Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs

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

Liao, Qifeng, E-mail: liaoqf@shanghaitech.edu.cn; Lin, Guang, E-mail: guanglin@purdue.edu

2016-07-15

In this paper we present a reduced basis ANOVA approach for partial deferential equations (PDEs) with random inputs. The ANOVA method combined with stochastic collocation methods provides model reduction in high-dimensional parameter space through decomposing high-dimensional inputs into unions of low-dimensional inputs. In this work, to further reduce the computational cost, we investigate spatial low-rank structures in the ANOVA-collocation method, and develop efficient spatial model reduction techniques using hierarchically generated reduced bases. We present a general mathematical framework of the methodology, validate its accuracy and demonstrate its efficiency with numerical experiments.

Spatial transformation abilities and their relation to later mathematics performance.

PubMed

Frick, Andrea

2018-04-10

Using a longitudinal approach, this study investigated the relational structure of different spatial transformation skills at kindergarten age, and how these spatial skills relate to children's later mathematics performance. Children were tested at three time points, in kindergarten, first grade, and second grade (N = 119). Exploratory factor analyses revealed two subcomponents of spatial transformation skills: one representing egocentric transformations (mental rotation and spatial scaling), and one representing allocentric transformations (e.g., cross-sectioning, perspective taking). Structural equation modeling suggested that egocentric transformation skills showed their strongest relation to the part of the mathematics test tapping arithmetic operations, whereas allocentric transformations were strongly related to Numeric-Logical and Spatial Functions as well as geometry. The present findings point to a tight connection between early mental transformation skills, particularly the ones requiring a high level of spatial flexibility and a strong sense for spatial magnitudes, and children's mathematics performance at the beginning of their school career.

Spatial evolutionary epidemiology of spreading epidemics

PubMed Central

2016-01-01

Most spatial models of host–parasite interactions either neglect the possibility of pathogen evolution or consider that this process is slow enough for epidemiological dynamics to reach an equilibrium on a fast timescale. Here, we propose a novel approach to jointly model the epidemiological and evolutionary dynamics of spatially structured host and pathogen populations. Starting from a multi-strain epidemiological model, we use a combination of spatial moment equations and quantitative genetics to analyse the dynamics of mean transmission and virulence in the population. A key insight of our approach is that, even in the absence of long-term evolutionary consequences, spatial structure can affect the short-term evolution of pathogens because of the build-up of spatial differentiation in mean virulence. We show that spatial differentiation is driven by a balance between epidemiological and genetic effects, and this quantity is related to the effect of kin competition discussed in previous studies of parasite evolution in spatially structured host populations. Our analysis can be used to understand and predict the transient evolutionary dynamics of pathogens and the emergence of spatial patterns of phenotypic variation. PMID:27798295

Spatial evolutionary epidemiology of spreading epidemics.

PubMed

Lion, S; Gandon, S

2016-10-26

Most spatial models of host-parasite interactions either neglect the possibility of pathogen evolution or consider that this process is slow enough for epidemiological dynamics to reach an equilibrium on a fast timescale. Here, we propose a novel approach to jointly model the epidemiological and evolutionary dynamics of spatially structured host and pathogen populations. Starting from a multi-strain epidemiological model, we use a combination of spatial moment equations and quantitative genetics to analyse the dynamics of mean transmission and virulence in the population. A key insight of our approach is that, even in the absence of long-term evolutionary consequences, spatial structure can affect the short-term evolution of pathogens because of the build-up of spatial differentiation in mean virulence. We show that spatial differentiation is driven by a balance between epidemiological and genetic effects, and this quantity is related to the effect of kin competition discussed in previous studies of parasite evolution in spatially structured host populations. Our analysis can be used to understand and predict the transient evolutionary dynamics of pathogens and the emergence of spatial patterns of phenotypic variation. © 2016 The Author(s).

Predator attack rate evolution in space: the role of ecology mediated by complex emergent spatial structure and self-shading.

PubMed

Messinger, Susanna M; Ostling, Annette

2013-11-01

Predation interactions are an important element of ecological communities. Population spatial structure has been shown to influence predator evolution, resulting in the evolution of a reduced predator attack rate; however, the evolutionary role of traits governing predator and prey ecology is unknown. The evolutionary effect of spatial structure on a predator's attack rate has primarily been explored assuming a fixed metapopulation spatial structure, and understood in terms of group selection. But endogenously generated, emergent spatial structure is common in nature. Furthermore, the evolutionary influence of ecological traits may be mediated through the spatial self-structuring process. Drawing from theory on pathogens, the evolutionary effect of emergent spatial structure can be understood in terms of self-shading, where a voracious predator limits its long-term invasion potential by reducing local prey availability. Here we formalize the effects of self-shading for predators using spatial moment equations. Then, through simulations, we show that in a spatial context self-shading leads to relationships between predator-prey ecology and the predator's attack rate that are not expected in a non-spatial context. Some relationships are analogous to relationships already shown for host-pathogen interactions, but others represent new trait dimensions. Finally, since understanding the effects of ecology using existing self-shading theory requires simplifications of the emergent spatial structure that do not apply well here, we also develop metrics describing the complex spatial structure of the predator and prey populations to help us explain the evolutionary effect of predator and prey ecology in the context of self-shading. The identification of these metrics may provide a step towards expansion of the predictive domain of self-shading theory to more complex spatial dynamics. Copyright © 2013 Elsevier Inc. All rights reserved.

Numerical Treatment of the Boltzmann Equation for Self-Propelled Particle Systems

NASA Astrophysics Data System (ADS)

Thüroff, Florian; Weber, Christoph A.; Frey, Erwin

2014-10-01

Kinetic theories constitute one of the most promising tools to decipher the characteristic spatiotemporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides a natural translation between a particle-level description of the system's dynamics and the corresponding hydrodynamic fields. Yet, the intricate mathematical structure of the Boltzmann equation substantially limits the progress toward a full understanding of this equation by solely analytical means. Here, we propose a general framework to numerically solve the Boltzmann equation for self-propelled particle systems in two spatial dimensions and with arbitrary boundary conditions. We discuss potential applications of this numerical framework to active matter systems and use the algorithm to give a detailed analysis to a model system of self-propelled particles with polar interactions. In accordance with previous studies, we find that spatially homogeneous isotropic and broken-symmetry states populate two distinct regions in parameter space, which are separated by a narrow region of spatially inhomogeneous, density-segregated moving patterns. We find clear evidence that these three regions in parameter space are connected by first-order phase transitions and that the transition between the spatially homogeneous isotropic and polar ordered phases bears striking similarities to liquid-gas phase transitions in equilibrium systems. Within the density-segregated parameter regime, we find a novel stable limit-cycle solution of the Boltzmann equation, which consists of parallel lanes of polar clusters moving in opposite directions, so as to render the overall symmetry of the system's ordered state nematic, despite purely polar interactions on the level of single particles.

Nonlinear diffusion and viral spread through the leaf of a plant

NASA Astrophysics Data System (ADS)

Edwards, Maureen P.; Waterhouse, Peter M.; Munoz-Lopez, María Jesús; Anderssen, Robert S.

2016-10-01

The spread of a virus through the leaf of a plant is both spatially and temporally causal in that the present status depends on the past and the spatial spread is compactly supported and progresses outwards. Such spatial spread is known to occur for certain nonlinear diffusion processes. The first compactly supported solution for nonlinear diffusion equations appears to be that of Pattle published in 1959. In that paper, no explanation is given as to how the solution was derived. Here, we show how the solution can be derived using Lie symmetry analysis. This lays a foundation for exploring the behavior of other choices for nonlinear diffusion and exploring the addition of reaction terms which do not eliminate the compactly supported structure. The implications associated with using the reaction-diffusion equation to model the spatial-temporal spread of a virus through the leaf of a plant are discussed.

Compatible Spatial Discretizations for Partial Differential Equations

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

Arnold, Douglas, N, ed.

From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide varietymore » of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical simulations. + Identification and design of compatible spatial discretizations of PDEs, their classification, analysis, and relations. + Relationships between different compatible spatial discretization methods and concepts which have been developed; + Impact of compatible spatial discretizations upon physical fidelity, verification and validation of simulations, especially in large-scale, multiphysics settings. + How solvers address the demands placed upon them by compatible spatial discretizations. This report provides information about the program and abstracts of all the presentations.« less

Nonlinear periodic wavetrains in thin liquid films falling on a uniformly heated horizontal plate

NASA Astrophysics Data System (ADS)

Issokolo, Remi J. Noumana; Dikandé, Alain M.

