from which the percent removal corresponding to each load of fluoride is determined. The mechanism of fluoride adsorption is governed by the zero point charge of laterite and follows a first-order rate equation. pH has a vital role influencing the surface characteristics of laterite. To simulate the flow dynamics, fluoride solution was run through a fixed bed column. The pattern of breakthrough curves for different influent fluoride concentration, pH, and column bed height was characterized. The column efficiency was tested from the bed depth-service time model. The elution of the retained fluoride was studied and the effectiveness of column operation was determined by the retention-elution cycles.

Stability analysis of BWR nuclear-coupled thermal-hyraulics using a simple model

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

Karve, A.A.; Rizwan-uddin; Dorning, J.J.

1995-09-01

A simple mathematical model is developed to describe the dynamics of the nuclear-coupled thermal-hydraulics in a boiling water reactor (BWR) core. The model, which incorporates the essential features of neutron kinetics, and single-phase and two-phase thermal-hydraulics, leads to simple dynamical system comprised of a set of nonlinear ordinary differential equations (ODEs). The stability boundary is determined and plotted in the inlet-subcooling-number (enthalpy)/external-reactivity operating parameter plane. The eigenvalues of the Jacobian matrix of the dynamical system also are calculated at various steady-states (fixed points); the results are consistent with those of the direct stability analysis and indicate that a Hopf bifurcationmore » occurs as the stability boundary in the operating parameter plane is crossed. Numerical simulations of the time-dependent, nonlinear ODEs are carried out for selected points in the operating parameter plane to obtain the actual damped and growing oscillations in the neutron number density, the channel inlet flow velocity, and the other phase variables. These indicate that the Hopf bifurcation is subcritical, hence, density wave oscillations with growing amplitude could result from a finite perturbation of the system even where the steady-state is stable. The power-flow map, frequently used by reactor operators during start-up and shut-down operation of a BWR, is mapped to the inlet-subcooling-number/neutron-density (operating-parameter/phase-variable) plane, and then related to the stability boundaries for different fixed inlet velocities corresponding to selected points on the flow-control line. The stability boundaries for different fixed inlet subcooling numbers corresponding to those selected points, are plotted in the neutron-density/inlet-velocity phase variable plane and then the points on the flow-control line are related to their respective stability boundaries in this plane.« less

Some issues on modeling atmospheric turbulence experienced by helicopter rotor blades

NASA Technical Reports Server (NTRS)

Costello, Mark; Gaonkar, G. H.; Prasad, J. V. R.; Schrage, D. P.

1992-01-01

The atmospheric turbulence velocities seen by nonrotating aircraft components and rotating blades can be substantially different. The differences are due to the spatial motion of the rotor blades, which move fore and aft through the gust waves. Body-fixed atmospheric turbulence refers to the actual atmospheric turbulence experienced by a point fixed on a nonrotating aircraft component such as the aircraft's center of gravity or the rotor hub, while blade-fixed atmospheric turbulence refers to the atmospheric turbulence experienced by an element of the rotating rotor blade. An example is presented, which, though overly simplified, shows important differences between blade- and body-fixed rotorcraft atmospheric turbulence models. All of the information necessary to develop the dynamic equations describing the atmospheric turbulence velocity field experienced by an aircraft is contained in the atmospheric turbulence velocity correlation matrix. It is for this reason that a generalized formulation of the correlation matrix describing atmospheric turbulence that a rotating blade encounters is developed. From this correlation matrix, earlier treated cases restricted to a rotor flying straight and level directly into the mean wind can be recovered as special cases.

A solution to Schroder's equation in several variables

DOE PAGES

Bridges, Robert A.

2016-03-04

For this paper, let φ be an analytic self-map of the n -ball, having 0 as the attracting fixed point and having full-rank near 0. We consider the generalized Schroder's equation, F °φ=φ'(0) kF with ka positive integer and prove there is always a solution F with linearly independent component functions, but that such an F cannot have full rank except possibly when k=1. Furthermore, when k=1 (Schroder's equation), necessary and sufficient conditions on φ are given to ensure F has full rank near 0 without the added assumption of diagonalizability as needed in the 2003 Cowen/MacCluer paper. In responsemore » to Enoch's 2007 paper, it is proven that any formal power series solution indeed represents an analytic function on the whole unit ball. Finally, how exactly resonance can lead to an obstruction of a full rank solution is discussed as well as some consequences of having solutions to Schroder's equation.« less

Simplified stock markets described by number operators

NASA Astrophysics Data System (ADS)

Bagarello, F.

2009-06-01

In this paper we continue our systematic analysis of the operatorial approach previously proposed in an economical context and we discuss a mixed toy model of a simplified stock market, i.e. a model in which the price of the shares is given as an input. We deduce the time evolution of the portfolio of the various traders of the market, as well as of other observable quantities. As in a previous paper, we solve the equations of motion by means of a fixed point like approximation.

Causal structure of oscillations in gene regulatory networks: Boolean analysis of ordinary differential equation attractors.

PubMed

Sun, Mengyang; Cheng, Xianrui; Socolar, Joshua E S

2013-06-01

A common approach to the modeling of gene regulatory networks is to represent activating or repressing interactions using ordinary differential equations for target gene concentrations that include Hill function dependences on regulator gene concentrations. An alternative formulation represents the same interactions using Boolean logic with time delays associated with each network link. We consider the attractors that emerge from the two types of models in the case of a simple but nontrivial network: a figure-8 network with one positive and one negative feedback loop. We show that the different modeling approaches give rise to the same qualitative set of attractors with the exception of a possible fixed point in the ordinary differential equation model in which concentrations sit at intermediate values. The properties of the attractors are most easily understood from the Boolean perspective, suggesting that time-delay Boolean modeling is a useful tool for understanding the logic of regulatory networks.

Some Remarks on GMRES for Transport Theory

NASA Technical Reports Server (NTRS)

Patton, Bruce W.; Holloway, James Paul

2003-01-01

We review some work on the application of GMRES to the solution of the discrete ordinates transport equation in one-dimension. We note that GMRES can be applied directly to the angular flux vector, or it can be applied to only a vector of flux moments as needed to compute the scattering operator of the transport equation. In the former case we illustrate both the delights and defects of ILU right-preconditioners for problems with anisotropic scatter and for problems with upscatter. When working with flux moments we note that GMRES can be used as an accelerator for any existing transport code whose solver is based on a stationary fixed-point iteration, including transport sweeps and DSA transport sweeps. We also provide some numerical illustrations of this idea. We finally show how space can be traded for speed by taking multiple transport sweeps per GMRES iteration. Key Words: transport equation, GMRES, Krylov subspace

Convergence of discrete Aubry–Mather model in the continuous limit

NASA Astrophysics Data System (ADS)

Su, Xifeng; Thieullen, Philippe

2018-05-01

We develop two approximation schemes for solving the cell equation and the discounted cell equation using Aubry–Mather–Fathi theory. The Hamiltonian is supposed to be Tonelli, time-independent and periodic in space. By Legendre transform it is equivalent to find a fixed point of some nonlinear operator, called Lax-Oleinik operator, which may be discounted or not. By discretizing in time, we are led to solve an additive eigenvalue problem involving a discrete Lax–Oleinik operator. We show how to approximate the effective Hamiltonian and some weak KAM solutions by letting the time step in the discrete model tend to zero. We also obtain a selected discrete weak KAM solution as in Davini et al (2016 Invent. Math. 206 29–55), and show that it converges to a particular solution of the cell equation. In order to unify the two settings, continuous and discrete, we develop a more general formalism of the short-range interactions.

Floating-to-Fixed-Point Conversion for Digital Signal Processors

NASA Astrophysics Data System (ADS)

Menard, Daniel; Chillet, Daniel; Sentieys, Olivier

2006-12-01

Digital signal processing applications are specified with floating-point data types but they are usually implemented in embedded systems with fixed-point arithmetic to minimise cost and power consumption. Thus, methodologies which establish automatically the fixed-point specification are required to reduce the application time-to-market. In this paper, a new methodology for the floating-to-fixed point conversion is proposed for software implementations. The aim of our approach is to determine the fixed-point specification which minimises the code execution time for a given accuracy constraint. Compared to previous methodologies, our approach takes into account the DSP architecture to optimise the fixed-point formats and the floating-to-fixed-point conversion process is coupled with the code generation process. The fixed-point data types and the position of the scaling operations are optimised to reduce the code execution time. To evaluate the fixed-point computation accuracy, an analytical approach is used to reduce the optimisation time compared to the existing methods based on simulation. The methodology stages are described and several experiment results are presented to underline the efficiency of this approach.

Will there be again a transition from acceleration to deceleration in course of the dark energy evolution of the universe?

NASA Astrophysics Data System (ADS)

Pan, Supriya; Chakraborty, Subenoy

2013-09-01

In this work we consider the evolution of the interactive dark fluids in the background of homogeneous and isotropic FRW model of the universe. The dark fluids consist of a warm dark matter and a dark energy and both are described as perfect fluid with barotropic equation of state. The dark species interact non-gravitationally through an additional term in the energy conservation equations. An autonomous system is formed in the energy density spaces and fixed points are analyzed. A general expression for the deceleration parameter has been obtained and it is possible to have more than one zero of the deceleration parameter. Finally, vanishing of the deceleration parameter has been examined with some examples.

Application of chaos theory to the particle dynamics of asymmetry-induced transport

NASA Astrophysics Data System (ADS)

Eggleston, D. L.

2018-03-01

The techniques of chaos theory are employed in an effort to better understand the complex single-particle dynamics of asymmetry-induced transport in non-neutral plasmas. The dynamical equations are re-conceptualized as describing time-independent trajectories in a four-dimensional space consisting of the radius r, rotating frame angle ψ, axial position z, and axial velocity v. Results include the identification of an integral of the motion, fixed-point analysis of the dynamical equations, the construction and interpretation of Poincaré sections to visualize the dynamics, and, for the case of chaotic motion, numerical calculation of the largest Lyapunov exponent. Chaotic cases are shown to be associated with the overlap of resonance islands formed by the applied asymmetry.

A fast dynamic grid adaption scheme for meteorological flows

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

Fiedler, B.H.; Trapp, R.J.

1993-10-01

The continuous dynamic grid adaption (CDGA) technique is applied to a compressible, three-dimensional model of a rising thermal. The computational cost, per grid point per time step, of using CDGA instead of a fixed, uniform Cartesian grid is about 53% of the total cost of the model with CDGA. The use of general curvilinear coordinates contributes 11.7% to this total, calculating and moving the grid 6.1%, and continually updating the transformation relations 20.7%. Costs due to calculations that involve the gridpoint velocities (as well as some substantial unexplained costs) contribute the remaining 14.5%. A simple way to limit the costmore » of calculating the grid is presented. The grid is adapted by solving an elliptic equation for gridpoint coordinates on a coarse grid and then interpolating the full finite-difference grid. In this application, the additional costs per grid point of CDGA are shown to be easily offset by the savings resulting from the reduction in the required number of grid points. In simulation of the thermal costs are reduced by a factor of 3, as compared with those of a companion model with a fixed, uniform Cartesian grid. 8 refs., 8 figs.« less

Selection of floating-point or fixed-point for adaptive noise canceller in somatosensory evoked potential measurement.

PubMed

Shen, Chongfei; Liu, Hongtao; Xie, Xb; Luk, Keith Dk; Hu, Yong

2007-01-01

Adaptive noise canceller (ANC) has been used to improve signal to noise ratio (SNR) of somsatosensory evoked potential (SEP). In order to efficiently apply the ANC in hardware system, fixed-point algorithm based ANC can achieve fast, cost-efficient construction, and low-power consumption in FPGA design. However, it is still questionable whether the SNR improvement performance by fixed-point algorithm is as good as that by floating-point algorithm. This study is to compare the outputs of ANC by floating-point and fixed-point algorithm ANC when it was applied to SEP signals. The selection of step-size parameter (micro) was found different in fixed-point algorithm from floating-point algorithm. In this simulation study, the outputs of fixed-point ANC showed higher distortion from real SEP signals than that of floating-point ANC. However, the difference would be decreased with increasing micro value. In the optimal selection of micro, fixed-point ANC can get as good results as floating-point algorithm.

Model Comparison of Nonlinear Structural Equation Models with Fixed Covariates.

ERIC Educational Resources Information Center

Lee, Sik-Yum; Song, Xin-Yuan

2003-01-01

Proposed a new nonlinear structural equation model with fixed covariates to deal with some complicated substantive theory and developed a Bayesian path sampling procedure for model comparison. Illustrated the approach with an illustrative example using data from an international study. (SLD)

The QCD Equation of state and critical end-point estimates at O (μB6)

NASA Astrophysics Data System (ADS)

Sharma, Sayantan; Bielefeld-BNL-CCNU Collaboration

2017-11-01

We present results for the QCD Equation of State at non-zero chemical potentials corresponding to the conserved charges in QCD using Taylor expansion upto sixth order in the baryon number, electric charge and strangeness chemical potentials. The latter two are constrained by the strangeness neutrality and a fixed electric charge to baryon number ratio. In our calculations, we use the Highly Improved Staggered Quarks (HISQ) discretization scheme at physical quark masses and at different values of the lattice spacings to control lattice cut-off effects. Furthermore we calculate the pressure along lines of constant energy density, which serve as proxies for the freeze-out conditions and discuss their dependence on μB, which is necessary for hydrodynamic modelling near freezeout. We also provide an estimate of the radius of convergence of the Taylor series from the 6th order coefficients which provides a new constraint on the location of the critical end-point in the T-μB plane of the QCD phase diagram.

Breaking of scale invariance in the time dependence of correlation functions in isotropic and homogeneous turbulence

NASA Astrophysics Data System (ADS)

Tarpin, Malo; Canet, Léonie; Wschebor, Nicolás

2018-05-01

In this paper, we present theoretical results on the statistical properties of stationary, homogeneous, and isotropic turbulence in incompressible flows in three dimensions. Within the framework of the non-perturbative renormalization group, we derive a closed renormalization flow equation for a generic n-point correlation (and response) function for large wave-numbers with respect to the inverse integral scale. The closure is obtained from a controlled expansion and relies on extended symmetries of the Navier-Stokes field theory. It yields the exact leading behavior of the flow equation at large wave-numbers |p→ i| and for arbitrary time differences ti in the stationary state. Furthermore, we obtain the form of the general solution of the corresponding fixed point equation, which yields the analytical form of the leading wave-number and time dependence of n-point correlation functions, for large wave-numbers and both for small ti and in the limit ti → ∞. At small ti, the leading contribution at large wave-numbers is logarithmically equivalent to -α (ɛL ) 2 /3|∑tip→ i|2, where α is a non-universal constant, L is the integral scale, and ɛ is the mean energy injection rate. For the 2-point function, the (tp)2 dependence is known to originate from the sweeping effect. The derived formula embodies the generalization of the effect of sweeping to n-point correlation functions. At large wave-numbers and large ti, we show that the ti2 dependence in the leading order contribution crosses over to a |ti| dependence. The expression of the correlation functions in this regime was not derived before, even for the 2-point function. Both predictions can be tested in direct numerical simulations and in experiments.

Collapsed heteroclinic snaking near a heteroclinic chain in dragged meniscus problems.

PubMed

Tseluiko, D; Galvagno, M; Thiele, U

2014-04-01

A liquid film is studied that is deposited onto a flat plate that is inclined at a constant angle to the horizontal and is extracted from a liquid bath at a constant speed. We analyse steady-state solutions of a long-wave evolution equation for the film thickness. Using centre manifold theory, we first obtain an asymptotic expansion of solutions in the bath region. The presence of an additional temperature gradient along the plate that induces a Marangoni shear stress significantly changes these expansions and leads to the presence of logarithmic terms that are absent otherwise. Next, we numerically obtain steady solutions and analyse their behaviour as the plate velocity is changed. We observe that the bifurcation curve exhibits collapsed (or exponential) heteroclinic snaking when the plate inclination angle is above a certain critical value. Otherwise, the bifurcation curve is monotonic. The steady profiles along these curves are characterised by a foot-like structure that is formed close to the meniscus and is preceded by a thin precursor film further up the plate. The length of the foot increases along the bifurcation curve. Finally, we prove with a Shilnikov-type method that the snaking behaviour of the bifurcation curves is caused by the existence of an infinite number of heteroclinic orbits close to a heteroclinic chain that connects in an appropriate three-dimensional phase space the fixed point corresponding to the precursor film with the fixed point corresponding to the foot and then with the fixed point corresponding to the bath.

The renormalization group method in statistical hydrodynamics

NASA Astrophysics Data System (ADS)

Eyink, Gregory L.

1994-09-01

This paper gives a first principles formulation of a renormalization group (RG) method appropriate to study of turbulence in incompressible fluids governed by Navier-Stokes equations. The present method is a momentum-shell RG of Kadanoff-Wilson type based upon the Martin-Siggia-Rose (MSR) field-theory formulation of stochastic dynamics. A simple set of diagrammatic rules are developed which are exact within perturbation theory (unlike the well-known Ma-Mazenko prescriptions). It is also shown that the claim of Yakhot and Orszag (1986) is false that higher-order terms are irrelevant in the ɛ expansion RG for randomly forced Navier-Stokes (RFNS) with power-law force spectrum F̂(k)=D0k-d+(4-ɛ). In fact, as a consequence of Galilei covariance, there are an infinite number of higher-order nonlinear terms marginal by power counting in the RG analysis of the power-law RFNS, even when ɛ≪4. The difficulty does not occur in the Forster-Nelson-Stephen (FNS) RG analysis of thermal fluctuations in an equilibrium NS fluid, which justifies a linear regression law for d≳2. On the other hand, the problem occurs also at the nontrivial fixed point in the FNS Model A, or its Burgers analog, when d<2. The marginal terms can still be present at the strong-coupling fixed point in true NS turbulence. If so, infinitely many fixed points may exist in turbulence and be associated to a somewhat surprising phenomenon: nonuniversality of the inertial-range scaling laws depending upon the dissipation-range dynamics.

The Simple Map for a Single-null Divertor Tokamak: How to Find the Footprint of Field lines

NASA Astrophysics Data System (ADS)

Figgins, Montoya; Ali, Halima; Punjabi, Alkesh

2000-10-01

We are working with the Simple Map^1 to find the footprint of field lines on the diverter plate in a single-null tokamak. Footprint of a field line is the position of the line when it escapes across the divertor plate. The Simple Map represents the magnetic field in a single-null divertor tokamak. The path of a field line is given by the equations: X_n+1=X_n-kY_n(1-Y_n) and Y_n+1=Y_n+kX_n+1. In order to find the footprint, we must first find the last good surface which is Y=0.997135768 and X=0. The value of k is fixed at 0.6. The starting values X0 are fixed at X_0=0. We use 10,000 points between the last good surface and the X-point. The X-point is located at (0,1). We also use the Continuous Analog of the Simple Map given by the equations: X(φ)=X_0-kY0 (1-Y_0)φ and Y(φ)=Y_0+kX(φ)φ. This will tell us what the (φ,X) is which represents the field lines crossing the divertor plate. The divertor plate is located at Y=1. When graphed, the footprint of field lines looks like the rings of Saturn. This work is supported by US DOES OFES. Ms. Montoya Figgins is HU CFRT Summer Fusion High School Scholar from E. E. Smith High School in North Carolina. She is supported by NASA under its NASA SHARP Plus Program. 1. Punjabi A, Verma A, and Boozer A, Phys Rev Lett, 69, 3322 (1992) and J Plasma Phys, 52, 91 (1994)

The effect of Cr, Co, Al, Mo and Ta on a series of cast Ni-base superalloys on the stability of an aluminide coating during cyclic oxidation in Mach 0.3 burner rig

NASA Technical Reports Server (NTRS)

Zaplatynsky, I.; Barrett, C. A.

1986-01-01

The influence of varying the content of Co, Cr, Mo, Ta, and Al in a series of cast Ni-based gamma/gamma'superalloys on the behavior of aluminide coatings was studied in burner rig cyclic oxidation tests at 1100 C. The alloys had nominally fixed levels of Ti, W, Cb, Zr, C, and B. The alloy compositions were based on a full 2(sup 5)-fractional statistical design supplemented by 10 star point alloys and a center point alloy. This full central composite design of 43 alloys plus two additional alloys with extreme Al levels allowed a complete second degree estimating equation to be derived from the 5-compositional variables. The weight change/time data for the coated samples fitted well to the paralinear oxidation model and enabled a modified oxidation attack parameter, K'(sub a) to be derived to rank the alloys and log K' (sub a ) to be used as the dependent variable in the estimating equation to determine the oxidation resistance of the coating as a function of the underlying alloy content. The most protective aluminide coatings are associated with the highest possible base ally contents of CR and Al and at a 4 percent Ta level. The Mo and Co effects interact but at fixed levels of 0, 5, or 10% Co. A 4% Mo level is optimum.

Turbulent compressible fluid: Renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Lučivjanský, T.

2017-03-01

We study a model of fully developed turbulence of a compressible fluid, based on the stochastic Navier-Stokes equation, by means of the field-theoretic renormalization group. In this approach, scaling properties are related to the fixed points of the renormalization group equations. Previous analysis of this model near the real-world space dimension 3 identified a scaling regime [N. V. Antonov et al., Theor. Math. Phys. 110, 305 (1997), 10.1007/BF02630456]. The aim of the present paper is to explore the existence of additional regimes, which could not be found using the direct perturbative approach of the previous work, and to analyze the crossover between different regimes. It seems possible to determine them near the special value of space dimension 4 in the framework of double y and ɛ expansion, where y is the exponent associated with the random force and ɛ =4 -d is the deviation from the space dimension 4. Our calculations show that there exists an additional fixed point that governs scaling behavior. Turbulent advection of a passive scalar (density) field by this velocity ensemble is considered as well. We demonstrate that various correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. The corresponding anomalous exponents, identified as scaling dimensions of certain composite fields, can be systematically calculated as a series in y and ɛ . All calculations are performed in the leading one-loop approximation.

Instantons in Self-Organizing Logic Gates

NASA Astrophysics Data System (ADS)

Bearden, Sean R. B.; Manukian, Haik; Traversa, Fabio L.; Di Ventra, Massimiliano

2018-03-01

Self-organizing logic is a recently suggested framework that allows the solution of Boolean truth tables "in reverse"; i.e., it is able to satisfy the logical proposition of gates regardless to which terminal(s) the truth value is assigned ("terminal-agnostic logic"). It can be realized if time nonlocality (memory) is present. A practical realization of self-organizing logic gates (SOLGs) can be done by combining circuit elements with and without memory. By employing one such realization, we show, numerically, that SOLGs exploit elementary instantons to reach equilibrium points. Instantons are classical trajectories of the nonlinear equations of motion describing SOLGs and connect topologically distinct critical points in the phase space. By linear analysis at those points, we show that these instantons connect the initial critical point of the dynamics, with at least one unstable direction, directly to the final fixed point. We also show that the memory content of these gates affects only the relaxation time to reach the logically consistent solution. Finally, we demonstrate, by solving the corresponding stochastic differential equations, that, since instantons connect critical points, noise and perturbations may change the instanton trajectory in the phase space but not the initial and final critical points. Therefore, even for extremely large noise levels, the gates self-organize to the correct solution. Our work provides a physical understanding of, and can serve as an inspiration for, models of bidirectional logic gates that are emerging as important tools in physics-inspired, unconventional computing.

Nonlinear Resonance and Duffing's Spring Equation

ERIC Educational Resources Information Center

Fay, Temple H.

2006-01-01

This note discusses the boundary in the frequency--amplitude plane for boundedness of solutions to the forced spring Duffing type equation. For fixed initial conditions and fixed parameter [epsilon] results are reported of a systematic numerical investigation on the global stability of solutions to the initial value problem as the parameters F and…

Is scale-invariance in gauge-Yukawa systems compatible with the graviton?

NASA Astrophysics Data System (ADS)

Christiansen, Nicolai; Eichhorn, Astrid; Held, Aaron

2017-10-01

We explore whether perturbative interacting fixed points in matter systems can persist under the impact of quantum gravity. We first focus on semisimple gauge theories and show that the leading order gravity contribution evaluated within the functional Renormalization Group framework preserves the perturbative fixed-point structure in these models discovered in [J. K. Esbensen, T. A. Ryttov, and F. Sannino, Phys. Rev. D 93, 045009 (2016)., 10.1103/PhysRevD.93.045009]. We highlight that the quantum-gravity contribution alters the scaling dimension of the gauge coupling, such that the system exhibits an effective dimensional reduction. We secondly explore the effect of metric fluctuations on asymptotically safe gauge-Yukawa systems which feature an asymptotically safe fixed point [D. F. Litim and F. Sannino, J. High Energy Phys. 12 (2014) 178., 10.1007/JHEP12(2014)178]. The same effective dimensional reduction that takes effect in pure gauge theories also impacts gauge-Yukawa systems. There, it appears to lead to a split of the degenerate free fixed point into an interacting infrared attractive fixed point and a partially ultraviolet attractive free fixed point. The quantum-gravity induced infrared fixed point moves towards the asymptotically safe fixed point of the matter system, and annihilates it at a critical value of the gravity coupling. Even after that fixed-point annihilation, graviton effects leave behind new partially interacting fixed points for the matter sector.

Computational simulations of vocal fold vibration: Bernoulli versus Navier-Stokes.

PubMed

Decker, Gifford Z; Thomson, Scott L

2007-05-01

The use of the mechanical energy (ME) equation for fluid flow, an extension of the Bernoulli equation, to predict the aerodynamic loading on a two-dimensional finite element vocal fold model is examined. Three steady, one-dimensional ME flow models, incorporating different methods of flow separation point prediction, were compared. For two models, determination of the flow separation point was based on fixed ratios of the glottal area at separation to the minimum glottal area; for the third model, the separation point determination was based on fluid mechanics boundary layer theory. Results of flow rate, separation point, and intraglottal pressure distribution were compared with those of an unsteady, two-dimensional, finite element Navier-Stokes model. Cases were considered with a rigid glottal profile as well as with a vibrating vocal fold. For small glottal widths, the three ME flow models yielded good predictions of flow rate and intraglottal pressure distribution, but poor predictions of separation location. For larger orifice widths, the ME models were poor predictors of flow rate and intraglottal pressure, but they satisfactorily predicted separation location. For the vibrating vocal fold case, all models resulted in similar predictions of mean intraglottal pressure, maximum orifice area, and vibration frequency, but vastly different predictions of separation location and maximum flow rate.

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

Critical behavior of reduced QED4 ,3 and dynamical fermion gap generation in graphene

NASA Astrophysics Data System (ADS)

Kotikov, A. V.; Teber, S.

2016-12-01

The dynamical generation of a fermion gap in graphene is studied at the infra-red Lorentz-invariant fixed point where the system is described by an effective relativistic-like field theory: reduced QED4 ,3 with N four-component fermions (N =2 for graphene), where photons are (3 +1 ) dimensional and mediate a fully retarded interaction among (2 +1 )-dimensional fermions. A correspondence between reduced QED4 ,3 and QED3 allows us to derive an exact gap equation for QED4 ,3 up to next-to-leading order. Our results show that a dynamical gap is generated for α >αc, where 1.03 <αc<1.08 in the case N =2 or for N

Predator prey oscillations in a simple cascade model of drift wave turbulence

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

Berionni, V.; Guercan, Oe. D.

2011-11-15

A reduced three shell limit of a simple cascade model of drift wave turbulence, which emphasizes nonlocal interactions with a large scale mode, is considered. It is shown to describe both the well known predator prey dynamics between the drift waves and zonal flows and to reduce to the standard three wave interaction equations. Here, this model is considered as a dynamical system whose characteristics are investigated. The analytical solutions for the purely nonlinear limit are given in terms of the Jacobi elliptic functions. An approximate analytical solution involving Jacobi elliptic functions and exponential growth is computed using scale separationmore » for the case of unstable solutions that are observed when the energy injection rate is high. The fixed points of the system are determined, and the behavior around these fixed points is studied. The system is shown to display periodic solutions corresponding to limit cycle oscillations, apparently chaotic phase space orbits, as well as unstable solutions that grow slowly while oscillating rapidly. The period doubling route to transition to chaos is examined.« less

Phase-plane analysis of the totally asymmetric simple exclusion process with binding kinetics and switching between antiparallel lanes

PubMed Central

Kuan, Hui-Shun; Betterton, Meredith D.

2016-01-01

Motor protein motion on biopolymers can be described by models related to the totally asymmetric simple exclusion process (TASEP). Inspired by experiments on the motion of kinesin-4 motors on antiparallel microtubule overlaps, we analyze a model incorporating the TASEP on two antiparallel lanes with binding kinetics and lane switching. We determine the steady-state motor density profiles using phase-plane analysis of the steady-state mean field equations and kinetic Monte Carlo simulations. We focus on the density-density phase plane, where we find an analytic solution to the mean field model. By studying the phase-space flows, we determine the model’s fixed points and their changes with parameters. Phases previously identified for the single-lane model occur for low switching rate between lanes. We predict a multiple coexistence phase due to additional fixed points that appear as the switching rate increases: switching moves motors from the higher-density to the lower-density lane, causing local jamming and creating multiple domain walls. We determine the phase diagram of the model for both symmetric and general boundary conditions. PMID:27627345

Comparative Study of Two InGaAs-Based Reference Radiation Thermometers

NASA Astrophysics Data System (ADS)

Nasibov, H.; Diril, A.; Pehlivan, O.; Kalemci, M.

2017-07-01

More than one decade ago, an InGaAs detector-based transfer standard infrared radiation thermometer working in the temperature range from 150 {^{circ }}\\hbox {C} to 1100 {^{circ }}\\hbox {C} was built at TUBITAK UME in the scope of collaboration with IMGC (INRIM since 2006). During this timescale, the radiation thermometer was used for the dissemination of the radiation temperature scale below the silver fixed-point temperature. Recently, a new radiation thermometer with the same design but with different spectral responsivity was constructed and employed in the laboratory. In this work, we present the comparative study of these thermometers. Furthermore, the paper describes the measurement results of the thermometer's main characteristics such as the size-of-source effect, spectral responsivity, gain ratio, and linearity. Besides, both thermometers were calibrated at the freezing temperatures of indium, tin, zinc, aluminum, and copper reference fixed-point blackbodies. The main study is focused on the impact of the spectral responsivity of thermometers on the interpolation parameters of the Sakuma-Hattori equation. Furthermore, the calibration results and the uncertainty sources are discussed in this paper.

Algebraic solution for the forward displacement analysis of the general 6-6 stewart mechanism

NASA Astrophysics Data System (ADS)

Wei, Feng; Wei, Shimin; Zhang, Ying; Liao, Qizheng

2016-01-01

The solution for the forward displacement analysis(FDA) of the general 6-6 Stewart mechanism(i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane) has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra(CGA). The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Gröbner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Gröbner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9´9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix.

47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.

Code of Federal Regulations, 2013 CFR

2013-10-01

... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations. Private...

47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.

Code of Federal Regulations, 2011 CFR

2011-10-01

... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations. Private...

47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.

Code of Federal Regulations, 2012 CFR

2012-10-01

... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations. Private...

47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.

Code of Federal Regulations, 2014 CFR

2014-10-01

... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations. Private...

47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.

Code of Federal Regulations, 2010 CFR

2010-10-01

... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations. Private...

Dynamic reduction with applications to mathematical biology and other areas.

PubMed

Sacker, Robert J; Von Bremen, Hubertus F

2007-10-01

In a difference or differential equation one is usually interested in finding solutions having certain properties, either intrinsic properties (e.g. bounded, periodic, almost periodic) or extrinsic properties (e.g. stable, asymptotically stable, globally asymptotically stable). In certain instances it may happen that the dependence of these equations on the state variable is such that one may (1) alter that dependency by replacing part of the state variable by a function from a class having some of the above properties and (2) solve the 'reduced' equation for a solution having the remaining properties and lying in the same class. This then sets up a mapping Τ of the class into itself, thus reducing the original problem to one of finding a fixed point of the mapping. The procedure is applied to obtain a globally asymptotically stable periodic solution for a system of difference equations modeling the interaction of wild and genetically altered mosquitoes in an environment yielding periodic parameters. It is also shown that certain coupled periodic systems of difference equations may be completely decoupled so that the mapping Τ is established by solving a set of scalar equations. Periodic difference equations of extended Ricker type and also rational difference equations with a finite number of delays are also considered by reducing them to equations without delays but with a larger period. Conditions are given guaranteeing the existence and global asymptotic stability of periodic solutions.

New matrix bounds and iterative algorithms for the discrete coupled algebraic Riccati equation

NASA Astrophysics Data System (ADS)

Liu, Jianzhou; Wang, Li; Zhang, Juan

2017-11-01

The discrete coupled algebraic Riccati equation (DCARE) has wide applications in control theory and linear system. In general, for the DCARE, one discusses every term of the coupled term, respectively. In this paper, we consider the coupled term as a whole, which is different from the recent results. When applying eigenvalue inequalities to discuss the coupled term, our method has less error. In terms of the properties of special matrices and eigenvalue inequalities, we propose several upper and lower matrix bounds for the solution of DCARE. Further, we discuss the iterative algorithms for the solution of the DCARE. In the fixed point iterative algorithms, the scope of Lipschitz factor is wider than the recent results. Finally, we offer corresponding numerical examples to illustrate the effectiveness of the derived results.

Nonlinear Resonance and Duffing's Spring Equation II

ERIC Educational Resources Information Center

Fay, T. H.; Joubert, Stephan V.

2007-01-01

The paper discusses the boundary in the frequency-amplitude plane for boundedness of solutions to the forced spring Duffing type equation x[umlaut] + x + [epsilon]x[cubed] = F cos[omega]t. For fixed initial conditions and for representative fixed values of the parameter [epsilon], the results are reported of a systematic numerical investigation…

Highly eccentric hip-hop solutions of the 2 N-body problem

NASA Astrophysics Data System (ADS)

Barrabés, Esther; Cors, Josep M.; Pinyol, Conxita; Soler, Jaume

2010-02-01

We show the existence of families of hip-hop solutions in the equal-mass 2 N-body problem which are close to highly eccentric planar elliptic homographic motions of 2 N bodies plus small perpendicular non-harmonic oscillations. By introducing a parameter ɛ, the homographic motion and the small amplitude oscillations can be uncoupled into a purely Keplerian homographic motion of fixed period and a vertical oscillation described by a Hill type equation. Small changes in the eccentricity induce large variations in the period of the perpendicular oscillation and give rise, via a Bolzano argument, to resonant periodic solutions of the uncoupled system in a rotating frame. For small ɛ≠0, the topological transversality persists and Brouwer’s fixed point theorem shows the existence of this kind of solutions in the full system.

Optimal Harvesting in a Periodic Food Chain Model with Size Structures in Predators

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

Zhang, Feng-Qin, E-mail: zhafq@263.net; Liu, Rong; Chen, Yuming, E-mail: ychen@wlu.ca

In this paper, we investigate a periodic food chain model with harvesting, where the predators have size structures and are described by first-order partial differential equations. First, we establish the existence of a unique non-negative solution by using the Banach fixed point theorem. Then, we provide optimality conditions by means of normal cone and adjoint system. Finally, we derive the existence of an optimal strategy by means of Ekeland’s variational principle. Here the objective functional represents the net economic benefit yielded from harvesting.

Scaling for the SOL/separatrix χ ⊥ following from the heuristic drift model for the power scrape-off layer width

NASA Astrophysics Data System (ADS)

Huber, A.; Chankin, A. V.

2017-06-01

A simple two-point representation of the tokamak scrape-off layer (SOL) in the conduction limited regime, based on the parallel and perpendicular energy balance equations in combination with the heat flux width predicted by a heuristic drift-based model, was used to derive a scaling for the cross-field thermal diffusivity {χ }\\perp . For fixed plasma shape and neglecting weak power dependence indexes 1/8, the scaling {χ }\\perp \\propto {P}{{S}{{O}}{{L}}}/(n{B}θ {R}2) is derived.