2018-05-01

A thin liquid film falling on a uniformly heated horizontal plate spreads into fingering ripples that can display a complex dynamics ranging from continuous waves, nonlinear spatially localized periodic wave patterns (i.e., rivulet structures) to modulated nonlinear wavetrain structures. Some of these structures have been observed experimentally; however, conditions under which they form are still not well understood. In this work, we examine profiles of nonlinear wave patterns formed by a thin liquid film falling on a uniformly heated horizontal plate. For this purpose, the Benney model is considered assuming a uniform temperature distribution along the film propagation on the horizontal surface. It is shown that for strong surface tension but a relatively small Biot number, spatially localized periodic-wave structures can be analytically obtained by solving the governing equation under appropriate conditions. In the regime of weak nonlinearity, a multiple-scale expansion combined with the reductive perturbation method leads to a complex Ginzburg-Landau equation: the solutions of which are modulated periodic pulse trains which amplitude and width and period are expressed in terms of characteristic parameters of the model.

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

Two-dimensional integrating matrices on rectangular grids. [solving differential equations associated with rotating structures

NASA Technical Reports Server (NTRS)

Lakin, W. D.

1981-01-01

The use of integrating matrices in solving differential equations associated with rotating beam configurations is examined. In vibration problems, by expressing the equations of motion of the beam in matrix notation, utilizing the integrating matrix as an operator, and applying the boundary conditions, the spatial dependence is removed from the governing partial differential equations and the resulting ordinary differential equations can be cast into standard eigenvalue form. Integrating matrices are derived based on two dimensional rectangular grids with arbitrary grid spacings allowed in one direction. The derivation of higher dimensional integrating matrices is the initial step in the generalization of the integrating matrix methodology to vibration and stability problems involving plates and shells.

On the thermodynamics of the Swift-Hohenberg theory

NASA Astrophysics Data System (ADS)

Espath, L. F. R.; Sarmiento, A. F.; Dalcin, L.; Calo, V. M.

2017-11-01

We present the microbalance including the microforces, the first- and second-order microstresses for the Swift-Hohenberg equation concomitantly with their constitutive equations, which are consistent with the free-energy imbalance. We provide an explicit form for the microstress structure for a free-energy functional endowed with second-order spatial derivatives. Additionally, we generalize the Swift-Hohenberg theory via a proper constitutive process. Finally, we present one highly resolved three-dimensional numerical simulation to demonstrate the particular form of the resulting microstresses and their interactions in the evolution of the Swift-Hohenberg equation.

Structural stability and chaotic solutions of perturbed Benjamin-Ono equations

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

Birnir, B.; Morrison, P.J.

1986-11-01

A method for proving chaos in partial differential equations is discussed and applied to the Benjamin-Ono equation subject to perturbations. The perturbations are of two types: one that corresponds to viscous dissipation, the so-called Burger's term, and one that involves the Hilbert transform and has been used to model Landau damping. The method proves chaos in the PDE by proving temporal chaos in its pole solutions. The spatial structure of the pole solutions remains intact, but their positions are chaotic in time. Melnikov's method is invoked to show this temporal chaos. It is discovered that the pole behavior is verymore » sensitive to the Burger's perturbation, but is quite insensitive to the perturbation involving the Hilbert transform.« less

A high-order gas-kinetic Navier-Stokes flow solver

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

Li Qibing, E-mail: lqb@tsinghua.edu.c; Xu Kun, E-mail: makxu@ust.h; Fu Song, E-mail: fs-dem@tsinghua.edu.c

2010-09-20

The foundation for the development of modern compressible flow solver is based on the Riemann solution of the inviscid Euler equations. The high-order schemes are basically related to high-order spatial interpolation or reconstruction. In order to overcome the low-order wave interaction mechanism due to the Riemann solution, the temporal accuracy of the scheme can be improved through the Runge-Kutta method, where the dynamic deficiencies in the first-order Riemann solution is alleviated through the sub-step spatial reconstruction in the Runge-Kutta process. The close coupling between the spatial and temporal evolution in the original nonlinear governing equations seems weakened due to itsmore » spatial and temporal decoupling. Many recently developed high-order methods require a Navier-Stokes flux function under piece-wise discontinuous high-order initial reconstruction. However, the piece-wise discontinuous initial data and the hyperbolic-parabolic nature of the Navier-Stokes equations seem inconsistent mathematically, such as the divergence of the viscous and heat conducting terms due to initial discontinuity. In this paper, based on the Boltzmann equation, we are going to present a time-dependent flux function from a high-order discontinuous reconstruction. The theoretical basis for such an approach is due to the fact that the Boltzmann equation has no specific requirement on the smoothness of the initial data and the kinetic equation has the mechanism to construct a dissipative wave structure starting from an initially discontinuous flow condition on a time scale being larger than the particle collision time. The current high-order flux evaluation method is an extension of the second-order gas-kinetic BGK scheme for the Navier-Stokes equations (BGK-NS). The novelty for the easy extension from a second-order to a higher order is due to the simple particle transport and collision mechanism on the microscopic level. This paper will present a hierarchy to construct such a high-order method. The necessity to couple spatial and temporal evolution nonlinearly in the flux evaluation can be clearly observed through the numerical performance of the scheme for the viscous flow computations.« less

Assessing the role of spatial correlations during collective cell spreading

PubMed Central

Treloar, Katrina K.; Simpson, Matthew J.; Binder, Benjamin J.; McElwain, D. L. Sean; Baker, Ruth E.

2014-01-01

Spreading cell fronts are essential features of development, repair and disease processes. Many mathematical models used to describe the motion of cell fronts, such as Fisher's equation, invoke a mean–field assumption which implies that there is no spatial structure, such as cell clustering, present. Here, we examine the presence of spatial structure using a combination of in vitro circular barrier assays, discrete random walk simulations and pair correlation functions. In particular, we analyse discrete simulation data using pair correlation functions to show that spatial structure can form in a spreading population of cells either through sufficiently strong cell–to–cell adhesion or sufficiently rapid cell proliferation. We analyse images from a circular barrier assay describing the spreading of a population of MM127 melanoma cells using the same pair correlation functions. Our results indicate that the spreading melanoma cell populations remain very close to spatially uniform, suggesting that the strength of cell–to–cell adhesion and the rate of cell proliferation are both sufficiently small so as not to induce any spatial patterning in the spreading populations. PMID:25026987

Concave omnidirectional imaging device for cylindrical object based on catadioptric panoramic imaging

NASA Astrophysics Data System (ADS)

Wu, Xiaojun; Wu, Yumei; Wen, Peizhi

2018-03-01

To obtain information on the outer surface of a cylinder object, we propose a catadioptric panoramic imaging system based on the principle of uniform spatial resolution for vertical scenes. First, the influence of the projection-equation coefficients on the spatial resolution and astigmatism of the panoramic system are discussed, respectively. Through parameter optimization, we obtain the appropriate coefficients for the projection equation, and so the imaging quality of the entire imaging system can reach an optimum value. Finally, the system projection equation is calibrated, and an undistorted rectangular panoramic image is obtained using the cylindrical-surface projection expansion method. The proposed 360-deg panoramic-imaging device overcomes the shortcomings of existing surface panoramic-imaging methods, and it has the advantages of low cost, simple structure, high imaging quality, and small distortion, etc. The experimental results show the effectiveness of the proposed method.

Spatially variant periodic structures in electromagnetics.

PubMed

Rumpf, Raymond C; Pazos, Javier J; Digaum, Jennefir L; Kuebler, Stephen M

2015-08-28

Spatial transforms are a popular technique for designing periodic structures that are macroscopically inhomogeneous. The structures are often required to be anisotropic, provide a magnetic response, and to have extreme values for the constitutive parameters in Maxwell's equations. Metamaterials and photonic crystals are capable of providing these, although sometimes only approximately. The problem still remains about how to generate the geometry of the final lattice when it is functionally graded, or spatially varied. This paper describes a simple numerical technique to spatially vary any periodic structure while minimizing deformations to the unit cells that would weaken or destroy the electromagnetic properties. New developments in this algorithm are disclosed that increase efficiency, improve the quality of the lattices and provide the ability to design aplanatic metasurfaces. The ability to spatially vary a lattice in this manner enables new design paradigms that are not possible using spatial transforms, three of which are discussed here. First, spatially variant self-collimating photonic crystals are shown to flow unguided waves around very tight bends using ordinary materials with low refractive index. Second, multi-mode waveguides in spatially variant band gap materials are shown to guide waves around bends without mixing power between the modes. Third, spatially variant anisotropic materials are shown to sculpt the near-field around electric components. This can be used to improve electromagnetic compatibility between components in close proximity. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Spatially variant periodic structures in electromagnetics

PubMed Central

Rumpf, Raymond C.; Pazos, Javier J.; Digaum, Jennefir L.; Kuebler, Stephen M.

2015-01-01

Spatial transforms are a popular technique for designing periodic structures that are macroscopically inhomogeneous. The structures are often required to be anisotropic, provide a magnetic response, and to have extreme values for the constitutive parameters in Maxwell's equations. Metamaterials and photonic crystals are capable of providing these, although sometimes only approximately. The problem still remains about how to generate the geometry of the final lattice when it is functionally graded, or spatially varied. This paper describes a simple numerical technique to spatially vary any periodic structure while minimizing deformations to the unit cells that would weaken or destroy the electromagnetic properties. New developments in this algorithm are disclosed that increase efficiency, improve the quality of the lattices and provide the ability to design aplanatic metasurfaces. The ability to spatially vary a lattice in this manner enables new design paradigms that are not possible using spatial transforms, three of which are discussed here. First, spatially variant self-collimating photonic crystals are shown to flow unguided waves around very tight bends using ordinary materials with low refractive index. Second, multi-mode waveguides in spatially variant band gap materials are shown to guide waves around bends without mixing power between the modes. Third, spatially variant anisotropic materials are shown to sculpt the near-field around electric components. This can be used to improve electromagnetic compatibility between components in close proximity. PMID:26217058

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

NASA Technical Reports Server (NTRS)

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

1983-01-01

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

Stanley Corrsin Award Talk: The role of singularities in hydrodynamics

NASA Astrophysics Data System (ADS)

Eggers, Jens

2017-11-01

If a tap is opened slowly, a drop will form. The separation of the drop is described by a singularity of the Navier-Stokes equation with a free surface. Shock waves are singular solutions of the equations of ideal, compressible hydrodynamics. These examples show that singularities are characteristic for the tendency of the hydrodynamic equations to develop small scale features spontaneously, starting from smooth initial conditions. As a result, new structures are created, which form the building blocks of more complicated flows. The mathematical structure of singularities is self-similar, and their characteristics are fixed by universal properties. This will be illustrated by physical examples, as well as by applications to engineering problems such as printing, coating, or air entrainment. Finally, more recent developments will be discussed: the increasing complexity underlying the self-similar behavior of some singularities, and the spatial structure of shock waves.

Regularization of the Perturbed Spatial Restricted Three-Body Problem by L-Transformations

NASA Astrophysics Data System (ADS)

Poleshchikov, S. M.

2018-03-01

Equations of motion for the perturbed circular restricted three-body problem have been regularized in canonical variables in a moving coordinate system. Two different L-matrices of the fourth order are used in the regularization. Conditions for generalized symplecticity of the constructed transform have been checked. In the unperturbed case, the regular equations have a polynomial structure. The regular equations have been numerically integrated using the Runge-Kutta-Fehlberg method. The results of numerical experiments are given for the Earth-Moon system parameters taking into account the perturbation of the Sun for different L-matrices.

The Fourier transforms for the spatially homogeneous Boltzmann equation and Landau equation

NASA Astrophysics Data System (ADS)

Meng, Fei; Liu, Fang

2018-03-01

In this paper, we study the Fourier transforms for two equations arising in the kinetic theory. The first equation is the spatially homogeneous Boltzmann equation. The Fourier transform of the spatially homogeneous Boltzmann equation has been first addressed by Bobylev (Sov Sci Rev C Math Phys 7:111-233, 1988) in the Maxwellian case. Alexandre et al. (Arch Ration Mech Anal 152(4):327-355, 2000) investigated the Fourier transform of the gain operator for the Boltzmann operator in the cut-off case. Recently, the Fourier transform of the Boltzmann equation is extended to hard or soft potential with cut-off by Kirsch and Rjasanow (J Stat Phys 129:483-492, 2007). We shall first establish the relation between the results in Alexandre et al. (2000) and Kirsch and Rjasanow (2007) for the Fourier transform of the Boltzmann operator in the cut-off case. Then we give the Fourier transform of the spatially homogeneous Boltzmann equation in the non cut-off case. It is shown that our results cover previous works (Bobylev 1988; Kirsch and Rjasanow 2007). The second equation is the spatially homogeneous Landau equation, which can be obtained as a limit of the Boltzmann equation when grazing collisions prevail. Following the method in Kirsch and Rjasanow (2007), we can also derive the Fourier transform for Landau equation.

A Model for the Oxidation of Carbon Silicon Carbide Composite Structures

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2004-01-01

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of carbon silicon carbide (C/SiC) composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The numerical method is demonstrated by utilizing the method to model the carbon oxidation and weight loss behavior of C/SiC specimens during thermogravimetric experiments. The numerical method is used to study the physics of carbon oxidation in carbon silicon carbide composites.

Quaternion Regularization of the Equations of the Perturbed Spatial Restricted Three-Body Problem: I

NASA Astrophysics Data System (ADS)

Chelnokov, Yu. N.

2017-11-01

We develop a quaternion method for regularizing the differential equations of the perturbed spatial restricted three-body problem by using the Kustaanheimo-Stiefel variables, which is methodologically closely related to the quaternion method for regularizing the differential equations of perturbed spatial two-body problem, which was proposed by the author of the present paper. A survey of papers related to the regularization of the differential equations of the two- and threebody problems is given. The original Newtonian equations of perturbed spatial restricted three-body problem are considered, and the problem of their regularization is posed; the energy relations and the differential equations describing the variations in the energies of the system in the perturbed spatial restricted three-body problem are given, as well as the first integrals of the differential equations of the unperturbed spatial restricted circular three-body problem (Jacobi integrals); the equations of perturbed spatial restricted three-body problem written in terms of rotating coordinate systems whose angular motion is described by the rotation quaternions (Euler (Rodrigues-Hamilton) parameters) are considered; and the differential equations for angular momenta in the restricted three-body problem are given. Local regular quaternion differential equations of perturbed spatial restricted three-body problem in the Kustaanheimo-Stiefel variables, i.e., equations regular in a neighborhood of the first and second body of finite mass, are obtained. The equations are systems of nonlinear nonstationary eleventhorder differential equations. These equations employ, as additional dependent variables, the energy characteristics of motion of the body under study (a body of a negligibly small mass) and the time whose derivative with respect to a new independent variable is equal to the distance from the body of negligibly small mass to the first or second body of finite mass. The equations obtained in the paper permit developing regular methods for determining solutions, in analytical or numerical form, of problems difficult for classicalmethods, such as the motion of a body of negligibly small mass in a neighborhood of the other two bodies of finite masses.

The properties of fast and slow oblique solitons in a magnetized plasma

NASA Astrophysics Data System (ADS)

McKenzie, J. F.; Doyle, T. B.

2002-01-01

This work builds on a recent treatment by McKenzie and Doyle [Phys. Plasmas 8, 4367 (2001)], on oblique solitons in a cold magnetized plasma, to include the effects of plasma thermal pressure. Conservation of total momentum in the direction of wave propagation immediately shows that if the flow is supersonic, compressive (rarefactive) changes in the magnetic pressure induce decelerations (accelerations) in the flow speed, whereas if the flow is subsonic, compressive (rarefactive) changes in the magnetic pressure induce accelerations (decelerations) in the flow speed. Such behavior is characteristic of a Bernoulli-type plasma momentum flux which exhibits a minimum at the plasma sonic point. The plasma energy flux (kinetic plus enthalpy) also shows similar Bernoulli-type behavior. This transonic effect is manifest in the spatial structure equation for the flow speed (in the direction of propagation) which shows that soliton structures may exist if the wave speed lies either (i) in the range between the fast and Alfven speeds or (ii) between the sound and slow mode speed. These conditions follow from the requirement that a defined, characteristic "soliton parameter" m exceeds unity. It is in this latter slow soliton regime that the effects of plasma pressure are most keenly felt. The equilibrium points of the structure equation define the center of the wave. The structure of both fast and slow solitons is elucidated through the properties of the energy integral function of the structure equation. In particular, the slow soliton, which owes its existence to plasma pressure, may have either a compressive or rarefactive nature, and exhibits a rich structure, which is revealed through the spatial structure of the longitudinal speed and its corresponding transverse velocity hodograph.