Cosmology of a covariant Galilean field.

PubMed

De Felice, Antonio; Tsujikawa, Shinji

2010-09-10

We study the cosmology of a covariant scalar field respecting a Galilean symmetry in flat space-time. We show the existence of a tracker solution that finally approaches a de Sitter fixed point responsible for cosmic acceleration today. The viable region of model parameters is clarified by deriving conditions under which ghosts and Laplacian instabilities of scalar and tensor perturbations are absent. The field equation of state exhibits a peculiar phantomlike behavior along the tracker, which allows a possibility to observationally distinguish the Galileon gravity from the cold dark matter model with a cosmological constant.

Stability properties of a general class of nonlinear dynamical systems

NASA Astrophysics Data System (ADS)

Gléria, I. M.; Figueiredo, A.; Rocha Filho, T. M.

2001-05-01

We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format.

Differential geometry based solvation model. III. Quantum formulation

PubMed Central

Chen, Zhan; Wei, Guo-Wei

2011-01-01

Solvation is of fundamental importance to biomolecular systems. Implicit solvent models, particularly those based on the Poisson-Boltzmann equation for electrostatic analysis, are established approaches for solvation analysis. However, ad hoc solvent-solute interfaces are commonly used in the implicit solvent theory. Recently, we have introduced differential geometry based solvation models which allow the solvent-solute interface to be determined by the variation of a total free energy functional. Atomic fixed partial charges (point charges) are used in our earlier models, which depends on existing molecular mechanical force field software packages for partial charge assignments. As most force field models are parameterized for a certain class of molecules or materials, the use of partial charges limits the accuracy and applicability of our earlier models. Moreover, fixed partial charges do not account for the charge rearrangement during the solvation process. The present work proposes a differential geometry based multiscale solvation model which makes use of the electron density computed directly from the quantum mechanical principle. To this end, we construct a new multiscale total energy functional which consists of not only polar and nonpolar solvation contributions, but also the electronic kinetic and potential energies. By using the Euler-Lagrange variation, we derive a system of three coupled governing equations, i.e., the generalized Poisson-Boltzmann equation for the electrostatic potential, the generalized Laplace-Beltrami equation for the solvent-solute boundary, and the Kohn-Sham equations for the electronic structure. We develop an iterative procedure to solve three coupled equations and to minimize the solvation free energy. The present multiscale model is numerically validated for its stability, consistency and accuracy, and is applied to a few sets of molecules, including a case which is difficult for existing solvation models. Comparison is made to many other classic and quantum models. By using experimental data, we show that the present quantum formulation of our differential geometry based multiscale solvation model improves the prediction of our earlier models, and outperforms some explicit solvation model. PMID:22112067

Euler/Navier-Stokes calculations of transonic flow past fixed- and rotary-wing aircraft configurations

NASA Technical Reports Server (NTRS)

Deese, J. E.; Agarwal, R. K.

1989-01-01

Computational fluid dynamics has an increasingly important role in the design and analysis of aircraft as computer hardware becomes faster and algorithms become more efficient. Progress is being made in two directions: more complex and realistic configurations are being treated and algorithms based on higher approximations to the complete Navier-Stokes equations are being developed. The literature indicates that linear panel methods can model detailed, realistic aircraft geometries in flow regimes where this approximation is valid. As algorithms including higher approximations to the Navier-Stokes equations are developed, computer resource requirements increase rapidly. Generation of suitable grids become more difficult and the number of grid points required to resolve flow features of interest increases. Recently, the development of large vector computers has enabled researchers to attempt more complex geometries with Euler and Navier-Stokes algorithms. The results of calculations for transonic flow about a typical transport and fighter wing-body configuration using thin layer Navier-Stokes equations are described along with flow about helicopter rotor blades using both Euler/Navier-Stokes equations.

Computational Study of Chaotic and Ordered Solutions of the Kuramoto-Sivashinsky Equation

NASA Technical Reports Server (NTRS)

Smyrlis, Yiorgos S.; Papageorgiou, Demetrios T.

1996-01-01

We report the results of extensive numerical experiments on the Kuramoto-Sivashinsky equation in the strongly chaotic regime as the viscosity parameter is decreased and increasingly more linearly unstable modes enter the dynamics. General initial conditions are used and evolving states do not assume odd-parity. A large number of numerical experiments are employed in order to obtain quantitative characteristics of the dynamics. We report on different routes to chaos and provide numerical evidence and construction of strange attractors with self-similar characteristics. As the 'viscosity' parameter decreases the dynamics becomes increasingly more complicated and chaotic. In particular it is found that regular behavior in the form of steady state or steady state traveling waves is supported amidst the time-dependent and irregular motions. We show that multimodal steady states emerge and are supported on decreasing windows in parameter space. In addition we invoke a self-similarity property of the equation, to show that these profiles are obtainable from global fixed point attractors of the Kuramoto-Sivashinsky equation at much larger values of the viscosity.

Wall shear stress fixed points in blood flow

NASA Astrophysics Data System (ADS)

Arzani, Amirhossein; Shadden, Shawn

2017-11-01

Patient-specific computational fluid dynamics produces large datasets, and wall shear stress (WSS) is one of the most important parameters due to its close connection with the biological processes at the wall. While some studies have investigated WSS vectorial features, the WSS fixed points have not received much attention. In this talk, we will discuss the importance of WSS fixed points from three viewpoints. First, we will review how WSS fixed points relate to the flow physics away from the wall. Second, we will discuss how certain types of WSS fixed points lead to high biochemical surface concentration in cardiovascular mass transport problems. Finally, we will introduce a new measure to track the exposure of endothelial cells to WSS fixed points.

Effect of Impurities on the Freezing Point of Zinc

NASA Astrophysics Data System (ADS)

Sun, Jianping; Rudtsch, Steffen; Niu, Yalu; Zhang, Lin; Wang, Wei; Den, Xiaolong

2017-03-01

The knowledge of the liquidus slope of impurities in fixed-point metal defined by the International Temperature Scale of 1990 is important for the estimation of uncertainties and correction of fixed point with the sum of individual estimates method. Great attentions are paid to the effect of ultra-trace impurities on the freezing point of zinc in the National Institute of Metrology. In the present work, the liquidus slopes of Ga-Zn, Ge-Zn were measured with the slim fixed-point cell developed through the doping experiments, and the temperature characteristics of the phase diagram of Fe-Zn were furthermore investigated. A quasi-adiabatic Zn fixed-point cell was developed with the thermometer well surrounded by the crucible with the pure metal, and the temperature uniformity of less than 20 mK in the region where the metal is located was obtained. The previous doping experiment of Pb-Zn with slim fixed-point cell was checked with quasi-adiabatic Zn fixed-point cell, and the result supports the previous liquidus slope measured with the traditional fixed-point realization.

Amplitudes on plane waves from ambitwistor strings

NASA Astrophysics Data System (ADS)

Adamo, Tim; Casali, Eduardo; Mason, Lionel; Nekovar, Stefan

2017-11-01

In marked contrast to conventional string theory, ambitwistor strings remain solvable worldsheet theories when coupled to curved background fields. We use this fact to consider the quantization of ambitwistor strings on plane wave metric and plane wave gauge field backgrounds. In each case, the worldsheet model is anomaly free as a consequence of the background satisfying the field equations. We derive vertex operators (in both fixed and descended picture numbers) for gravitons and gluons on these backgrounds from the worldsheet CFT, and study the 3-point functions of these vertex operators on the Riemann sphere. These worldsheet correlation functions reproduce the known results for 3-point scattering amplitudes of gravitons and gluons in gravitational and gauge theoretic plane wave backgrounds, respectively.

Development of Advanced Methods of Structural and Trajectory Analysis for Transport Aircraft

NASA Technical Reports Server (NTRS)

Ardema, Mark D.; Windhorst, Robert; Phillips, James

1998-01-01

This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.

Optimization of Supersonic Transport Trajectories

NASA Technical Reports Server (NTRS)

Ardema, Mark D.; Windhorst, Robert; Phillips, James

1998-01-01

This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.

Uncovering novel phase structures in \\Box ^k scalar theories with the renormalization group

NASA Astrophysics Data System (ADS)

Safari, M.; Vacca, G. P.

2018-03-01

We present a detailed version of our recent work on the RG approach to multicritical scalar theories with higher derivative kinetic term φ (-\\Box )^kφ and upper critical dimension d_c = 2nk/(n-1). Depending on whether the numbers k and n have a common divisor two classes of theories have been distinguished. For coprime k and n-1 the theory admits a Wilson-Fisher type fixed point. We derive in this case the RG equations of the potential and compute the scaling dimensions and some OPE coefficients, mostly at leading order in ɛ . While giving new results, the critical data we provide are compared, when possible, and accord with a recent alternative approach using the analytic structure of conformal blocks. Instead when k and n-1 have a common divisor we unveil a novel interacting structure at criticality. \\Box ^2 theories with odd n, which fall in this class, are analyzed in detail. Using the RG flows it is shown that a derivative interaction is unavoidable at the critical point. In particular there is an infrared fixed point with a pure derivative interaction at which we compute the scaling dimensions and, for the particular example of \\Box ^2 theory in d_c=6, also some OPE coefficients.

TESS: A RELATIVISTIC HYDRODYNAMICS CODE ON A MOVING VORONOI MESH

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

Duffell, Paul C.; MacFadyen, Andrew I., E-mail: pcd233@nyu.edu, E-mail: macfadyen@nyu.edu

2011-12-01

We have generalized a method for the numerical solution of hyperbolic systems of equations using a dynamic Voronoi tessellation of the computational domain. The Voronoi tessellation is used to generate moving computational meshes for the solution of multidimensional systems of conservation laws in finite-volume form. The mesh-generating points are free to move with arbitrary velocity, with the choice of zero velocity resulting in an Eulerian formulation. Moving the points at the local fluid velocity makes the formulation effectively Lagrangian. We have written the TESS code to solve the equations of compressible hydrodynamics and magnetohydrodynamics for both relativistic and non-relativistic fluidsmore » on a dynamic Voronoi mesh. When run in Lagrangian mode, TESS is significantly less diffusive than fixed mesh codes and thus preserves contact discontinuities to high precision while also accurately capturing strong shock waves. TESS is written for Cartesian, spherical, and cylindrical coordinates and is modular so that auxiliary physics solvers are readily integrated into the TESS framework and so that this can be readily adapted to solve general systems of equations. We present results from a series of test problems to demonstrate the performance of TESS and to highlight some of the advantages of the dynamic tessellation method for solving challenging problems in astrophysical fluid dynamics.« less

Common fixed points in best approximation for Banach operator pairs with Ciric type I-contractions

NASA Astrophysics Data System (ADS)

Hussain, N.

2008-02-01

The common fixed point theorems, similar to those of Ciric [Lj.B. Ciric, On a common fixed point theorem of a Gregus type, Publ. Inst. Math. (Beograd) (N.S.) 49 (1991) 174-178; Lj.B. Ciric, On Diviccaro, Fisher and Sessa open questions, Arch. Math. (Brno) 29 (1993) 145-152; Lj.B. Ciric, On a generalization of Gregus fixed point theorem, Czechoslovak Math. J. 50 (2000) 449-458], Fisher and Sessa [B. Fisher, S. Sessa, On a fixed point theorem of Gregus, Internat. J. Math. Math. Sci. 9 (1986) 23-28], Jungck [G. Jungck, On a fixed point theorem of Fisher and Sessa, Internat. J. Math. Math. Sci. 13 (1990) 497-500] and Mukherjee and Verma [R.N. Mukherjee, V. Verma, A note on fixed point theorem of Gregus, Math. Japon. 33 (1988) 745-749], are proved for a Banach operator pair. As applications, common fixed point and approximation results for Banach operator pair satisfying Ciric type contractive conditions are obtained without the assumption of linearity or affinity of either T or I. Our results unify and generalize various known results to a more general class of noncommuting mappings.

Miniature Fixed Points as Temperature Standards for In Situ Calibration of Temperature Sensors

NASA Astrophysics Data System (ADS)

Hao, X. P.; Sun, J. P.; Xu, C. Y.; Wen, P.; Song, J.; Xu, M.; Gong, L. Y.; Ding, L.; Liu, Z. L.

2017-06-01

Miniature Ga and Ga-In alloy fixed points as temperature standards are developed at National Institute of Metrology, China for the in situ calibration of temperature sensors. A quasi-adiabatic vacuum measurement system is constructed to study the phase-change plateaus of the fixed points. The system comprises a high-stability bath, a quasi-adiabatic vacuum chamber and a temperature control and measurement system. The melting plateau of the Ga fixed point is longer than 2 h at 0.008 W. The standard deviation of the melting temperature of the Ga and Ga-In alloy fixed points is better than 2 mK. The results suggest that the melting temperature of the Ga or Ga-In alloy fixed points is linearly related with the heating power.

Transport equations of electrodiffusion processes in the laboratory reference frame.

PubMed

Garrido, Javier

2006-02-23

The transport equations of electrodiffusion processes use three reference frames for defining the fluxes: Fick's reference in diffusion, solvent-fixed reference in transference numbers, and laboratory fluxes in electric conductivity. The convenience of using only one reference frame is analyzed here from the point of view of the thermodynamics of irreversible processes. A relation between the fluxes of ions and solvent and the electric current density is deduced first from a mass and volume balance. This is then used to show that (i) the laboratory and Fick's diffusion coefficients are identical and (ii) the transference numbers of both the solvent and the ion in the laboratory reference frame are related. Finally, four experimental methods for the measurement of ion transference numbers are analyzed critically. New expressions for evaluating transference numbers for the moving boundary method and the chronopotentiometry technique are deduced. It is concluded that the ion transport equation in the laboratory reference frame plays a key role in the description of electrodiffusion processes.

Bifurcation Analysis and Nonlinear Decay of a Tumor in the Presence of an Immune Response

NASA Astrophysics Data System (ADS)

López, Álvaro G.; Seoane, Jesús M.; Sanjuán, Miguel A. F.

2017-12-01

The decay of a planar compact surface that is reduced through its boundary is considered. The interest of this problem lies in the fact that it can represent the destruction of a solid tumor by a population of immune cells. The theory of curves is utilized to derive the rate at which the area of the set decreases. Firstly, the process is represented as a discrete dynamical system. A recurrence equation describing the shrinkage of the area at any step is deduced. Then, a continuum limit is attained to derive an ordinary differential equation that governs the decay of the set. The solutions to the differential equation and its implications are discussed, and numerical simulations are carried out to test the accuracy of the decay law. Finally, the dynamics of a tumor-immune aggregate is inspected using this law and the theory of bifurcations. As the ratio of immune destruction to tumor growth increases, a saddle-node bifurcation stabilizes the tumor-free fixed point.

Wall shear stress fixed points in cardiovascular fluid mechanics.

PubMed

Arzani, Amirhossein; Shadden, Shawn C

2018-05-17

Complex blood flow in large arteries creates rich wall shear stress (WSS) vectorial features. WSS acts as a link between blood flow dynamics and the biology of various cardiovascular diseases. WSS has been of great interest in a wide range of studies and has been the most popular measure to correlate blood flow to cardiovascular disease. Recent studies have emphasized different vectorial features of WSS. However, fixed points in the WSS vector field have not received much attention. A WSS fixed point is a point on the vessel wall where the WSS vector vanishes. In this article, WSS fixed points are classified and the aspects by which they could influence cardiovascular disease are reviewed. First, the connection between WSS fixed points and the flow topology away from the vessel wall is discussed. Second, the potential role of time-averaged WSS fixed points in biochemical mass transport is demonstrated using the recent concept of Lagrangian WSS structures. Finally, simple measures are proposed to quantify the exposure of the endothelial cells to WSS fixed points. Examples from various arterial flow applications are demonstrated. Copyright © 2018 Elsevier Ltd. All rights reserved.

On the stability and dynamics of stochastic spiking neuron models: Nonlinear Hawkes process and point process GLMs

PubMed Central

Truccolo, Wilson

2017-01-01

Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a stability framework for data-driven PP-GLMs and shed new light on the stochastic dynamics of state-of-the-art statistical models of neuronal spiking activity. PMID:28234899

On the stability and dynamics of stochastic spiking neuron models: Nonlinear Hawkes process and point process GLMs.

PubMed

Gerhard, Felipe; Deger, Moritz; Truccolo, Wilson

2017-02-01

Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a stability framework for data-driven PP-GLMs and shed new light on the stochastic dynamics of state-of-the-art statistical models of neuronal spiking activity.

Beyond Poisson-Boltzmann: Fluctuation effects and correlation functions

NASA Astrophysics Data System (ADS)

Netz, R. R.; Orland, H.

2000-02-01

We formulate the exact non-linear field theory for a fluctuating counter-ion distribution in the presence of a fixed, arbitrary charge distribution. The Poisson-Boltzmann equation is obtained as the saddle-point of the field-theoretic action, and the effects of counter-ion fluctuations are included by a loop-wise expansion around this saddle point. The Poisson equation is obeyed at each order in this loop expansion. We explicitly give the expansion of the Gibbs potential up to two loops. We then apply our field-theoretic formalism to the case of a single impenetrable wall with counter ions only (in the absence of salt ions). We obtain the fluctuation corrections to the electrostatic potential and the counter-ion density to one-loop order without further approximations. The relative importance of fluctuation corrections is controlled by a single parameter, which is proportional to the cube of the counter-ion valency and to the surface charge density. The effective interactions and correlation functions between charged particles close to the charged wall are obtained on the one-loop level.

Thin-plate spline quadrature of geodetic integrals

NASA Technical Reports Server (NTRS)

Vangysen, Herman

1989-01-01

Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in the analytical continuation solution of Molodensky's problem. These rules are exact for interpolating thin-plate splines. In cases where the integration data are distributed irregularly, a system of linear equations needs to be solved for the quadrature coefficients. Formulae are given for the terms appearing in these equations. In case the data are regularly distributed, the coefficients may be determined once-and-for-all. Examples are given of some fixed-point rules. With such rules successive evaluation, within a circular disk, of the terms in Molodensky's series becomes relatively easy. The spline quadrature technique presented complements other techniques such as ring integration for intermediate integration zones.

Accelerated perturbation-resilient block-iterative projection methods with application to image reconstruction

PubMed Central

Nikazad, T; Davidi, R; Herman, G. T.

2013-01-01

We study the convergence of a class of accelerated perturbation-resilient block-iterative projection methods for solving systems of linear equations. We prove convergence to a fixed point of an operator even in the presence of summable perturbations of the iterates, irrespective of the consistency of the linear system. For a consistent system, the limit point is a solution of the system. In the inconsistent case, the symmetric version of our method converges to a weighted least squares solution. Perturbation resilience is utilized to approximate the minimum of a convex functional subject to the equations. A main contribution, as compared to previously published approaches to achieving similar aims, is a more than an order of magnitude speed-up, as demonstrated by applying the methods to problems of image reconstruction from projections. In addition, the accelerated algorithms are illustrated to be better, in a strict sense provided by the method of statistical hypothesis testing, than their unaccelerated versions for the task of detecting small tumors in the brain from X-ray CT projection data. PMID:23440911

Accelerated perturbation-resilient block-iterative projection methods with application to image reconstruction.

PubMed

Nikazad, T; Davidi, R; Herman, G T

2012-03-01

We study the convergence of a class of accelerated perturbation-resilient block-iterative projection methods for solving systems of linear equations. We prove convergence to a fixed point of an operator even in the presence of summable perturbations of the iterates, irrespective of the consistency of the linear system. For a consistent system, the limit point is a solution of the system. In the inconsistent case, the symmetric version of our method converges to a weighted least squares solution. Perturbation resilience is utilized to approximate the minimum of a convex functional subject to the equations. A main contribution, as compared to previously published approaches to achieving similar aims, is a more than an order of magnitude speed-up, as demonstrated by applying the methods to problems of image reconstruction from projections. In addition, the accelerated algorithms are illustrated to be better, in a strict sense provided by the method of statistical hypothesis testing, than their unaccelerated versions for the task of detecting small tumors in the brain from X-ray CT projection data.

A Numerical Study of Three Moving-Grid Methods for One-Dimensional Partial Differential Equations Which Are Based on the Method of Lines

NASA Astrophysics Data System (ADS)

Furzeland, R. M.; Verwer, J. G.; Zegeling, P. A.

1990-08-01

In recent years, several sophisticated packages based on the method of lines (MOL) have been developed for the automatic numerical integration of time-dependent problems in partial differential equations (PDEs), notably for problems in one space dimension. These packages greatly benefit from the very successful developments of automatic stiff ordinary differential equation solvers. However, from the PDE point of view, they integrate only in a semiautomatic way in the sense that they automatically adjust the time step sizes, but use just a fixed space grid, chosen a priori, for the entire calculation. For solutions possessing sharp spatial transitions that move, e.g., travelling wave fronts or emerging boundary and interior layers, a grid held fixed for the entire calculation is computationally inefficient, since for a good solution this grid often must contain a very large number of nodes. In such cases methods which attempt automatically to adjust the sizes of both the space and the time steps are likely to be more successful in efficiently resolving critical regions of high spatial and temporal activity. Methods and codes that operate this way belong to the realm of adaptive or moving-grid methods. Following the MOL approach, this paper is devoted to an evaluation and comparison, mainly based on extensive numerical tests, of three moving-grid methods for 1D problems, viz., the finite-element method of Miller and co-workers, the method published by Petzold, and a method based on ideas adopted from Dorfi and Drury. Our examination of these three methods is aimed at assessing which is the most suitable from the point of view of retaining the acknowledged features of reliability, robustness, and efficiency of the conventional MOL approach. Therefore, considerable attention is paid to the temporal performance of the methods.

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow

NASA Astrophysics Data System (ADS)

Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M.

2018-02-01

The nonequilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed nonplanar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. We observe that the anisotropic hydrodynamics is able to match up to high numerical accuracy the attractor of the exact solution while the second-order hydrodynamical theories fail to describe it. We show that the IS and DNMR asymptotic series expansions diverge and use resurgence techniques to perform the resummation of these divergences. We also comment on a possible link between the manifold of steepest descent paths in path integrals and the basin of attraction for the attractors via Lyapunov functions that opens a new horizon toward an effective field theory description of hydrodynamics. Our findings indicate that the reorganization of the expansion series carried out by anisotropic hydrodynamics resums the Knudsen and inverse Reynolds numbers to all orders and thus, it can be understood as an effective theory for the far-from-equilibrium fluid dynamics.

47 CFR 101.101 - Frequency availability.

Code of Federal Regulations, 2012 CFR

2012-10-01

... Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE...—(Part 78) CC: Common Carrier Fixed Point-to-Point Microwave Service—(Part 101, Subparts C & I) DBS... Distribution Service—(Part 21) OFS: Private Operational Fixed Point-to-Point Microwave Service—(Part 101...

47 CFR 101.101 - Frequency availability.

Code of Federal Regulations, 2013 CFR

2013-10-01

... Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE...—(Part 78) CC: Common Carrier Fixed Point-to-Point Microwave Service—(Part 101, Subparts C & I) DBS... Distribution Service—(Part 21) OFS: Private Operational Fixed Point-to-Point Microwave Service—(Part 101...

47 CFR 101.21 - Technical content of applications.

Code of Federal Regulations, 2013 CFR

2013-10-01

... SERVICES FIXED MICROWAVE SERVICES Applications and Licenses General Filing Requirements § 101.21 Technical... Private Operational Fixed Point-to-Point Microwave Service and the Common Carrier Fixed Point-to-Point Microwave Service must include the following information: Applicant's name and address. Transmitting station...

47 CFR 101.21 - Technical content of applications.

Code of Federal Regulations, 2014 CFR

2014-10-01

... SERVICES FIXED MICROWAVE SERVICES Applications and Licenses General Filing Requirements § 101.21 Technical... Private Operational Fixed Point-to-Point Microwave Service and the Common Carrier Fixed Point-to-Point Microwave Service must include the following information: Applicant's name and address. Transmitting station...

47 CFR 101.107 - Frequency tolerance.

Code of Federal Regulations, 2011 CFR

2011-10-01

... Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE... to private operational fixed point-to-point microwave and stations providing MVDDS. 5 For private operational fixed point-to-point microwave systems, with a channel greater than or equal to 50 KHz bandwidth...

47 CFR 101.101 - Frequency availability.

Code of Federal Regulations, 2014 CFR

2014-10-01

... Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE...—(Part 78) CC: Common Carrier Fixed Point-to-Point Microwave Service—(Part 101, Subparts C & I) DBS... Distribution Service—(Part 21) OFS: Private Operational Fixed Point-to-Point Microwave Service—(Part 101...

Seeking fixed points in multiple coupling scalar theories in the ɛ expansion

NASA Astrophysics Data System (ADS)

Osborn, Hugh; Stergiou, Andreas

2018-05-01

Fixed points for scalar theories in 4 - ɛ, 6 - ɛ and 3 - ɛ dimensions are discussed. It is shown how a large range of known fixed points for the four dimensional case can be obtained by using a general framework with two couplings. The original maximal symmetry, O( N), is broken to various subgroups, both discrete and continuous. A similar discussion is applied to the six dimensional case. Perturbative applications of the a-theorem are used to help classify potential fixed points. At lowest order in the ɛ-expansion it is shown that at fixed points there is a lower bound for a which is saturated at bifurcation points.

Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data.

PubMed

van Maanen, Leendert; Couto, Joaquina; Lebreton, Mael

2016-01-01

The notion of "mixtures" has become pervasive in behavioral and cognitive sciences, due to the success of dual-process theories of cognition. However, providing support for such dual-process theories is not trivial, as it crucially requires properties in the data that are specific to mixture of cognitive processes. In theory, one such property could be the fixed-point property of binary mixture data, applied-for instance- to response times. In that case, the fixed-point property entails that response time distributions obtained in an experiment in which the mixture proportion is manipulated would have a common density point. In the current article, we discuss the application of the fixed-point property and identify three boundary conditions under which the fixed-point property will not be interpretable. In Boundary condition 1, a finding in support of the fixed-point will be mute because of a lack of difference between conditions. Boundary condition 2 refers to the case in which the extreme conditions are so different that a mixture may display bimodality. In this case, a mixture hypothesis is clearly supported, yet the fixed-point may not be found. In Boundary condition 3 the fixed-point may also not be present, yet a mixture might still exist but is occluded due to additional changes in behavior. Finding the fixed-property provides strong support for a dual-process account, yet the boundary conditions that we identify should be considered before making inferences about underlying psychological processes.

Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data

PubMed Central

Couto, Joaquina; Lebreton, Mael

2016-01-01

The notion of “mixtures” has become pervasive in behavioral and cognitive sciences, due to the success of dual-process theories of cognition. However, providing support for such dual-process theories is not trivial, as it crucially requires properties in the data that are specific to mixture of cognitive processes. In theory, one such property could be the fixed-point property of binary mixture data, applied–for instance- to response times. In that case, the fixed-point property entails that response time distributions obtained in an experiment in which the mixture proportion is manipulated would have a common density point. In the current article, we discuss the application of the fixed-point property and identify three boundary conditions under which the fixed-point property will not be interpretable. In Boundary condition 1, a finding in support of the fixed-point will be mute because of a lack of difference between conditions. Boundary condition 2 refers to the case in which the extreme conditions are so different that a mixture may display bimodality. In this case, a mixture hypothesis is clearly supported, yet the fixed-point may not be found. In Boundary condition 3 the fixed-point may also not be present, yet a mixture might still exist but is occluded due to additional changes in behavior. Finding the fixed-property provides strong support for a dual-process account, yet the boundary conditions that we identify should be considered before making inferences about underlying psychological processes. PMID:27893868

47 CFR 101.21 - Technical content of applications.

Code of Federal Regulations, 2010 CFR

2010-10-01

... SERVICES FIXED MICROWAVE SERVICES Applications and Licenses General Filing Requirements § 101.21 Technical...) [Reserved] (e) Each application in the Private Operational Fixed Point-to-Point Microwave Service and the Common Carrier Fixed Point-to-Point Microwave Service must include the following information: Applicant's...

47 CFR 101.5 - Station authorization required.

Code of Federal Regulations, 2014 CFR

2014-10-01

... SERVICES FIXED MICROWAVE SERVICES Applications and Licenses General Filing Requirements § 101.5 Station... stations authorized under subpart H (Private Operational Fixed Point-to-Point Microwave Service), subpart I (Common Carrier Fixed Point-to-Point Microwave Service), and subpart L of this part (Local Multipoint...

47 CFR 101.5 - Station authorization required.

Code of Federal Regulations, 2010 CFR

2010-10-01

... SERVICES FIXED MICROWAVE SERVICES Applications and Licenses General Filing Requirements § 101.5 Station... stations authorized under subpart H (Private Operational Fixed Point-to-Point Microwave Service), subpart I (Common Carrier Fixed Point-to-Point Microwave Service), and subpart L of this part (Local Multipoint...

47 CFR 101.21 - Technical content of applications.

Code of Federal Regulations, 2011 CFR

2011-10-01

... SERVICES FIXED MICROWAVE SERVICES Applications and Licenses General Filing Requirements § 101.21 Technical...) [Reserved] (e) Each application in the Private Operational Fixed Point-to-Point Microwave Service and the Common Carrier Fixed Point-to-Point Microwave Service must include the following information: Applicant's...

47 CFR 101.21 - Technical content of applications.

Code of Federal Regulations, 2012 CFR

2012-10-01

... SERVICES FIXED MICROWAVE SERVICES Applications and Licenses General Filing Requirements § 101.21 Technical...) [Reserved] (e) Each application in the Private Operational Fixed Point-to-Point Microwave Service and the Common Carrier Fixed Point-to-Point Microwave Service must include the following information: Applicant's...

47 CFR 101.5 - Station authorization required.

Code of Federal Regulations, 2013 CFR

2013-10-01

... SERVICES FIXED MICROWAVE SERVICES Applications and Licenses General Filing Requirements § 101.5 Station... stations authorized under subpart H (Private Operational Fixed Point-to-Point Microwave Service), subpart I (Common Carrier Fixed Point-to-Point Microwave Service), and subpart L of this part (Local Multipoint...

47 CFR 101.5 - Station authorization required.

Code of Federal Regulations, 2012 CFR

2012-10-01

... SERVICES FIXED MICROWAVE SERVICES Applications and Licenses General Filing Requirements § 101.5 Station... stations authorized under subpart H (Private Operational Fixed Point-to-Point Microwave Service), subpart I (Common Carrier Fixed Point-to-Point Microwave Service), and subpart L of this part (Local Multipoint...

47 CFR 101.5 - Station authorization required.

Code of Federal Regulations, 2011 CFR

2011-10-01

... SERVICES FIXED MICROWAVE SERVICES Applications and Licenses General Filing Requirements § 101.5 Station... stations authorized under subpart H (Private Operational Fixed Point-to-Point Microwave Service), subpart I (Common Carrier Fixed Point-to-Point Microwave Service), and subpart L of this part (Local Multipoint...

Homogenization of Winkler-Steklov spectral conditions in three-dimensional linear elasticity

NASA Astrophysics Data System (ADS)

Gómez, D.; Nazarov, S. A.; Pérez, M. E.

2018-04-01

We consider a homogenization Winkler-Steklov spectral problem that consists of the elasticity equations for a three-dimensional homogeneous anisotropic elastic body which has a plane part of the surface subject to alternating boundary conditions on small regions periodically placed along the plane. These conditions are of the Dirichlet type and of the Winkler-Steklov type, the latter containing the spectral parameter. The rest of the boundary of the body is fixed, and the period and size of the regions, where the spectral parameter arises, are of order ɛ . For fixed ɛ , the problem has a discrete spectrum, and we address the asymptotic behavior of the eigenvalues {β _k^ɛ }_{k=1}^{∞} as ɛ → 0. We show that β _k^ɛ =O(ɛ ^{-1}) for each fixed k, and we observe a common limit point for all the rescaled eigenvalues ɛ β _k^ɛ while we make it evident that, although the periodicity of the structure only affects the boundary conditions, a band-gap structure of the spectrum is inherited asymptotically. Also, we provide the asymptotic behavior for certain "groups" of eigenmodes.

Fixed-ratio discrimination: effects of response-produced blackouts1

PubMed Central

Lydersen, Tore; Crossman, E. K.

1974-01-01

For three pigeons, reinforcement depended upon a left side-key response after execution of a fixed ratio 10 on the center key, and upon a right side-key response after fixed ratio 20. Each response during the fixed ratios produced a 0.5-sec blackout. The time between the first and last response in fixed ratio 10 was then equated with the time between the first and last response in fixed ratio 20 by increasing the blackout duration. The accuracy of side-key choice was disrupted, thereby suggesting that time, rather than number of responses, controlled choice responding. When the time between the first and last response was equated during both ratios, asymptotic accuracy was approximately equal to (two birds) or somewhat higher than (one bird) that obtained previously. The results of probes with intermediate fixed ratios and blackouts suggested that control of side-key choice had transferred from the time between the first and last response in ratios to blackout duration. PMID:16811819

Mixed Spin-1/2 and Spin-5/2 Model by Renormalization Group Theory: Recursion Equations and Thermodynamic Study

NASA Astrophysics Data System (ADS)

Antari, A. El; Zahir, H.; Hasnaoui, A.; Hachem, N.; Alrajhi, A.; Madani, M.; Bouziani, M. El

2018-04-01

Using the renormalization group approximation, specifically the Migdal-Kadanoff technique, we investigate the Blume-Capel model with mixed spins S = 1/2 and S = 5/2 on d-dimensional hypercubic lattice. The flow in the parameter space of the Hamiltonian and the thermodynamic functions are determined. The phase diagram of this model is plotted in the (anisotropy, temperature) plane for both cases d = 2 and d = 3 in which the system exhibits the first and second order phase transitions and critical end-points. The associated fixed points are drawn up in a table, and by linearizing the transformation at the vicinity of these points, we determine the critical exponents for d = 2 and d = 3. We have also presented a variation of the free energy derivative at the vicinity of the first and second order transitions. Finally, this work is completed by a discussion and comparison with other approximation.

Multilevel Dynamic Generalized Structured Component Analysis for Brain Connectivity Analysis in Functional Neuroimaging Data.

PubMed

Jung, Kwanghee; Takane, Yoshio; Hwang, Heungsun; Woodward, Todd S

2016-06-01

We extend dynamic generalized structured component analysis (GSCA) to enhance its data-analytic capability in structural equation modeling of multi-subject time series data. Time series data of multiple subjects are typically hierarchically structured, where time points are nested within subjects who are in turn nested within a group. The proposed approach, named multilevel dynamic GSCA, accommodates the nested structure in time series data. Explicitly taking the nested structure into account, the proposed method allows investigating subject-wise variability of the loadings and path coefficients by looking at the variance estimates of the corresponding random effects, as well as fixed loadings between observed and latent variables and fixed path coefficients between latent variables. We demonstrate the effectiveness of the proposed approach by applying the method to the multi-subject functional neuroimaging data for brain connectivity analysis, where time series data-level measurements are nested within subjects.

Non-linear vibrating systems excited by a nonideal energy source with a large slope characteristic

NASA Astrophysics Data System (ADS)

González-Carbajal, Javier; Domínguez, Jaime

2017-11-01

This paper revisits the problem of an unbalanced motor attached to a fixed frame by means of a nonlinear spring and a linear damper. The excitation provided by the motor is, in general, nonideal, which means it is affected by the vibratory response. Since the system behaviour is highly dependent on the order of magnitude of the motor characteristic slope, the case of large slope is considered herein. Some Perturbation Methods are applied to the system of equations, which allows transforming the original 4D system into a much simpler 2D system. The fixed points of this reduced system and their stability are carefully studied. We find the existence of a Hopf bifurcation which, to the authors' knowledge, has not been addressed before in the literature. These analytical results are supported by numerical simulations. We also compare our approach and results with those published by other authors.

Theoretical study of the incompressible Navier-Stokes equations by the least-squares method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Loh, Ching Y.; Povinelli, Louis A.

1994-01-01

Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis.

A new solution procedure for a nonlinear infinite beam equation of motion

NASA Astrophysics Data System (ADS)

Jang, T. S.

2016-10-01

Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.

Renormalization group equations and the Lifshitz point in noncommutative Landau-Ginsburg theory

NASA Astrophysics Data System (ADS)

Chen, Guang-Hong; Wu, Yong-Shi

2002-02-01

A one-loop renormalization group (RG) analysis is performed for noncommutative Landau-Ginsburg theory in an arbitrary dimension. We adopt a modern version of the Wilsonian RG approach, in which a shell integration in momentum space bypasses the potential IR singularities due to UV-IR mixing. The momentum-dependent trigonometric factors in interaction vertices, characteristic of noncommutative geometry, are marginal under RG transformations, and their marginality is preserved at one loop. A negative Θ-dependent anomalous dimension is discovered as a novel effect of the UV-IR mixing. We also found a noncommutative Wilson-Fisher (NCWF) fixed point in less than four dimensions. At large noncommutativity, a momentum space instability is induced by quantum fluctuations, and a consequential first-order phase transition is identified together with a Lifshitz point in the phase diagram. In the vicinity of the Lifshitz point, we introduce two critical exponents νm and βk, whose values are determined to be 1/4 and 1/2, respectively, at mean-field level.

Dynamic Analysis of a Reaction-Diffusion Rumor Propagation Model

NASA Astrophysics Data System (ADS)

Zhao, Hongyong; Zhu, Linhe

2016-06-01

The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. Rumor propagation in social networks has brought new challenges to network security and social stability. This paper, based on partial differential equations (PDEs), proposes a new SIS rumor propagation model by considering the effect of the communication between the different rumor infected users on rumor propagation. The stabilities of a nonrumor equilibrium point and a rumor-spreading equilibrium point are discussed by linearization technique and the upper and lower solutions method, and the existence of a traveling wave solution is established by the cross-iteration scheme accompanied by the technique of upper and lower solutions and Schauder’s fixed point theorem. Furthermore, we add the time delay to rumor propagation and deduce the conditions of Hopf bifurcation and stability switches for the rumor-spreading equilibrium point by taking the time delay as the bifurcation parameter. Finally, numerical simulations are performed to illustrate the theoretical results.

Arbitrary Steady-State Solutions with the K-epsilon Model

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.; Pettersson Reif, B. A.; Gatski, Thomas B.

2006-01-01

Widely-used forms of the K-epsilon turbulence model are shown to yield arbitrary steady-state converged solutions that are highly dependent on numerical considerations such as initial conditions and solution procedure. These solutions contain pseudo-laminar regions of varying size. By applying a nullcline analysis to the equation set, it is possible to clearly demonstrate the reasons for the anomalous behavior. In summary, the degenerate solution acts as a stable fixed point under certain conditions, causing the numerical method to converge there. The analysis also suggests a methodology for preventing the anomalous behavior in steady-state computations.

Square Turing patterns in reaction-diffusion systems with coupled layers

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

Li, Jing; Wang, Hongli, E-mail: hlwang@pku.edu.cn, E-mail: qi@pku.edu.cn; Center for Quantitative Biology, Peking University, Beijing 100871

Square Turing patterns are usually unstable in reaction-diffusion systems and are rarely observed in corresponding experiments and simulations. We report here an example of spontaneous formation of square Turing patterns with the Lengyel-Epstein model of two coupled layers. The squares are found to be a result of the resonance between two supercritical Turing modes with an appropriate ratio. Besides, the spatiotemporal resonance of Turing modes resembles to the mode-locking phenomenon. Analysis of the general amplitude equations for square patterns reveals that the fixed point corresponding to square Turing patterns is stationary when the parameters adopt appropriate values.

Gradient calculations for dynamic recurrent neural networks: a survey.

PubMed

Pearlmutter, B A

1995-01-01

Surveys learning algorithms for recurrent neural networks with hidden units and puts the various techniques into a common framework. The authors discuss fixed point learning algorithms, namely recurrent backpropagation and deterministic Boltzmann machines, and nonfixed point algorithms, namely backpropagation through time, Elman's history cutoff, and Jordan's output feedback architecture. Forward propagation, an on-line technique that uses adjoint equations, and variations thereof, are also discussed. In many cases, the unified presentation leads to generalizations of various sorts. The author discusses advantages and disadvantages of temporally continuous neural networks in contrast to clocked ones continues with some "tricks of the trade" for training, using, and simulating continuous time and recurrent neural networks. The author presents some simulations, and at the end, addresses issues of computational complexity and learning speed.

Eigensolutions of nonviscously damped systems based on the fixed-point iteration

NASA Astrophysics Data System (ADS)

Lázaro, Mario

2018-03-01

In this paper, nonviscous, nonproportional, symmetric vibrating structures are considered. Nonviscously damped systems present dissipative forces depending on the time history of the response via kernel hereditary functions. Solutions of the free motion equation leads to a nonlinear eigenvalue problem involving mass, stiffness and damping matrices, this latter as dependent on frequency. Viscous damping can be considered as a particular case, involving damping forces as function of the instantaneous velocity of the degrees of freedom. In this work, a new numerical procedure to compute eigensolutions is proposed. The method is based on the construction of certain recursive functions which, under a iterative scheme, allow to reach eigenvalues and eigenvectors simultaneously and avoiding computation of eigensensitivities. Eigenvalues can be read then as fixed-points of those functions. A deep analysis of the convergence is carried out, focusing specially on relating the convergence conditions and error-decay rate to the damping model features, such as the nonproportionality and the viscoelasticity. The method is validated using two 6 degrees of freedom numerical examples involving both nonviscous and viscous damping and a continuous system with a local nonviscous damper. The convergence and the sequences behavior are in agreement with the results foreseen by the theory.

Perturbation analysis of the limit cycle of the free van der Pol equation

NASA Technical Reports Server (NTRS)

Dadfar, M. B.; Geer, J.; Anderson, C. M.

1983-01-01

A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Pade approximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon.

Solution of effective Hamiltonian of impurity hopping between two sites in a metal

NASA Astrophysics Data System (ADS)

Ye, Jinwu

1998-03-01

We analyze in detail all the possible fixed points of the effective Hamiltonian of a non-magnetic impurity hopping between two sites in a metal obtained by Moustakas and Fisher(MF). We find a line of non-fermi liquid fixed points which continuously interpolates between the 2-channel Kondo fixed point(2CK) and the one channel, two impurity Kondo (2IK) fixed point. There is one relevant direction with scaling dimension 1/2 and one leading irrelevant operator with dimension 3/2. There is also one marginal operator in the spin sector moving along this line. The additional non-fermi liquid fixed point found by MF has the same symmetry as the 2IK, it has two relevant directions with scaling dimension 1/2, therefore also unstable. The system is shown to flow to a line of fermi-liquid fixed points which continuously interpolates between the non-interacting fixed point and the 2 channel spin-flavor Kondo fixed point (2CSFK) discussed by the author previously. The effect of particle-hole symmetry breaking is discussed. The effective Hamiltonian in the external magnetic field is analysed. The scaling functions for the physical measurable quantities are derived in the different regimes; their predictions for the experiments are given. Finally the implications are given for a non-magnetic impurity hopping around three sites with triangular symmetry discussed by MF.

Variable Step Integration Coupled with the Method of Characteristics Solution for Water-Hammer Analysis, A Case Study

NASA Technical Reports Server (NTRS)

Turpin, Jason B.

2004-01-01

One-dimensional water-hammer modeling involves the solution of two coupled non-linear hyperbolic partial differential equations (PDEs). These equations result from applying the principles of conservation of mass and momentum to flow through a pipe, and usually the assumption that the speed at which pressure waves propagate through the pipe is constant. In order to solve these equations for the interested quantities (i.e. pressures and flow rates), they must first be converted to a system of ordinary differential equations (ODEs) by either approximating the spatial derivative terms with numerical techniques or using the Method of Characteristics (MOC). The MOC approach is ideal in that no numerical approximation errors are introduced in converting the original system of PDEs into an equivalent system of ODEs. Unfortunately this resulting system of ODEs is bound by a time step constraint so that when integrating the equations the solution can only be obtained at fixed time intervals. If the fluid system to be modeled also contains dynamic components (i.e. components that are best modeled by a system of ODEs), it may be necessary to take extremely small time steps during certain points of the model simulation in order to achieve stability and/or accuracy in the solution. Coupled together, the fixed time step constraint invoked by the MOC, and the occasional need for extremely small time steps in order to obtain stability and/or accuracy, can greatly increase simulation run times. As one solution to this problem, a method for combining variable step integration (VSI) algorithms with the MOC was developed for modeling water-hammer in systems with highly dynamic components. A case study is presented in which reverse flow through a dual-flapper check valve introduces a water-hammer event. The predicted pressure responses upstream of the check-valve are compared with test data.

International Conference on Fixed Point Theory and Applications (Colloque International Theorie Du Point Fixe et Applications)

DTIC Science & Technology

1989-06-09

Theorem and the Perron - Frobenius Theorem in matrix theory. We use the Hahn-Banach theorem and do not use any fixed-point related concepts. 179 A...games defined b’, tions 87 Isac G. Fixed point theorems on convex cones , generalized pseudo-contractive mappings and the omplementarity problem 89...and (II), af(x) ° denotes the negative polar cone ot of(x). This condition are respectively called "inward" and "outward". Indeed, when X is convex

High Agreement was Obtained Across Scores from Multiple Equated Scales for Social Anxiety Disorder using Item Response Theory.

PubMed

Sunderland, Matthew; Batterham, Philip; Calear, Alison; Carragher, Natacha; Baillie, Andrew; Slade, Tim

2018-04-10

There is no standardized approach to the measurement of social anxiety. Researchers and clinicians are faced with numerous self-report scales with varying strengths, weaknesses, and psychometric properties. The lack of standardization makes it difficult to compare scores across populations that utilise different scales. Item response theory offers one solution to this problem via equating different scales using an anchor scale to set a standardized metric. This study is the first to equate several scales for social anxiety disorder. Data from two samples (n=3,175 and n=1,052), recruited from the Australian community using online advertisements, were utilised to equate a network of 11 self-report social anxiety scales via a fixed parameter item calibration method. Comparisons between actual and equated scores for most of the scales indicted a high level of agreement with mean differences <0.10 (equivalent to a mean difference of less than one point on the standardized metric). This study demonstrates that scores from multiple scales that measure social anxiety can be converted to a common scale. Re-scoring observed scores to a common scale provides opportunities to combine research from multiple studies and ultimately better assess social anxiety in treatment and research settings. Copyright © 2018. Published by Elsevier Inc.

Pose-free structure from motion using depth from motion constraints.

PubMed

Zhang, Ji; Boutin, Mireille; Aliaga, Daniel G

2011-10-01

Structure from motion (SFM) is the problem of recovering the geometry of a scene from a stream of images taken from unknown viewpoints. One popular approach to estimate the geometry of a scene is to track scene features on several images and reconstruct their position in 3-D. During this process, the unknown camera pose must also be recovered. Unfortunately, recovering the pose can be an ill-conditioned problem which, in turn, can make the SFM problem difficult to solve accurately. We propose an alternative formulation of the SFM problem with fixed internal camera parameters known a priori. In this formulation, obtained by algebraic variable elimination, the external camera pose parameters do not appear. As a result, the problem is better conditioned in addition to involving much fewer variables. Variable elimination is done in three steps. First, we take the standard SFM equations in projective coordinates and eliminate the camera orientations from the equations. We then further eliminate the camera center positions. Finally, we also eliminate all 3-D point positions coordinates, except for their depths with respect to the camera center, thus obtaining a set of simple polynomial equations of degree two and three. We show that, when there are merely a few points and pictures, these "depth-only equations" can be solved in a global fashion using homotopy methods. We also show that, in general, these same equations can be used to formulate a pose-free cost function to refine SFM solutions in a way that is more accurate than by minimizing the total reprojection error, as done when using the bundle adjustment method. The generalization of our approach to the case of varying internal camera parameters is briefly discussed. © 2011 IEEE

Hybrid state vector methods for structural dynamic and aeroelastic boundary value problems

NASA Technical Reports Server (NTRS)

Lehman, L. L.

1982-01-01

A computational technique is developed that is suitable for performing preliminary design aeroelastic and structural dynamic analyses of large aspect ratio lifting surfaces. The method proves to be quite general and can be adapted to solving various two point boundary value problems. The solution method, which is applicable to both fixed and rotating wing configurations, is based upon a formulation of the structural equilibrium equations in terms of a hybrid state vector containing generalized force and displacement variables. A mixed variational formulation is presented that conveniently yields a useful form for these state vector differential equations. Solutions to these equations are obtained by employing an integrating matrix method. The application of an integrating matrix provides a discretization of the differential equations that only requires solutions of standard linear matrix systems. It is demonstrated that matrix partitioning can be used to reduce the order of the required solutions. Results are presented for several example problems in structural dynamics and aeroelasticity to verify the technique and to demonstrate its use. These problems examine various types of loading and boundary conditions and include aeroelastic analyses of lifting surfaces constructed from anisotropic composite materials.

Neural network based online simultaneous policy update algorithm for solving the HJI equation in nonlinear H∞ control.

PubMed

Wu, Huai-Ning; Luo, Biao

2012-12-01

It is well known that the nonlinear H∞ state feedback control problem relies on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that has proven to be impossible to solve analytically. In this paper, a neural network (NN)-based online simultaneous policy update algorithm (SPUA) is developed to solve the HJI equation, in which knowledge of internal system dynamics is not required. First, we propose an online SPUA which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment. The proposed online SPUA updates control and disturbance policies simultaneously; thus, only one iterative loop is needed. Second, the convergence of the online SPUA is established by proving that it is mathematically equivalent to Newton's method for finding a fixed point in a Banach space. Third, we develop an actor-critic structure for the implementation of the online SPUA, in which only one critic NN is needed for approximating the cost function, and a least-square method is given for estimating the NN weight parameters. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed algorithm.

Validation of a single-stage fixed-rate step test for the prediction of maximal oxygen uptake in healthy adults.

PubMed

Hansen, Dominique; Jacobs, Nele; Thijs, Herbert; Dendale, Paul; Claes, Neree

2016-09-01

Healthcare professionals with limited access to ergospirometry remain in need of valid and simple submaximal exercise tests to predict maximal oxygen uptake (VO2max ). Despite previous validation studies concerning fixed-rate step tests, accurate equations for the estimation of VO2max remain to be formulated from a large sample of healthy adults between age 18-75 years (n > 100). The aim of this study was to develop a valid equation to estimate VO2max from a fixed-rate step test in a larger sample of healthy adults. A maximal ergospirometry test, with assessment of cardiopulmonary parameters and VO2max , and a 5-min fixed-rate single-stage step test were executed in 112 healthy adults (age 18-75 years). During the step test and subsequent recovery, heart rate was monitored continuously. By linear regression analysis, an equation to predict VO2max from the step test was formulated. This equation was assessed for level of agreement by displaying Bland-Altman plots and calculation of intraclass correlations with measured VO2max . Validity further was assessed by employing a Jackknife procedure. The linear regression analysis generated the following equation to predict VO2max (l min(-1) ) from the step test: 0·054(BMI)+0·612(gender)+3·359(body height in m)+0·019(fitness index)-0·012(HRmax)-0·011(age)-3·475. This equation explained 78% of the variance in measured VO2max (F = 66·15, P<0·001). The level of agreement and intraclass correlation was high (ICC = 0·94, P<0·001) between measured and predicted VO2max . From this study, a valid fixed-rate single-stage step test equation has been developed to estimate VO2max in healthy adults. This tool could be employed by healthcare professionals with limited access to ergospirometry. © 2015 Scandinavian Society of Clinical Physiology and Nuclear Medicine. Published by John Wiley & Sons Ltd.

Nonperturbative renormalization group study of the stochastic Navier-Stokes equation.

PubMed

Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

2012-07-01

We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4-2ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.

Guiding brine shrimp through mazes by solving reaction diffusion equations

NASA Astrophysics Data System (ADS)

Singal, Krishma; Fenton, Flavio

Excitable systems driven by reaction diffusion equations have been shown to not only find solutions to mazes but to also to find the shortest path between the beginning and the end of the maze. In this talk we describe how we can use the Fitzhugh-Nagumo model, a generic model for excitable media, to solve a maze by varying the basin of attraction of its two fixed points. We demonstrate how two dimensional mazes are solved numerically using a Java Applet and then accelerated to run in real time by using graphic processors (GPUs). An application of this work is shown by guiding phototactic brine shrimp through a maze solved by the algorithm. Once the path is obtained, an Arduino directs the shrimp through the maze using lights from LEDs placed at the floor of the Maze. This method running in real time could be eventually used for guiding robots and cars through traffic.

Minimal wave speed for a class of non-cooperative reaction-diffusion systems of three equations

NASA Astrophysics Data System (ADS)

Zhang, Tianran

2017-05-01

In this paper, we study the traveling wave solutions and minimal wave speed for a class of non-cooperative reaction-diffusion systems consisting of three equations. Based on the eigenvalues, a pair of upper-lower solutions connecting only the invasion-free equilibrium are constructed and the Schauder's fixed-point theorem is applied to show the existence of traveling semi-fronts for an auxiliary system. Then the existence of traveling semi-fronts of original system is obtained by limit arguments. The traveling semi-fronts are proved to connect another equilibrium if natural birth and death rates are not considered and to be persistent if these rates are incorporated. Then non-existence of bounded traveling semi-fronts is obtained by two-sided Laplace transform. Then the above results are applied to some disease-transmission models and a predator-prey model.

Markov Chain Monte Carlo from Lagrangian Dynamics.

PubMed

Lan, Shiwei; Stathopoulos, Vasileios; Shahbaba, Babak; Girolami, Mark

2015-04-01

Hamiltonian Monte Carlo (HMC) improves the computational e ciency of the Metropolis-Hastings algorithm by reducing its random walk behavior. Riemannian HMC (RHMC) further improves the performance of HMC by exploiting the geometric properties of the parameter space. However, the geometric integrator used for RHMC involves implicit equations that require fixed-point iterations. In some cases, the computational overhead for solving implicit equations undermines RHMC's benefits. In an attempt to circumvent this problem, we propose an explicit integrator that replaces the momentum variable in RHMC by velocity. We show that the resulting transformation is equivalent to transforming Riemannian Hamiltonian dynamics to Lagrangian dynamics. Experimental results suggests that our method improves RHMC's overall computational e ciency in the cases considered. All computer programs and data sets are available online (http://www.ics.uci.edu/~babaks/Site/Codes.html) in order to allow replication of the results reported in this paper.

Exact Solution for Capillary Bridges Properties by Shooting Method

NASA Astrophysics Data System (ADS)

Qiang-Nian, Li; Jia-Qi, Zhang; Feng-Xi, Zhou

2017-04-01

The investigation of liquid bridge force acting between wet particles has great significance in many fields. In this article, the exact solution of capillary force between two unequal-sized spherical particles is investigated. Firstly, The Young-Laplace equation with moving boundary is converted into a set of ordinary differential equations with two fix point boundary using variable substitution technique, in which the gravity effects have been neglected. The geometry of the liquid bridge between two particles is solved by shooting method. After that, the gorge method is applied to calculate the capillary-bridge force that is consists of contributions from the capillary suction and surface tension. Finally, the effect of various parameters including distance between two spheres, radii of spheres, and contact angles on the capillary force are investigated. It is shown that the presented approach is an efficient and accurate algorithm for capillary force between two particles in complex situations.

Homotopy approach to optimal, linear quadratic, fixed architecture compensation

NASA Technical Reports Server (NTRS)

Mercadal, Mathieu

1991-01-01

Optimal linear quadratic Gaussian compensators with constrained architecture are a sensible way to generate good multivariable feedback systems meeting strict implementation requirements. The optimality conditions obtained from the constrained linear quadratic Gaussian are a set of highly coupled matrix equations that cannot be solved algebraically except when the compensator is centralized and full order. An alternative to the use of general parameter optimization methods for solving the problem is to use homotopy. The benefit of the method is that it uses the solution to a simplified problem as a starting point and the final solution is then obtained by solving a simple differential equation. This paper investigates the convergence properties and the limitation of such an approach and sheds some light on the nature and the number of solutions of the constrained linear quadratic Gaussian problem. It also demonstrates the usefulness of homotopy on an example of an optimal decentralized compensator.

A Comparison of Deterministic and Stochastic Modeling Approaches for Biochemical Reaction Systems: On Fixed Points, Means, and Modes.

PubMed

Hahl, Sayuri K; Kremling, Andreas

2016-01-01

In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still expected to provide relevant indications on the underlying dynamics.

The Examination of the Classification of Students into Performance Categories by Two Different Equating Methods

ERIC Educational Resources Information Center

Keller, Lisa A.; Keller, Robert R.; Parker, Pauline A.

2011-01-01

This study investigates the comparability of two item response theory based equating methods: true score equating (TSE), and estimated true equating (ETE). Additionally, six scaling methods were implemented within each equating method: mean-sigma, mean-mean, two versions of fixed common item parameter, Stocking and Lord, and Haebara. Empirical…

Implicit Contractive Mappings in Modular Metric and Fuzzy Metric Spaces

PubMed Central

Hussain, N.; Salimi, P.

2014-01-01

The notion of modular metric spaces being a natural generalization of classical modulars over linear spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, and Calderon-Lozanovskii spaces was recently introduced. In this paper we investigate the existence of fixed points of generalized α-admissible modular contractive mappings in modular metric spaces. As applications, we derive some new fixed point theorems in partially ordered modular metric spaces, Suzuki type fixed point theorems in modular metric spaces and new fixed point theorems for integral contractions. In last section, we develop an important relation between fuzzy metric and modular metric and deduce certain new fixed point results in triangular fuzzy metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results. PMID:25003157

Adaptive moving mesh methods for simulating one-dimensional groundwater problems with sharp moving fronts

USGS Publications Warehouse

Huang, W.; Zheng, Lingyun; Zhan, X.

2002-01-01

Accurate modelling of groundwater flow and transport with sharp moving fronts often involves high computational cost, when a fixed/uniform mesh is used. In this paper, we investigate the modelling of groundwater problems using a particular adaptive mesh method called the moving mesh partial differential equation approach. With this approach, the mesh is dynamically relocated through a partial differential equation to capture the evolving sharp fronts with a relatively small number of grid points. The mesh movement and physical system modelling are realized by solving the mesh movement and physical partial differential equations alternately. The method is applied to the modelling of a range of groundwater problems, including advection dominated chemical transport and reaction, non-linear infiltration in soil, and the coupling of density dependent flow and transport. Numerical results demonstrate that sharp moving fronts can be accurately and efficiently captured by the moving mesh approach. Also addressed are important implementation strategies, e.g. the construction of the monitor function based on the interpolation error, control of mesh concentration, and two-layer mesh movement. Copyright ?? 2002 John Wiley and Sons, Ltd.

A Kronecker product splitting preconditioner for two-dimensional space-fractional diffusion equations

NASA Astrophysics Data System (ADS)

Chen, Hao; Lv, Wen; Zhang, Tongtong

2018-05-01

We study preconditioned iterative methods for the linear system arising in the numerical discretization of a two-dimensional space-fractional diffusion equation. Our approach is based on a formulation of the discrete problem that is shown to be the sum of two Kronecker products. By making use of an alternating Kronecker product splitting iteration technique we establish a class of fixed-point iteration methods. Theoretical analysis shows that the new method converges to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameters and the corresponding asymptotic convergence rate are computed exactly when the eigenvalues of the system matrix are all real. The basic iteration is accelerated by a Krylov subspace method like GMRES. The corresponding preconditioner is in a form of a Kronecker product structure and requires at each iteration the solution of a set of discrete one-dimensional fractional diffusion equations. We use structure preserving approximations to the discrete one-dimensional fractional diffusion operators in the action of the preconditioning matrix. Numerical examples are presented to illustrate the effectiveness of this approach.

Computed torque control of a free-flying cooperat ing-arm robot

NASA Technical Reports Server (NTRS)

Koningstein, Ross; Ullman, Marc; Cannon, Robert H., Jr.

1989-01-01

The unified approach to solving free-floating space robot manipulator end-point control problems is presented using a control formulation based on an extension of computed torque. Once the desired end-point accelerations have been specified, the kinematic equations are used with momentum conservation equations to solve for the joint accelerations in any of the robot's possible configurations: fixed base or free-flying with open/closed chain grasp. The joint accelerations can then be used to calculate the arm control torques and internal forces using a recursive order N algorithm. Initial experimental verification of these techniques has been performed using a laboratory model of a two-armed space robot. This fully autonomous spacecraft system experiences the drag-free, zero G characteristics of space in two dimensions through the use of an air cushion support system. Results of these initial experiments are included which validate the correctness of the proposed methodology. The further problem of control in the large where not only the manipulator tip positions but the entire system consisting of base and arms must be controlled is also presented. The availability of a physical testbed has brought a keener insight into the subtleties of the problem at hand.

H2, fixed architecture, control design for large scale systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Mercadal, Mathieu

1990-01-01

The H2, fixed architecture, control problem is a classic linear quadratic Gaussian (LQG) problem whose solution is constrained to be a linear time invariant compensator with a decentralized processing structure. The compensator can be made of p independent subcontrollers, each of which has a fixed order and connects selected sensors to selected actuators. The H2, fixed architecture, control problem allows the design of simplified feedback systems needed to control large scale systems. Its solution becomes more complicated, however, as more constraints are introduced. This work derives the necessary conditions for optimality for the problem and studies their properties. It is found that the filter and control problems couple when the architecture constraints are introduced, and that the different subcontrollers must be coordinated in order to achieve global system performance. The problem requires the simultaneous solution of highly coupled matrix equations. The use of homotopy is investigated as a numerical tool, and its convergence properties studied. It is found that the general constrained problem may have multiple stabilizing solutions, and that these solutions may be local minima or saddle points for the quadratic cost. The nature of the solution is not invariant when the parameters of the system are changed. Bifurcations occur, and a solution may continuously transform into a nonstabilizing compensator. Using a modified homotopy procedure, fixed architecture compensators are derived for models of large flexible structures to help understand the properties of the constrained solutions and compare them to the corresponding unconstrained ones.

Computation of a controlled store separation from a cavity

NASA Technical Reports Server (NTRS)

Atwood, Christopher A.

1993-01-01

Coupling of the Reynolds-averaged Navier-Stokes equations, rigid-body dynamics, and a pitch attitude control law is demonstrated in two- and three-dimensions. The application problem was the separation of a canard-controlled store from an open-flow rectangular cavity bay at a freestream Mach number of 1.2. The transient flowfield was computed using a diagonal scheme in an overset mesh framework, with the resultant aerodynamic loads used as the forcing functions in the nonlinear dynamics equations. The proportional and rate gyro sensitivities were computed a priori using pole placement techniques for the linearized dynamical equations. These fixed gain values were used in the controller for the nonlinear simulation. Reasonable comparison between the full and linearized equations for a perturbed two-dimensional missile was found. Also in two-dimensions, a controlled store was found to possess improved separation characteristics over a canard-fixed store. In three-dimensions, trajectory comparisons with wind-tunnel data for the canard-fixed case will be made. In addition, it will be determined if a canard-controlled store is an effective means of improving cavity store separation characteristics.

Automated system for measuring temperature profiles inside ITS-90 fixed-point cells

NASA Astrophysics Data System (ADS)

Hiti, Miha; Bojkovski, Jovan; Batagelj, Valentin; Drnovsek, Janko

2005-11-01

The defining fixed points of the International Temperature Scale of 1990 (ITS-90) are temperature reference points for temperature calibration. The measured temperature inside the fixed-point cell depends on thermometer immersion, since measurements are made below the surface of the fixed-point material and the additional effect of the hydrostatic pressure has to be taken into account. Also, the heat flux along the thermometer stem can affect the measured temperature. The paper presents a system that enables accurate and reproducible immersion profile measurements for evaluation of measurement sensitivity and adequacy of thermometer immersion. It makes immersion profile measurements possible, where a great number of repetitions and long measurement periods are required, and reduces the workload on the user for performing such measurements. The system is flexible and portable and was developed for application to existing equipment in the laboratory. Results of immersion profile measurements in a triple point of water fixed-point cell are presented.

Linear Power-Flow Models in Multiphase Distribution Networks: Preprint

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

Bernstein, Andrey; Dall'Anese, Emiliano

This paper considers multiphase unbalanced distribution systems and develops approximate power-flow models where bus-voltages, line-currents, and powers at the point of common coupling are linearly related to the nodal net power injections. The linearization approach is grounded on a fixed-point interpretation of the AC power-flow equations, and it is applicable to distribution systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. The proposed linear models can facilitate the development of computationally-affordable optimization and control applications -- frommore » advanced distribution management systems settings to online and distributed optimization routines. Performance of the proposed models is evaluated on different test feeders.« less

Geometrical and Graphical Solutions of Quadratic Equations.

ERIC Educational Resources Information Center

Hornsby, E. John, Jr.

1990-01-01

Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

Random-Effects Models for Meta-Analytic Structural Equation Modeling: Review, Issues, and Illustrations

ERIC Educational Resources Information Center

Cheung, Mike W.-L.; Cheung, Shu Fai

2016-01-01

Meta-analytic structural equation modeling (MASEM) combines the techniques of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed-effects and random-effects models can be defined in MASEM.…

3D reconstruction of laser projective point with projection invariant generated from five points on 2D target.

PubMed

Xu, Guan; Yuan, Jing; Li, Xiaotao; Su, Jian

2017-08-01

Vision measurement on the basis of structured light plays a significant role in the optical inspection research. The 2D target fixed with a line laser projector is designed to realize the transformations among the world coordinate system, the camera coordinate system and the image coordinate system. The laser projective point and five non-collinear points that are randomly selected from the target are adopted to construct a projection invariant. The closed form solutions of the 3D laser points are solved by the homogeneous linear equations generated from the projection invariants. The optimization function is created by the parameterized re-projection errors of the laser points and the target points in the image coordinate system. Furthermore, the nonlinear optimization solutions of the world coordinates of the projection points, the camera parameters and the lens distortion coefficients are contributed by minimizing the optimization function. The accuracy of the 3D reconstruction is evaluated by comparing the displacements of the reconstructed laser points with the actual displacements. The effects of the image quantity, the lens distortion and the noises are investigated in the experiments, which demonstrate that the reconstruction approach is effective to contribute the accurate test in the measurement system.

A conserved quantity in thin body dynamics

NASA Astrophysics Data System (ADS)

Hanna, James; Pendar, Hodjat

We use an example from textile processing to illustrate the utility of a conserved quantity associated with metric symmetry in a thin body. This quantity, when combined with the usual linear and angular momentum currents, allows us to construct a four-parameter family of curves representing the equilibria of a rotating, flowing string. To achieve this, we introduce a non-material action of mixed Lagrangian-Eulerian type, applicable to fixed windows of axially-moving systems. We will point out intriguing similarities with Bernoulli's equation, discuss the effects of axial flow on rotating conservative systems, and make connections with 19th- and 20th-century results on the dynamics of cables.

Plate falling in a fluid: Regular and chaotic dynamics of finite-dimensional models

NASA Astrophysics Data System (ADS)

Kuznetsov, Sergey P.

2015-05-01

Results are reviewed concerning the planar problem of a plate falling in a resisting medium studied with models based on ordinary differential equations for a small number of dynamical variables. A unified model is introduced to conduct a comparative analysis of the dynamical behaviors of models of Kozlov, Tanabe-Kaneko, Belmonte-Eisenberg-Moses and Andersen-Pesavento-Wang using common dimensionless variables and parameters. It is shown that the overall structure of the parameter spaces for the different models manifests certain similarities caused by the same inherent symmetry and by the universal nature of the phenomena involved in nonlinear dynamics (fixed points, limit cycles, attractors, and bifurcations).

Common fixed point theorems for maps under a contractive condition of integral type

NASA Astrophysics Data System (ADS)

Djoudi, A.; Merghadi, F.

2008-05-01

Two common fixed point theorems for mapping of complete metric space under a general contractive inequality of integral type and satisfying minimal commutativity conditions are proved. These results extend and improve several previous results, particularly Theorem 4 of Rhoades [B.E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 63 (2003) 4007-4013] and Theorem 4 of Sessa [S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.) 32 (46) (1982) 149-153].

Stability of libration points in the restricted four-body problem with variable mass

NASA Astrophysics Data System (ADS)

Mittal, Amit; Aggarwal, Rajiv; Suraj, Md. Sanam; Bisht, Virender Singh

2016-10-01

We have investigated the stability of the Lagrangian solutions for the restricted four-body problem with variable mass. It has been assumed that the three primaries with masses m1, m2 and m3 form an equilateral triangle, wherein m2=m3. According to Jeans' law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), the infinitesimal body varies its mass m with time. The space-time transformations of Meshcherskii (Studies on the Mechanics of Bodies of Variable Mass, GITTL, Moscow, 1949) are used by taking the values of the parameters q=1/2, k=0, n=1. The equations of motion of the infinitesimal body with variable mass have been determined. The equations of motion of the current problem differ from the ones of the restricted four-body problem with constant mass. There exist eight libration points, out of which two are collinear with the primary m1 and the rest are non-collinear for a fixed value of parameters γ (m {at time} t/m {at initial time}, 0<γ≤1 ), α (the proportionality constant in Jeans' law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), 0≤α≤2.2) and μ=0.019 (the mass parameter). All the libration points are found to be unstable. The zero velocity surfaces (ZVS) are also drawn and regions of motion are discussed.

Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion

NASA Astrophysics Data System (ADS)

Zhang, Wei-Guo; Li, Zhe; Liu, Yong-Jun

2018-01-01

In this paper, we study the pricing problem of the continuously monitored fixed and floating strike geometric Asian power options in a mixed fractional Brownian motion environment. First, we derive both closed-form solutions and mixed fractional partial differential equations for fixed and floating strike geometric Asian power options based on delta-hedging strategy and partial differential equation method. Second, we present the lower and upper bounds of the prices of fixed and floating strike geometric Asian power options under the assumption that both risk-free interest rate and volatility are interval numbers. Finally, numerical studies are performed to illustrate the performance of our proposed pricing model.

The Strong Effects Of On-Axis Focal Shift And Its Nonlinear Variation In Ultrasound Beams Radiated By Low Fresnel Number Transducers

NASA Astrophysics Data System (ADS)

Makov, Y. N.; Espinosa, V.; Sánchez-Morcillo, V. J.; Ramis, J.; Cruañes, J.; Camarena, F.

2006-05-01

On the basis of theoretical concepts, an accurate and complete experimental and numerical examination of the on-axis distribution and the corresponding temporal profiles for low-Fresnel-number focused ultrasound beams under increasing transducer input voltage has been performed. For a real focusing transducer with sufficiently small Fresnel number, a strong initial (linear) shift of the main on-axis pressure maximum from geometrical focal point towards the transducer, and its following displacement towards the focal point and backward motion as the driving transducer voltage increase until highly nonlinear regimes were fixed. The simultaneous monitoring of the temporal waveform modifications determines the real roles and interplay between different nonlinear effects (refraction and attenuation) in the observed dynamics of on-axis pressure maximum. The experimental results are in good agreement with numerical solutions of KZK equation, confirming that the observed dynamic shift of the maximum pressure point is related only to the interplay between diffraction, dissipation and nonlinearity of the acoustic wave.

The statistics of peaks of Gaussian random fields. [cosmological density fluctuations

NASA Technical Reports Server (NTRS)

Bardeen, J. M.; Bond, J. R.; Kaiser, N.; Szalay, A. S.