Turbulent solutions of the equations of fluid motion

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1984-01-01

Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. Initial three-dimensional cosine velocity fluctuations and periodic boundary conditions are used in most of the work considered. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations, the initially nonrandom flow develops into an apparently random turbulence. Thus randomness or turbulence can arise as a consequence of the structure of the Navier-Stokes equations. The cases considered include turbulence which is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A mean shear is present in some cases. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components, and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.

Numerical solution of the wave equation with variable wave speed on nonconforming domains by high-order difference potentials

NASA Astrophysics Data System (ADS)

Britt, S.; Tsynkov, S.; Turkel, E.

2018-02-01

We solve the wave equation with variable wave speed on nonconforming domains with fourth order accuracy in both space and time. This is accomplished using an implicit finite difference (FD) scheme for the wave equation and solving an elliptic (modified Helmholtz) equation at each time step with fourth order spatial accuracy by the method of difference potentials (MDP). High-order MDP utilizes compact FD schemes on regular structured grids to efficiently solve problems on nonconforming domains while maintaining the design convergence rate of the underlying FD scheme. Asymptotically, the computational complexity of high-order MDP scales the same as that for FD.

Spatiotemporal canards in neural field equations

NASA Astrophysics Data System (ADS)

Avitabile, D.; Desroches, M.; Knobloch, E.

2017-04-01

Canards are special solutions to ordinary differential equations that follow invariant repelling slow manifolds for long time intervals. In realistic biophysical single-cell models, canards are responsible for several complex neural rhythms observed experimentally, but their existence and role in spatially extended systems is largely unexplored. We identify and describe a type of coherent structure in which a spatial pattern displays temporal canard behavior. Using interfacial dynamics and geometric singular perturbation theory, we classify spatiotemporal canards and give conditions for the existence of folded-saddle and folded-node canards. We find that spatiotemporal canards are robust to changes in the synaptic connectivity and firing rate. The theory correctly predicts the existence of spatiotemporal canards with octahedral symmetry in a neural field model posed on the unit sphere.

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

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

Prediction and experimental observation of damage dependent damping in laminated composite beams

NASA Technical Reports Server (NTRS)

Allen, D. H.; Harris, C. E.; Highsmith, A. L.

1987-01-01

The equations of motion are developed for laminated composite beams with load-induced matrix cracking. The damage is accounted for by utilizing internal state variables. The net result of these variables on the field equations is the introduction of both enhanced damping, and degraded stiffness. Both quantities are history dependent and spatially variable, thus resulting in nonlinear equations of motion. It is explained briefly how these equations may be quasi-linearized for laminated polymeric composites under certain types of structural loading. The coupled heat conduction equation is developed, and it is shown that an enhanced Zener damping effect is produced by the introduction of microstructural damage. The resulting equations are utilized to demonstrate how damage dependent material properties may be obtained from dynamic experiments. Finaly, experimental results are compared to model predictions for several composite layups.

A Finite-Volume approach for compressible single- and two-phase flows in flexible pipelines with fluid-structure interaction

NASA Astrophysics Data System (ADS)

Daude, F.; Galon, P.

2018-06-01

A Finite-Volume scheme for the numerical computations of compressible single- and two-phase flows in flexible pipelines is proposed based on an approximate Godunov-type approach. The spatial discretization is here obtained using the HLLC scheme. In addition, the numerical treatment of abrupt changes in area and network including several pipelines connected at junctions is also considered. The proposed approach is based on the integral form of the governing equations making it possible to tackle general equations of state. A coupled approach for the resolution of fluid-structure interaction of compressible fluid flowing in flexible pipes is considered. The structural problem is solved using Euler-Bernoulli beam finite elements. The present Finite-Volume method is applied to ideal gas and two-phase steam-water based on the Homogeneous Equilibrium Model (HEM) in conjunction with a tabulated equation of state in order to demonstrate its ability to tackle general equations of state. The extensive application of the scheme for both shock tube and other transient flow problems demonstrates its capability to resolve such problems accurately and robustly. Finally, the proposed 1-D fluid-structure interaction model appears to be computationally efficient.

Propagation of localized structures in relativistic magnetized electron-positron plasmas using particle-in-cell simulations

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

López, Rodrigo A.; Muñoz, Víctor; Viñas, Adolfo F.

2015-09-15

We use a particle-in-cell simulation to study the propagation of localized structures in a magnetized electron-positron plasma with relativistic finite temperature. We use as initial condition for the simulation an envelope soliton solution of the nonlinear Schrödinger equation, derived from the relativistic two fluid equations in the strongly magnetized limit. This envelope soliton turns out not to be a stable solution for the simulation and splits in two localized structures propagating in opposite directions. However, these two localized structures exhibit a soliton-like behavior, as they keep their profile after they collide with each other due to the periodic boundary conditions.more » We also observe the formation of localized structures in the evolution of a spatially uniform circularly polarized Alfvén wave. In both cases, the localized structures propagate with an amplitude independent velocity.« less

Tendency to occupy a statistically dominant spatial state of the flow as a driving force for turbulent transition.

PubMed

Chekmarev, Sergei F

2013-03-01

The transition from laminar to turbulent fluid motion occurring at large Reynolds numbers is generally associated with the instability of the laminar flow. On the other hand, since the turbulent flow characteristically appears in the form of spatially localized structures (e.g., eddies) filling the flow field, a tendency to occupy such a structured state of the flow cannot be ruled out as a driving force for turbulent transition. To examine this possibility, we propose a simple analytical model that treats the flow as a collection of localized spatial structures, each of which consists of elementary cells in which the behavior of the particles (atoms or molecules) is uncorrelated. This allows us to introduce the Reynolds number, associating it with the ratio between the total phase volume for the system and that for the elementary cell. Using the principle of maximum entropy to calculate the most probable size distribution of the localized structures, we show that as the Reynolds number increases, the elementary cells group into the localized structures, which successfully explains turbulent transition and some other general properties of turbulent flows. An important feature of the present model is that a bridge between the spatial-statistical description of the flow and hydrodynamic equations is established. We show that the basic assumptions underlying the model, i.e., that the particles are indistinguishable and elementary volumes of phase space exist in which the state of the particles is uncertain, are involved in the derivation of the Navier-Stokes equation. Taking into account that the model captures essential features of turbulent flows, this suggests that the driving force for the turbulent transition is basically the same as in the present model, i.e., the tendency of the system to occupy a statistically dominant state plays a key role. The instability of the flow at high Reynolds numbers can then be a mechanism to initiate structural rearrangement of the flow to find this state.

Distribution of thermal neutrons in a temperature gradient

NASA Astrophysics Data System (ADS)

Molinari, V. G.; Pollachini, L.

A method to determine the spatial distribution of the thermal spectrum of neutrons in heterogeneous systems is presented. The method is based on diffusion concepts and has a simple mathematical structure which increases computing efficiency. The application of this theory to the neutron thermal diffusion induced by a temperature gradient, as found in nuclear reactors, is described. After introducing approximations, a nonlinear equation system representing the neutron temperature is given. Values of the equation parameters and its dependence on geometrical factors and media characteristics are discussed.

Coarse-grained description of cosmic structure from Szekeres models

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

Sussman, Roberto A.; Gaspar, I. Delgado; Hidalgo, Juan Carlos, E-mail: sussman@nucleares.unam.mx, E-mail: ismael.delgadog@uaem.edu.mx, E-mail: hidalgo@fis.unam.mx

2016-03-01

We show that the full dynamical freedom of the well known Szekeres models allows for the description of elaborated 3-dimensional networks of cold dark matter structures (over-densities and/or density voids) undergoing ''pancake'' collapse. By reducing Einstein's field equations to a set of evolution equations, which themselves reduce in the linear limit to evolution equations for linear perturbations, we determine the dynamics of such structures, with the spatial comoving location of each structure uniquely specified by standard early Universe initial conditions. By means of a representative example we examine in detail the density contrast, the Hubble flow and peculiar velocities ofmore » structures that evolved, from linear initial data at the last scattering surface, to fully non-linear 10–20 Mpc scale configurations today. To motivate further research, we provide a qualitative discussion on the connection of Szekeres models with linear perturbations and the pancake collapse of the Zeldovich approximation. This type of structure modelling provides a coarse grained—but fully relativistic non-linear and non-perturbative —description of evolving large scale cosmic structures before their virialisation, and as such it has an enormous potential for applications in cosmological research.« less

Robust manipulation of light using topologically protected plasmonic modes.