1986-01-01

A set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed. The point process equation is discussed, giving the general formula for the average number density of peaks. The problem of the proper conditional probability constraints appropriate to maxima are examined using a one-dimensional illustration. The average density of maxima of a general three-dimensional Gaussian field is calculated as a function of heights of the maxima, and the average density of 'upcrossing' points on density contour surfaces is computed. The number density of peaks subject to the constraint that the large-scale density field be fixed is determined and used to discuss the segregation of high peaks from the underlying mass distribution. The machinery to calculate n-point peak-peak correlation functions is determined, as are the shapes of the profiles about maxima.

Verification and Planning Based on Coinductive Logic Programming

NASA Technical Reports Server (NTRS)

Bansal, Ajay; Min, Richard; Simon, Luke; Mallya, Ajay; Gupta, Gopal

2008-01-01

Coinduction is a powerful technique for reasoning about unfounded sets, unbounded structures, infinite automata, and interactive computations [6]. Where induction corresponds to least fixed point's semantics, coinduction corresponds to greatest fixed point semantics. Recently coinduction has been incorporated into logic programming and an elegant operational semantics developed for it [11, 12]. This operational semantics is the greatest fix point counterpart of SLD resolution (SLD resolution imparts operational semantics to least fix point based computations) and is termed co- SLD resolution. In co-SLD resolution, a predicate goal p( t) succeeds if it unifies with one of its ancestor calls. In addition, rational infinite terms are allowed as arguments of predicates. Infinite terms are represented as solutions to unification equations and the occurs check is omitted during the unification process. Coinductive Logic Programming (Co-LP) and Co-SLD resolution can be used to elegantly perform model checking and planning. A combined SLD and Co-SLD resolution based LP system forms the common basis for planning, scheduling, verification, model checking, and constraint solving [9, 4]. This is achieved by amalgamating SLD resolution, co-SLD resolution, and constraint logic programming [13] in a single logic programming system. Given that parallelism in logic programs can be implicitly exploited [8], complex, compute-intensive applications (planning, scheduling, model checking, etc.) can be executed in parallel on multi-core machines. Parallel execution can result in speed-ups as well as in larger instances of the problems being solved. In the remainder we elaborate on (i) how planning can be elegantly and efficiently performed under real-time constraints, (ii) how real-time systems can be elegantly and efficiently model- checked, as well as (iii) how hybrid systems can be verified in a combined system with both co-SLD and SLD resolution. Implementations of co-SLD resolution as well as preliminary implementations of the planning and verification applications have been developed [4]. Co-LP and Model Checking: The vast majority of properties that are to be verified can be classified into safety properties and liveness properties. It is well known within model checking that safety properties can be verified by reachability analysis, i.e, if a counter-example to the property exists, it can be finitely determined by enumerating all the reachable states of the Kripke structure.

Implicit solution of Navier-Stokes equations on staggered curvilinear grids using a Newton-Krylov method with a novel analytical Jacobian.

NASA Astrophysics Data System (ADS)

Borazjani, Iman; Asgharzadeh, Hafez

2015-11-01

Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.

PCC Framework for Program-Generators

NASA Technical Reports Server (NTRS)

Kong, Soonho; Choi, Wontae; Yi, Kwangkeun

2009-01-01

In this paper, we propose a proof-carrying code framework for program-generators. The enabling technique is abstract parsing, a static string analysis technique, which is used as a component for generating and validating certificates. Our framework provides an efficient solution for certifying program-generators whose safety properties are expressed in terms of the grammar representing the generated program. The fixed-point solution of the analysis is generated and attached with the program-generator on the code producer side. The consumer receives the code with a fixed-point solution and validates that the received fixed point is indeed a fixed point of the received code. This validation can be done in a single pass.

Metal Carbon Eutectics to Extend the Use of the Fixed-Point Technique in Precision IR Thermometry

NASA Astrophysics Data System (ADS)

Battuello, M.; Girard, F.; Florio, M.

2008-06-01

The high-temperature extension of the fixed-point technique for primary calibration of precision infrared (IR) thermometers was investigated both through mathematical simulations and laboratory investigations. Simulations were performed with Co C (1,324°C) and Pd C (1, 492°C) eutectic fixed points, and a precision IR thermometer was calibrated from the In point (156.5985°C) up to the Co C point. Mathematical simulations suggested the possibility of directly deriving the transition temperature of the Co C and Pd C points by extrapolating the calibration derived from fixed-point measurements from In to the Cu point. Both temperatures, as a result of the low uncertainty associated with the In Cu calibration and the high number of fixed points involved in the calibration process, can be derived with an uncertainty of 0.11°C for Co C and 0.18°C for Pd C. A transition temperature of 1,324.3°C for Co C was determined from the experimental verification, a value higher than, but compatible with, the one proposed by the thermometry community for inclusion as a secondary reference point for ITS-90 dissemination, i.e., 1,324.0°C.

The succinonitrile triple-point standard: a fixed point to improve the accuracy of temperature measurements in the clinical laboratory.

PubMed

Mangum, B W

1983-07-01

In an investigation of the melting and freezing behavior of succinonitrile, the triple-point temperature was determined to be 58.0805 degrees C, with an estimated uncertainty of +/- 0.0015 degrees C relative to the International Practical Temperature Scale of 1968 (IPTS-68). The triple-point temperature of this material is evaluated as a temperature-fixed point, and some clinical laboratory applications of this fixed point are proposed. In conjunction with the gallium and ice points, the availability of succinonitrile permits thermistor thermometers to be calibrated accurately and easily on the IPTS-68.

A method for the determination of the coefficient of rolling friction using cycloidal pendulum

NASA Astrophysics Data System (ADS)

Ciornei, M. C.; Alaci, S.; Ciornei, F. C.; Romanu, I. C.

2017-08-01

The paper presents a method for experimental finding of coefficient of rolling friction appropriate for biomedical applications based on the theory of cycloidal pendulum. When a mobile circle rolls over a fixed straight line, the points from the circle describe trajectories called normal cycloids. To materialize this model, it is sufficient that a small region from boundary surfaces of a moving rigid body is spherical. Assuming pure rolling motion, the equation of motion of the cycloidal pendulum is obtained - an ordinary nonlinear differential equation. The experimental device is composed by two interconnected balls rolling over the material to be studied. The inertial characteristics of the pendulum can be adjusted via weights placed on a rod. A laser spot oscillates together to the pendulum and provides the amplitude of oscillations. After finding the experimental parameters necessary in differential equation of motion, it can be integrated using the Runge-Kutta of fourth order method. The equation was integrated for several materials and found values of rolling friction coefficients. Two main conclusions are drawn: the coefficient of rolling friction influenced significantly the amplitude of oscillation but the effect upon the period of oscillation is practically imperceptible. A methodology is proposed for finding the rolling friction coefficient and the pure rolling condition is verified.

ADAPTIVE METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS VIA NATURAL EMBEDDINGS AND REJECTION SAMPLING WITH MEMORY.

PubMed

Rackauckas, Christopher; Nie, Qing

2017-01-01

Adaptive time-stepping with high-order embedded Runge-Kutta pairs and rejection sampling provides efficient approaches for solving differential equations. While many such methods exist for solving deterministic systems, little progress has been made for stochastic variants. One challenge in developing adaptive methods for stochastic differential equations (SDEs) is the construction of embedded schemes with direct error estimates. We present a new class of embedded stochastic Runge-Kutta (SRK) methods with strong order 1.5 which have a natural embedding of strong order 1.0 methods. This allows for the derivation of an error estimate which requires no additional function evaluations. Next we derive a general method to reject the time steps without losing information about the future Brownian path termed Rejection Sampling with Memory (RSwM). This method utilizes a stack data structure to do rejection sampling, costing only a few floating point calculations. We show numerically that the methods generate statistically-correct and tolerance-controlled solutions. Lastly, we show that this form of adaptivity can be applied to systems of equations, and demonstrate that it solves a stiff biological model 12.28x faster than common fixed timestep algorithms. Our approach only requires the solution to a bridging problem and thus lends itself to natural generalizations beyond SDEs.

ADAPTIVE METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS VIA NATURAL EMBEDDINGS AND REJECTION SAMPLING WITH MEMORY

PubMed Central

Rackauckas, Christopher

2017-01-01

Adaptive time-stepping with high-order embedded Runge-Kutta pairs and rejection sampling provides efficient approaches for solving differential equations. While many such methods exist for solving deterministic systems, little progress has been made for stochastic variants. One challenge in developing adaptive methods for stochastic differential equations (SDEs) is the construction of embedded schemes with direct error estimates. We present a new class of embedded stochastic Runge-Kutta (SRK) methods with strong order 1.5 which have a natural embedding of strong order 1.0 methods. This allows for the derivation of an error estimate which requires no additional function evaluations. Next we derive a general method to reject the time steps without losing information about the future Brownian path termed Rejection Sampling with Memory (RSwM). This method utilizes a stack data structure to do rejection sampling, costing only a few floating point calculations. We show numerically that the methods generate statistically-correct and tolerance-controlled solutions. Lastly, we show that this form of adaptivity can be applied to systems of equations, and demonstrate that it solves a stiff biological model 12.28x faster than common fixed timestep algorithms. Our approach only requires the solution to a bridging problem and thus lends itself to natural generalizations beyond SDEs. PMID:29527134

High Frequency Acoustic Propagation using Level Set Methods

DTIC Science & Technology

2007-01-01

solution of the high frequency approximation to the wave equation. Traditional solutions to the Eikonal equation in high frequency acoustics are...the Eikonal equation derived from the high frequency approximation to the wave equation, ucuH ∇±=∇ )(),( xx , with the nonnegative function c(x...For simplicity, we only consider the case ucuH ∇+=∇ )(),( xx . Two difficulties must be addressed when solving the Eikonal equation in a fixed

Scaling theory of topological phase transitions

NASA Astrophysics Data System (ADS)

Chen, Wei

2016-02-01

Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may be Berry curvature, Berry connection, or other quantities depending on the system. Akin to stretching a messy string to reveal the number of knots it contains, a scaling procedure is proposed for the curvature function in inversion symmetric systems, from which the topological phase transition can be identified from the flow of the driving energy parameters that control the topology (hopping, chemical potential, etc) under scaling. At an infinitesimal operation, one obtains the renormalization group (RG) equations for the driving energy parameters. A length scale defined from the curvature function near the gap-closing momentum is suggested to characterize the scale invariance at critical points and fixed points, and displays a universal critical behavior in a variety of systems examined.

Rotational isomerism of molecules in condensed phases

NASA Astrophysics Data System (ADS)

Sakka, Tetsuo; Iwasaki, Matae; Ogata, Yukio

1991-08-01

A statistical mechanical model is developed for the description of the conformational distribution of organic molecules in the liquid and solid phases. In the model, they are assumed to have one internal freedom of rotation. The molecules are fixed to lattice sites and have two types of ordering, conformational and distributional. The latter is supposed to represent an ordering typical of solid state. The model is compared with the experimental results of the rotational-isomeric ratio of 1,2-dichloro-1,1-difluoroethane, in the temperature range from 77 to 300 K. It explains successfully the experimental results, especially the behavior near the melting point. From the point of view of melting, the present model is an extension of the Lennard-Jones and Devonshire model, because, when the distinctions between the two conformers are neglected, the parameter representing the distributional ordering of the molecules results in the same equation as that derived from the Lennard-Jones and Devonshire model.

Realization of the Temperature Scale in the Range from 234.3 K (Hg Triple Point) to 1084.62°C (Cu Freezing Point) in Croatia

NASA Astrophysics Data System (ADS)

Zvizdic, Davor; Veliki, Tomislav; Grgec Bermanec, Lovorka

2008-06-01

This article describes the realization of the International Temperature Scale in the range from 234.3 K (mercury triple point) to 1084.62°C (copper freezing point) at the Laboratory for Process Measurement (LPM), Faculty of Mechanical Engineering and Naval Architecture (FSB), University of Zagreb. The system for the realization of the ITS-90 consists of the sealed fixed-point cells (mercury triple point, water triple point and gallium melting point) and the apparatus designed for the optimal realization of open fixed-point cells which include the gallium melting point, tin freezing point, zinc freezing point, aluminum freezing point, and copper freezing point. The maintenance of the open fixed-point cells is described, including the system for filling the cells with pure argon and for maintaining the pressure during the realization.

Exact results for the O( N ) model with quenched disorder

NASA Astrophysics Data System (ADS)

Delfino, Gesualdo; Lamsen, Noel

2018-04-01

We use scale invariant scattering theory to exactly determine the lines of renormalization group fixed points for O( N )-symmetric models with quenched disorder in two dimensions. Random fixed points are characterized by two disorder parameters: a modulus that vanishes when approaching the pure case, and a phase angle. The critical lines fall into three classes depending on the values of the disorder modulus. Besides the class corresponding to the pure case, a second class has maximal value of the disorder modulus and includes Nishimori-like multicritical points as well as zero temperature fixed points. The third class contains critical lines that interpolate, as N varies, between the first two classes. For positive N , it contains a single line of infrared fixed points spanning the values of N from √{2}-1 to 1. The symmetry sector of the energy density operator is superuniversal (i.e. N -independent) along this line. For N = 2 a line of fixed points exists only in the pure case, but accounts also for the Berezinskii-Kosterlitz-Thouless phase observed in presence of disorder.

Establishment of the Co-C Eutectic Fixed-Point Cell for Thermocouple Calibrations at NIMT

NASA Astrophysics Data System (ADS)

Ongrai, O.; Elliott, C. J.

2017-08-01

In 2015, NIMT first established a Co-C eutectic temperature reference (fixed-point) cell measurement capability for thermocouple calibration to support the requirements of Thailand's heavy industries and secondary laboratories. The Co-C eutectic fixed-point cell is a facility transferred from NPL, where the design was developed through European and UK national measurement system projects. In this paper, we describe the establishment of a Co-C eutectic fixed-point cell for thermocouple calibration at NIMT. This paper demonstrates achievement of the required furnace uniformity, the Co-C plateau realization and the comparison data between NIMT and NPL Co-C cells by using the same standard Pt/Pd thermocouple, demonstrating traceability. The NIMT measurement capability for noble metal type thermocouples at the new Co-C eutectic fixed point (1324.06°C) is estimated to be within ± 0.60 K (k=2). This meets the needs of Thailand's high-temperature thermocouple users—for which previously there has been no traceable calibration facility.

Selection of Common Items as an Unrecognized Source of Variability in Test Equating: A Bootstrap Approximation Assuming Random Sampling of Common Items

ERIC Educational Resources Information Center

Michaelides, Michalis P.; Haertel, Edward H.

2014-01-01

The standard error of equating quantifies the variability in the estimation of an equating function. Because common items for deriving equated scores are treated as fixed, the only source of variability typically considered arises from the estimation of common-item parameters from responses of samples of examinees. Use of alternative, equally…

High-order boundary integral equation solution of high frequency wave scattering from obstacles in an unbounded linearly stratified medium

NASA Astrophysics Data System (ADS)

Barnett, Alex H.; Nelson, Bradley J.; Mahoney, J. Matthew

2015-09-01

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve, the square of the wavenumber (refractive index) varies linearly in one coordinate, i.e. (Δ + E +x2) u (x1 ,x2) = 0 where E is a constant; this models quantum particles of fixed energy in a uniform gravitational field, and has broader applications to stratified media in acoustics, optics and seismology. We evaluate the fundamental solution efficiently with exponential accuracy via numerical saddle-point integration, using the truncated trapezoid rule with typically 102 nodes, with an effort that is independent of the frequency parameter E. By combining with a high-order Nyström quadrature, we are able to solve the scattering from obstacles 50 wavelengths across to 11 digits of accuracy in under a minute on a desktop or laptop.

Using Global Invariant Manifolds to Understand Metastability in the Burgers Equation With Small Viscosity

NASA Astrophysics Data System (ADS)

Beck, Margaret; Wayne, C. Eugene

2009-01-01

The large-time behavior of solutions to the Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context means that solutions spend a very long time near the family of solutions known as diffusive N-waves before finally converging to a stable self-similar diffusion wave. More precisely, it is shown that in terms of similarity, or scaling, variables in an algebraically weighted L^2 space, the self-similar diffusion waves correspond to a one-dimensional global center manifold of stationary solutions. Through each of these fixed points there exists a one-dimensional, global, attractive, invariant manifold corresponding to the diffusive N-waves. Thus, metastability corresponds to a fast transient in which solutions approach this metastable manifold of diffusive N-waves, followed by a slow decay along this manifold, and, finally, convergence to the self-similar diffusion wave.

Performance of a cavity-method-based algorithm for the prize-collecting Steiner tree problem on graphs

NASA Astrophysics Data System (ADS)

Biazzo, Indaco; Braunstein, Alfredo; Zecchina, Riccardo

2012-08-01

We study the behavior of an algorithm derived from the cavity method for the prize-collecting steiner tree (PCST) problem on graphs. The algorithm is based on the zero temperature limit of the cavity equations and as such is formally simple (a fixed point equation resolved by iteration) and distributed (parallelizable). We provide a detailed comparison with state-of-the-art algorithms on a wide range of existing benchmarks, networks, and random graphs. Specifically, we consider an enhanced derivative of the Goemans-Williamson heuristics and the dhea solver, a branch and cut integer linear programming based approach. The comparison shows that the cavity algorithm outperforms the two algorithms in most large instances both in running time and quality of the solution. Finally we prove a few optimality properties of the solutions provided by our algorithm, including optimality under the two postprocessing procedures defined in the Goemans-Williamson derivative and global optimality in some limit cases.

A Nonlinear Elasticity Model of Macromolecular Conformational Change Induced by Electrostatic Forces

PubMed Central

Zhou, Y. C.; Holst, Michael; McCammon, J. Andrew

2008-01-01

In this paper we propose a nonlinear elasticity model of macromolecular conformational change (deformation) induced by electrostatic forces generated by an implicit solvation model. The Poisson-Boltzmann equation for the electrostatic potential is analyzed in a domain varying with the elastic deformation of molecules, and a new continuous model of the electrostatic forces is developed to ensure solvability of the nonlinear elasticity equations. We derive the estimates of electrostatic forces corresponding to four types of perturbations to an electrostatic potential field, and establish the existance of an equilibrium configuration using a fixed-point argument, under the assumption that the change in the ionic strength and charges due to the additional molecules causing the deformation are sufficiently small. The results are valid for elastic models with arbitrarily complex dielectric interfaces and cavities, and can be generalized to large elastic deformation caused by high ionic strength, large charges, and strong external fields by using continuation methods. PMID:19461946

Cosmology in generalized Proca theories

NASA Astrophysics Data System (ADS)

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

2016-06-01

We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological implications of such generalized Proca theories are investigated for both the background and the linear perturbation by taking into account the Lagrangian up to quintic order. In the presence of a matter fluid with a temporal component of the vector field, we derive the background equations of motion and show the existence of de Sitter solutions relevant to the late-time cosmic acceleration. We also obtain conditions for the absence of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations in the small-scale limit. Our results are applied to concrete examples of the general functions in the theory, which encompass vector Galileons as a specific case. In such examples, we show that the de Sitter fixed point is always a stable attractor and study viable parameter spaces in which the no-ghost and stability conditions are satisfied during the cosmic expansion history.

Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network.

PubMed

Landajuela, Mikel; Vergara, Christian; Gerbi, Antonello; Dedé, Luca; Formaggia, Luca; Quarteroni, Alfio

2018-03-25

In this work, we consider the numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network. The mathematical model couples the 3D elastodynamics and bidomain equations for the electrophysiology in the myocardium with the 1D monodomain equation in the Purkinje network. For the numerical solution of the coupled problem, we consider a fixed-point iterative algorithm that enables a partitioned solution of the myocardium and Purkinje network problems. Different levels of myocardium-Purkinje network splitting are considered and analyzed. The results are compared with those obtained using standard strategies proposed in the literature to trigger the electrical activation. Finally, we present a numerical study that, although performed in an idealized computational domain, features all the physiological issues that characterize a heartbeat simulation, including the initiation of the signal in the Purkinje network and the systolic and diastolic phases. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.

On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density

NASA Astrophysics Data System (ADS)

Dorini, F. A.; Cecconello, M. S.; Dorini, L. B.

2016-04-01

It is recognized that handling uncertainty is essential to obtain more reliable results in modeling and computer simulation. This paper aims to discuss the logistic equation subject to uncertainties in two parameters: the environmental carrying capacity, K, and the initial population density, N0. We first provide the closed-form results for the first probability density function of time-population density, N(t), and its inflection point, t*. We then use the Maximum Entropy Principle to determine both K and N0 density functions, treating such parameters as independent random variables and considering fluctuations of their values for a situation that commonly occurs in practice. Finally, closed-form results for the density functions and statistical moments of N(t), for a fixed t > 0, and of t* are provided, considering the uniform distribution case. We carried out numerical experiments to validate the theoretical results and compared them against that obtained using Monte Carlo simulation.

Critical behavior and dimension crossover of pion superfluidity

NASA Astrophysics Data System (ADS)

Wang, Ziyue; Zhuang, Pengfei

2016-09-01

We investigate the critical behavior of pion superfluidity in the framework of the functional renormalization group (FRG). By solving the flow equations in the SU(2) linear sigma model at finite temperature and isospin density, and making comparison with the fixed point analysis of a general O (N ) system with continuous dimension, we find that the pion superfluidity is a second order phase transition subject to an O (2 ) universality class with a dimension crossover from dc=4 to dc=3 . This phenomenon provides a concrete example of dimension reduction in thermal field theory. The large-N expansion gives a temperature independent critical exponent β and agrees with the FRG result only at zero temperature.

Fixed points and limit cycles in the population dynamics of lysogenic viruses and their hosts

NASA Astrophysics Data System (ADS)

Wang, Zhenyu; Goldenfeld, Nigel

2010-07-01

Starting with stochastic rate equations for the fundamental interactions between microbes and their viruses, we derive a mean-field theory for the population dynamics of microbe-virus systems, including the effects of lysogeny. In the absence of lysogeny, our model is a generalization of that proposed phenomenologically by Weitz and Dushoff. In the presence of lysogeny, we analyze the possible states of the system, identifying a limit cycle, which we interpret physically. To test the robustness of our mean-field calculations to demographic fluctuations, we have compared our results with stochastic simulations using the Gillespie algorithm. Finally, we estimate the range of parameters that delineate the various steady states of our model.

Combining states without scale hierarchies with ordered parton showers

DOE PAGES

Fischer, Nadine; Prestel, Stefan

2017-09-12

Here, we present a parameter-free scheme to combine fixed-order multi-jet results with parton-shower evolution. The scheme produces jet cross sections with leading-order accuracy in the complete phase space of multiple emissions, resumming large logarithms when appropriate, while not arbitrarily enforcing ordering on momentum configurations beyond the reach of the parton-shower evolution equation. This then requires the development of a matrix-element correction scheme for complex phase-spaces including ordering conditions as well as a systematic scale-setting procedure for unordered phase-space points. Our algorithm does not require a merging-scale parameter. We implement the new method in the Vincia framework and compare to LHCmore » data.« less

A Fast Solver for Implicit Integration of the Vlasov--Poisson System in the Eulerian Framework

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

Garrett, C. Kristopher; Hauck, Cory D.

In this paper, we present a domain decomposition algorithm to accelerate the solution of Eulerian-type discretizations of the linear, steady-state Vlasov equation. The steady-state solver then forms a key component in the implementation of fully implicit or nearly fully implicit temporal integrators for the nonlinear Vlasov--Poisson system. The solver relies on a particular decomposition of phase space that enables the use of sweeping techniques commonly used in radiation transport applications. The original linear system for the phase space unknowns is then replaced by a smaller linear system involving only unknowns on the boundary between subdomains, which can then be solvedmore » efficiently with Krylov methods such as GMRES. Steady-state solves are combined to form an implicit Runge--Kutta time integrator, and the Vlasov equation is coupled self-consistently to the Poisson equation via a linearized procedure or a nonlinear fixed-point method for the electric field. Finally, numerical results for standard test problems demonstrate the efficiency of the domain decomposition approach when compared to the direct application of an iterative solver to the original linear system.« less

Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface

NASA Astrophysics Data System (ADS)

Shao, Songdong; Lo, Edmond Y. M.

An incompressible smoothed particle hydrodynamics (SPH) method is presented to simulate Newtonian and non-Newtonian flows with free surfaces. The basic equations solved are the incompressible mass conservation and Navier-Stokes equations. The method uses prediction-correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting deviation of particle density is then implicitly projected onto a divergence-free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. Various SPH formulations are employed in the discretization of the relevant gradient, divergence and Laplacian terms. Free surfaces are identified by the particles whose density is below a set point. Wall boundaries are represented by particles whose positions are fixed. The SPH formulation is also extended to non-Newtonian flows and demonstrated using the Cross rheological model. The incompressible SPH method is tested by typical 2-D dam-break problems in which both water and fluid mud are considered. The computations are in good agreement with available experimental data. The different flow features between Newtonian and non-Newtonian flows after the dam-break are discussed.

A Fast Solver for Implicit Integration of the Vlasov--Poisson System in the Eulerian Framework

DOE PAGES

Garrett, C. Kristopher; Hauck, Cory D.

2018-04-05

In this paper, we present a domain decomposition algorithm to accelerate the solution of Eulerian-type discretizations of the linear, steady-state Vlasov equation. The steady-state solver then forms a key component in the implementation of fully implicit or nearly fully implicit temporal integrators for the nonlinear Vlasov--Poisson system. The solver relies on a particular decomposition of phase space that enables the use of sweeping techniques commonly used in radiation transport applications. The original linear system for the phase space unknowns is then replaced by a smaller linear system involving only unknowns on the boundary between subdomains, which can then be solvedmore » efficiently with Krylov methods such as GMRES. Steady-state solves are combined to form an implicit Runge--Kutta time integrator, and the Vlasov equation is coupled self-consistently to the Poisson equation via a linearized procedure or a nonlinear fixed-point method for the electric field. Finally, numerical results for standard test problems demonstrate the efficiency of the domain decomposition approach when compared to the direct application of an iterative solver to the original linear system.« less

47 CFR 101.701 - Eligibility.

Code of Federal Regulations, 2014 CFR

2014-10-01

... Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Common Carrier Fixed Point-to-Point Microwave Service § 101.701 Eligibility. (a) Authorizations... the customers (or points of service) on the microwave system involved, including those served through...

47 CFR 101.701 - Eligibility.

Code of Federal Regulations, 2011 CFR

2011-10-01

... Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Common Carrier Fixed Point-to-Point Microwave Service § 101.701 Eligibility. (a) Authorizations... the customers (or points of service) on the microwave system involved, including those served through...

47 CFR 101.701 - Eligibility.

Code of Federal Regulations, 2013 CFR

2013-10-01

... Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Common Carrier Fixed Point-to-Point Microwave Service § 101.701 Eligibility. (a) Authorizations... the customers (or points of service) on the microwave system involved, including those served through...

47 CFR 101.701 - Eligibility.

Code of Federal Regulations, 2012 CFR

2012-10-01

... Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Common Carrier Fixed Point-to-Point Microwave Service § 101.701 Eligibility. (a) Authorizations... the customers (or points of service) on the microwave system involved, including those served through...

Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models.

PubMed

Antonov, N V; Gulitskiy, N M; Kostenko, M M; Malyshev, A V

2018-03-01

In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E∝k^{1-y} and the dispersion law ω∝k^{2-η}. The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.

Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Malyshev, A. V.

2018-03-01

In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E ∝k1 -y and the dispersion law ω ∝k2 -η . The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.

A numerical analysis of phase-change problems including natural convection

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

Cao, Y.; Faghri, A.

1990-08-01

Fixed grid solutions for phase-change problems remove the need to satisfy conditions at the phase-change front and can be easily extended to multidimensional problems. The two most important and widely used methods are enthalpy methods and temperature-based equivalent heat capacity methods. Both methods in this group have advantages and disadvantages. Enthalpy methods (Shamsundar and Sparrow, 1975; Voller and Prakash, 1987; Cao et al., 1989) are flexible and can handle phase-change problems occurring both at a single temperature and over a temperature range. The drawback of this method is that although the predicted temperature distributions and melting fronts are reasonable, themore » predicted time history of the temperature at a typical grid point may have some oscillations. The temperature-based fixed grid methods (Morgan, 1981; Hsiao and Chung, 1984) have no such time history problems and are more convenient with conjugate problems involving an adjacent wall, but have to deal with the severe nonlinearity of the governing equations when the phase-change temperature range is small. In this paper, a new temperature-based fixed-grid formulation is proposed, and the reason that the original equivalent heat capacity model is subject to such restrictions on the time step, mesh size, and the phase-change temperature range will also be discussed.« less

Stability analysis of an autocatalytic protein model

NASA Astrophysics Data System (ADS)

Lee, Julian

2016-05-01

A self-regulatory genetic circuit, where a protein acts as a positive regulator of its own production, is known to be the simplest biological network with a positive feedback loop. Although at least three components—DNA, RNA, and the protein—are required to form such a circuit, stability analysis of the fixed points of this self-regulatory circuit has been performed only after reducing the system to a two-component system, either by assuming a fast equilibration of the DNA component or by removing the RNA component. Here, stability of the fixed points of the three-component positive feedback loop is analyzed by obtaining eigenvalues of the full three-dimensional Hessian matrix. In addition to rigorously identifying the stable fixed points and saddle points, detailed information about the system can be obtained, such as the existence of complex eigenvalues near a fixed point.

Electromagnetic scattering and emission by a fixed multi-particle object in local thermal equilibrium: General formalism.

PubMed

Mishchenko, Michael I

2017-10-01

The majority of previous studies of the interaction of individual particles and multi-particle groups with electromagnetic field have focused on either elastic scattering in the presence of an external field or self-emission of electromagnetic radiation. In this paper we apply semi-classical fluctuational electrodynamics to address the ubiquitous scenario wherein a fixed particle or a fixed multi-particle group is exposed to an external quasi-polychromatic electromagnetic field as well as thermally emits its own electromagnetic radiation. We summarize the main relevant axioms of fluctuational electrodynamics, formulate in maximally rigorous mathematical terms the general scattering-emission problem for a fixed object, and derive such fundamental corollaries as the scattering-emission volume integral equation, the Lippmann-Schwinger equation for the dyadic transition operator, the multi-particle scattering-emission equations, and the far-field limit. We show that in the framework of fluctuational electrodynamics, the computation of the self-emitted component of the total field is completely separated from that of the elastically scattered field. The same is true of the computation of the emitted and elastically scattered components of quadratic/bilinear forms in the total electromagnetic field. These results pave the way to the practical computation of relevant optical observables.

Fixed-point theorems for families of weakly non-expansive maps

NASA Astrophysics Data System (ADS)

Mai, Jie-Hua; Liu, Xin-He

2007-10-01

In this paper, we present some fixed-point theorems for families of weakly non-expansive maps under some relatively weaker and more general conditions. Our results generalize and improve several results due to Jungck [G. Jungck, Fixed points via a generalized local commutativity, Int. J. Math. Math. Sci. 25 (8) (2001) 497-507], Jachymski [J. Jachymski, A generalization of the theorem by Rhoades and Watson for contractive type mappings, Math. Japon. 38 (6) (1993) 1095-1102], Guo [C. Guo, An extension of fixed point theorem of Krasnoselski, Chinese J. Math. (P.O.C.) 21 (1) (1993) 13-20], Rhoades [B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290], and others.

Common Coupled Fixed Point Theorems for Two Hybrid Pairs of Mappings under φ-ψ Contraction

PubMed Central

Handa, Amrish

2014-01-01

We introduce the concept of (EA) property and occasional w-compatibility for hybrid pair F : X × X → 2X and f : X → X. We also introduce common (EA) property for two hybrid pairs F, G : X → 2X and f, g : X → X. We establish some common coupled fixed point theorems for two hybrid pairs of mappings under φ-ψ contraction on noncomplete metric spaces. An example is also given to validate our results. We improve, extend and generalize several known results. The results of this paper generalize the common fixed point theorems for hybrid pairs of mappings and essentially contain fixed point theorems for hybrid pair of mappings. PMID:27340688

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.

47 CFR 101.101 - Frequency availability.

Code of Federal Regulations, 2011 CFR

2011-10-01

... Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE... Television Relay Service—(Part 78) CC: Common Carrier Fixed Point-to-Point Microwave Service—(Part 101...-Point Microwave Service—(Part 101, Subparts C & H) PCS: Personal Communications Service—(Part 24) PET...

Focus on quantum Einstein gravity Focus on quantum Einstein gravity

NASA Astrophysics Data System (ADS)

Ambjorn, Jan; Reuter, Martin; Saueressig, Frank

2012-09-01

The gravitational asymptotic safety program summarizes the attempts to construct a consistent and predictive quantum theory of gravity within Wilson's generalized framework of renormalization. Its key ingredient is a non-Gaussian fixed point of the renormalization group flow which controls the behavior of the theory at trans-Planckian energies and renders gravity safe from unphysical divergences. Provided that the fixed point comes with a finite number of ultraviolet-attractive (relevant) directions, this construction gives rise to a consistent quantum field theory which is as predictive as an ordinary, perturbatively renormalizable one. This opens up the exciting possibility of establishing quantum Einstein gravity as a fundamental theory of gravity, without introducing supersymmetry or extra dimensions, and solely based on quantization techniques that are known to work well for the other fundamental forces of nature. While the idea of gravity being asymptotically safe was proposed by Steven Weinberg more than 30 years ago [1], the technical tools for investigating this scenario only emerged during the last decade. Here a key role is played by the exact functional renormalization group equation for gravity, which allows the construction of non-perturbative approximate solutions for the RG-flow of the gravitational couplings. Most remarkably, all solutions constructed to date exhibit a suitable non-Gaussian fixed point, lending strong support to the asymptotic safety conjecture. Moreover, the functional renormalization group also provides indications that the central idea of a non-Gaussian fixed point providing a safe ultraviolet completion also carries over to more realistic scenarios where gravity is coupled to a suitable matter sector like the standard model. These theoretical successes also triggered a wealth of studies focusing on the consequences of asymptotic safety in a wide range of phenomenological applications covering the physics of black holes, early time cosmology and the big bang, as well as TeV-scale gravity models testable at the Large Hadron Collider. On different grounds, Monte-Carlo studies of the gravitational partition function based on the discrete causal dynamical triangulations approach provide an a priori independent avenue towards unveiling the non-perturbative features of gravity. As a highlight, detailed simulations established that the phase diagram underlying causal dynamical triangulations contains a phase where the triangulations naturally give rise to four-dimensional, macroscopic universes. Moreover, there are indications for a second-order phase transition that naturally forms the discrete analog of the non-Gaussian fixed point seen in the continuum computations. Thus there is a good chance that the discrete and continuum computations will converge to the same fundamental physics. This focus issue collects a series of papers that outline the current frontiers of the gravitational asymptotic safety program. We hope that readers get an impression of the depth and variety of this research area as well as our excitement about the new and ongoing developments. References [1] Weinberg S 1979 General Relativity, an Einstein Centenary Survey ed S W Hawking and W Israel (Cambridge: Cambridge University Press)

Liquidus slopes of impurities in ITS-90 fixed points from the mercury point to the copper point in the low concentration limit

NASA Astrophysics Data System (ADS)

Pearce, Jonathan V.; Gisby, John A.; Steur, Peter P. M.

2016-08-01

A knowledge of the effect of impurities at the level of parts per million on the freezing temperature of very pure metals is essential for realisation of ITS-90 fixed points. New information has become available for use with the thermodynamic modelling software MTDATA, permitting calculation of liquidus slopes, in the low concentration limit, of a wider range of binary alloy systems than was previously possible. In total, calculated values for 536 binary systems are given. In addition, new experimental determinations of phase diagrams, in the low impurity concentration limit, have recently appeared. All available data have been combined to provide a comprehensive set of liquidus slopes for impurities in ITS-90 metal fixed points. In total, liquidus slopes for 838 systems are tabulated for the fixed points Hg, Ga, In, Sn, Zn, Al, Ag, Au, and Cu. It is shown that the value of the liquidus slope as a function of impurity element atomic number can be approximated using a simple formula, and good qualitative agreement with the existing data is observed for the fixed points Al, Ag, Au and Cu, but curiously the formula is not applicable to the fixed points Hg, Ga, In, Sn, and Zn. Some discussion is made concerning the influence of oxygen on the liquidus slopes, and some calculations using MTDATA are discussed. The BIPM’s consultative committee for thermometry has long recognised that the sum of individual estimates method is the ideal approach for assessing uncertainties due to impurities, but the community has been largely powerless to use the model due to lack of data. Here, not only is data provided, but a simple model is given to enable known thermophysical data to be used directly to estimate impurity effects for a large fraction of the ITS-90 fixed points.

47 CFR 101.107 - Frequency tolerance.

Code of Federal Regulations, 2014 CFR

2014-10-01

... Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE...-point microwave and stations providing MVDDS. 5 For private operational fixed point-to-point microwave... noted in the table of paragraph (a) of this section. (b) Heterodyne microwave radio systems may be...

47 CFR 101.107 - Frequency tolerance.

Code of Federal Regulations, 2012 CFR

2012-10-01

... Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE...-point microwave and stations providing MVDDS. 5 For private operational fixed point-to-point microwave... noted in the table of paragraph (a) of this section. (b) Heterodyne microwave radio systems may be...

47 CFR 101.107 - Frequency tolerance.

Code of Federal Regulations, 2013 CFR

2013-10-01

... Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE...-point microwave and stations providing MVDDS. 5 For private operational fixed point-to-point microwave... noted in the table of paragraph (a) of this section. (b) Heterodyne microwave radio systems may be...

A new deflection solution and application of a fiber Bragg grating-based inclinometer for monitoring internal displacements in slopes

NASA Astrophysics Data System (ADS)

Zheng, Yong; Huang, Da; Shi, Lin

2018-05-01

Landslide monitoring is critical for predicting the stability of slopes to ensure the safety of life and property. Considering the potential advantages of fiber Bragg gratings (FBGs), such as immunity to electromagnetic interference, resistance to hostile environments, light weight, and high measurement precision and real time response, a self-designed, FBG-based in situ inclinometer combining a traditional inclinometer and FBG technology was designed to monitor the inner deformation of a slope. In practical landslide monitoring, the inclinometer can be regarded as a cantilever beam with one end fixed. Based on the deflection curve equation of a normal beam and the composite Simpson integral equation, a theoretical deflection equation of the FBG-based inclinometer versus longitudinal strain was established. A FBG-based inclinometer was fabricated and calibrated in the laboratory and a calibration strain sensitivity coefficient was obtained. The results of calibration tests show that the displacements measured by dial indicators are in good agreement with the theoretical displacements calculated using the proposed equation. A series of FBG-based inclinometers were installed into three vertical boreholes located at different points on the profile of an actual reinforced slope. The in situ monitoring results show that the FBG-based inclinometer can effectively capture the real-time internal displacements and potential sliding surface of the slope, proving the validity of the proposed theoretical equation as well the reliability and practicality of the proposed FBG-based inclinometer in engineering applications.

Nuclear-coupled thermal-hydraulic stability analysis of boiling water reactors

NASA Astrophysics Data System (ADS)

Karve, Atul A.

We have studied the nuclear-coupled thermal-hydraulic stability of boiling water reactors (BWRs) using a model we developed from: the space-time modal neutron kinetics equations based on spatial omega-modes, the equations for two-phase flow in parallel boiling channels, the fuel rod heat conduction equations, and a simple model for the recirculation loop. The model is represented as a dynamical system comprised of time-dependent nonlinear ordinary differential equations, and it is studied using stability analysis, modern bifurcation theory, and numerical simulations. We first determine the stability boundary (SB) in the most relevant parameter plane, the inlet-subcooling-number/external-pressure-drop plane, for a fixed control rod induced external reactivity equal to the 100% rod line value and then transform the SB to the practical power-flow map. Using this SB, we show that the normal operating point at 100% power is very stable, stability of points on the 100% rod line decreases as the flow rate is reduced, and that points are least stable in the low-flow/high-power region. We also determine the SB when the modal kinetics is replaced by simple point reactor kinetics and show that the first harmonic mode has no significant effect on the SB. Later we carry out the relevant numerical simulations where we first show that the Hopf bifurcation, that occurs as a parameter is varied across the SB is subcritical, and that, in the important low-flow/high-power region, growing oscillations can result following small finite perturbations of stable steady-states on the 100% rod line. Hence, a point on the 100% rod line in the low-flow/high-power region, although stable, may nevertheless be a point at which a BWR should not be operated. Numerical simulations are then done to calculate the decay ratios (DRs) and frequencies of oscillations for various points on the 100% rod line. It is determined that the NRC requirement of DR < 0.75-0.8 is not rigorously satisfied in the low-flow/high-power region and hence these points should be avoided during normal startup and shutdown operations. The frequency of oscillation is shown to decrease as the flow rate is reduced and the frequency of 0.5Hz observed in the low-flow/high-power region is consistent with those observed during actual instability incidents. Additional numerical simulations show that in the low-flow/high-power region, for the same initial conditions, the use of point kinetics leads to damped oscillations, whereas the model that includes the modal kinetics equations results in growing nonlinear oscillations. Thus, we show that side-by-side out-of-phase growing power oscillations result due to the very important first harmonic mode effect and that the use of point kinetics, which fails to predict these growing oscillations, leads to dramatically nonconservative results. Finally, the effect of a simple recirculation loop model that we develop is studied by carrying out additional stability analyses and additional numerical simulations. It is shown that the loop has a stabilizing effect on certain points on the 100% rod line for time delays equal to integer multiples of the natural period of oscillation, whereas it has a destabilizing effect for half-integer multiples. However, for more practical time delays, it is determined that the overall effect generally is destabilizing.

Renorming c0 and closed, bounded, convex sets with fixed point property for affine nonexpansive mappings

NASA Astrophysics Data System (ADS)

Nezir, Veysel; Mustafa, Nizami

2017-04-01

In 2008, P.K. Lin provided the first example of a nonreflexive space that can be renormed to have fixed point property for nonexpansive mappings. This space was the Banach space of absolutely summable sequences l1 and researchers aim to generalize this to c0, Banach space of null sequences. Before P.K. Lin's intriguing result, in 1979, Goebel and Kuczumow showed that there is a large class of non-weak* compact closed, bounded, convex subsets of l1 with fixed point property for nonexpansive mappings. Then, P.K. Lin inspired by Goebel and Kuczumow's ideas to give his result. Similarly to P.K. Lin's study, Hernández-Linares worked on L1 and in his Ph.D. thesis, supervisored under Maria Japón, showed that L1 can be renormed to have fixed point property for affine nonexpansive mappings. Then, related questions for c0 have been considered by researchers. Recently, Nezir constructed several equivalent norms on c0 and showed that there are non-weakly compact closed, bounded, convex subsets of c0 with fixed point property for affine nonexpansive mappings. In this study, we construct a family of equivalent norms containing those developed by Nezir as well and show that there exists a large class of non-weakly compact closed, bounded, convex subsets of c0 with fixed point property for affine nonexpansive mappings.

Analyzing survival curves at a fixed point in time for paired and clustered right-censored data

PubMed Central

Su, Pei-Fang; Chi, Yunchan; Lee, Chun-Yi; Shyr, Yu; Liao, Yi-De

2018-01-01

In clinical trials, information about certain time points may be of interest in making decisions about treatment effectiveness. Rather than comparing entire survival curves, researchers can focus on the comparison at fixed time points that may have a clinical utility for patients. For two independent samples of right-censored data, Klein et al. (2007) compared survival probabilities at a fixed time point by studying a number of tests based on some transformations of the Kaplan-Meier estimators of the survival function. However, to compare the survival probabilities at a fixed time point for paired right-censored data or clustered right-censored data, their approach would need to be modified. In this paper, we extend the statistics to accommodate the possible within-paired correlation and within-clustered correlation, respectively. We use simulation studies to present comparative results. Finally, we illustrate the implementation of these methods using two real data sets. PMID:29456280

APMP Scale Comparison with Three Radiation Thermometers and Six Fixed-Point Blackbodies

NASA Astrophysics Data System (ADS)

Yamada, Y.; Shimizu, Y.; Ishii, J.

2015-08-01

New Asia Pacific Metrology Programme (APMP) comparisons of radiation thermometry standards, APMP TS-11, and -12, have recently been initiated. These new APMP comparisons cover the temperature range from to . Three radiation thermometers with central wavelengths of 1.6 , 0.9 , and 0.65 are the transfer devices for the radiation thermometer scale comparison conducted in the so-called star configuration. In parallel, a compact fixed-point blackbody furnace that houses six types of fixed-point cells of In, Sn, Zn, Al, Ag, and Cu is circulated, again in a star-type comparison, to substantiate fixed-point calibration capabilities. Twelve APMP national metrology institutes are taking part in this endeavor, in which the National Metrology Institute of Japan acts as the pilot. In this article, the comparison scheme is described with emphasis on the features of the transfer devices, i.e., the radiation thermometers and the fixed-point blackbodies. Results of preliminary evaluations of the performance and characteristic of these instruments as well as the evaluation method of the comparison results are presented.

Long-Term Stability of WC-C Peritectic Fixed Point

NASA Astrophysics Data System (ADS)

Khlevnoy, B. B.; Grigoryeva, I. A.

2015-03-01

The tungsten carbide-carbon peritectic (WC-C) melting transition is an attractive high-temperature fixed point with a temperature of . Earlier investigations showed high repeatability, small melting range, low sensitivity to impurities, and robustness of WC-C that makes it a prospective candidate for the highest fixed point of the temperature scale. This paper presents further study of the fixed point, namely the investigation of the long-term stability of the WC-C melting temperature. For this purpose, a new WC-C cell of the blackbody type was built using tungsten powder of 99.999 % purity. The stability of the cell was investigated during the cell aging for 50 h at the cell working temperature that tooks 140 melting/freezing cycles. The method of investigation was based on the comparison of the WC-C tested cell with a reference Re-C fixed-point cell that reduces an influence of the probable instability of a radiation thermometer. It was shown that after the aging period, the deviation of the WC-C cell melting temperature was with an uncertainty of.

Renormalization group fixed points of foliated gravity-matter systems

NASA Astrophysics Data System (ADS)

Biemans, Jorn; Platania, Alessia; Saueressig, Frank

2017-05-01

We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) "time"- direction. In this work, we provide a detailed derivation of the renormalization group flow of Newton's constant and the cosmological constant on a flat Friedmann-Robertson-Walker background. Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters d g d λ . We classify the resulting fixed point structure as a function of these parameters finding that the existence of non-Gaussian renormalization group fixed points is rather generic. In particular the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety. Moreover, we find non-Gaussian fixed points for any number of scalar matter fields, making the scenario attractive for cosmological model building.

Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications☆

PubMed Central

Bíró, Oszkár; Koczka, Gergely; Preis, Kurt

2014-01-01

An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer. PMID:24829517

Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications.

PubMed

Bíró, Oszkár; Koczka, Gergely; Preis, Kurt

2014-05-01

An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.

Vibrational and rotational transitions in low-energy electron-diatomic-molecule collisions. I - Close-coupling theory in the moving body-fixed frame. II - Hybrid theory and close-coupling theory: An /l subscript z-prime/-conserving close-coupling approximation

NASA Technical Reports Server (NTRS)

Choi, B. H.; Poe, R. T.

1977-01-01

A detailed vibrational-rotational (V-R) close-coupling formulation of electron-diatomic-molecule scattering is developed in which the target molecular axis is chosen to be the z-axis and the resulting coupled differential equation is solved in the moving body-fixed frame throughout the entire interaction region. The coupled differential equation and asymptotic boundary conditions in the body-fixed frame are given for each parity, and procedures are outlined for evaluating V-R transition cross sections on the basis of the body-fixed transition and reactance matrix elements. Conditions are discussed for obtaining identical results from the space-fixed and body-fixed formulations in the case where a finite truncated basis set is used. The hybrid theory of Chandra and Temkin (1976) is then reformulated, relevant expressions and formulas for the simultaneous V-R transitions of the hybrid theory are obtained in the same forms as those of the V-R close-coupling theory, and distorted-wave Born-approximation expressions for the cross sections of the hybrid theory are presented. A close-coupling approximation that conserves the internuclear axis component of the incident electronic angular momentum (l subscript z-prime) is derived from the V-R close-coupling formulation in the moving body-fixed frame.

47 CFR 101.133 - Limitations on use of transmitters.

Code of Federal Regulations, 2011 CFR

2011-10-01

... SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.133 Limitations on use of transmitters. (a...) Private operational fixed point-to-point microwave stations authorized in this service may communicate...-point microwave licenses may use the same transmitting equipment under the following terms and...

47 CFR 101.133 - Limitations on use of transmitters.

Code of Federal Regulations, 2013 CFR

2013-10-01

... SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.133 Limitations on use of transmitters. (a...) Private operational fixed point-to-point microwave stations authorized in this service may communicate...-point microwave licenses may use the same transmitting equipment under the following terms and...

47 CFR 101.133 - Limitations on use of transmitters.

Code of Federal Regulations, 2014 CFR

2014-10-01

... SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.133 Limitations on use of transmitters. (a...) Private operational fixed point-to-point microwave stations authorized in this service may communicate...-point microwave licenses may use the same transmitting equipment under the following terms and...

47 CFR 101.133 - Limitations on use of transmitters.

Code of Federal Regulations, 2012 CFR

2012-10-01

... SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.133 Limitations on use of transmitters. (a...) Private operational fixed point-to-point microwave stations authorized in this service may communicate...-point microwave licenses may use the same transmitting equipment under the following terms and...

47 CFR 101.133 - Limitations on use of transmitters.

Code of Federal Regulations, 2010 CFR

2010-10-01

... SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.133 Limitations on use of transmitters. (a...) Private operational fixed point-to-point microwave stations authorized in this service may communicate...-point microwave licenses may use the same transmitting equipment under the following terms and...

Anderson Acceleration for Fixed-Point Iterations

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

Walker, Homer F.

The purpose of this grant was to support research on acceleration methods for fixed-point iterations, with applications to computational frameworks and simulation problems that are of interest to DOE.

Approach to the origin of turbulence on the basis of two-point kinetic theory

NASA Technical Reports Server (NTRS)

Tsuge, S.

1974-01-01

Equations for the fluctuation correlation in an incompressible shear flow are derived on the basis of kinetic theory, utilizing the two-point distribution function which obeys the BBGKY hierarchy equation truncated with the hypothesis of 'ternary' molecular chaos. The step from the molecular to the hydrodynamic description is accomplished by a moment expansion which is a two-point version of the thirteen-moment method, and which leads to a series of correlation equations, viz., the two-point counterparts of the continuity equation, the Navier-Stokes equation, etc. For almost parallel shearing flows the two-point equation is separable and reduces to two Orr-Sommerfeld equations with different physical implications.

Dynamic optimization and its relation to classical and quantum constrained systems

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo

2017-08-01

We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop λ-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton-Jacobi-Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Ψ(x , t) =e iS(x , t) in the quantum Schrödinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton-Jacobi-Bellman equation, when S(x , t) is identified with the optimal value function. Thus, the Hamilton-Jacobi-Bellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem.

Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics

NASA Astrophysics Data System (ADS)

Rangan, Aaditya V.; Cai, David; Tao, Louis

2007-02-01

Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear boundary conditions. The PDEs themselves are self-consistently specified by parameters which are functions of the boundary values of the solution. The moment equations can be stiff in space and time. Numerical methods are presented here for efficiently and accurately solving these moment equations. The essential ingredients in our numerical methods include: (i) the system is discretized in time with an implicit Euler method within a spectral deferred correction framework, therefore, the PDEs of the kinetic theory are reduced to a sequence, in time, of boundary value problems (BVPs) with nonlinear boundary conditions; (ii) a set of auxiliary parameters is introduced to recast the original BVP with nonlinear boundary conditions as BVPs with linear boundary conditions - with additional algebraic constraints on the auxiliary parameters; (iii) a careful combination of two Newton's iterates for the nonlinear BVP with linear boundary condition, interlaced with a Newton's iterate for solving the associated algebraic constraints is constructed to achieve quadratic convergence for obtaining the solutions with self-consistent parameters. It is shown that a simple fixed-point iteration can only achieve a linear convergence for the self-consistent parameters. The practicability and efficiency of our numerical methods for solving the moment equations of the kinetic theory are illustrated with numerical examples. It is further demonstrated that the moment equations derived from the kinetic theory of neuronal network dynamics can very well capture the coarse-grained dynamical properties of integrate-and-fire neuronal networks.

Side Effects in Time Discounting Procedures: Fixed Alternatives Become the Reference Point

PubMed Central

2016-01-01

Typical research on intertemporal choice utilizes a two-alternative forced choice (2AFC) paradigm requiring participants to choose between a smaller sooner and larger later payoff. In the adjusting-amount procedure (AAP) one of the alternatives is fixed and the other is adjusted according to particular choices made by the participant. Such a method makes the alternatives unequal in status and is speculated to make the fixed alternative a reference point for choices, thereby affecting the decision made. The current study shows that fixing different alternatives in the AAP influences discount rates in intertemporal choices. Specifically, individuals’ (N = 283) choices were affected to just the same extent by merely fixing an alternative as when choices were preceded by scenarios explicitly imposing reference points. PMID:27768759

Multidirectional hybrid algorithm for the split common fixed point problem and application to the split common null point problem.

PubMed

Li, Xia; Guo, Meifang; Su, Yongfu

2016-01-01

In this article, a new multidirectional monotone hybrid iteration algorithm for finding a solution to the split common fixed point problem is presented for two countable families of quasi-nonexpansive mappings in Banach spaces. Strong convergence theorems are proved. The application of the result is to consider the split common null point problem of maximal monotone operators in Banach spaces. Strong convergence theorems for finding a solution of the split common null point problem are derived. This iteration algorithm can accelerate the convergence speed of iterative sequence. The results of this paper improve and extend the recent results of Takahashi and Yao (Fixed Point Theory Appl 2015:87, 2015) and many others .

Fixed-Rate Compressed Floating-Point Arrays.

PubMed

Lindstrom, Peter

2014-12-01

Current compression schemes for floating-point data commonly take fixed-precision values and compress them to a variable-length bit stream, complicating memory management and random access. We present a fixed-rate, near-lossless compression scheme that maps small blocks of 4(d) values in d dimensions to a fixed, user-specified number of bits per block, thereby allowing read and write random access to compressed floating-point data at block granularity. Our approach is inspired by fixed-rate texture compression methods widely adopted in graphics hardware, but has been tailored to the high dynamic range and precision demands of scientific applications. Our compressor is based on a new, lifted, orthogonal block transform and embedded coding, allowing each per-block bit stream to be truncated at any point if desired, thus facilitating bit rate selection using a single compression scheme. To avoid compression or decompression upon every data access, we employ a software write-back cache of uncompressed blocks. Our compressor has been designed with computational simplicity and speed in mind to allow for the possibility of a hardware implementation, and uses only a small number of fixed-point arithmetic operations per compressed value. We demonstrate the viability and benefits of lossy compression in several applications, including visualization, quantitative data analysis, and numerical simulation.

Response of a Rotating Propeller to Aerodynamic Excitation

NASA Technical Reports Server (NTRS)

Arnoldi, Walter E.

1949-01-01

The flexural vibration of a rotating propeller blade with clamped shank is analyzed with the object of presenting, in matrix form, equations for the elastic bending moments in forced vibration resulting from aerodynamic forces applied at a fixed multiple of rotational speed. Matrix equations are also derived which define the critical speeds end mode shapes for any excitation order and the relation between critical speed and blade angle. Reference is given to standard works on the numerical solution of matrix equations of the forms derived. The use of a segmented blade as an approximation to a continuous blade provides a simple means for obtaining the matrix solution from the integral equation of equilibrium, so that, in the numerical application of the method presented, the several matrix arrays of the basic physical characteristics of the propeller blade are of simple form, end their simplicity is preserved until, with the solution in sight, numerical manipulations well-known in matrix algebra yield the desired critical speeds and mode shapes frame which the vibration at any operating condition may be synthesized. A close correspondence between the familiar Stodola method and the matrix method is pointed out, indicating that any features of novelty are characteristic not of the analytical procedure but only of the abbreviation, condensation, and efficient organization of the numerical procedure made possible by the use of classical matrix theory.

Anderson acceleration and application to the three-temperature energy equations

NASA Astrophysics Data System (ADS)

An, Hengbin; Jia, Xiaowei; Walker, Homer F.

2017-10-01

The Anderson acceleration method is an algorithm for accelerating the convergence of fixed-point iterations, including the Picard method. Anderson acceleration was first proposed in 1965 and, for some years, has been used successfully to accelerate the convergence of self-consistent field iterations in electronic-structure computations. Recently, the method has attracted growing attention in other application areas and among numerical analysts. Compared with a Newton-like method, an advantage of Anderson acceleration is that there is no need to form the Jacobian matrix. Thus the method is easy to implement. In this paper, an Anderson-accelerated Picard method is employed to solve the three-temperature energy equations, which are a type of strong nonlinear radiation-diffusion equations. Two strategies are used to improve the robustness of the Anderson acceleration method. One strategy is to adjust the iterates when necessary to satisfy the physical constraint. Another strategy is to monitor and, if necessary, reduce the matrix condition number of the least-squares problem in the Anderson-acceleration implementation so that numerical stability can be guaranteed. Numerical results show that the Anderson-accelerated Picard method can solve the three-temperature energy equations efficiently. Compared with the Picard method without acceleration, Anderson acceleration can reduce the number of iterations by at least half. A comparison between a Jacobian-free Newton-Krylov method, the Picard method, and the Anderson-accelerated Picard method is conducted in this paper.

Solving the hypersingular boundary integral equation for the Burton and Miller formulation.

PubMed

Langrenne, Christophe; Garcia, Alexandre; Bonnet, Marc

2015-11-01

This paper presents an easy numerical implementation of the Burton and Miller (BM) formulation, where the hypersingular Helmholtz integral is regularized by identities from the associated Laplace equation and thus needing only the evaluation of weakly singular integrals. The Helmholtz equation and its normal derivative are combined directly with combinations at edge or corner collocation nodes not used when the surface is not smooth. The hypersingular operators arising in this process are regularized and then evaluated by an indirect procedure based on discretized versions of the Calderón identities linking the integral operators for associated Laplace problems. The method is valid for acoustic radiation and scattering problems involving arbitrarily shaped three-dimensional bodies. Unlike other approaches using direct evaluation of hypersingular integrals, collocation points still coincide with mesh nodes, as is usual when using conforming elements. Using higher-order shape functions (with the boundary element method model size kept fixed) reduces the overall numerical integration effort while increasing the solution accuracy. To reduce the condition number of the resulting BM formulation at low frequencies, a regularized version α = ik/(k(2 )+ λ) of the classical BM coupling factor α = i/k is proposed. Comparisons with the combined Helmholtz integral equation Formulation method of Schenck are made for four example configurations, two of them featuring non-smooth surfaces.

Triple points and phase diagrams in the extended phase space of charged Gauss-Bonnet black holes in AdS space

NASA Astrophysics Data System (ADS)

Wei, Shao-Wen; Liu, Yu-Xiao

2014-08-01

We study the triple points and phase diagrams in the extended phase space of the charged Gauss-Bonnet black holes in d-dimensional anti-de Sitter space, where the cosmological constant appears as a dynamical pressure of the system and its conjugate quantity is the thermodynamic volume of the black holes. Employing the equation of state T=T(v,P), we demonstrate that the information of the phase transition and behavior of the Gibbs free energy are potential encoded in the T-v (T-rh) line with fixed pressure P. We get the phase diagrams for the charged Gauss-Bonnet black holes with different values of the charge Q and dimension d. The result shows that the small/large black hole phase transitions appear for any d, which is reminiscent of the liquid/gas transition of a Van der Waals type. Moreover, the interesting thermodynamic phenomena, i.e., the triple points and the small/intermediate/large black hole phase transitions are observed for d=6 and Q ∈(0.1705,0.1946).

Statistical Study of Turbulence: Spectral Functions and Correlation Coefficients

NASA Technical Reports Server (NTRS)

Frenkiel, Francois N.

1958-01-01

In reading the publications on turbulence of different authors, one often runs the risk of confusing the various correlation coefficients and turbulence spectra. We have made a point of defining, by appropriate concepts, the differences which exist between these functions. Besides, we introduce in the symbols a few new characteristics of turbulence. In the first chapter, we study some relations between the correlation coefficients and the different turbulence spectra. Certain relations are given by means of demonstrations which could be called intuitive rather than mathematical. In this way we demonstrate that the correlation coefficients between the simultaneous turbulent velocities at two points are identical, whether studied in Lagrange's or in Euler's systems. We then consider new spectra of turbulence, obtained by study of the simultaneous velocities along a straight line of given direction. We determine some relations between these spectra and the correlation coefficients. Examining the relation between the spectrum of the turbulence measured at a fixed point and the longitudinal-correlation curve given by G. I. Taylor, we find that this equation is exact only when the coefficient is very small.

Solution of the effective Hamiltonian of impurity hopping between two sites in a metal

NASA Astrophysics Data System (ADS)

Ye, Jinwu

1997-07-01

We analyze in detail all the possible fixed points of the effective Hamiltonian of a nonmagnetic impurity hopping between two sites in a metal obtained by Moustakas and Fisher (MF). We find a line of non-Fermi liquid fixed points which continuously interpolates between the two-channel Kondo fixed point (2CK) and the one-channel, two-impurity Kondo (2IK) fixed point. There is one relevant direction with scaling dimension 12 and one leading irrelevant operator with dimension 32. There is also one marginal operator in the spin sector moving along this line. The marginal operator, combined with the leading irrelevant operator, will generate the relevant operator. For the general position on this line, the leading low-temperature exponents of the specific heat, the hopping susceptibility and the electron conductivity Cimp,χhimp,σ(T) are the same as those of the 2CK, but the finite-size spectrum depends on the position on the line. No universal ratios can be formed from the amplitudes of the three quantities except at the 2CK point on this line where the universal ratios can be formed. At the 2IK point on this line, σ(T)~2σu(1+aT3/2), no universal ratio can be formed either. The additional non-Fermi-liquid fixed point found by MF has the same symmetry as the 2IK, it has two relevant directions with scaling dimension 12, and is therefore also unstable. The leading low-temperature behaviors are Cimp~T,χhimp~lnT,σ(T)~2σu(1+aT3/2) no universal ratios can be formed. The system is shown to flow to a line of Fermi-liquid fixed points which continuously interpolates between the noninteracting fixed point and the two-channel spin-flavor Kondo fixed point discussed by the author previously. The effect of particle-hole symmetry breaking is discussed. The effective Hamiltonian in the external magnetic field is analyzed. The scaling functions for the physical measurable quantities are derived in the different regimes; their predictions for the experiments are given. Finally the implications are given for a nonmagnetic impurity hopping around three sites with triangular symmetry discussed by MF.

Infrared fixed point of SU(2) gauge theory with six flavors

NASA Astrophysics Data System (ADS)

Leino, Viljami; Rummukainen, Kari; Suorsa, Joni; Tuominen, Kimmo; Tähtinen, Sara

2018-06-01

We compute the running of the coupling in SU(2) gauge theory with six fermions in the fundamental representation of the gauge group. We find strong evidence that this theory has an infrared stable fixed point at strong coupling and measure also the anomalous dimension of the fermion mass operator at the fixed point. This theory therefore likely lies close to the boundary of the conformal window and will display novel infrared dynamics if coupled with the electroweak sector of the Standard Model.

A dynamical system approach to Bianchi III cosmology for Hu-Sawicki type f( R) gravity

NASA Astrophysics Data System (ADS)

Banik, Sebika Kangsha; Banik, Debika Kangsha; Bhuyan, Kalyan

2018-02-01

The cosmological dynamics of spatially homogeneous but anisotropic Bianchi type-III space-time is investigated in presence of a perfect fluid within the framework of Hu-Sawicki model. We use the dynamical system approach to perform a detailed analysis of the cosmological behaviour of this model for the model parameters n=1, c_1=1, determining all the fixed points, their stability and corresponding cosmological evolution. We have found stable fixed points with de Sitter solution along with unstable radiation like fixed points. We have identified a matter like point which act like an unstable spiral and when the initial conditions of a trajectory are very close to this point, it stabilizes at a stable accelerating point. Thus, in this model, the universe can naturally approach to a phase of accelerated expansion following a radiation or a matter dominated phase. It is also found that the isotropisation of this model is affected by the spatial curvature and that all the isotropic fixed points are found to be spatially flat.

On the nature of control algorithms for free-floating space manipulators

NASA Technical Reports Server (NTRS)

Papadopoulos, Evangelos; Dubowsky, Steven

1991-01-01

It is suggested that nearly any control algorithm that can be used for fixed-based manipulators also can be employed in the control of free-floating space manipulator systems, with the additional conditions of estimating or measuring a spacecraft's orientation and of avoiding dynamic singularities. This result is based on the structural similarities between the kinematic and dynamic equations for the same manipulator but with a fixed base. Barycenters are used to formulate the kinematic and dynamic equations of free-floating space manipulators. A control algorithm for a space manipulator system is designed to demonstrate the value of the analysis.

Study on the fixed point in crustal deformation before strong earthquake

NASA Astrophysics Data System (ADS)

Niu, A.; Li, Y.; Yan, W. Mr

2017-12-01

Usually, scholars believe that the fault pre-sliding or expansion phenomenon will be observed near epicenter area before strong earthquake, but more and more observations show that the crust deformation nearby epicenter area is smallest(Zhou, 1997; Niu,2009,2012;Bilham, 2005; Amoruso et al., 2010). The theory of Fixed point t is a branch of mathematics that arises from the theory of topological transformation and has important applications in obvious model analysis. An important precursory was observed by two tilt-meter sets, installed at Wenchuan Observatory in the epicenter area, that the tilt changes were the smallest compared with the other 8 stations around them in one year before the Wenchuan earthquake. To subscribe the phenomenon, we proposed the minimum annual variation range that used as a topological transformation. The window length is 1 year, and the sliding length is 1 day. The convergence of points with minimum annual change in the 3 years before the Wenchuan earthquake is studied. And the results show that the points with minimum deformation amplitude basically converge to the epicenter region before the earthquake. The possible mechanism of fixed point of crustal deformation was explored. Concerning the fixed point of crust deformation, the liquidity of lithospheric medium and the isostasy theory are accepted by many scholars (Bott &Dean, 1973; Merer et al.1988; Molnar et al., 1975,1978; Tapponnier et al., 1976; Wang et al., 2001). To explain the fixed point of crust deformation before earthquakes, we study the plate bending model (Bai, et al., 2003). According to plate bending model and real deformation data, we have found that the earthquake rupture occurred around the extreme point of plate bending, where the velocities of displacement, tilt, strain, gravity and so on are close to zero, and the fixed points are located around the epicenter.The phenomenon of fixed point of crust deformation is different from former understandings about the earthquake rupture precursor. 1) The observations for crust deformation in natural conditions are different with dry and static experiments, and the former had the meaning of stress wave.2)The earthquake rupture has a special triggering mechanism that is different from the experiment with limited scale rock fracture.

Alternative supply specifications and estimates of regional supply and demand for stumpage.

Treesearch

Kent P. Connaughton; David H. Jackson; Gerard A. Majerus

1988-01-01

Four plausible sets of stumpage supply and demand equations were developed and estimated; the demand equation was the same for each set, although the supply equation differed. The supply specifications varied from the model of regional excess demand in which National Forest harvest levels were assumed fixed to a more realistic model in which the harvest on the National...

Improvements in the realization of the ITS-90 over the temperature range from the melting point of gallium to the freezing point of silver at NIM

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

Sun, J.; Zhang, J. T.; Ping, Q.

2013-09-11

The temperature primary standard over the range from the melting point of gallium to the freezing point of silver in National institute of Metrology (NIM), China, was established in the early 1990s. The performance of all of fixed-point furnaces degraded and needs to be updated due to many years of use. Nowadays, the satisfactory fixed point materials can be available with the development of the modern purification techniques. NIM plans to use a group of three cells for each defining fixed point temperature. In this way the eventual drift of individual cells can be evidenced by periodic intercomparison and thismore » will increase the reliability in disseminating the ITS-90 in China. This article describes the recent improvements in realization of ITS-90 over temperature range from the melting point of gallium to the freezing point of silver at NIM. Taking advantages of the technological advances in the design and manufacture of furnaces, the new three-zone furnaces and the open-type fixed points were developed from the freezing point of indium to the freezing point of silver, and a furnace with the three-zone semiconductor cooling was designed to automatically realize the melting point of gallium. The reproducibility of the new melting point of gallium and the new open-type freezing points of In, Sn, Zn. Al and Ag is improved, especially the freezing points of Al and Ag with the reproducibility of 0.2mK and 0.5mK respectively. The expanded uncertainty in the realization of these defining fixed point temperatures is 0.34mK, 0.44mK, 0.54mK, 0.60mK, 1.30mK and 1.88mK respectively.« less

Structure of Lie point and variational symmetry algebras for a class of odes

NASA Astrophysics Data System (ADS)

Ndogmo, J. C.

2018-04-01

It is known for scalar ordinary differential equations, and for systems of ordinary differential equations of order not higher than the third, that their Lie point symmetry algebras is of maximal dimension if and only if they can be reduced by a point transformation to the trivial equation y(n)=0. For arbitrary systems of ordinary differential equations of order n ≥ 3 reducible by point transformations to the trivial equation, we determine the complete structure of their Lie point symmetry algebras as well as that for their variational, and their divergence symmetry algebras. As a corollary, we obtain the maximal dimension of the Lie point symmetry algebra for any system of linear or nonlinear ordinary differential equations.

A Spaceborne Synthetic Aperture Radar Partial Fixed-Point Imaging System Using a Field- Programmable Gate Array—Application-Specific Integrated Circuit Hybrid Heterogeneous Parallel Acceleration Technique

PubMed Central

Li, Bingyi; Chen, Liang; Wei, Chunpeng; Xie, Yizhuang; Chen, He; Yu, Wenyue

2017-01-01

With the development of satellite load technology and very large scale integrated (VLSI) circuit technology, onboard real-time synthetic aperture radar (SAR) imaging systems have become a solution for allowing rapid response to disasters. A key goal of the onboard SAR imaging system design is to achieve high real-time processing performance with severe size, weight, and power consumption constraints. In this paper, we analyse the computational burden of the commonly used chirp scaling (CS) SAR imaging algorithm. To reduce the system hardware cost, we propose a partial fixed-point processing scheme. The fast Fourier transform (FFT), which is the most computation-sensitive operation in the CS algorithm, is processed with fixed-point, while other operations are processed with single precision floating-point. With the proposed fixed-point processing error propagation model, the fixed-point processing word length is determined. The fidelity and accuracy relative to conventional ground-based software processors is verified by evaluating both the point target imaging quality and the actual scene imaging quality. As a proof of concept, a field- programmable gate array—application-specific integrated circuit (FPGA-ASIC) hybrid heterogeneous parallel accelerating architecture is designed and realized. The customized fixed-point FFT is implemented using the 130 nm complementary metal oxide semiconductor (CMOS) technology as a co-processor of the Xilinx xc6vlx760t FPGA. A single processing board requires 12 s and consumes 21 W to focus a 50-km swath width, 5-m resolution stripmap SAR raw data with a granularity of 16,384 × 16,384. PMID:28672813

A Spaceborne Synthetic Aperture Radar Partial Fixed-Point Imaging System Using a Field- Programmable Gate Array-Application-Specific Integrated Circuit Hybrid Heterogeneous Parallel Acceleration Technique.