PubMed

Liu, Chenxu; Gurudev Dutt, M V; Pekker, David

2018-02-05

We propose using a topological plasmonic crystal structure composed of an array of nearly parallel nanowires with unequal spacing for manipulating light. In the paraxial approximation, the Helmholtz equation that describes the propagation of light along the nanowires maps onto the Schrödinger equation of the Su-Schrieffer-Heeger (SSH) model. Using a full three-dimensional finite difference time domain solution of the Maxwell equations, we verify the existence of topological defect modes, with sub-wavelength localization, bound to domain walls of the plasmonic crystal. We show that by manipulating domain walls we can construct spatial mode filters that couple bulk modes to topological defect modes, and topological beam-splitters that couple two topological defect modes. Finally, we show that the structures are tolerant to fabrication errors with an inverse length-scale smaller than the topological band gap.

Recurrent noise-induced phase singularities in drifting patterns.

PubMed

Clerc, M G; Coulibaly, S; del Campo, F; Garcia-Nustes, M A; Louvergneaux, E; Wilson, M

2015-11-01

We show that the key ingredients for creating recurrent traveling spatial phase defects in drifting patterns are a noise-sustained structure regime together with the vicinity of a phase transition, that is, a spatial region where the control parameter lies close to the threshold for pattern formation. They both generate specific favorable initial conditions for local spatial gradients, phase, and/or amplitude. Predictions from the stochastic convective Ginzburg-Landau equation with real coefficients agree quite well with experiments carried out on a Kerr medium submitted to shifted optical feedback that evidence noise-induced traveling phase slips and vortex phase-singularities.

Nonlinear dynamics of drift structures in a magnetized dissipative plasma

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

Aburjania, G. D.; Rogava, D. L.; Kharshiladze, O. A.

2011-06-15

A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous magnetized dissipative plasma. A nonlinear transport equation for long-wavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the magnetic and collisional viscosity of the medium and its friction. The dynamic equation describes two types of nonlinearity: scalar (due to the temperature inhomogeneity) and vector (due to the convectively polarized motion of the particles of the medium). The equation is fourth order in the spatial derivatives, in contrast to the second-order Hasegawa-Mima equations. Anmore » analytic steady solution to the nonlinear equation is obtained that describes a new type of solitary dipole vortex. The nonlinear dynamic equation is integrated numerically. A new algorithm and a new finite difference scheme for solving the equation are proposed, and it is proved that the solution so obtained is unique. The equation is used to investigate how the initially steady dipole vortex constructed here behaves unsteadily under the action of the factors just mentioned. Numerical simulations revealed that the role of the vector nonlinearity is twofold: it helps the dispersion or the scalar nonlinearity (depending on their magnitude) to ensure the mutual equilibrium and, thereby, promote self-organization of the vortical structures. It is shown that dispersion breaks the initial dipole vortex into a set of tightly packed, smaller scale, less intense monopole vortices-alternating cyclones and anticyclones. When the dispersion of the evolving initial dipole vortex is weak, the scalar nonlinearity symmetrically breaks a cyclone-anticyclone pair into a cyclone and an anticyclone, which are independent of one another and have essentially the same intensity, shape, and size. The stronger the dispersion, the more anisotropic the process whereby the structures break: the anticyclone is more intense and localized, while the cyclone is less intense and has a larger size. In the course of further evolution, the cyclone persists for a relatively longer time, while the anticyclone breaks into small-scale vortices and dissipation hastens this process. It is found that the relaxation of the vortex by viscous dissipation differs in character from that by the frictional force. The time scale on which the vortex is damped depends strongly on its typical size: larger scale vortices are longer lived structures. It is shown that, as the instability develops, the initial vortex is amplified and the lifetime of the dipole pair components-cyclone and anticyclone-becomes longer. As time elapses, small-scale noise is generated in the system, and the spatial structure of the perturbation potential becomes irregular. The pattern of interaction of solitary vortex structures among themselves and with the medium shows that they can take part in strong drift turbulence and anomalous transport of heat and matter in an inhomogeneous magnetized plasma.« less

On the three dimensional structure of stratospheric material transport associated with various types of waves

NASA Astrophysics Data System (ADS)

Kinoshita, T.; Sato, K.

2016-12-01

The Transformed Eulerian-Mean (TEM) equations were derived by Andrews and McIntyre (1976, 1978) and have been widely used to examine wave-mean flow interaction in the meridional cross section. According to previous studies, the Brewer-Dobson circulation in the stratosphere is driven by planetary waves, baroclinic waves, and inertia-gravity waves, and that the meridional circulation from the summer hemisphere to the winter hemisphere in the mesosphere is mainly driven by gravity waves (e.g., Garcia and Boville 1994; Plumb and Semeniuk 2003; Watanabe et al. 2008; Okamoto et al. 2011). However, the TEM equations do not provide the three-dimensional view of the transport, so that the three dimensional TEM equations have been formulated (Hoskins et al. 1983, Trenberth 1986, Plumb 1985, 1986, Takaya and Nakamura 1997, 2001, Miyahara 2006, Kinoshita et al. 2010, Noda 2010, Kinoshita and Sato 2013a, b, and Noda 2014). On the other hand, the TEM equations cannot properly treat the lower boundary and unstable waves. The Mass-weighted Isentropic Mean (MIM) equations derived by Iwasaki (1989, 1990) are the equations that overcome those problems and the formulation of three-dimensional MIM equations have been studied. The present study applies the three-dimensional TEM and MIM equations to the ERA-Interim reanalysis data and examines the climatological character of three-dimensional structure of Stratospheric Brewer-Dobson circulation. Next, we will discuss how to treat the flow associated with spatial structure of stationary waves.

Landscape structure affects specialists but not generalists in naturally fragmented grasslands

USGS Publications Warehouse

Miller, Jesse E.D.; Damschen, Ellen Ingman; Harrison, Susan P.; Grace, James B.

2015-01-01

Understanding how biotic communities respond to landscape spatial structure is critically important for conservation management as natural landscapes become increasingly fragmented. However, empirical studies of the effects of spatial structure on plant species richness have found inconsistent results, suggesting that more comprehensive approaches are needed. In this study, we asked how landscape structure affects total plant species richness and the richness of a guild of specialized plants in a multivariate context. We sampled herbaceous plant communities at 56 dolomite glades (insular, fire-adapted grasslands) across the Missouri Ozarks, and used structural equation modeling (SEM) to analyze the relative importance of landscape structure, soil resource availability, and fire history for plant communities. We found that landscape spatial structure-defined as the area-weighted proximity of glade habitat surrounding study sites (proximity index)-had a significant effect on total plant species richness, but only after we controlled for environmental covariates. Richness of specialist species, but not generalists, was positively related to landscape spatial structure. Our results highlight that local environmental filters must be considered to understand the influence of landscape structure on communities, and that unique species guilds may respond differently to landscape structure than the community as a whole. These findings suggest that both local environment and landscape context should be considered when developing management strategies for species of conservation concern in fragmented habitats.

Analysis and modeling of localized invariant solutions in pipe flow

NASA Astrophysics Data System (ADS)

Ritter, Paul; Zammert, Stefan; Song, Baofang; Eckhardt, Bruno; Avila, Marc

2018-01-01

Turbulent spots surrounded by laminar flow are a landmark of transitional shear flows, but the dependence of their kinematic properties on spatial structure is poorly understood. We here investigate this dependence in pipe flow for Reynolds numbers between 1500 and 5000. We compute spatially localized relative periodic orbits in long pipes and show that their upstream and downstream fronts decay exponentially towards the laminar profile. This allows us to model the fronts by employing the linearized Navier-Stokes equations, and the resulting model yields the spatial decay rate and the front velocity profiles of the periodic orbits as a function of Reynolds number, azimuthal wave number, and propagation speed. In addition, when applied to a localized turbulent puff, the model is shown to accurately approximate the spatial decay rate of its upstream and downstream tails. Our study provides insight into the relationship between the kinematics and spatial structure of localized turbulence and more generally into the physics of localization.