PubMed

Yang, Chen; Li, Bingyi; Chen, Liang; Wei, Chunpeng; Xie, Yizhuang; Chen, He; Yu, Wenyue

2017-06-24

With the development of satellite load technology and very large scale integrated (VLSI) circuit technology, onboard real-time synthetic aperture radar (SAR) imaging systems have become a solution for allowing rapid response to disasters. A key goal of the onboard SAR imaging system design is to achieve high real-time processing performance with severe size, weight, and power consumption constraints. In this paper, we analyse the computational burden of the commonly used chirp scaling (CS) SAR imaging algorithm. To reduce the system hardware cost, we propose a partial fixed-point processing scheme. The fast Fourier transform (FFT), which is the most computation-sensitive operation in the CS algorithm, is processed with fixed-point, while other operations are processed with single precision floating-point. With the proposed fixed-point processing error propagation model, the fixed-point processing word length is determined. The fidelity and accuracy relative to conventional ground-based software processors is verified by evaluating both the point target imaging quality and the actual scene imaging quality. As a proof of concept, a field- programmable gate array-application-specific integrated circuit (FPGA-ASIC) hybrid heterogeneous parallel accelerating architecture is designed and realized. The customized fixed-point FFT is implemented using the 130 nm complementary metal oxide semiconductor (CMOS) technology as a co-processor of the Xilinx xc6vlx760t FPGA. A single processing board requires 12 s and consumes 21 W to focus a 50-km swath width, 5-m resolution stripmap SAR raw data with a granularity of 16,384 × 16,384.

Mass eigenstates in bimetric theory with matter coupling

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

Schmidt-May, Angnis, E-mail: angnis.schmidt-may@fysik.su.se

2015-01-01

In this paper we study the ghost-free bimetric action extended by a recently proposed coupling to matter through a composite metric. The equations of motion for this theory are derived using a method which avoids varying the square-root matrix that appears in the matter coupling. We make an ansatz for which the metrics are proportional to each other and find that it can solve the equations provided that one parameter in the action is fixed. In this case, the proportional metrics as well as the effective metric that couples to matter solve Einstein's equations of general relativity including a mattermore » source. Around these backgrounds we derive the quadratic action for perturbations and diagonalize it into generalized mass eigenstates. It turns out that matter only interacts with the massless spin-2 mode whose equation of motion has exactly the form of the linearized Einstein equations, while the field with Fierz-Pauli mass term is completely decoupled. Hence, bimetric theory, with one parameter fixed such that proportional solutions exist, is degenerate with general relativity up to linear order around these backgrounds.« less

47 CFR 101.143 - Minimum path length requirements.

Code of Federal Regulations, 2011 CFR

2011-10-01

... SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.143 Minimum path length requirements. (a) The... carrier fixed point-to-point microwave services must equal or exceed the value set forth in the table...

47 CFR 101.143 - Minimum path length requirements.

Code of Federal Regulations, 2012 CFR

2012-10-01

... SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.143 Minimum path length requirements. (a) The... carrier fixed point-to-point microwave services must equal or exceed the value set forth in the table...

47 CFR 101.143 - Minimum path length requirements.

Code of Federal Regulations, 2014 CFR

2014-10-01

... SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.143 Minimum path length requirements. (a) The... carrier fixed point-to-point microwave services must equal or exceed the value set forth in the table...

47 CFR 101.143 - Minimum path length requirements.

Code of Federal Regulations, 2010 CFR

2010-10-01

... SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.143 Minimum path length requirements. (a) The... carrier fixed point-to-point microwave services must equal or exceed the value set forth in the table...

47 CFR 101.143 - Minimum path length requirements.

Code of Federal Regulations, 2013 CFR

2013-10-01

... SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.143 Minimum path length requirements. (a) The... carrier fixed point-to-point microwave services must equal or exceed the value set forth in the table...

Modelling and simulation of a dynamical system with the Atangana-Baleanu fractional derivative

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.

2018-01-01

In this paper, we model an ecological system consisting of a predator and two preys with the newly derived two-step fractional Adams-Bashforth method via the Atangana-Baleanu derivative in the Caputo sense. We analyze the dynamical system for correct choice of parameter values that are biologically meaningful. The local analysis of the main model is based on the application of qualitative theory for ordinary differential equations. By using the fixed point theorem idea, we establish the existence and uniqueness of the solutions. Convergence results of the new scheme are verified in both space and time. Dynamical wave phenomena of solutions are verified via some numerical results obtained for different values of the fractional index, which have some interesting ecological implications.

Evidence for equivalence of diffusion processes of passive scalar and magnetic fields in anisotropic Navier-Stokes turbulence.

PubMed

Jurčišinová, E; Jurčišin, M

2017-05-01

The influence of the uniaxial small-scale anisotropy on the kinematic magnetohydrodynamic turbulence is investigated by using the field theoretic renormalization group technique in the one-loop approximation of a perturbation theory. The infrared stable fixed point of the renormalization group equations, which drives the scaling properties of the model in the inertial range, is investigated as the function of the anisotropy parameters and it is shown that, at least at the one-loop level of approximation, the diffusion processes of the weak passive magnetic field in the anisotropically driven kinematic magnetohydrodynamic turbulence are completely equivalent to the corresponding diffusion processes of passively advected scalar fields in the anisotropic Navier-Stokes turbulent environments.

Ecological communities with Lotka-Volterra dynamics

NASA Astrophysics Data System (ADS)

Bunin, Guy

2017-04-01

Ecological communities in heterogeneous environments assemble through the combined effect of species interaction and migration. Understanding the effect of these processes on the community properties is central to ecology. Here we study these processes for a single community subject to migration from a pool of species, with population dynamics described by the generalized Lotka-Volterra equations. We derive exact results for the phase diagram describing the dynamical behaviors, and for the diversity and species abundance distributions. A phase transition is found from a phase where a unique globally attractive fixed point exists to a phase where multiple dynamical attractors exist, leading to history-dependent community properties. The model is shown to possess a symmetry that also establishes a connection with other well-known models.

Ecological communities with Lotka-Volterra dynamics.

PubMed

Bunin, Guy

2017-04-01

Ecological communities in heterogeneous environments assemble through the combined effect of species interaction and migration. Understanding the effect of these processes on the community properties is central to ecology. Here we study these processes for a single community subject to migration from a pool of species, with population dynamics described by the generalized Lotka-Volterra equations. We derive exact results for the phase diagram describing the dynamical behaviors, and for the diversity and species abundance distributions. A phase transition is found from a phase where a unique globally attractive fixed point exists to a phase where multiple dynamical attractors exist, leading to history-dependent community properties. The model is shown to possess a symmetry that also establishes a connection with other well-known models.

Stationary equatorial MHD flows in general relativity

NASA Astrophysics Data System (ADS)

Daigne, F.; Drenkhahn, G.

2002-01-01

We derive a new formulation of the fully general relativistic equations describing a stationary equatorial MHD outflow from a rotating central object. The wind solution appears as a level contour of a ``Bernoulli'' function fixed by the requirements that it must pass through the slow and fast critical points. This approach is the general relativistic extension to the classical treatment of Sakurai (\\cite{sakurai:85}). We discuss in details how the efficiency of the magnetic to kinetic energy conversion depends mainly on the geometry of the flux tubes and show that the magnetic acceleration can work very well under some conditions. We show how this tool can be used for the study of several astrophysical phenomena, among which gamma-ray bursts.

Dynamic transition between fixed- and mobile-bed: mathematical and numerical aspects

NASA Astrophysics Data System (ADS)

Zugliani, Daniel; Pasqualini, Matteo; Rosatti, Giorgio

2017-04-01

Free-surface flows with high sediment transport (as debris flow or hyper-concentrated flow) are composed by a mixture of fluid and solid phase, usually water and sediment. When these flows propagate over loose beds, particles constituting the mixture of water and sediments strongly interact with the ones forming the bed, leading to erosion or deposition. However, there are lots of other situations when the mixture flows over rigid bedrocks or over artificially paved transects, so there is no mass exchange between bed and mixture. The two situations are usually referred to as, respectively, mobile- and fixed-bed conditions. From a mathematical point of view, the systems of Partial Differential Equations (PDEs) that describe these flows derive from mass and momentum balance of both phases, but, the two resulting PDEs systems are different. The main difference concerns the concentration: in the mobile-bed condition, the concentration is linked to the local flow conditions by means of a suitable rheological relation, while in the fixed-bed case, the concentration is an unknown of the problem. It is quite common that a free surface flow with high sediment transport, in its path, encounters both conditions. In the recent work of Rosatti & Zugliani 2015, the mathematical and numerical description of the transition between fixed- and mobile-bed was successfully resolved, for the case of low sediment transport phenomena, by the introduction of a suitable erodibility variable and satisfactory results were obtained. The main disadvantage of the approach is related to the erodibility variable, that changes in space, based on bed characteristics, but remains constant in time. However, the nature of the bed can change dynamically as result of deposition over fixed bed or high erosion over mobile bed. With this work, we extend the applicability of the mentioned approach to the more complex PDEs describing the hyper-concentrated flow. Moreover, we introduce a strategy that allows a dynamic time variation of the erodibility variable. The issue of the dynamic transition between fixed- and mobile-bed condition is tackled, from a numerical point of view, using a particular predictor corrector technique that compare the transported concentration related with the fixed bed and the equilibrium concentration, deriving from a closure relation, associated to the mobile bed condition. Through a comparison between exact solution, built using the generalized Rankine - Hugoniot condition, and the numeric results, we highlight capabilities and limits of this enhanced technique. Bibliography: G. Rosatti and D. Zugliani, 2015. "Modelling the transition between fixed and mobile bed conditions in two-phase free-surface flows: The Composite Riemann Problem and its numerical solution". Journal of Computational Physics, 285:226-250

The study of correlation among different scattering parameters in an aggregate dust model

NASA Astrophysics Data System (ADS)

Mazarbhuiya, A. M.; Das, H. S.

2017-09-01

We study the light scattering properties of aggregate particles in a wide range of complex refractive indices (m = n + i k, where 1.4 ≤ n ≤ 2.0, 0.001 ≤ k ≤1.0) and wavelengths (0.45 ≤ λ≤1.25 μ m) to investigate the correlation among different parameters e.g., the positive polarization maximum (P_{max}), the amplitude of the negative polarization (P_{min}), geometric albedo (A), (n,k) and λ. Numerical computations are performed by the Superposition T-matrix code with Ballistic Cluster-Cluster Aggregate (BCCA) particles of 128 monomers and Ballistic Aggregates (BA) particles of 512 monomers, where monomer's radius of aggregates is considered to be 0.1 μm. At a fixed value of k, P_{max} and n are correlated via a quadratic regression equation and this nature is observed at all wavelengths. Further, P_{max} and k are found to be related via a polynomial regression equation when n is taken to be fixed. The degree of the equation depends on the wavelength, higher the wavelength lower is the degree. We find that A and P_{max} are correlated via a cubic regression at λ= 0.45 μ m whereas this correlation is quadratic at higher wavelengths. We notice that |P_{min}| increases with the decrease of P_{max} and a strong linear correlation between them is observed when n is fixed at some value and k is changed from higher to lower value. Further, at a fix value of k, P_{min} and P_{max} can be fitted well via a quartic regression equation when n is changed from higher to lower value. We also find that P_{max} increases with λ and they are correlated via a quartic regression.

A Markov model for the temporal dynamics of balanced random networks of finite size

PubMed Central

Lagzi, Fereshteh; Rotter, Stefan

2014-01-01

The balanced state of recurrent networks of excitatory and inhibitory spiking neurons is characterized by fluctuations of population activity about an attractive fixed point. Numerical simulations show that these dynamics are essentially nonlinear, and the intrinsic noise (self-generated fluctuations) in networks of finite size is state-dependent. Therefore, stochastic differential equations with additive noise of fixed amplitude cannot provide an adequate description of the stochastic dynamics. The noise model should, rather, result from a self-consistent description of the network dynamics. Here, we consider a two-state Markovian neuron model, where spikes correspond to transitions from the active state to the refractory state. Excitatory and inhibitory input to this neuron affects the transition rates between the two states. The corresponding nonlinear dependencies can be identified directly from numerical simulations of networks of leaky integrate-and-fire neurons, discretized at a time resolution in the sub-millisecond range. Deterministic mean-field equations, and a noise component that depends on the dynamic state of the network, are obtained from this model. The resulting stochastic model reflects the behavior observed in numerical simulations quite well, irrespective of the size of the network. In particular, a strong temporal correlation between the two populations, a hallmark of the balanced state in random recurrent networks, are well represented by our model. Numerical simulations of such networks show that a log-normal distribution of short-term spike counts is a property of balanced random networks with fixed in-degree that has not been considered before, and our model shares this statistical property. Furthermore, the reconstruction of the flow from simulated time series suggests that the mean-field dynamics of finite-size networks are essentially of Wilson-Cowan type. We expect that this novel nonlinear stochastic model of the interaction between neuronal populations also opens new doors to analyze the joint dynamics of multiple interacting networks. PMID:25520644

Using structural equation modeling for network meta-analysis.

PubMed

Tu, Yu-Kang; Wu, Yun-Chun

2017-07-14

Network meta-analysis overcomes the limitations of traditional pair-wise meta-analysis by incorporating all available evidence into a general statistical framework for simultaneous comparisons of several treatments. Currently, network meta-analyses are undertaken either within the Bayesian hierarchical linear models or frequentist generalized linear mixed models. Structural equation modeling (SEM) is a statistical method originally developed for modeling causal relations among observed and latent variables. As random effect is explicitly modeled as a latent variable in SEM, it is very flexible for analysts to specify complex random effect structure and to make linear and nonlinear constraints on parameters. The aim of this article is to show how to undertake a network meta-analysis within the statistical framework of SEM. We used an example dataset to demonstrate the standard fixed and random effect network meta-analysis models can be easily implemented in SEM. It contains results of 26 studies that directly compared three treatment groups A, B and C for prevention of first bleeding in patients with liver cirrhosis. We also showed that a new approach to network meta-analysis based on the technique of unrestricted weighted least squares (UWLS) method can also be undertaken using SEM. For both the fixed and random effect network meta-analysis, SEM yielded similar coefficients and confidence intervals to those reported in the previous literature. The point estimates of two UWLS models were identical to those in the fixed effect model but the confidence intervals were greater. This is consistent with results from the traditional pairwise meta-analyses. Comparing to UWLS model with common variance adjusted factor, UWLS model with unique variance adjusted factor has greater confidence intervals when the heterogeneity was larger in the pairwise comparison. The UWLS model with unique variance adjusted factor reflects the difference in heterogeneity within each comparison. SEM provides a very flexible framework for univariate and multivariate meta-analysis, and its potential as a powerful tool for advanced meta-analysis is still to be explored.

A new high pressure and temperature equation of state of fcc cobalt

DOE PAGES

Armentrout, Matthew M.; Kavner, Abby

2015-11-20

The high pressure and temperature equation of state of cobalt metal in the face-centered cubic phase was measured up to 57 GPa and 2400 K using the laser heated diamond anvil cell in conjunction with synchrotron X-ray diffraction. The measured region is bisected by a ferromagnetic to paramagnetic transition across the Curie temperature necessitating use of an equation of state that incorporates a 2nd order phase transition within its formalism. A third order Birch-Murnaghan equation of state with a Mie-Grüneisen-Debye thermal correction and a Hillert-Jarl magnetic correction is employed to describe the data above and below the Curie temperature. Furthermore,more » we find best fit parameters of V 0 = 6.753 (fixed) cm 3/mol, K 0 – 196 (3) GPa, K' – 4.7 (2), γ 0 – 2.00 (11), q – 1.3 (5), and θ 0 – 385 K (fixed).« less

The Ptolemaic Approach to Ionospheric Electrodynamics

NASA Astrophysics Data System (ADS)

Vasyliunas, V. M.

2010-12-01

The conventional treatment of ionospheric electrodynamics (as expounded in standard textbooks and tutorial publications) consists of a set of equations, plus verbal descriptions of the physical processes supposedly represented by the equations. Key assumptions underlying the equations are: electric field equal to the gradient of a potential, electric current driven by an Ohm's law (with both electric-field and neutral-wind terms), continuity of current then giving a second-order elliptic differential equation for calculating the potential; as a separate assumption, ion and electron bulk flows are determined by ExB drifts plus collision effects. The verbal descriptions are in several respects inconsistent with the equations; furthermore, both the descriptions and the equations are not compatible with the more rigorous physical understanding derived from the complete plasma and Maxwell's equations. The conventional ionospheric equations are applicable under restricted conditions, corresponding to a quasi-steady-state equilibrium limit, and are thus intrinsically incapable of answering questions about causal relations or dynamic developments. Within their limited range of applicability, however, the equations are in most cases adequate to explain the observations, despite the deficient treatment of plasma physics. (A historical precedent that comes to mind is that of astronomical theory at the time of Copernicus and for some decades afterwards, when the Ptolemaic scheme could explain the observations at least as well if not better than the Copernican. Some of the verbal descriptions in conventional ionospheric electrodynamics might be considered Ptolemaic also in the more literal sense of being formulated exclusively in terms of a fixed Earth.) I review the principal differences between the two approaches, point out some questions where the conventional ionospheric theory does not provide unambiguous answers even within its range of validity (e.g., topside and bottomside boundary conditions on electrodynamics), and illustrate with some simple examples of how a neutral-wind dynamo really develops.

On the equivalence of the dual-wavelength and polarimetric equations for estimation of the raindrop size distribution

NASA Technical Reports Server (NTRS)

Meneghini, Robert; Liao, Liang

2006-01-01

In writing the integral equations for the median mass diameter and particle concentration, or comparable parameters of the raindrop size distribution, it is apparent that when attenuation effects are included, the forms of the equations for polarimetric and dual wavelength radars are identical. In both sets of equations, differences in the backscattering and extinction cross sections appear: in the polarimetric equations, the differences are taken with respect polarization at a fixed frequency while for the dual wavelength equations, the differences are taken with respect to wavelength at a fixed polarization. Because the forms of the equations are the same, the ways in which they can be solved are similar as well. To avoid instabilities in the forward recursion procedure, the equations can be expressed in the form of a final-value. Solving the equations in this way traditionally has required estimates of the path attenuations to the final gate: either the attenuations at horizontal and vertical polarizations at the same frequency or attenuations at two frequencies with the same polarization. This has been done for dual-frequency (air/spaceborne case) and polarimetric radars by the respective use of the surface reference technique and the differential phase shift. An alternative to solving the constrained version of the equations is an iterative procedure recently proposed in which independent estimates of path attenuation are not required. Although the procedure has limitations, it appears to be quite useful. Simulations of the retrievals help clarify the relationship between the constrained and unconstrained approaches and their application to the polarimetric and dual-wavelength equations.

Choice in situations of time-based diminishing returns: immediate versus delayed consequences of action.

PubMed Central

Hackenberg, T D; Hineline, P N

1992-01-01

Pigeons chose between two schedules of food presentation, a fixed-interval schedule and a progressive-interval schedule that began at 0 s and increased by 20 s with each food delivery provided by that schedule. Choosing one schedule disabled the alternate schedule and stimuli until the requirements of the chosen schedule were satisfied, at which point both schedules were again made available. Fixed-interval duration remained constant within individual sessions but varied across conditions. Under reset conditions, completing the fixed-interval schedule not only produced food but also reset the progressive interval to its minimum. Blocks of sessions under the reset procedure were interspersed with sessions under a no-reset procedure, in which the progressive schedule value increased independent of fixed-interval choices. Median points of switching from the progressive to the fixed schedule varied systematically with fixed-interval value, and were consistently lower during reset than during no-reset conditions. Under the latter, each subject's choices of the progressive-interval schedule persisted beyond the point at which its requirements equaled those of the fixed-interval schedule at all but the highest fixed-interval value. Under the reset procedure, switching occurred at or prior to that equality point. These results qualitatively confirm molar analyses of schedule preference and some versions of optimality theory, but they are more adequately characterized by a model of schedule preference based on the cumulated values of multiple reinforcers, weighted in inverse proportion to the delay between the choice and each successive reinforcer. PMID:1548449

Entanglement entropy at infinite-randomness fixed points in higher dimensions.

PubMed

Lin, Yu-Cheng; Iglói, Ferenc; Rieger, Heiko

2007-10-05

The entanglement entropy of the two-dimensional random transverse Ising model is studied with a numerical implementation of the strong-disorder renormalization group. The asymptotic behavior of the entropy per surface area diverges at, and only at, the quantum phase transition that is governed by an infinite-randomness fixed point. Here we identify a double-logarithmic multiplicative correction to the area law for the entanglement entropy. This contrasts with the pure area law valid at the infinite-randomness fixed point in the diluted transverse Ising model in higher dimensions.

Fixed Point Results of Locally Contractive Mappings in Ordered Quasi-Partial Metric Spaces

PubMed Central

Arshad, Muhammad; Ahmad, Jamshaid

2013-01-01

Fixed point results for a self-map satisfying locally contractive conditions on a closed ball in an ordered 0-complete quasi-partial metric space have been established. Instead of monotone mapping, the notion of dominated mappings is applied. We have used weaker metric, weaker contractive conditions, and weaker restrictions to obtain unique fixed points. An example is given which shows that how this result can be used when the corresponding results cannot. Our results generalize, extend, and improve several well-known conventional results. PMID:24062629

Fixed point theorems for generalized α -β-weakly contraction mappings in metric spaces and applications.

PubMed

Latif, Abdul; Mongkolkeha, Chirasak; Sintunavarat, Wutiphol

2014-01-01

We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011) to generalized α-β-weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph.

Singularity-free solutions for anisotropic charged fluids with Chaplygin equation of state

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

Rahaman, Farook; Ray, Saibal; Jafry, Abdul Kayum

2010-11-15

We extend the Krori-Barua analysis of the static, spherically symmetric, Einstein-Maxwell field equations and consider charged fluid sources with anisotropic stresses. The inclusion of a new variable (tangential pressure) allows the use of a nonlinear, Chaplygin-type equation of state with coefficients fixed by the matching conditions at the boundary of the source. Some physical features are briefly discussed.

A Solution Space for a System of Null-State Partial Differential Equations: Part 1

NASA Astrophysics Data System (ADS)

Flores, Steven M.; Kleban, Peter

2015-01-01

This article is the first of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations (PDEs) in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE). In CFT, these are null-state equations and conformal Ward identities. They govern partition functions for the continuum limit of a statistical cluster or loop-gas model, such as percolation, or more generally the Potts models and O( n) models, at the statistical mechanical critical point. (SLE partition functions also satisfy these equations.) For such a lattice model in a polygon with its 2 N sides exhibiting a free/fixed side-alternating boundary condition , this partition function is proportional to the CFT correlation function where the w i are the vertices of and where is a one-leg corner operator. (Partition functions for "crossing events" in which clusters join the fixed sides of in some specified connectivity are linear combinations of such correlation functions.) When conformally mapped onto the upper half-plane, methods of CFT show that this correlation function satisfies the system of PDEs that we consider. In this first article, we use methods of analysis to prove that the dimension of this solution space is no more than C N , the Nth Catalan number. While our motivations are based in CFT, our proofs are completely rigorous. This proof is contained entirely within this article, except for the proof of Lemma 14, which constitutes the second article (Flores and Kleban, in Commun Math Phys, arXiv:1404.0035, 2014). In the third article (Flores and Kleban, in Commun Math Phys, arXiv:1303.7182, 2013), we use the results of this article to prove that the solution space of this system of PDEs has dimension C N and is spanned by solutions constructed with the CFT Coulomb gas (contour integral) formalism. In the fourth article (Flores and Kleban, in Commun Math Phys, arXiv:1405.2747, 2014), we prove further CFT-related properties about these solutions, some useful for calculating cluster-crossing probabilities of critical lattice models in polygons.

Experiments with conjugate gradient algorithms for homotopy curve tracking

NASA Technical Reports Server (NTRS)

Irani, Kashmira M.; Ribbens, Calvin J.; Watson, Layne T.; Kamat, Manohar P.; Walker, Homer F.

1991-01-01

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.

Different femorotibial contact points between fixed- and mobile-bearing TKAs do not show clinical impact.

PubMed

van Stralen, R A; Heesterbeek, P J C; Wymenga, A B

2015-11-01

In anteroposterior (AP)-gliding mobile-bearing total knee arthroplasty (TKA), the femoral component can theoretically slide forward resulting in a more anterior contact point, causing pain due to impingement. A lower lever arm of the extensor apparatus can also attribute to higher patella pressures and pain. The goal of this study was to determine the contact point in a cohort of mobile- and fixed-bearing TKAs, to determine whether the contact point lies more anteriorly in mobile-bearing TKA and to confirm whether this results in anterior knee pain. We used 38 fixed-bearing TKA and 40 mobile-bearing TKA from a randomized trial with straight lateral knee X-rays and measured the contact point. The functional outcome was measured by Knee Society Score at 12 months postoperatively. Pain scores were analysed using a VAS score (0-100 mm) in all patients at rest and when moving. Difficulty at rising up out of a chair was also assessed using a VAS score. The contact point in mobile-bearing TKA was situated at 59.5 % of the AP distance of the tibia and in the fixed-bearing TKA group at 66.1 % (P< 0.05). Patients with mobile- and fixed-bearing TKAs had similar knee scores, pain scores and difficulty in chair rise. No significant correlation was found between contact point and knee pain. The hypothesis of a more anterior contact point in the mobile-bearing cohort was confirmed but no correlation with functional and pain scores in this cohort could be found. The tibiofemoral contact point could not be correlated with a different clinical outcome and higher incidence of anterior knee pain. This study further adds to the knowledge on possible differences between mobile- and fixed-bearing prostheses. Next to that, bad outcomes could not be explained by CP. Case series, Level IV.

The Melting Point of Palladium Using Miniature Fixed Points of Different Ceramic Materials: Part II—Analysis of Melting Curves and Long-Term Investigation

NASA Astrophysics Data System (ADS)

Edler, F.; Huang, K.

2016-12-01

Fifteen miniature fixed-point cells made of three different ceramic crucible materials (Al2O3, ZrO2, and Al2O3(86 %)+ZrO2(14 %)) were filled with pure palladium and used to calibrate type B thermocouples (Pt30 %Rh/Pt6 %Rh). A critical point by using miniature fixed points with small amounts of fixed-point material is the analysis of the melting curves, which are characterized by significant slopes during the melting process compared to flat melting plateaus obtainable using conventional fixed-point cells. The method of the extrapolated starting point temperature using straight line approximation of the melting plateau was applied to analyze the melting curves. This method allowed an unambiguous determination of an electromotive force (emf) assignable as melting temperature. The strict consideration of two constraints resulted in a unique, repeatable and objective method to determine the emf at the melting temperature within an uncertainty of about 0.1 μ V. The lifetime and long-term stability of the miniature fixed points was investigated by performing more than 100 melt/freeze cycles for each crucible of the different ceramic materials. No failure of the crucibles occurred indicating an excellent mechanical stability of the investigated miniature cells. The consequent limitation of heating rates to values below {± }3.5 K min^{-1} above 1100° C and the carefully and completely filled crucibles (the liquid palladium occupies the whole volume of the crucible) are the reasons for successfully preventing the crucibles from breaking. The thermal stability of the melting temperature of palladium was excellent when using the crucibles made of Al2O3(86 %)+ZrO2(14 %) and ZrO2. Emf drifts over the total duration of the long-term investigation were below a temperature equivalent of about 0.1 K-0.2 K.

Onsite Calibration of a Precision IPRT Based on Gallium and Gallium-Based Small-Size Eutectic Points

NASA Astrophysics Data System (ADS)

Sun, Jianping; Hao, Xiaopeng; Zeng, Fanchao; Zhang, Lin; Fang, Xinyun

2017-04-01

Onsite thermometer calibration with temperature scale transfer technology based on fixed points can effectively improve the level of industrial temperature measurement and calibration. The present work performs an onsite calibration of a precision industrial platinum resistance thermometer near room temperature. The calibration is based on a series of small-size eutectic points, including Ga-In (15.7°C), Ga-Sn (20.5°C), Ga-Zn (25.2°C), and a Ga fixed point (29.7°C), developed in a portable multi-point automatic realization apparatus. The temperature plateaus of the Ga-In, Ga-Sn, and Ga-Zn eutectic points and the Ga fixed point last for longer than 2 h, and their reproducibility was better than 5 mK. The device is suitable for calibrating non-detachable temperature sensors in advanced environmental laboratories and industrial fields.

Addressing the unemployment-mortality conundrum: non-linearity is the answer.

PubMed

Bonamore, Giorgio; Carmignani, Fabrizio; Colombo, Emilio

2015-02-01

The effect of unemployment on mortality is the object of a lively literature. However, this literature is characterized by sharply conflicting results. We revisit this issue and suggest that the relationship might be non-linear. We use data for 265 territorial units (regions) within 23 European countries over the period 2000-2012 to estimate a multivariate regression of mortality. The estimating equation allows for a quadratic relationship between unemployment and mortality. We control for various other determinants of mortality at regional and national level and we include region-specific and time-specific fixed effects. The model is also extended to account for the dynamic adjustment of mortality and possible lagged effects of unemployment. We find that the relationship between mortality and unemployment is U shaped. In the benchmark regression, when the unemployment rate is low, at 3%, an increase by one percentage point decreases average mortality by 0.7%. As unemployment increases, the effect decays: when the unemployment rate is 8% (sample average) a further increase by one percentage point decreases average mortality by 0.4%. The effect changes sign, turning from negative to positive, when unemployment is around 17%. When the unemployment rate is 25%, a further increase by one percentage point raises average mortality by 0.4%. Results hold for different causes of death and across different specifications of the estimating equation. We argue that the non-linearity arises because the level of unemployment affects the psychological and behavioural response of individuals to worsening economic conditions. Copyright © 2014 Elsevier Ltd. All rights reserved.

Scaling in the vicinity of the four-state Potts fixed point

NASA Astrophysics Data System (ADS)

Blöte, H. W. J.; Guo, Wenan; Nightingale, M. P.

2017-08-01

We study a self-dual generalization of the Baxter-Wu model, employing results obtained by transfer matrix calculations of the magnetic scaling dimension and the free energy. While the pure critical Baxter-Wu model displays the critical behavior of the four-state Potts fixed point in two dimensions, in the sense that logarithmic corrections are absent, the introduction of different couplings in the up- and down triangles moves the model away from this fixed point, so that logarithmic corrections appear. Real couplings move the model into the first-order range, away from the behavior displayed by the nearest-neighbor, four-state Potts model. We also use complex couplings, which bring the model in the opposite direction characterized by the same type of logarithmic corrections as present in the four-state Potts model. Our finite-size analysis confirms in detail the existing renormalization theory describing the immediate vicinity of the four-state Potts fixed point.

How to Assess the Existence of Competing Strategies in Cognitive Tasks: A Primer on the Fixed-Point Property

PubMed Central

van Maanen, Leendert; de Jong, Ritske; van Rijn, Hedderik

2014-01-01

When multiple strategies can be used to solve a type of problem, the observed response time distributions are often mixtures of multiple underlying base distributions each representing one of these strategies. For the case of two possible strategies, the observed response time distributions obey the fixed-point property. That is, there exists one reaction time that has the same probability of being observed irrespective of the actual mixture proportion of each strategy. In this paper we discuss how to compute this fixed-point, and how to statistically assess the probability that indeed the observed response times are generated by two competing strategies. Accompanying this paper is a free R package that can be used to compute and test the presence or absence of the fixed-point property in response time data, allowing for easy to use tests of strategic behavior. PMID:25170893

Matrix product density operators: Renormalization fixed points and boundary theories

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

Cirac, J.I.; Pérez-García, D., E-mail: dperezga@ucm.es; ICMAT, Nicolas Cabrera, Campus de Cantoblanco, 28049 Madrid

We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well asmore » to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).« less

Fixed Point Learning Based Intelligent Traffic Control System

NASA Astrophysics Data System (ADS)

Zongyao, Wang; Cong, Sui; Cheng, Shao

2017-10-01

Fixed point learning has become an important tool to analyse large scale distributed system such as urban traffic network. This paper presents a fixed point learning based intelligence traffic network control system. The system applies convergence property of fixed point theorem to optimize the traffic flow density. The intelligence traffic control system achieves maximum road resources usage by averaging traffic flow density among the traffic network. The intelligence traffic network control system is built based on decentralized structure and intelligence cooperation. No central control is needed to manage the system. The proposed system is simple, effective and feasible for practical use. The performance of the system is tested via theoretical proof and simulations. The results demonstrate that the system can effectively solve the traffic congestion problem and increase the vehicles average speed. It also proves that the system is flexible, reliable and feasible for practical use.

Assessment of tungsten/rhenium thermocouples with metal-carbon eutectic fixed points up to 1500°C

NASA Astrophysics Data System (ADS)

Gotoh, M.

2013-09-01

Four Type A thermocouples and two Type C thermocouples were calibrated at the Au fixed point and Co-C and Pd-C eutectic fixed points. The thermocouples were exposed to 1330 °C for a total of 100 hours. The maximum drift due to the exposure was found to be 4.8 °C. The fixed-point calibration EMF of these thermocouples deviated by less than 0.86% from the temperature specified by the standards ASTM E230-2003 for Type C and GOSTR 8.585-2001 for Type A. The length of one of Type A thermocouples A52 is longer than the others by 150mm. Making use of this provision it was possible to place annealed part of A52 to the temperature gradient part of calibration arrangement every time. Therefore observed aging effect was as low as 0.5 °C compared to the other thermocouples.

More asymptotic safety guaranteed

NASA Astrophysics Data System (ADS)

Bond, Andrew D.; Litim, Daniel F.

2018-04-01

We study interacting fixed points and phase diagrams of simple and semisimple quantum field theories in four dimensions involving non-Abelian gauge fields, fermions and scalars in the Veneziano limit. Particular emphasis is put on new phenomena which arise due to the semisimple nature of the theory. Using matter field multiplicities as free parameters, we find a large variety of interacting conformal fixed points with stable vacua and crossovers inbetween. Highlights include semisimple gauge theories with exact asymptotic safety, theories with one or several interacting fixed points in the IR, theories where one of the gauge sectors is both UV free and IR free, and theories with weakly interacting fixed points in the UV and the IR limits. The phase diagrams for various simple and semisimple settings are also given. Further aspects such as perturbativity beyond the Veneziano limit, conformal windows, and implications for model building are discussed.

Aircraft Pitch Control With Fixed Order LQ Compensators

NASA Technical Reports Server (NTRS)

Green, James; Ashokkumar, C. R.; Homaifar, Abdollah

1997-01-01

This paper considers a given set of fixed order compensators for aircraft pitch control problem. By augmenting compensator variables to the original state equations of the aircraft, a new dynamic model is considered to seek a LQ controller. While the fixed order compensators can achieve a set of desired poles in a specified region, LQ formulation provides the inherent robustness properties. The time response for ride quality is significantly improved with a set of dynamic compensators.

Aircraft Pitch Control with Fixed Order LQ Compensators

NASA Technical Reports Server (NTRS)

Green, James; Ashokkumar, Cr.; Homaifar, A.

1997-01-01

This paper considers a given set of fixed order compensators for aircraft pitch control problem. By augmenting compensator variables to the original state equations of the aircraft, a new dynamic model is considered to seek a LQ controller. While the fixed order compensators can achieve a set of desired poles in a specified region, LQ formulation provides the inherent robustness properties. The time response for ride quality is significantly improved with a set of dynamic compensators.

High order multi-grid methods to solve the Poisson equation

NASA Technical Reports Server (NTRS)

Schaffer, S.