Optimized growth and reorientation of anisotropic material based on evolution equations

NASA Astrophysics Data System (ADS)

Jantos, Dustin R.; Junker, Philipp; Hackl, Klaus

2018-07-01

Modern high-performance materials have inherent anisotropic elastic properties. The local material orientation can thus be considered to be an additional design variable for the topology optimization of structures containing such materials. In our previous work, we introduced a variational growth approach to topology optimization for isotropic, linear-elastic materials. We solved the optimization problem purely by application of Hamilton's principle. In this way, we were able to determine an evolution equation for the spatial distribution of density mass, which can be evaluated in an iterative process within a solitary finite element environment. We now add the local material orientation described by a set of three Euler angles as additional design variables into the three-dimensional model. This leads to three additional evolution equations that can be separately evaluated for each (material) point. Thus, no additional field unknown within the finite element approach is needed, and the evolution of the spatial distribution of density mass and the evolution of the Euler angles can be evaluated simultaneously.

S{sub 2}SA preconditioning for the S{sub n} equations with strictly non negative spatial discretization

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

Bruss, D. E.; Morel, J. E.; Ragusa, J. C.

2013-07-01

Preconditioners based upon sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D S{sub n} transport equation using a strictly non negative nonlinear spatial closure. Linear and nonlinear preconditioners have been analyzed. The effectiveness of various combinations of these preconditioners are compared. In one dimension, nonlinear sweep preconditioning is shown to be superior to linear sweep preconditioning, and DSA preconditioning using nonlinear sweeps in conjunction with a linear diffusion equation is found to be essentially equivalent to nonlinear sweeps in conjunction with a nonlinear diffusion equation. The ability to use amore » linear diffusion equation has important implications for preconditioning the S{sub n} equations with a strictly non negative spatial discretization in multiple dimensions. (authors)« less

Power-law spatial dispersion from fractional Liouville equation

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

Tarasov, Vasily E.

2013-10-15

A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.

Covariant Hamiltonian tetrad approach to numerical relativity

NASA Astrophysics Data System (ADS)

Hamilton, Andrew J. S.

2017-12-01

A Hamiltonian approach to the equations of general relativity is proposed using the powerful mathematical language of multivector-valued differential forms. In the approach, the gravitational coordinates are the 12 spatial components of the line interval (the vierbein) including their antisymmetric parts, and their 12 conjugate momenta. A feature of the proposed formalism is that it allows Lorentz gauge freedoms to be imposed on the Lorentz connections rather than on the vierbein, which may facilitate numerical integration in some challenging problems. The 40 Hamilton's equations comprise 12 +12 =24 equations of motion, ten constraint equations (first class constraints, which must be arranged on the initial hypersurface of constant time, but which are guaranteed thereafter by conservation laws), and six identities (second class constraints). The six identities define a trace-free spatial tensor that is the gravitational analog of the magnetic field of electromagnetism. If the gravitational magnetic field is promoted to an independent field satisfying its own equation of motion, then the system becomes the Wahlquist-Estabrook-Buchman-Bardeen (WEBB) system, which is known to be strongly hyperbolic. Some other approaches, including Arnowitt-Deser-Misner, Baumgarte-Shapiro-Shibata-Nakamura, WEBB, and loop quantum gravity, are translated into the language of multivector-valued forms, bringing out their underlying mathematical structure.

Generation mechanisms of fundamental rogue wave spatial-temporal structure.

PubMed

Ling, Liming; Zhao, Li-Chen; Yang, Zhan-Ying; Guo, Boling

2017-08-01

We discuss the generation mechanism of fundamental rogue wave structures in N-component coupled systems, based on analytical solutions of the nonlinear Schrödinger equation and modulational instability analysis. Our analysis discloses that the pattern of a fundamental rogue wave is determined by the evolution energy and growth rate of the resonant perturbation that is responsible for forming the rogue wave. This finding allows one to predict the rogue wave pattern without the need to solve the N-component coupled nonlinear Schrödinger equation. Furthermore, our results show that N-component coupled nonlinear Schrödinger systems may possess N different fundamental rogue wave patterns at most. These results can be extended to evaluate the type and number of fundamental rogue wave structure in other coupled nonlinear systems.

Sine-Gordon Equation in (1+2) and (1+3) dimensions: Existence and Classification of Traveling-Wave Solutions.

PubMed

Zarmi, Yair

2015-01-01

The (1+1)-dimensional Sine-Gordon equation passes integrability tests commonly applied to nonlinear evolution equations. Its kink solutions (one-dimensional fronts) are obtained by a Hirota algorithm. In higher space-dimensions, the equation does not pass these tests. Although it has been derived over the years for quite a few physical systems that have nothing to do with Special Relativity, the Sine-Gordon equation emerges as a non-linear relativistic wave equation. This opens the way for exploiting the tools of the Theory of Special Relativity. Using no more than the relativistic kinematics of tachyonic momentum vectors, from which the solutions are constructed through the Hirota algorithm, the existence and classification of N-moving-front solutions of the (1+2)- and (1+3)-dimensional equations for all N ≥ 1 are presented. In (1+2) dimensions, each multi-front solution propagates rigidly at one velocity. The solutions are divided into two subsets: Solutions whose velocities are lower than a limiting speed, c = 1, or are greater than or equal to c. To connect with concepts of the Theory of Special Relativity, c will be called "the speed of light." In (1+3)-dimensions, multi-front solutions are characterized by spatial structure and by velocity composition. The spatial structure is either planar (rotated (1+2)-dimensional solutions), or genuinely three-dimensional--branes. Planar solutions, propagate rigidly at one velocity, which is lower than, equal to, or higher than c. Branes must contain clusters of fronts whose speed exceeds c = 1. Some branes are "hybrids": different clusters of fronts propagate at different velocities. Some velocities may be lower than c but some must be equal to, or exceed, c. Finally, the speed of light cannot be approached from within the subset of slower-than-light solutions in both (1+2) and (1+3) dimensions.

Identification of spatially-localized initial conditions via sparse PCA

NASA Astrophysics Data System (ADS)

Dwivedi, Anubhav; Jovanovic, Mihailo

2017-11-01

Principal Component Analysis involves maximization of a quadratic form subject to a quadratic constraint on the initial flow perturbations and it is routinely used to identify the most energetic flow structures. For general flow configurations, principal components can be efficiently computed via power iteration of the forward and adjoint governing equations. However, the resulting flow structures typically have a large spatial support leading to a question of physical realizability. To obtain spatially-localized structures, we modify the quadratic constraint on the initial condition to include a convex combination with an additional regularization term which promotes sparsity in the physical domain. We formulate this constrained optimization problem as a nonlinear eigenvalue problem and employ an inverse power-iteration-based method to solve it. The resulting solution is guaranteed to converge to a nonlinear eigenvector which becomes increasingly localized as our emphasis on sparsity increases. We use several fluids examples to demonstrate that our method indeed identifies the most energetic initial perturbations that are spatially compact. This work was supported by Office of Naval Research through Grant Number N00014-15-1-2522.

On small beams with large topological charge: II. Photons, electrons and gravitational waves

NASA Astrophysics Data System (ADS)

Krenn, Mario; Zeilinger, Anton

2018-06-01

Beams of light with a large topological charge significantly change their spatial structure when they are focused strongly. Physically, it can be explained by an emerging electromagnetic field component in the direction of propagation, which is neglected in the simplified scalar wave picture in optics. Here we ask: is this a specific photonic behavior, or can similar phenomena also be predicted for other species of particles? We show that the same modification of the spatial structure exists for relativistic electrons as well as for focused gravitational waves. However, this is for different physical reasons: for electrons, which are described by the Dirac equation, the spatial structure changes due to a spin–orbit coupling in the relativistic regime. In gravitational waves described with linearized general relativity, the curvature of space–time between the transverse and propagation direction leads to the modification of the spatial structure. Thus, this universal phenomenon exists for both massive and massless elementary particles with spin 1/2, 1 and 2. It would be very interesting whether other types of particles such as composite systems (neutrons or C60) or neutrinos show a similar behavior and how this phenomenon can be explained in a unified physical way.

Ecological and evolutionary consequences of explicit spatial structure in exploiter-victim systems

NASA Astrophysics Data System (ADS)

Klopfer, Eric David

One class of spatial model which has been widely used in ecology has been termed "pseudo-spatial models" and classically employs various types of aggregation in studying the coexistence of competing parasitoids. Yet, little is known about the relative effects of each of these aggregation behaviors. Thus, in Chapter 1 I chose to examine three types of aggregation and explore their relative strengths in promoting coexistence of two competing parasitoids. A striking shortcoming of spatial models in ecology to date is that there is a relative lack of use of spatial models to investigate problems on the evolutionary as opposed to ecological time scale. Consequently, in Chapter 2 I chose to start with a classic problem of evolutionary time scale--the evolution of virulence and predation rates. Debate about this problem has continued through several decades, yet many instances are not adequately explained by current models. In this study I explored the effect of explicit spatial structure on exploitation rates by comparing a cellular automata (CA) exploiter-victim model which incorporates local dynamics to a metapopulation model which does not include such dynamics. One advantage of CA models is that they are defined by simple rules rather than the often complex equations of other types of spatial models. This is an extremely useful attribute when one wants to convey results of models to an audience with an applied bent that is often uncomfortable with hard-to-understand equations. Thus, in Chapter 3, through the use of CA models I show that there are spatial phenomena which alter the impact of introduced predators and that these phenomena are potentially important in the implementation of biocontrol programs. The relatively recent incorporation of spatial models into the ecological literature has left most ecologists and evolutionary biologists without the ability to understand, let alone employ, spatial models in evolutionary problems. In order to give the next generation of potential ecologists a better understanding of these models, in Chapter 4 I present an interactive tutorial in which students are able to explore the most well studied of these models (the evolution of cooperation in a spatial environment).

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

NASA Technical Reports Server (NTRS)

Givoli, D.; Rand, O.

1992-01-01

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

Thin-film Faraday patterns in three dimensions

NASA Astrophysics Data System (ADS)

Richter, Sebastian; Bestehorn, Michael

2017-04-01

We investigate the long time evolution of a thin fluid layer in three spatial dimensions located on a horizontal planar substrate. The substrate is subjected to time-periodic external vibrations in normal and in tangential direction with respect to the plane surface. The governing partial differential equation system of our model is obtained from the incompressible Navier-Stokes equations considering the limit of a thin fluid geometry and using the long wave lubrication approximation. It includes inertia and viscous friction. Numerical simulations evince the existence of persistent spatially complex surface patterns (periodic and quasiperiodic) for certain superpositions of two vertical excitations and initial conditions. Additional harmonic lateral excitations cause deformations but retain the basic structure of the patterns. Horizontal ratchet-shaped forces lead to a controllable lateral movement of the fluid. A Floquet analysis is used to determine the stability of the linearized system.

A Structural Equation Model Explaining 8th Grade Students' Mathematics Achievements

ERIC Educational Resources Information Center

Yurt, Eyüp; Sünbül, Ali Murat

2014-01-01

The purpose of this study is to investigate, via a model, the explanatory and predictive relationships among the following variables: Mathematical Problem Solving and Reasoning Skills, Sources of Mathematics Self-Efficacy, Spatial Ability, and Mathematics Achievements of Secondary School 8th Grade Students. The sample group of the study, itself…

The Architecture, Dynamics, and Development of Mental Processing: Greek, Chinese, or Universal?

ERIC Educational Resources Information Center

Demetriou, A.; Kui, Z.X.; Spanoudis, G.; Christou, C.; Kyriakides, L.; Platsidou, M.

2005-01-01

This study compared Greeks with Chinese, from 8 to 14 years of age, on measures of processing efficiency, working memory, and reasoning. All processes were addressed through three domains of relations: verbal/propositional, quantitative, and visuo/spatial. Structural equations modelling and rating scale analysis showed that the architecture and…

Resolvent analysis of shear flows using One-Way Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Rigas, Georgios; Schmidt, Oliver; Towne, Aaron; Colonius, Tim

2017-11-01

For three-dimensional flows, questions of stability, receptivity, secondary flows, and coherent structures require the solution of large partial-derivative eigenvalue problems. Reduced-order approximations are thus required for engineering prediction since these problems are often computationally intractable or prohibitively expensive. For spatially slowly evolving flows, such as jets and boundary layers, the One-Way Navier-Stokes (OWNS) equations permit a fast spatial marching procedure that results in a huge reduction in computational cost. Here, an adjoint-based optimization framework is proposed and demonstrated for calculating optimal boundary conditions and optimal volumetric forcing. The corresponding optimal response modes are validated against modes obtained in terms of global resolvent analysis. For laminar base flows, the optimal modes reveal modal and non-modal transition mechanisms. For turbulent base flows, they predict the evolution of coherent structures in a statistical sense. Results from the application of the method to three-dimensional laminar wall-bounded flows and turbulent jets will be presented. This research was supported by the Office of Naval Research (N00014-16-1-2445) and Boeing Company (CT-BA-GTA-1).

Quantum spatial propagation of squeezed light in a degenerate parametric amplifier

NASA Technical Reports Server (NTRS)

Deutsch, Ivan H.; Garrison, John C.

1992-01-01

Differential equations which describe the steady state spatial evolution of nonclassical light are established using standard quantum field theoretic techniques. A Schroedinger equation for the state vector of the optical field is derived using the quantum analog of the slowly varying envelope approximation (SVEA). The steady state solutions are those that satisfy the time independent Schroedinger equation. The resulting eigenvalue problem then leads to the spatial propagation equations. For the degenerate parametric amplifier this method shows that the squeezing parameter obey nonlinear differential equations coupled by the amplifier gain and phase mismatch. The solution to these differential equations is equivalent to one obtained from the classical three wave mixing steady state solution to the parametric amplifier with a nondepleted pump.

A selfsimilar behavior of the urban structure in the spatially inhomogeneous model

NASA Astrophysics Data System (ADS)

Echkina, E. Y.; Inovenkov, O. I.; Kostomarov, D. P.

2006-03-01

At present there is a strong tendency to use new methods for the description of the regional and spatial economy. In increasing frequency we consider that any economic activity is spatially dependent. The problem of the evolution of internal urban formation can be described with the exact supposition. So that is why we use partial derivative equations set with the appropriate boundary and initial conditions for the solving the problem of the urban evolution. Here we describe the model of urban population's density modification taking into account a modification of the housing quality. A program has been created which realizes difference method of mixed problem solution for population's density. For the wide class of coefficients it has been shown that the problem's solution “quickly forgets” the parts of the initial conditions and comes out to the intermediate asymptotic form, which nature depends only on the problem's operator. Actually it means that the urban structure does not depend on external circumstances and is formed by the internal structure of the model.

Stochastic population dynamics in spatially extended predator-prey systems

NASA Astrophysics Data System (ADS)

Dobramysl, Ulrich; Mobilia, Mauro; Pleimling, Michel; Täuber, Uwe C.

2018-02-01

Spatially extended population dynamics models that incorporate demographic noise serve as case studies for the crucial role of fluctuations and correlations in biological systems. Numerical and analytic tools from non-equilibrium statistical physics capture the stochastic kinetics of these complex interacting many-particle systems beyond rate equation approximations. Including spatial structure and stochastic noise in models for predator-prey competition invalidates the neutral Lotka-Volterra population cycles. Stochastic models yield long-lived erratic oscillations stemming from a resonant amplification mechanism. Spatially extended predator-prey systems display noise-stabilized activity fronts that generate persistent correlations. Fluctuation-induced renormalizations of the oscillation parameters can be analyzed perturbatively via a Doi-Peliti field theory mapping of the master equation; related tools allow detailed characterization of extinction pathways. The critical steady-state and non-equilibrium relaxation dynamics at the predator extinction threshold are governed by the directed percolation universality class. Spatial predation rate variability results in more localized clusters, enhancing both competing species’ population densities. Affixing variable interaction rates to individual particles and allowing for trait inheritance subject to mutations induces fast evolutionary dynamics for the rate distributions. Stochastic spatial variants of three-species competition with ‘rock-paper-scissors’ interactions metaphorically describe cyclic dominance. These models illustrate intimate connections between population dynamics and evolutionary game theory, underscore the role of fluctuations to drive populations toward extinction, and demonstrate how space can support species diversity. Two-dimensional cyclic three-species May-Leonard models are characterized by the emergence of spiraling patterns whose properties are elucidated by a mapping onto a complex Ginzburg-Landau equation. Multiple-species extensions to general ‘food networks’ can be classified on the mean-field level, providing both fundamental understanding of ensuing cooperativity and profound insight into the rich spatio-temporal features and coarsening kinetics in the corresponding spatially extended systems. Novel space-time patterns emerge as a result of the formation of competing alliances; e.g. coarsening domains that each incorporate rock-paper-scissors competition games.