1981-01-01

High order multigrid methods based on finite difference discretization of the model problem are examined. The following methods are described: (1) a fixed high order FMG-FAS multigrid algorithm; (2) the high order methods; and (3) results are presented on four problems using each method with the same underlying fixed FMG-FAS algorithm.

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

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

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

On the orbital stability of pendulum-like vibrations of a rigid body carrying a rotor

NASA Astrophysics Data System (ADS)

Yehia, Hamad M.; El-Hadidy, E. G.

2013-09-01

One of the most notable effects in mechanics is the stabilization of the unstable upper equilibrium position of a symmetric body fixed from one point on its axis of symmetry, either by giving the body a suitable angular velocity or by adding a suitably spinned rotor along its axis. This effect is widely used in technology and in space dynamics. The aim of the present article is to explore the effect of the presence of a rotor on a simple periodic motion of the rigid body and its motion as a physical pendulum. The equation in the variation for pendulum vibrations takes the form in which α depends on the moments of inertia, ρ on the gyrostatic momentum of the rotor and ν (the modulus of the elliptic function) depends on the total energy of the motion. This equation, which reduces to Lame's equation when ρ = 0, has not been studied to any extent in the literature. The determination of the zones of stability and instability of plane motion reduces to finding conditions for the existence of primitive periodic solutions (with periods 4 K( ν), 8 K( ν)) with those parameters. Complete analysis of primitive periodic solutions of this equation is performed analogously to that of Ince for Lame's equation. Zones of stability and instability are determined analytically and illustrated in a graphical form by plotting surfaces separating them in the three-dimensional space of parameters. The problem is also solved numerically in certain regions of the parameter space, and results are compared to analytical ones.

Inflation, quintessence, and the origin of mass

NASA Astrophysics Data System (ADS)

Wetterich, C.

2015-08-01

In a unified picture both inflation and present dynamical dark energy arise from the same scalar field. The history of the Universe describes a crossover from a scale invariant "past fixed point" where all particles are massless, to a "future fixed point" for which spontaneous breaking of the exact scale symmetry generates the particle masses. The cosmological solution can be extrapolated to the infinite past in physical time - the universe has no beginning. This is seen most easily in a frame where particle masses and the Planck mass are field-dependent and increase with time. In this "freeze frame" the Universe shrinks and heats up during radiation and matter domination. In the equivalent, but singular Einstein frame cosmic history finds the familiar big bang description. The vicinity of the past fixed point corresponds to inflation. It ends at a first stage of the crossover. A simple model with no more free parameters than ΛCDM predicts for the primordial fluctuations a relation between the tensor amplitude r and the spectral index n, r = 8.19 (1 - n) - 0.137. The crossover is completed by a second stage where the beyond-standard-model sector undergoes the transition to the future fixed point. The resulting increase of neutrino masses stops a cosmological scaling solution, relating the present dark energy density to the present neutrino mass. At present our simple model seems compatible with all observational tests. We discuss how the fixed points can be rooted within quantum gravity in a crossover between ultraviolet and infrared fixed points. Then quantum properties of gravity could be tested both by very early and late cosmology.

47 CFR 101.705 - Special showing for renewal of common carrier station facilities using frequency diversity.

Code of Federal Regulations, 2014 CFR

2014-10-01

... COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Common Carrier Fixed Point-to-Point Microwave Service § 101.705 Special showing for renewal of common carrier station...

47 CFR 101.705 - Special showing for renewal of common carrier station facilities using frequency diversity.

Code of Federal Regulations, 2013 CFR

2013-10-01

... COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Common Carrier Fixed Point-to-Point Microwave Service § 101.705 Special showing for renewal of common carrier station...

47 CFR 101.705 - Special showing for renewal of common carrier station facilities using frequency diversity.

Code of Federal Regulations, 2012 CFR

2012-10-01

... COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Common Carrier Fixed Point-to-Point Microwave Service § 101.705 Special showing for renewal of common carrier station...

47 CFR 101.705 - Special showing for renewal of common carrier station facilities using frequency diversity.

Code of Federal Regulations, 2011 CFR

2011-10-01

... COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Common Carrier Fixed Point-to-Point Microwave Service § 101.705 Special showing for renewal of common carrier station...

Heron Triangles with Two Fixed Sides

DTIC Science & Technology

2006-10-08

number of divisors of the positive integer n. Theorem 2.3. If a and b are fixed, then H(a, b) ≤ 4τ(ab)2. Proof. We start with the following observation...obtain a more precise result which improves upon [2]. Theorem 2.4. If p and q are two fixed primes, then H(p, q) is  = 0 if both p and q are...conclude the proof of Theorem 2.4, it suffices to show that if p and q are fixed, then at most five of the above eight equations can produce integer

Meshless method for solving fixed boundary problem of plasma equilibrium

NASA Astrophysics Data System (ADS)

Imazawa, Ryota; Kawano, Yasunori; Itami, Kiyoshi

2015-07-01

This study solves the Grad-Shafranov equation with a fixed plasma boundary by utilizing a meshless method for the first time. Previous studies have utilized a finite element method (FEM) to solve an equilibrium inside the fixed separatrix. In order to avoid difficulties of FEM (such as mesh problem, difficulty of coding, expensive calculation cost), this study focuses on the meshless methods, especially RBF-MFS and KANSA's method to solve the fixed boundary problem. The results showed that CPU time of the meshless methods was ten to one hundred times shorter than that of FEM to obtain the same accuracy.

Exploring the nonlinear cloud and rain equation

NASA Astrophysics Data System (ADS)

Koren, Ilan; Tziperman, Eli; Feingold, Graham

2017-01-01

Marine stratocumulus cloud decks are regarded as the reflectors of the climate system, returning back to space a significant part of the income solar radiation, thus cooling the atmosphere. Such clouds can exist in two stable modes, open and closed cells, for a wide range of environmental conditions. This emergent behavior of the system, and its sensitivity to aerosol and environmental properties, is captured by a set of nonlinear equations. Here, using linear stability analysis, we express the transition from steady to a limit-cycle state analytically, showing how it depends on the model parameters. We show that the control of the droplet concentration (N), the environmental carrying-capacity (H0), and the cloud recovery parameter (τ) can be linked by a single nondimensional parameter (μ=√{N }/(ατH0) ) , suggesting that for deeper clouds the transition from open (oscillating) to closed (stable fixed point) cells will occur for higher droplet concentration (i.e., higher aerosol loading). The analytical calculations of the possible states, and how they are affected by changes in aerosol and the environmental variables, provide an enhanced understanding of the complex interactions of clouds and rain.

Cosmology in generalized Proca theories

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

Felice, Antonio De; Mukohyama, Shinji; Heisenberg, Lavinia

2016-06-01

We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological implications of such generalized Proca theories are investigated for both the background and the linear perturbation by taking into account the Lagrangian up to quintic order. In the presence of a matter fluid with a temporal component of the vector field, we derive the background equations of motion and show the existence of de Sitter solutions relevant to the late-time cosmic acceleration. We also obtain conditions for themore » absence of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations in the small-scale limit. Our results are applied to concrete examples of the general functions in the theory, which encompass vector Galileons as a specific case. In such examples, we show that the de Sitter fixed point is always a stable attractor and study viable parameter spaces in which the no-ghost and stability conditions are satisfied during the cosmic expansion history.« less

Bimodal pair f-KdV dynamics in star-forming clouds

NASA Astrophysics Data System (ADS)

Karmakar, Pralay Kumar; Haloi, Archana; Roy, Supriya

2018-04-01

A theoretical formalism for investigating the bimodal conjugational mode dynamics of hybrid source, dictated by a unique pair of forced Korteweg-de Vries (f-KdV) equations in a complex turbo-magnetized star-forming cloud, is reported. It uses a standard multi-scale analysis executed over the cloud-governing equations in a closure form to derive the conjugated pair f-KdV system. We numerically see the structural features of two distinctive classes of eigenmode patterns stemming from the conjoint gravito-electrostatic interplay. The electrostatic compressive monotonic aperiodic shock-like patterns and gravitational compressive non-monotonic oscillatory shock-like structures are excitable. It is specifically revealed that the constitutive grain-charge (grain-mass) acts as electrostatic stabilizer (gravitational destabilizer) against the global cloud collapse dynamics. The basic features of the nonlinear coherent structures are confirmed in systematic phase-plane landscapes, indicating electrostatic irregular non-homoclinic open trajectories and gravitational atypical non-chaotic homoclinic fixed-point attractors. The relevance in the real astro-cosmic scenarios of the early phases of structure formation via wave-driven fluid-accretive transport processes is summarily emphasized.

Convergence of Distributed Optimal Controls on the Internal Energy in Mixed Elliptic Problems when the Heat Transfer Coefficient Goes to Infinity

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

Gariboldi, C.; E-mail: cgariboldi@exa.unrc.edu.ar; Tarzia, D.

2003-05-21

We consider a steady-state heat conduction problem P{sub {alpha}} with mixed boundary conditions for the Poisson equation depending on a positive parameter {alpha} , which represents the heat transfer coefficient on a portion {gamma} {sub 1} of the boundary of a given bounded domain in R{sup n} . We formulate distributed optimal control problems over the internal energy g for each {alpha}. We prove that the optimal control g{sub o}p{sub {alpha}} and its corresponding system u{sub go}p{sub {alpha}}{sub {alpha}} and adjoint p{sub go}p{sub {alpha}}{sub {alpha}} states for each {alpha} are strongly convergent to g{sub op},u{sub gop} and p{sub gop} ,more » respectively, in adequate functional spaces. We also prove that these limit functions are respectively the optimal control, and the system and adjoint states corresponding to another distributed optimal control problem for the same Poisson equation with a different boundary condition on the portion {gamma}{sub 1} . We use the fixed point and elliptic variational inequality theories.« less

Optimal four-impulse rendezvous between coplanar elliptical orbits

NASA Astrophysics Data System (ADS)

Wang, JianXia; Baoyin, HeXi; Li, JunFeng; Sun, FuChun

2011-04-01

Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods proposed for fuel optimal orbital rendezvous, Lawden's primer vector theory is favored by many researchers with its clear physical concept and simplicity in solution. Prussing has applied the primer vector optimization theory to minimum-fuel, multiple-impulse, time-fixed orbital rendezvous in a near circular orbit and achieved great success. Extending Prussing's work, this paper will employ the primer vector theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous. Based on linearized equations of relative motion on elliptical reference orbit (referred to as T-H equations), the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar, coaxial elliptical orbits with arbitrary large eccentricity. A parameter adjustment method is developed for the prime vector to satisfy the Lawden's necessary condition for the optimal solution. Finally, the optimal multiple-impulse rendezvous solution including the time, direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem. The rendezvous error of the linearized equation is also analyzed. The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentricity case and is large for the higher eccentricity. For better rendezvous accuracy of high eccentricity orbits, a combined method of multiplier penalty function with the simplex search method is used for local optimization. The simplex search method is sensitive to the initial values of optimization variables, but the simulation results show that initial values with the primer vector theory, and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence, because the optimal results obtained by the primer vector theory are already very close to the actual optimal solution. If the initial values are taken randomly, it is difficult to converge to the optimal solution.

Fabrication of a mini multi-fixed-point cell for the calibration of industrial platinum resistance thermometers

NASA Astrophysics Data System (ADS)

Ragay-Enot, Monalisa; Lee, Young Hee; Kim, Yong-Gyoo

2017-07-01

A mini multi-fixed-point cell (length 118 mm, diameter 33 mm) containing three materials (In-Zn eutectic (mass fraction 3.8% Zn), Sn and Pb) in a single crucible was designed and fabricated for the easy and economical fixed-point calibration of industrial platinum resistance thermometers (IPRTs) for use in industrial temperature measurements. The melting and freezing behaviors of the metals were investigated and the phase transition temperatures were determined using a commercial dry-block calibrator. Results showed that the melting plateaus are generally easy to realize and are reproducible, flatter and of longer duration. On the other hand, the freezing process is generally difficult, especially for Sn, due to the high supercooling required to initiate freezing. The observed melting temperatures at optimum set conditions were 143.11 °C (In-Zn), 231.70 °C (Sn) and 327.15 °C (Pb) with expanded uncertainties (k  = 2) of 0.12 °C, 0.10 °C and 0.13 °C, respectively. This multi-fixed-point cell can be treated as a sole reference temperature-generating system. Based on the results, the realization of melting points of the mini multi-fixed-point cell can be recommended for the direct calibration of IPRTs in industrial applications without the need for a reference thermometer.

Holography as a highly efficient renormalization group flow. I. Rephrasing gravity

NASA Astrophysics Data System (ADS)

Behr, Nicolas; Kuperstein, Stanislav; Mukhopadhyay, Ayan

2016-07-01

We investigate how the holographic correspondence can be reformulated as a generalization of Wilsonian renormalization group (RG) flow in a strongly interacting large-N quantum field theory. We first define a highly efficient RG flow as one in which the Ward identities related to local conservation of energy, momentum and charges preserve the same form at each scale. To achieve this, it is necessary to redefine the background metric and external sources at each scale as functionals of the effective single-trace operators. These redefinitions also absorb the contributions of the multitrace operators to these effective Ward identities. Thus, the background metric and external sources become effectively dynamical, reproducing the dual classical gravity equations in one higher dimension. Here, we focus on reconstructing the pure gravity sector as a highly efficient RG flow of the energy-momentum tensor operator, leaving the explicit constructive field theory approach for generating such RG flows to the second part of the work. We show that special symmetries of the highly efficient RG flows carry information through which we can decode the gauge fixing of bulk diffeomorphisms in the corresponding gravity equations. We also show that the highly efficient RG flow which reproduces a given classical gravity theory in a given gauge is unique provided the endpoint can be transformed to a nonrelativistic fixed point with a finite number of parameters under a universal rescaling. The results obtained here are used in the second part of this work, where we do an explicit field-theoretic construction of the RG flow and obtain the dual classical gravity theory.

Interactive Physical Simulation of Catheter Motion within Mayor Vessel Structures and Cavities for ASD/VSD Treatment

NASA Astrophysics Data System (ADS)

Becherer, Nico; Hesser, Jürgen; Kornmesser, Ulrike; Schranz, Dietmar; Männer, Reinhard

2007-03-01

Simulation systems are becoming increasingly essential in medical education. Hereby, capturing the physical behaviour of the real world requires a sophisticated modelling of instruments within the virtual environment. Most models currently used are not capable of user interactive simulations due to the computation of the complex underlying analytical equations. Alternatives are often based on simplifying mass-spring systems, being able to deliver high update rates that come at the cost of less realistic motion. In addition, most techniques are limited to narrow and tubular vessel structures or restrict shape alterations to two degrees of freedom, not allowing instrument deformations like torsion. In contrast, our approach combines high update rates with highly realistic motion and can in addition be used with respect to arbitrary structures like vessels or cavities (e.g. atrium, ventricle) without limiting the degrees of freedom. Based on energy minimization, bending energies and vessel structures are considered as linear elastic elements; energies are evaluated at regularly spaced points on the instrument, while the distance of the points is fixed, i.e. we simulate an articulated structure of joints with fixed connections between them. Arbitrary tissue structures are modeled through adaptive distance fields and are connected by nodes via an undirected graph system. The instrument points are linked to nodes by a system of rules. Energy minimization uses a Quasi Newton method without preconditioning and, hereby, gradients are estimated using a combination of analytical and numerical terms. Results show a high quality in motion simulation when compared to a phantom model. The approach is also robust and fast. Simulating an instrument with 100 joints runs at 100 Hz on a 3 GHz PC.

Weighted triangulation adjustment

USGS Publications Warehouse

Anderson, Walter L.

1969-01-01

The variation of coordinates method is employed to perform a weighted least squares adjustment of horizontal survey networks. Geodetic coordinates are required for each fixed and adjustable station. A preliminary inverse geodetic position computation is made for each observed line. Weights associated with each observed equation for direction, azimuth, and distance are applied in the formation of the normal equations in-the least squares adjustment. The number of normal equations that may be solved is twice the number of new stations and less than 150. When the normal equations are solved, shifts are produced at adjustable stations. Previously computed correction factors are applied to the shifts and a most probable geodetic position is found for each adjustable station. Pinal azimuths and distances are computed. These may be written onto magnetic tape for subsequent computation of state plane or grid coordinates. Input consists of punch cards containing project identification, program options, and position and observation information. Results listed include preliminary and final positions, residuals, observation equations, solution of the normal equations showing magnitudes of shifts, and a plot of each adjusted and fixed station. During processing, data sets containing irrecoverable errors are rejected and the type of error is listed. The computer resumes processing of additional data sets.. Other conditions cause warning-errors to be issued, and processing continues with the current data set.

Advances in Quantum Trajectory Approaches to Dynamics

NASA Astrophysics Data System (ADS)

Askar, Attila

2001-03-01

The quantum fluid dynamics (QFD) formulation is based on the separation of the amplitude and phase of the complex wave function in Schrodinger's equation. The approach leads to conservation laws for an equivalent "gas continuum". The Lagrangian [1] representation corresponds to following the particles of the fluid continuum, i. e. calculating "quantum trajectories". The Eulerian [2] representation on the other hand, amounts to observing the dynamics of the gas continuum at the points of a fixed coordinate frame. The combination of several factors leads to a most encouraging computational efficiency. QFD enables the numerical analysis to deal with near monotonic amplitude and phase functions. The Lagrangian description concentrates the computation effort to regions of highest probability as an optimal adaptive grid. The Eulerian representation allows the study of multi-coordinate problems as a set of one-dimensional problems within an alternating direction methodology. An explicit time integrator limits the increase in computational effort with the number of discrete points to linear. Discretization of the space via local finite elements [1,2] and global radial functions [3] will be discussed. Applications include wave packets in four-dimensional quadratic potentials and two coordinate photo-dissociation problems for NOCl and NO2. [1] "Quantum fluid dynamics (QFD) in the Lagrangian representation with applications to photo-dissociation problems", F. Sales, A. Askar and H. A. Rabitz, J. Chem. Phys. 11, 2423 (1999) [2] "Multidimensional wave-packet dynamics within the fluid dynamical formulation of the Schrodinger equation", B. Dey, A. Askar and H. A. Rabitz, J. Chem. Phys. 109, 8770 (1998) [3] "Solution of the quantum fluid dynamics equations with radial basis function interpolation", Xu-Guang Hu, Tak-San Ho, H. A. Rabitz and A. Askar, Phys. Rev. E. 61, 5967 (2000)

47 CFR 101.703 - Permissible communications.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 47 Telecommunication 5 2014-10-01 2014-10-01 false Permissible communications. 101.703 Section 101.703 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Common Carrier Fixed Point-to-Point Microwave Service § 101.703 Permissible...

47 CFR 101.601 - Eligibility.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 47 Telecommunication 5 2013-10-01 2013-10-01 false Eligibility. 101.601 Section 101.601 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Private Operational Fixed Point-to-Point Microwave Service § 101.601 Eligibility. Any person, or...

47 CFR 101.703 - Permissible communications.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 47 Telecommunication 5 2011-10-01 2011-10-01 false Permissible communications. 101.703 Section 101.703 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Common Carrier Fixed Point-to-Point Microwave Service § 101.703 Permissible...

47 CFR 101.135 - Shared use of radio stations and the offering of private carrier service.

Code of Federal Regulations, 2012 CFR

2012-10-01

... COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101... Operational Fixed Point-to-Point Microwave radio stations may share the use of their facilities on a non...

47 CFR 101.601 - Eligibility.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 47 Telecommunication 5 2010-10-01 2010-10-01 false Eligibility. 101.601 Section 101.601 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Private Operational Fixed Point-to-Point Microwave Service § 101.601 Eligibility. Any person, or...

47 CFR 101.601 - Eligibility.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 47 Telecommunication 5 2014-10-01 2014-10-01 false Eligibility. 101.601 Section 101.601 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Private Operational Fixed Point-to-Point Microwave Service § 101.601 Eligibility. Any person, or...

47 CFR 101.135 - Shared use of radio stations and the offering of private carrier service.

Code of Federal Regulations, 2010 CFR

2010-10-01

... COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101... Operational Fixed Point-to-Point Microwave radio stations may share the use of their facilities on a non...

47 CFR 101.703 - Permissible communications.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 47 Telecommunication 5 2013-10-01 2013-10-01 false Permissible communications. 101.703 Section 101.703 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Common Carrier Fixed Point-to-Point Microwave Service § 101.703 Permissible...

47 CFR 101.135 - Shared use of radio stations and the offering of private carrier service.

Code of Federal Regulations, 2011 CFR

2011-10-01

... COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101... Operational Fixed Point-to-Point Microwave radio stations may share the use of their facilities on a non...

47 CFR 101.601 - Eligibility.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 47 Telecommunication 5 2012-10-01 2012-10-01 false Eligibility. 101.601 Section 101.601 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Private Operational Fixed Point-to-Point Microwave Service § 101.601 Eligibility. Any person, or...

47 CFR 101.703 - Permissible communications.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 47 Telecommunication 5 2010-10-01 2010-10-01 false Permissible communications. 101.703 Section 101.703 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Common Carrier Fixed Point-to-Point Microwave Service § 101.703 Permissible...

47 CFR 101.135 - Shared use of radio stations and the offering of private carrier service.

Code of Federal Regulations, 2014 CFR

2014-10-01

... COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101... Operational Fixed Point-to-Point Microwave radio stations may share the use of their facilities on a non...

47 CFR 101.135 - Shared use of radio stations and the offering of private carrier service.

Code of Federal Regulations, 2013 CFR

2013-10-01

... COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101... Operational Fixed Point-to-Point Microwave radio stations may share the use of their facilities on a non...

47 CFR 101.601 - Eligibility.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 47 Telecommunication 5 2011-10-01 2011-10-01 false Eligibility. 101.601 Section 101.601 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Private Operational Fixed Point-to-Point Microwave Service § 101.601 Eligibility. Any person, or...

47 CFR 101.703 - Permissible communications.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 47 Telecommunication 5 2012-10-01 2012-10-01 false Permissible communications. 101.703 Section 101.703 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Common Carrier Fixed Point-to-Point Microwave Service § 101.703 Permissible...

Regulator dependence of fixed points in quantum Einstein gravity with R 2 truncation

NASA Astrophysics Data System (ADS)

Nagy, S.; Fazekas, B.; Peli, Z.; Sailer, K.; Steib, I.

2018-03-01

We performed a functional renormalization group analysis for the quantum Einstein gravity including a quadratic term in the curvature. The ultraviolet non-gaussian fixed point and its critical exponent for the correlation length are identified for different forms of regulators in case of dimension 3. We searched for that optimized regulator where the physical quantities show the least regulator parameter dependence. It is shown that the Litim regulator satisfies this condition. The infrared fixed point has also been investigated, it is found that the exponent is insensitive to the third coupling introduced by the R 2 term.

Fixed Point Results for G-α-Contractive Maps with Application to Boundary Value Problems

PubMed Central

Roshan, Jamal Rezaei

2014-01-01

We unify the concepts of G-metric, metric-like, and b-metric to define new notion of generalized b-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes of G-α-admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, some examples and an application to the existence of a solution for the first-order periodic boundary value problem are provided here to illustrate the usability of the obtained results. PMID:24895655

A regularity result for fixed points, with applications to linear response

NASA Astrophysics Data System (ADS)

Sedro, Julien

2018-04-01

In this paper, we show a series of abstract results on fixed point regularity with respect to a parameter. They are based on a Taylor development taking into account a loss of regularity phenomenon, typically occurring for composition operators acting on spaces of functions with finite regularity. We generalize this approach to higher order differentiability, through the notion of an n-graded family. We then give applications to the fixed point of a nonlinear map, and to linear response in the context of (uniformly) expanding dynamics (theorem 3 and corollary 2), in the spirit of Gouëzel-Liverani.

Context dependence of students' views about the role of equations in understanding biology.

PubMed

Watkins, Jessica; Elby, Andrew

2013-06-01

Students' epistemological views about biology--their ideas about what "counts" as learning and understanding biology--play a role in how they approach their courses and respond to reforms. As introductory biology courses incorporate more physics and quantitative reasoning, student attitudes about the role of equations in biology become especially relevant. However, as documented in research in physics education, students' epistemologies are not always stable and fixed entities; they can be dynamic and context-dependent. In this paper, we examine an interview with an introductory student in which she discusses the use of equations in her reformed biology course. In one part of the interview, she expresses what sounds like an entrenched negative stance toward the role equations can play in understanding biology. However, later in the interview, when discussing a different biology topic, she takes a more positive stance toward the value of equations. These results highlight how a given student can have diverse ways of thinking about the value of bringing physics and math into biology. By highlighting how attitudes can shift in response to different tasks, instructional environments, and contextual cues, we emphasize the need to attend to these factors, rather than treating students' beliefs as fixed and stable.

Multiple steady states in atmospheric chemistry

NASA Technical Reports Server (NTRS)

Stewart, Richard W.

1993-01-01

The equations describing the distributions and concentrations of trace species are nonlinear and may thus possess more than one solution. This paper develops methods for searching for multiple physical solutions to chemical continuity equations and applies these to subsets of equations describing tropospheric chemistry. The calculations are carried out with a box model and use two basic strategies. The first strategy is a 'search' method. This involves fixing model parameters at specified values, choosing a wide range of initial guesses at a solution, and using a Newton-Raphson technique to determine if different initial points converge to different solutions. The second strategy involves a set of techniques known as homotopy methods. These do not require an initial guess, are globally convergent, and are guaranteed, in principle, to find all solutions of the continuity equations. The first method is efficient but essentially 'hit or miss' in the sense that it cannot guarantee that all solutions which may exist will be found. The second method is computationally burdensome but can, in principle, determine all the solutions of a photochemical system. Multiple solutions have been found for models that contain a basic complement of photochemical reactions involving O(x), HO(x), NO(x), and CH4. In the present calculations, transitions occur between stable branches of a multiple solution set as a control parameter is varied. These transitions are manifestations of hysteresis phenomena in the photochemical system and may be triggered by increasing the NO flux or decreasing the CH4 flux from current mean tropospheric levels.

Optimal transfers between libration-point orbits in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Hiday, Lisa Ann

1992-09-01

A strategy is formulated to design optimal impulsive transfers between three-dimensional libration-point orbits in the vicinity of the interior L(1) libration point of the Sun-Earth/Moon barycenter system. Two methods of constructing nominal transfers, for which the fuel cost is to be minimized, are developed; both inferior and superior transfers between two halo orbits are considered. The necessary conditions for an optimal transfer trajectory are stated in terms of the primer vector. The adjoint equation relating reference and perturbed trajectories in this formulation of the elliptic restricted three-body problem is shown to be distinctly different from that obtained in the analysis of trajectories in the two-body problem. Criteria are established whereby the cost on a nominal transfer can be improved by the addition of an interior impulse or by the implementation of coastal arcs in the initial and final orbits. The necessary conditions for the local optimality of a time-fixed transfer trajectory possessing additional impulses are satisfied by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses. The optimality of a time-free transfer containing coastal arcs is surmised by examination of the slopes at the endpoints of a plot of the magnitude of the primer vector over the duration of the transfer path. If the initial and final slopes of the primer magnitude are zero, the transfer trajectory is optimal; otherwise, the execution of coasts is warranted. The position and timing of each interior impulse applied to a time-fixed transfer as well as the direction and length of coastal periods implemented on a time-free transfer are specified by the unconstrained minimization of the appropriate variation in cost utilizing a multivariable search technique. Although optimal solutions in some instances are elusive, the time-fixed and time-free optimization algorithms prove to be very successful in diminishing costs on nominal transfer trajectories. The inclusion of coastal arcs on time-free superior and inferior transfers results in significant modification of the transfer time of flight caused by shifts in departure and arrival locations on the halo orbits.

Synchronisation under shocks: The Lévy Kuramoto model

NASA Astrophysics Data System (ADS)

Roberts, Dale; Kalloniatis, Alexander C.

2018-04-01

We study the Kuramoto model of identical oscillators on Erdős-Rényi (ER) and Barabasi-Alberts (BA) scale free networks examining the dynamics when perturbed by a Lévy noise. Lévy noise exhibits heavier tails than Gaussian while allowing for their tempering in a controlled manner. This allows us to understand how 'shocks' influence individual oscillator and collective system behaviour of a paradigmatic complex system. Skewed α-stable Lévy noise, equivalent to fractional diffusion perturbations, are considered, but overlaid by exponential tempering of rate λ. In an earlier paper we found that synchrony takes a variety of forms for identical Kuramoto oscillators subject to stable Lévy noise, not seen for the Gaussian case, and changing with α: a noise-induced drift, a smooth α dependence of the point of cross-over of synchronisation point of ER and BA networks, and a severe loss of synchronisation at low values of α. In the presence of tempering we observe both analytically and numerically a dramatic change to the α < 1 behaviour where synchronisation is sustained over a larger range of values of the 'noise strength' σ, improved compared to the α > 1 tempered cases. Analytically we study the system close to the phase synchronised fixed point and solve the tempered fractional Fokker-Planck equation. There we observe that densities show stronger support in the basin of attraction at low α for fixed coupling, σ and tempering λ. We then perform numerical simulations for networks of size N = 1000 and average degree d ¯ = 10. There, we compute the order parameter r as a function of σ for fixed α and λ and observe values of r ≈ 1 over larger ranges of σ for α < 1 and λ ≠ 0. In addition we observe drift of both positive and negative slopes for different α and λ when native frequencies are equal, and confirm a sustainment of synchronisation down to low values of α. We propose a mechanism for this in terms of the basic shape of the tempered stable Lévy densities for various α and how it feeds into Kuramoto oscillator dynamics and illustrate this with examples of specific paths.

Asymptotic safety of quantum gravity beyond Ricci scalars

NASA Astrophysics Data System (ADS)

Falls, Kevin; King, Callum R.; Litim, Daniel F.; Nikolakopoulos, Kostas; Rahmede, Christoph

2018-04-01

We investigate the asymptotic safety conjecture for quantum gravity including curvature invariants beyond Ricci scalars. Our strategy is put to work for families of gravitational actions which depend on functions of the Ricci scalar, the Ricci tensor, and products thereof. Combining functional renormalization with high order polynomial approximations and full numerical integration we derive the renormalization group flow for all couplings and analyse their fixed points, scaling exponents, and the fixed point effective action as a function of the background Ricci curvature. The theory is characterized by three relevant couplings. Higher-dimensional couplings show near-Gaussian scaling with increasing canonical mass dimension. We find that Ricci tensor invariants stabilize the UV fixed point and lead to a rapid convergence of polynomial approximations. We apply our results to models for cosmology and establish that the gravitational fixed point admits inflationary solutions. We also compare findings with those from f (R ) -type theories in the same approximation and pin-point the key new effects due to Ricci tensor interactions. Implications for the asymptotic safety conjecture of gravity are indicated.

Universality of modular symmetries in two-dimensional magnetotransport

NASA Astrophysics Data System (ADS)

Olsen, K. S.; Limseth, H. S.; Lütken, C. A.

2018-01-01

We analyze experimental quantum Hall data from a wide range of different materials, including semiconducting heterojunctions, thin films, surface layers, graphene, mercury telluride, bismuth antimonide, and black phosphorus. The fact that these materials have little in common, except that charge transport is effectively two-dimensional, shows how robust and universal the quantum Hall phenomenon is. The scaling and fixed point data we analyzed appear to show that magnetotransport in two dimensions is governed by a small number of universality classes that are classified by modular symmetries, which are infinite discrete symmetries not previously seen in nature. The Hall plateaux are (infrared) stable fixed points of the scaling-flow, and quantum critical points (where the wave function is delocalized) are unstable fixed points of scaling. Modular symmetries are so rigid that they in some cases fix the global geometry of the scaling flow, and therefore predict the exact location of quantum critical points, as well as the shape of flow lines anywhere in the phase diagram. We show that most available experimental quantum Hall scaling data are in good agreement with these predictions.

Rigorous high-precision enclosures of fixed points and their invariant manifolds

NASA Astrophysics Data System (ADS)

Wittig, Alexander N.

The well established concept of Taylor Models is introduced, which offer highly accurate C0 enclosures of functional dependencies, combining high-order polynomial approximation of functions and rigorous estimates of the truncation error, performed using verified arithmetic. The focus of this work is on the application of Taylor Models in algorithms for strongly non-linear dynamical systems. A method is proposed to extend the existing implementation of Taylor Models in COSY INFINITY from double precision coefficients to arbitrary precision coefficients. Great care is taken to maintain the highest efficiency possible by adaptively adjusting the precision of higher order coefficients in the polynomial expansion. High precision operations are based on clever combinations of elementary floating point operations yielding exact values for round-off errors. An experimental high precision interval data type is developed and implemented. Algorithms for the verified computation of intrinsic functions based on the High Precision Interval datatype are developed and described in detail. The application of these operations in the implementation of High Precision Taylor Models is discussed. An application of Taylor Model methods to the verification of fixed points is presented by verifying the existence of a period 15 fixed point in a near standard Henon map. Verification is performed using different verified methods such as double precision Taylor Models, High Precision intervals and High Precision Taylor Models. Results and performance of each method are compared. An automated rigorous fixed point finder is implemented, allowing the fully automated search for all fixed points of a function within a given domain. It returns a list of verified enclosures of each fixed point, optionally verifying uniqueness within these enclosures. An application of the fixed point finder to the rigorous analysis of beam transfer maps in accelerator physics is presented. Previous work done by Johannes Grote is extended to compute very accurate polynomial approximations to invariant manifolds of discrete maps of arbitrary dimension around hyperbolic fixed points. The algorithm presented allows for automatic removal of resonances occurring during construction. A method for the rigorous enclosure of invariant manifolds of continuous systems is introduced. Using methods developed for discrete maps, polynomial approximations of invariant manifolds of hyperbolic fixed points of ODEs are obtained. These approximations are outfit with a sharp error bound which is verified to rigorously contain the manifolds. While we focus on the three dimensional case, verification in higher dimensions is possible using similar techniques. Integrating the resulting enclosures using the verified COSY VI integrator, the initial manifold enclosures are expanded to yield sharp enclosures of large parts of the stable and unstable manifolds. To demonstrate the effectiveness of this method, we construct enclosures of the invariant manifolds of the Lorenz system and show pictures of the resulting manifold enclosures. To the best of our knowledge, these enclosures are the largest verified enclosures of manifolds in the Lorenz system in existence.

Development of Fixed-Point Cells at the SMU

NASA Astrophysics Data System (ADS)

Ďuriš, S.; Ranostaj, J.; Palenčár, R.

2008-06-01

One of the research programs realized at the thermometry laboratory of the Slovak Institute of Metrology (SMU) in recent years has focused on the development of fixed-point cells. In the frame of this research, several primary cells for realization of the International Temperature Scale of 1990 (ITS-90) and several secondary cells for industrial thermometer calibrations were built and studied. This article discusses primary cells for the gallium and mercury fixed points and miniature cells for the zinc point that were developed at the SMU. Information about the cell designs is provided, the materials that were used are specified, and the procedures for their manufacture are described. Briefly, the realization of the fixed points of mercury, gallium, and zinc by using these cells is also described. Many experiments were carried out to study the characteristics of these cells. One of the gallium cells was compared with the circulating transfer cell during the key comparison CCT-K3, and it and the mercury cell were used for the EUROMET Project No. 552. The results of the experiments together with the results of the comparisons show the high quality of these cells. Secondary zinc-point cells were compared against SMU primary zinc-point cells. The comparison shows agreement within 0.12 mK.

Glassy phase in quenched disordered crystalline membranes

NASA Astrophysics Data System (ADS)

Coquand, O.; Essafi, K.; Kownacki, J.-P.; Mouhanna, D.

2018-03-01

We investigate the flat phase of D -dimensional crystalline membranes embedded in a d -dimensional space and submitted to both metric and curvature quenched disorders using a nonperturbative renormalization group approach. We identify a second-order phase transition controlled by a finite-temperature, finite-disorder fixed point unreachable within the leading order of ɛ =4 -D and 1 /d expansions. This critical point divides the flow diagram into two basins of attraction: that associated with the finite-temperature fixed point controlling the long-distance behavior of disorder-free membranes and that associated with the zero-temperature, finite-disorder fixed point. Our work thus strongly suggests the existence of a whole low-temperature glassy phase for quenched disordered crystalline membranes and, possibly, for graphene and graphene-like compounds.

INFLUENCES OF GENDER IDEOLOGY AND HOUSEWORK ALLOCATION ON WOMEN’S EMPLOYMENT OVER THE LIFE COURSE

PubMed Central

Cunningham, Mick

2008-01-01

The study investigates the influences of women’s attitudes about gender and couples’ housework allocation patterns on women’s employment status and work hours across the life course. The influence of these factors on the employment characteristics of continuously married women is investigated at four time points: 1977, 1980, 1985, and 1993. Data come from the Intergenerational Panel Study of Parents and Children and the analysis sample includes 556 continuously married women. Findings from structural equation, fixed effects, and tobit models offer consistent evidence of long-term positive influences of women’s egalitarian gender ideology and men’s participation in routine housework on women’s labor force participation. The results provide support for hypotheses based on the notion of lagged adaptation. PMID:19255608

An explicit solution to the exoatmospheric powered flight guidance and trajectory optimization problem for rocket propelled vehicles

NASA Technical Reports Server (NTRS)

Jaggers, R. F.

1977-01-01

A derivation of an explicit solution to the two point boundary-value problem of exoatmospheric guidance and trajectory optimization is presented. Fixed initial conditions and continuous burn, multistage thrusting are assumed. Any number of end conditions from one to six (throttling is required in the case of six) can be satisfied in an explicit and practically optimal manner. The explicit equations converge for off nominal conditions such as engine failure, abort, target switch, etc. The self starting, predictor/corrector solution involves no Newton-Rhapson iterations, numerical integration, or first guess values, and converges rapidly if physically possible. A form of this algorithm has been chosen for onboard guidance, as well as real time and preflight ground targeting and trajectory shaping for the NASA Space Shuttle Program.

Poisson's ratio of fiber-reinforced composites

NASA Astrophysics Data System (ADS)

Christiansson, Henrik; Helsing, Johan

1996-05-01

Poisson's ratio flow diagrams, that is, the Poisson's ratio versus the fiber fraction, are obtained numerically for hexagonal arrays of elastic circular fibers in an elastic matrix. High numerical accuracy is achieved through the use of an interface integral equation method. Questions concerning fixed point theorems and the validity of existing asymptotic relations are investigated and partially resolved. Our findings for the transverse effective Poisson's ratio, together with earlier results for random systems by other authors, make it possible to formulate a general statement for Poisson's ratio flow diagrams: For composites with circular fibers and where the phase Poisson's ratios are equal to 1/3, the system with the lowest stiffness ratio has the highest Poisson's ratio. For other choices of the elastic moduli for the phases, no simple statement can be made.

Indirect Determination of the Thermodynamic Temperature of a Gold Fixed-Point Cell

NASA Astrophysics Data System (ADS)

Battuello, M.; Girard, F.; Florio, M.

2010-09-01

Since the value T 90(Au) was fixed on the ITS-90, some determinations of the thermodynamic temperature of the gold point have been performed which form, with other renormalized results of previous measurements by radiation thermometry, the basis for the current best estimates of ( T - T 90)Au = 39.9 mK as elaborated by the CCT-WG4. Such a value, even if consistent with the behavior of T - T 90 differences at lower temperatures, is quite influenced by the low values of T Au as determined with few radiometric measurements. At INRIM, an independent indirect determination of the thermodynamic temperature of gold was performed by means of a radiation thermometry approach. A fixed-point technique was used to realize approximated thermodynamic scales from the Zn point up to the Cu point. A Si-based standard radiation thermometer working at 900 nm and 950 nm was used. The low uncertainty presently associated to the thermodynamic temperature of fixed points and the accuracy of INRIM realizations, allowed scales with an uncertainty lower than 0.03 K in terms of the thermodynamic temperature to be realized. A fixed-point cell filled with gold, 99.999 % in purity, was measured, and its freezing temperature was determined by both interpolation and extrapolation. An average T Au = 1337.395 K was found with a combined standard uncertainty of 23 mK. Such a value is 25 mK higher than the presently available value as derived by the CCT-WG4 value of ( T - T 90)Au = 39.9 mK.

ON THE LIMIT DISTRIBUTION OF THE NUMBER OF SOLUTIONS OF THE EQUATION x^k = a IN THE SYMMETRIC GROUP S_n

NASA Astrophysics Data System (ADS)

Pavlov, A. I.

1983-02-01

The limit distribution of the number of solutions of the equation x^k = a as n \\to \\infty is investigated for a fixed integer k \\geq 2, where a is in the symmetric group S_n of degree n.Bibliography: 2 titles.

Logistic Achievement Test Scaling and Equating with Fixed versus Estimated Lower Asymptotes.

ERIC Educational Resources Information Center

Phillips, S. E.

This study compared the lower asymptotes estimated by the maximum likelihood procedures of the LOGIST computer program with those obtained via application of the Norton methodology. The study also compared the equating results from the three-parameter logistic model with those obtained from the equipercentile, Rasch, and conditional…

Verifying the Hanging Chain Model

ERIC Educational Resources Information Center

Karls, Michael A.

2013-01-01

The wave equation with variable tension is a classic partial differential equation that can be used to describe the horizontal displacements of a vertical hanging chain with one end fixed and the other end free to move. Using a web camera and TRACKER software to record displacement data from a vibrating hanging chain, we verify a modified version…

The microcomputer scientific software series 5: the BIOMASS user's guide.

Treesearch

George E. Host; Stephen C. Westin; William G. Cole; Kurt S. Pregitzer

1989-01-01

BIOMASS is an interactive microcomputer program that uses allometric regression equations to calculate aboveground biomass of common tree species of the Lake States. The equations are species-specific and most use both diameter and height as independent variables. The program accommodates fixed area and variable radius sample designs and produces both individual tree...

Influence of the Cavity Length on the Behavior of Hybrid Fixed-Point Cells Constructed at INRIM

NASA Astrophysics Data System (ADS)

Battuello, M.; Girard, F.; Florio, M.

2015-03-01

Hybrid cells with double carbon/carbon sheets are used at the Istituto Nazionale di Ricerca Metrologica (INRIM) for the realization of both pure metal fixed points and high-temperature metal-carbon eutectic points. Cells for the Cu and Co-C fixed points have been prepared to be used in the high-temperature fixed-point project of the Comité Consultatif de Thermométrie. The results of the evaluation processes were not completely satisfactory for the INRIM cells because of their low transition temperatures with respect to the best cells, and of a rather large melting range for the Co-C cell. A new design of the cells was devised, and considerable improvements were achieved with respect to the transition temperature, and the plateau shape and duration. As for the Cu point, the duration of the freezing plateaux increased by more than 50 % and the freezing temperature increased by 18 mK. As for the Co-C point, the melting temperature, expressed in terms of the point of inflection of the melting curve, increased by about 70 mK. The melting range of the plateaux, expressed as a difference was reduced from about 180 mK to about 130 mK, with melting times increased by about 50 %, as a consequence of an improvement of flatness and run-off of the plateaux.

Towards apparent convergence in asymptotically safe quantum gravity

NASA Astrophysics Data System (ADS)

Denz, T.; Pawlowski, J. M.; Reichert, M.

2018-04-01

The asymptotic safety scenario in gravity is accessed within the systematic vertex expansion scheme for functional renormalisation group flows put forward in Christiansen et al. (Phys Lett B 728:114, 2014), Christiansen et al. (Phy Rev D 93:044036, 2016), and implemented in Christiansen et al. (Phys Rev D 92:121501, 2015) for propagators and three-point functions. In the present work this expansion scheme is extended to the dynamical graviton four-point function. For the first time, this provides us with a closed flow equation for the graviton propagator: all vertices and propagators involved are computed from their own flows. In terms of a covariant operator expansion the current approximation gives access to Λ , R, R^2 as well as R_{μ ν }^2 and higher derivative operators. We find a UV fixed point with three attractive and two repulsive directions, thus confirming previous studies on the relevance of the first three operators. In the infrared we find trajectories that correspond to classical general relativity and further show non-classical behaviour in some fluctuation couplings. We also find signatures for the apparent convergence of the systematic vertex expansion. This opens a promising path towards establishing asymptotically safe gravity in terms of apparent convergence.

The structure of non-hierarchical triple system stability regions

NASA Astrophysics Data System (ADS)

Martynova, A. I.; Orlov, V. V.; Rubinov, A. V.

2009-08-01

A detailed study of the two-dimensional initial conditions region section in the planar three-body problem is performed. The initial conditions for the three well-known stable periodic orbits (the Schubart’s orbit, the Broucke’s orbit and the eight-like orbit) belong to this section. Continuous stability regions (for the fixed integration interval) generated by these periodic orbits are found. Zones of the quick stability violation are outlined. The analysis of some concrete trajectories coming from various stability regions is performed. In particular, trajectories possessing varying number of “eights” formed by moving triple system components are discovered. Orbits with librations are also found. The new periodic orbit originated from the zone siding with the Schubart’s orbit region is discovered. This orbit has reversibility points (each of the outer bodies possess a reversibility point) and two points of close double approach of the central body to each of the outer bodies. The influence of the numerical integration accuracy on the results is studied. The stability regions structure is preserved during calculations with different values of the precision parameter, numerical integration methods and regularization algorithms of the equations of motion.

Turbulent mixing of a critical fluid: The non-perturbative renormalization

NASA Astrophysics Data System (ADS)

Hnatič, M.; Kalagov, G.; Nalimov, M.

2018-01-01

Non-perturbative Renormalization Group (NPRG) technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υjυi 〉 ∼ (Pji⊥ + αPji∥) /k d + ζ. Depending on the relations between the parameters ζ, α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow), but there is a new nonequilibrium regime (universality class) associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ) of possible scaling regimes in the system. The physical point d = 3, ζ = 4 / 3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α ≲ 2.26. Otherwise, in the case of "strong compressibility" α ≳ 2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.

Self-adaptive calibration for staring infrared sensors

NASA Astrophysics Data System (ADS)

Kendall, William B.; Stocker, Alan D.

1993-10-01

This paper presents a new, self-adaptive technique for the correlation of non-uniformities (fixed-pattern noise) in high-density infrared focal-plane detector arrays. We have developed a new approach to non-uniformity correction in which we use multiple image frames of the scene itself, and take advantage of the aim-point wander caused by jitter, residual tracking errors, or deliberately induced motion. Such wander causes each detector in the array to view multiple scene elements, and each scene element to be viewed by multiple detectors. It is therefore possible to formulate (and solve) a set of simultaneous equations from which correction parameters can be computed for the detectors. We have tested our approach with actual images collected by the ARPA-sponsored MUSIC infrared sensor. For these tests we employed a 60-frame (0.75-second) sequence of terrain images for which an out-of-date calibration was deliberately used. The sensor was aimed at a point on the ground via an operator-assisted tracking system having a maximum aim point wander on the order of ten pixels. With these data, we were able to improve the calibration accuracy by a factor of approximately 100.

Contractive type non-self mappings on metric spaces of hyperbolic type

NASA Astrophysics Data System (ADS)

Ciric, Ljubomir B.

2006-05-01

Let (X,d) be a metric space of hyperbolic type and K a nonempty closed subset of X. In this paper we study a class of mappings from K into X (not necessarily self-mappings on K), which are defined by the contractive condition (2.1) below, and a class of pairs of mappings from K into X which satisfy the condition (2.28) below. We present fixed point and common fixed point theorems which are generalizations of the corresponding fixed point theorems of Ciric [L.B. Ciric, Quasi-contraction non-self mappings on Banach spaces, Bull. Acad. Serbe Sci. Arts 23 (1998) 25-31; L.B. Ciric, J.S. Ume, M.S. Khan, H.K.T. Pathak, On some non-self mappings, Math. Nachr. 251 (2003) 28-33], Rhoades [B.E. Rhoades, A fixed point theorem for some non-self mappings, Math. Japon. 23 (1978) 457-459] and many other authors. Some examples are presented to show that our results are genuine generalizations of known results from this area.

The evolving Planck mass in classically scale-invariant theories

NASA Astrophysics Data System (ADS)

Kannike, K.; Raidal, M.; Spethmann, C.; Veermäe, H.

2017-04-01

We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale invariance is spontaneously broken. In these theories, however, the Planck mass becomes unstable in the presence of explicit sources of scale invariance breaking, such as non-relativistic matter and cosmological constant terms. We quantify the constraints on such classical models from Big Bang Nucleosynthesis that lead to an upper bound on the non-minimal coupling and require trans-Planckian field values. We show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg potential. The time-averaged motion of the evolving fixed point is strongly suppressed, thus the limits on the evolving gravitational constant from Big Bang Nucleosynthesis and other measurements do not presently constrain this class of theories. Field oscillations around the fixed point, if not damped, contribute to the dark matter density of the Universe.

Analysis and testing of numerical formulas for the initial value problem

NASA Technical Reports Server (NTRS)

Brown, R. L.; Kovach, K. R.; Popyack, J. L.

1980-01-01

Three computer programs for evaluating and testing numerical integration formulas used with fixed stepsize programs to solve initial value systems of ordinary differential equations are described. A program written in PASCAL SERIES, takes as input the differential equations and produces a FORTRAN subroutine for the derivatives of the system and for computing the actual solution through recursive power series techniques. Both of these are used by STAN, a FORTRAN program that interactively displays a discrete analog of the Liapunov stability region of any two dimensional subspace of the system. The derivatives may be used by CLMP, a FORTRAN program, to test the fixed stepsize formula against a good numerical result and interactively display the solutions.

Stability of iterative procedures with errors for approximating common fixed points of a couple of q-contractive-like mappings in Banach spaces

NASA Astrophysics Data System (ADS)

Zeng, Lu-Chuan; Yao, Jen-Chih

2006-09-01

Recently, Agarwal, Cho, Li and Huang [R.P. Agarwal, Y.J. Cho, J. Li, N.J. Huang, Stability of iterative procedures with errors approximating common fixed points for a couple of quasi-contractive mappings in q-uniformly smooth Banach spaces, J. Math. Anal. Appl. 272 (2002) 435-447] introduced the new iterative procedures with errors for approximating the common fixed point of a couple of quasi-contractive mappings and showed the stability of these iterative procedures with errors in Banach spaces. In this paper, we introduce a new concept of a couple of q-contractive-like mappings (q>1) in a Banach space and apply these iterative procedures with errors for approximating the common fixed point of the couple of q-contractive-like mappings. The results established in this paper improve, extend and unify the corresponding ones of Agarwal, Cho, Li and Huang [R.P. Agarwal, Y.J. Cho, J. Li, N.J. Huang, Stability of iterative procedures with errors approximating common fixed points for a couple of quasi-contractive mappings in q-uniformly smooth Banach spaces, J. Math. Anal. Appl. 272 (2002) 435-447], Chidume [C.E. Chidume, Approximation of fixed points of quasi-contractive mappings in Lp spaces, Indian J. Pure Appl. Math. 22 (1991) 273-386], Chidume and Osilike [C.E. Chidume, M.O. Osilike, Fixed points iterations for quasi-contractive maps in uniformly smooth Banach spaces, Bull. Korean Math. Soc. 30 (1993) 201-212], Liu [Q.H. Liu, On Naimpally and Singh's open questions, J. Math. Anal. Appl. 124 (1987) 157-164; Q.H. Liu, A convergence theorem of the sequence of Ishikawa iterates for quasi-contractive mappings, J. Math. Anal. Appl. 146 (1990) 301-305], Osilike [M.O. Osilike, A stable iteration procedure for quasi-contractive maps, Indian J. Pure Appl. Math. 27 (1996) 25-34; M.O. Osilike, Stability of the Ishikawa iteration method for quasi-contractive maps, Indian J. Pure Appl. Math. 28 (1997) 1251-1265] and many others in the literature.

50 CFR 86.13 - What is boating infrastructure?

Code of Federal Regulations, 2010 CFR

2010-10-01

..., currents, etc., that provide a temporary safe anchorage point or harbor of refuge during storms); (f) Floating docks and fixed piers; (g) Floating and fixed breakwaters; (h) Dinghy docks (floating or fixed...

Parallel Fixed Point Implementation of a Radial Basis Function Network in an FPGA

PubMed Central

de Souza, Alisson C. D.; Fernandes, Marcelo A. C.

2014-01-01

This paper proposes a parallel fixed point radial basis function (RBF) artificial neural network (ANN), implemented in a field programmable gate array (FPGA) trained online with a least mean square (LMS) algorithm. The processing time and occupied area were analyzed for various fixed point formats. The problems of precision of the ANN response for nonlinear classification using the XOR gate and interpolation using the sine function were also analyzed in a hardware implementation. The entire project was developed using the System Generator platform (Xilinx), with a Virtex-6 xc6vcx240t-1ff1156 as the target FPGA. PMID:25268918

Expected Number of Fixed Points in Boolean Networks with Arbitrary Topology.

PubMed

Mori, Fumito; Mochizuki, Atsushi

2017-07-14

Boolean network models describe genetic, neural, and social dynamics in complex networks, where the dynamics depend generally on network topology. Fixed points in a genetic regulatory network are typically considered to correspond to cell types in an organism. We prove that the expected number of fixed points in a Boolean network, with Boolean functions drawn from probability distributions that are not required to be uniform or identical, is one, and is independent of network topology if only a feedback arc set satisfies a stochastic neutrality condition. We also demonstrate that the expected number is increased by the predominance of positive feedback in a cycle.

An investigation of the convergence to the stationary state in the Hassell mapping

NASA Astrophysics Data System (ADS)

de Mendonça, Hans M. J.; Leonel, Edson D.; de Oliveira, Juliano A.

2017-01-01

We investigate the convergence to the fixed point and near it in a transcritical bifurcation observed in a Hassell mapping. We considered a phenomenological description which was reinforced by a theoretical description. At the bifurcation, we confirm the convergence for the fixed point is characterized by a homogeneous function with three exponents. Near the bifurcation the decay to the fixed point is exponential with a relaxation time given by a power law. Although the expression of the mapping is different from the traditional logistic mapping, at the bifurcation and near it, the local dynamics is essentially the same for either mappings.

Automated Parameter Studies Using a Cartesian Method

NASA Technical Reports Server (NTRS)

Murman, Scott M.; Aftosimis, Michael J.; Nemec, Marian

2004-01-01

Computational Fluid Dynamics (CFD) is now routinely used to analyze isolated points in a design space by performing steady-state computations at fixed flight conditions (Mach number, angle of attack, sideslip), for a fixed geometric configuration of interest. This "point analysis" provides detailed information about the flowfield, which aides an engineer in understanding, or correcting, a design. A point analysis is typically performed using high fidelity methods at a handful of critical design points, e.g. a cruise or landing configuration, or a sample of points along a flight trajectory.

Methods to Prescribe Particle Motion to Minimize Quadrature Error in Meshfree Methods

NASA Astrophysics Data System (ADS)

Templeton, Jeremy; Erickson, Lindsay; Morris, Karla; Poliakoff, David

2015-11-01

Meshfree methods are an attractive approach for simulating material systems undergoing large-scale deformation, such as spray break up, free surface flows, and droplets. Particles, which can be easily moved, are used as nodes and/or quadrature points rather than a relying on a fixed mesh. Most methods move particles according to the local fluid velocity that allows for the convection terms in the Navier-Stokes equations to be easily accounted for. However, this is a trade-off against numerical accuracy as the flow can often move particles to configurations with high quadrature error, and artificial compressibility is often required to prevent particles from forming undesirable regions of high and low concentrations. In this work, we consider the other side of the trade-off: moving particles based on reducing numerical error. Methods derived from molecular dynamics show that particles can be moved to minimize a surrogate for the solution error, resulting in substantially more accurate simulations at a fixed cost. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Demand Equations for Qualitatively Different Foods under Fixed-Ratio Schedules: A Comparison of Three Data Conversions

ERIC Educational Resources Information Center

Foster, T. Mary; Sumpter, Catherine E.; Temple, William; Flevill, Amanda; Poling, Alan

2009-01-01

Concurrent schedules were used to establish 6 hens' preferences for three foods. The resulting biases suggested wheat was preferred over honey-puffed and puffed wheat, and puffed wheat was the least preferred food. The hens then responded under fixed-ratio schedules for each food in 40-min (excluding reinforcer time) sessions, with the response…

Generalized contractive mappings and weakly α-admissible pairs in G-metric spaces.

PubMed

Hussain, N; Parvaneh, V; Hoseini Ghoncheh, S J

2014-01-01

The aim of this paper is to present some coincidence and common fixed point results for generalized (ψ, φ)-contractive mappings using partially weakly G-α-admissibility in the setup of G-metric space. As an application of our results, periodic points of weakly contractive mappings are obtained. We also derive certain new coincidence point and common fixed point theorems in partially ordered G-metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results.

Generalized Contractive Mappings and Weakly α-Admissible Pairs in G-Metric Spaces

PubMed Central

Hussain, N.; Parvaneh, V.; Hoseini Ghoncheh, S. J.

2014-01-01

The aim of this paper is to present some coincidence and common fixed point results for generalized (ψ, φ)-contractive mappings using partially weakly G-α-admissibility in the setup of G-metric space. As an application of our results, periodic points of weakly contractive mappings are obtained. We also derive certain new coincidence point and common fixed point theorems in partially ordered G-metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results. PMID:25202742

Asymptotics and numerics of a family of two-dimensional generalized surface quasi-geostrophic equations

NASA Astrophysics Data System (ADS)

Ohkitani, Koji

2012-09-01

We study the generalised 2D surface quasi-geostrophic (SQG) equation, where the active scalar is given by a fractional power α of Laplacian applied to the stream function. This includes the 2D SQG and Euler equations as special cases. Using Poincaré's successive approximation to higher α-derivatives of the active scalar, we derive a variational equation for describing perturbations in the generalized SQG equation. In particular, in the limit α → 0, an asymptotic equation is derived on a stretched time variable τ = αt, which unifies equations in the family near α = 0. The successive approximation is also discussed at the other extreme of the 2D Euler limit α = 2-0. Numerical experiments are presented for both limits. We consider whether the solution behaves in a more singular fashion, with more effective nonlinearity, when α is increased. Two competing effects are identified: the regularizing effect of a fractional inverse Laplacian (control by conservation) and cancellation by symmetry (nonlinearity depletion). Near α = 0 (complete depletion), the solution behaves in a more singular fashion as α increases. Near α = 2 (maximal control by conservation), the solution behave in a more singular fashion, as α decreases, suggesting that there may be some α in [0, 2] at which the solution behaves in the most singular manner. We also present some numerical results of the family for α = 0.5, 1, and 1.5. On the original time t, the H1 norm of θ generally grows more rapidly with increasing α. However, on the new time τ, this order is reversed. On the other hand, contour patterns for different α appear to be similar at fixed τ, even though the norms are markedly different in magnitude. Finally, point-vortex systems for the generalized SQG family are discussed to shed light on the above problems of time scale.

The Polyanalytic Ginibre Ensembles

NASA Astrophysics Data System (ADS)

Haimi, Antti; Hedenmalm, Haakan

2013-10-01

For integers n, q=1,2,3,… , let Pol n, q denote the -linear space of polynomials in z and , of degree ≤ n-1 in z and of degree ≤ q-1 in . We supply Pol n, q with the inner product structure of the resulting Hilbert space is denoted by Pol m, n, q . Here, it is assumed that m is a positive real. We let K m, n, q denote the reproducing kernel of Pol m, n, q , and study the associated determinantal process, in the limit as m, n→+∞ while n= m+O(1); the number q, the degree of polyanalyticity, is kept fixed. We call these processes polyanalytic Ginibre ensembles, because they generalize the Ginibre ensemble—the eigenvalue process of random (normal) matrices with Gaussian weight. There is a physical interpretation in terms of a system of free fermions in a uniform magnetic field so that a fixed number of the first Landau levels have been filled. We consider local blow-ups of the polyanalytic Ginibre ensembles around points in the spectral droplet, which is here the closed unit disk . We obtain asymptotics for the blow-up process, using a blow-up to characteristic distance m -1/2; the typical distance is the same both for interior and for boundary points of . This amounts to obtaining the asymptotical behavior of the generating kernel K m, n, q . Following (Ameur et al. in Commun. Pure Appl. Math. 63(12):1533-1584, 2010), the asymptotics of the K m, n, q are rather conveniently expressed in terms of the Berezin measure (and density) [Equation not available: see fulltext.] For interior points | z|<1, we obtain that in the weak-star sense, where δ z denotes the unit point mass at z. Moreover, if we blow up to the scale of m -1/2 around z, we get convergence to a measure which is Gaussian for q=1, but exhibits more complicated Fresnel zone behavior for q>1. In contrast, for exterior points | z|>1, we have instead that , where is the harmonic measure at z with respect to the exterior disk . For boundary points, | z|=1, the Berezin measure converges to the unit point mass at z, as with interior points, but the blow-up to the scale m -1/2 exhibits quite different behavior at boundary points compared with interior points. We also obtain the asymptotic boundary behavior of the 1-point function at the coarser local scale q 1/2 m -1/2.

Review: Hamiltonian Linearization of the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge: A Radiation Gauge for Background-Independent Gravitational Waves in a Post-Minkowskian Einstein Spacetime

NASA Astrophysics Data System (ADS)

Agresti, Juri; De Pietri, Roberto; Lusanna, Luca; Martucci, Luca

2004-05-01

In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy {\\hat E}ADM, we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of non-harmonic 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO) r_{\\bar a}(\\tau ,\\vec \\sigma ), \\pi_{\\bar a}(\\tau ,\\vec \\sigma ), \\bar a = 1,2. We define a Hamiltonian linearization of the theory, i.e. gravitational waves, without introducing any background 4-metric, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in {\\hat E}ADM. We solve all the constraints of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's r_{\\bar a}(\\tau ,\\vec \\sigma ), which replace the two polarizations of the TT harmonic gauge, and that linearized Einstein's equations are satisfied. Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation.

A New Method of High-Precision Positioning for an Indoor Pseudolite without Using the Known Point Initialization.

PubMed

Zhao, Yinzhi; Zhang, Peng; Guo, Jiming; Li, Xin; Wang, Jinling; Yang, Fei; Wang, Xinzhe

2018-06-20

Due to the great influence of multipath effect, noise, clock and error on pseudorange, the carrier phase double difference equation is widely used in high-precision indoor pseudolite positioning. The initial position is determined mostly by the known point initialization (KPI) method, and then the ambiguities can be fixed with the LAMBDA method. In this paper, a new method without using the KPI to achieve high-precision indoor pseudolite positioning is proposed. The initial coordinates can be quickly obtained to meet the accuracy requirement of the indoor LAMBDA method. The detailed processes of the method follows: Aiming at the low-cost single-frequency pseudolite system, the static differential pseudolite system (DPL) method is used to obtain the low-accuracy positioning coordinates of the rover station quickly. Then, the ambiguity function method (AFM) is used to search for the coordinates in the corresponding epoch. The real coordinates obtained by AFM can meet the initial accuracy requirement of the LAMBDA method, so that the double difference carrier phase ambiguities can be correctly fixed. Following the above steps, high-precision indoor pseudolite positioning can be realized. Several experiments, including static and dynamic tests, are conducted to verify the feasibility of the new method. According to the results of the experiments, the initial coordinates with the accuracy of decimeter level through the DPL can be obtained. For the AFM part, both a one-meter search scope and two-centimeter or four-centimeter search steps are used to ensure the precision at the centimeter level and high search efficiency. After dealing with the problem of multiple peaks caused by the ambiguity cosine function, the coordinate information of the maximum ambiguity function value (AFV) is taken as the initial value of the LAMBDA, and the ambiguities can be fixed quickly. The new method provides accuracies at the centimeter level for dynamic experiments and at the millimeter level for static ones.

Base units of the SI, fundamental constants and modern quantum physics.

PubMed

Bordé, Christian J

2005-09-15

Over the past 40 years, a number of discoveries in quantum physics have completely transformed our vision of fundamental metrology. This revolution starts with the frequency stabilization of lasers using saturation spectroscopy and the redefinition of the metre by fixing the velocity of light c. Today, the trend is to redefine all SI base units from fundamental constants and we discuss strategies to achieve this goal. We first consider a kinematical frame, in which fundamental constants with a dimension, such as the speed of light c, the Planck constant h, the Boltzmann constant k(B) or the electron mass m(e) can be used to connect and redefine base units. The various interaction forces of nature are then introduced in a dynamical frame, where they are completely characterized by dimensionless coupling constants such as the fine structure constant alpha or its gravitational analogue alpha(G). This point is discussed by rewriting the Maxwell and Dirac equations with new force fields and these coupling constants. We describe and stress the importance of various quantum effects leading to the advent of this new quantum metrology. In the second part of the paper, we present the status of the seven base units and the prospects of their possible redefinitions from fundamental constants in an experimental perspective. The two parts can be read independently and they point to these same conclusions concerning the redefinitions of base units. The concept of rest mass is directly related to the Compton frequency of a body, which is precisely what is measured by the watt balance. The conversion factor between mass and frequency is the Planck constant, which could therefore be fixed in a realistic and consistent new definition of the kilogram based on its Compton frequency. We discuss also how the Boltzmann constant could be better determined and fixed to replace the present definition of the kelvin.

50 CFR 660.212 - Fixed gear fishery-prohibitions.

Code of Federal Regulations, 2010 CFR

2010-10-01

..., Painted Cave, Anacapa Island, Carrington Point, Judith Rock, Skunk Point, Footprint, Gull Island, South... are specific to the limited entry fixed gear fisheries. General groundfish prohibitions are found at § 660.12, subpart C. In addition to the general groundfish prohibitions specified in § 660.12, subpart C...

L-fuzzy fixed points theorems for L-fuzzy mappings via βℱL-admissible pair.

PubMed

Rashid, Maliha; Azam, Akbar; Mehmood, Nayyar

2014-01-01

We define the concept of βℱL-admissible for a pair of L-fuzzy mappings and establish the existence of common L-fuzzy fixed point theorem. Our result generalizes some useful results in the literature. We provide an example to support our result.

Network Aggregation in Transportation Planning : Volume II : A Fixed Point Method for Treating Traffic Equilibria

DOT National Transportation Integrated Search

1978-04-01

Volume 2 defines a new algorithm for the network equilibrium model that works in the space of path flows and is based on the theory of fixed point method. The goals of the study were broadly defined as the identification of aggregation practices and ...

Weight of fitness deviation governs strict physical chaos in replicator dynamics.

PubMed

Pandit, Varun; Mukhopadhyay, Archan; Chakraborty, Sagar

2018-03-01

Replicator equation-a paradigm equation in evolutionary game dynamics-mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions-fixed points, periodic orbits, and chaotic trajectories-are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.

Fixed points of contractive mappings in b-metric-like spaces.

PubMed

Hussain, Nawab; Roshan, Jamal Rezaei; Parvaneh, Vahid; Kadelburg, Zoran

2014-01-01

We discuss topological structure of b-metric-like spaces and demonstrate a fundamental lemma for the convergence of sequences. As an application we prove certain fixed point results in the setup of such spaces for different types of contractive mappings. Finally, some periodic point results in b-metric-like spaces are obtained. Two examples are presented in order to verify the effectiveness and applicability of our main results.

A fixed energy fixed angle inverse scattering in interior transmission problem

NASA Astrophysics Data System (ADS)

Chen, Lung-Hui

2017-06-01

We study the inverse acoustic scattering problem in mathematical physics. The problem is to recover the index of refraction in an inhomogeneous medium by measuring the scattered wave fields in the far field. We transform the problem to the interior transmission problem in the study of the Helmholtz equation. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of spherical harmonics in the far field, we can determine uniquely the perturbation source for the radially symmetric perturbations.

Simulation of design-unbiased point-to-particle sampling compared to alternatives on plantation rows

Treesearch

Thomas B. Lynch; David Hamlin; Mark J. Ducey

2016-01-01

Total quantities of tree attributes can be estimated in plantations by sampling on plantation rows using several methods. At random sample points on a row, either fixed row lengths or variable row lengths with a fixed number of sample trees can be assessed. Ratio of means or mean of ratios estimators can be developed for the fixed number of trees option but are not...

Maximum Likelihood Analysis of a Two-Level Nonlinear Structural Equation Model with Fixed Covariates

ERIC Educational Resources Information Center

Lee, Sik-Yum; Song, Xin-Yuan

2005-01-01

In this article, a maximum likelihood (ML) approach for analyzing a rather general two-level structural equation model is developed for hierarchically structured data that are very common in educational and/or behavioral research. The proposed two-level model can accommodate nonlinear causal relations among latent variables as well as effects…

On a Simple Formulation of the Golf Ball Paradox

ERIC Educational Resources Information Center

Pujol, O.; Perez, J. Ph.

2007-01-01

The motion of a ball rolling without slipping on the lateral section inside a fixed vertical cylinder is analysed in the Earth referential frame which is assumed to be Galilean. Equations of motion are rapidly obtained and the golf ball paradox is understood: these equations describe a motion consisting of a vertical harmonic oscillation related…

Video Measurement of the Muzzle Velocity of a Potato Gun

ERIC Educational Resources Information Center

Jasperson, Christopher; Pollman, Anthony

2011-01-01

Using first principles, a theoretical equation for the maximum and actual muzzle velocities for a pneumatic cannon was recently derived. For a fixed barrel length, this equation suggests that the muzzle velocity can be enhanced by maximizing the product of the initial pressure and the volume of the propellant gas and decreasing the projectile…

Human body surface area: a theoretical approach.

PubMed

Wang, Jianfeng; Hihara, Eiji

2004-04-01

Knowledge of the human body surface area has important applications in medical practice, garment design, and other engineering sizing. Therefore, it is not surprising that several expressions correlating body surface area with direct measurements of body mass and length have been reported in the literature. In the present study, based on the assumption that the exterior shape of the human body is the result of convex and concave deformations from a basic cylinder, we derive a theoretical equation minimizing body surface area (BSA) at a fixed volume (V): BSA=(9pi VL)(0.5), where L is the reference length of the body. Assuming a body density value of 1,000 kg.m(-3), the equation becomes BSA=(BM.BH/35.37)(0.5), where BSA is in square meters, BM is the body mass in kilograms, and BH is the body height in meters. BSA values calculated by means of this equation fall within +/-7% of the values obtained by means of the equations available in the literature, in the range of BSA from children to adults. It is also suggested that the above equation, which is obtained by minimizing the outer body surface at a fixed volume, implies a fundamental relation set by the geometrical constraints governing the growth and the development of the human body.

Context Dependence of Students’ Views about the Role of Equations in Understanding Biology

PubMed Central

Watkins, Jessica; Elby, Andrew

2013-01-01

Students’ epistemological views about biology—their ideas about what “counts” as learning and understanding biology—play a role in how they approach their courses and respond to reforms. As introductory biology courses incorporate more physics and quantitative reasoning, student attitudes about the role of equations in biology become especially relevant. However, as documented in research in physics education, students’ epistemologies are not always stable and fixed entities; they can be dynamic and context-dependent. In this paper, we examine an interview with an introductory student in which she discusses the use of equations in her reformed biology course. In one part of the interview, she expresses what sounds like an entrenched negative stance toward the role equations can play in understanding biology. However, later in the interview, when discussing a different biology topic, she takes a more positive stance toward the value of equations. These results highlight how a given student can have diverse ways of thinking about the value of bringing physics and math into biology. By highlighting how attitudes can shift in response to different tasks, instructional environments, and contextual cues, we emphasize the need to attend to these factors, rather than treating students’ beliefs as fixed and stable. PMID:23737634