Effective equations governing an active poroelastic medium

PubMed Central

2017-01-01

In this work, we consider the spatial homogenization of a coupled transport and fluid–structure interaction model, to the end of deriving a system of effective equations describing the flow, elastic deformation and transport in an active poroelastic medium. The ‘active’ nature of the material results from a morphoelastic response to a chemical stimulant, in which the growth time scale is strongly separated from other elastic time scales. The resulting effective model is broadly relevant to the study of biological tissue growth, geophysical flows (e.g. swelling in coals and clays) and a wide range of industrial applications (e.g. absorbant hygiene products). The key contribution of this work is the derivation of a system of homogenized partial differential equations describing macroscale growth, coupled to transport of solute, that explicitly incorporates details of the structure and dynamics of the microscopic system, and, moreover, admits finite growth and deformation at the pore scale. The resulting macroscale model comprises a Biot-type system, augmented with additional terms pertaining to growth, coupled to an advection–reaction–diffusion equation. The resultant system of effective equations is then compared with other recent models under a selection of appropriate simplifying asymptotic limits. PMID:28293138

Generation of laser-induced periodic surface structures on transparent material-fused silica

NASA Astrophysics Data System (ADS)

Schwarz, Simon; Rung, Stefan; Hellmann, Ralf

2016-05-01

We report on a comparison between simulated and experimental results for the generation of laser-induced periodic surface structures with low spatial frequency on dielectrics. Using the established efficacy factor theory extended by a Drude model, we determine the required carrier density for the generation of low spatial frequency LIPSS (LSFL) and forecast their periodicity and orientation. In a subsequent calculative step, we determine the fluence of ultrashort laser pulses necessary to excite this required carrier density in due consideration of the pulse number dependent ablation threshold. The later calculation is based on a rate equation including photo- and avalanche ionization and derives appropriate process parameters for a selective generation of LSFL. Exemplarily, we apply this approach to the generation of LSFL on fused silica using a 1030 nm femtosecond laser. The experimental results for the orientation and spatial periodicity of LSFL reveal excellent agreement with the simulation.

Generation of laser-induced periodic surface structures on transparent material-fused silica

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

Schwarz, Simon; Rung, Stefan; Hellmann, Ralf

2016-05-02

We report on a comparison between simulated and experimental results for the generation of laser-induced periodic surface structures with low spatial frequency on dielectrics. Using the established efficacy factor theory extended by a Drude model, we determine the required carrier density for the generation of low spatial frequency LIPSS (LSFL) and forecast their periodicity and orientation. In a subsequent calculative step, we determine the fluence of ultrashort laser pulses necessary to excite this required carrier density in due consideration of the pulse number dependent ablation threshold. The later calculation is based on a rate equation including photo- and avalanche ionizationmore » and derives appropriate process parameters for a selective generation of LSFL. Exemplarily, we apply this approach to the generation of LSFL on fused silica using a 1030 nm femtosecond laser. The experimental results for the orientation and spatial periodicity of LSFL reveal excellent agreement with the simulation.« less

Rule-based spatial modeling with diffusing, geometrically constrained molecules.

PubMed

Gruenert, Gerd; Ibrahim, Bashar; Lenser, Thorsten; Lohel, Maiko; Hinze, Thomas; Dittrich, Peter

2010-06-07

We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined. For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided. Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa. We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly.

Rule-based spatial modeling with diffusing, geometrically constrained molecules

PubMed Central

2010-01-01

Background We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined. For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided. Results Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa. Conclusions We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly. PMID:20529264

Oxidation Behavior of Carbon Fiber-Reinforced Composites

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2008-01-01

OXIMAP is a numerical (FEA-based) solution tool capable of calculating the carbon fiber and fiber coating oxidation patterns within any arbitrarily shaped carbon silicon carbide composite structure as a function of time, temperature, and the environmental oxygen partial pressure. The mathematical formulation is derived from the mechanics of the flow of ideal gases through a chemically reacting, porous solid. The result of the formulation is a set of two coupled, non-linear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined at each time step using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The non-linear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual finite element method, allowing for the solution of the differential equations numerically.

Investigation of the Wave Propagation of Vector Modes of Light in a Spherically Symmetric Refractive Index Profile

NASA Astrophysics Data System (ADS)

Pozderac, Preston; Leary, Cody

We investigated the solutions to the Helmholtz equation in the case of a spherically symmetric refractive index using three different methods. The first method involves solving the Helmholtz equation for a step index profile and applying further constraints contained in Maxwell's equations. Utilizing these equations, we can simultaneously solve for the electric and magnetic fields as well as the allowed energies of photons propagating in this system. The second method applies a perturbative correction to these energies, which surfaces when deriving a Helmholtz type equation in a medium with an inhomogeneous refractive index. Applying first order perturbation theory, we examine how the correction term affects the energy of the photon. In the third method, we investigate the effects of the above perturbation upon solutions to the scalar Helmholtz equation, which are separable with respect to its polarization and spatial degrees of freedom. This work provides insights into the vector field structure of a photon guided by a glass microsphere.

Label-free nanoscale characterization of red blood cell structure and dynamics using single-shot transport of intensity equation

NASA Astrophysics Data System (ADS)

Poola, Praveen Kumar; John, Renu

2017-10-01

We report the results of characterization of red blood cell (RBC) structure and its dynamics with nanometric sensitivity using transport of intensity equation microscopy (TIEM). Conventional transport of intensity technique requires three intensity images and hence is not suitable for studying real-time dynamics of live biological samples. However, assuming the sample to be homogeneous, phase retrieval using transport of intensity equation has been demonstrated with single defocused measurement with x-rays. We adopt this technique for quantitative phase light microscopy of homogenous cells like RBCs. The main merits of this technique are its simplicity, cost-effectiveness, and ease of implementation on a conventional microscope. The phase information can be easily merged with regular bright-field and fluorescence images to provide multidimensional (three-dimensional spatial and temporal) information without any extra complexity in the setup. The phase measurement from the TIEM has been characterized using polymeric microbeads and the noise stability of the system has been analyzed. We explore the structure and real-time dynamics of RBCs and the subdomain membrane fluctuations using this technique.

Anomalous sea surface structures as an object of statistical topography

NASA Astrophysics Data System (ADS)

Klyatskin, V. I.; Koshel, K. V.

2015-06-01

By exploiting ideas of statistical topography, we analyze the stochastic boundary problem of emergence of anomalous high structures on the sea surface. The kinematic boundary condition on the sea surface is assumed to be a closed stochastic quasilinear equation. Applying the stochastic Liouville equation, and presuming the stochastic nature of a given hydrodynamic velocity field within the diffusion approximation, we derive an equation for a spatially single-point, simultaneous joint probability density of the surface elevation field and its gradient. An important feature of the model is that it accounts for stochastic bottom irregularities as one, but not a single, perturbation. Hence, we address the assumption of the infinitely deep ocean to obtain statistic features of the surface elevation field and the squared elevation gradient field. According to the calculations, we show that clustering in the absolute surface elevation gradient field happens with the unit probability. It results in the emergence of rare events such as anomalous high structures and deep gaps on the sea surface almost in every realization of a stochastic velocity field.

A positivity preserving and conservative variational scheme for phase-field modeling of two-phase flows

NASA Astrophysics Data System (ADS)

Joshi, Vaibhav; Jaiman, Rajeev K.

2018-05-01

We present a positivity preserving variational scheme for the phase-field modeling of incompressible two-phase flows with high density ratio. The variational finite element technique relies on the Allen-Cahn phase-field equation for capturing the phase interface on a fixed Eulerian mesh with mass conservative and energy-stable discretization. The mass conservation is achieved by enforcing a Lagrange multiplier which has both temporal and spatial dependence on the underlying solution of the phase-field equation. To make the scheme energy-stable in a variational sense, we discretize the spatial part of the Lagrange multiplier in the phase-field equation by the mid-point approximation. The proposed variational technique is designed to reduce the spurious and unphysical oscillations in the solution while maintaining the second-order accuracy of both spatial and temporal discretizations. We integrate the Allen-Cahn phase-field equation with the incompressible Navier-Stokes equations for modeling a broad range of two-phase flow and fluid-fluid interface problems. The coupling of the implicit discretizations corresponding to the phase-field and the incompressible flow equations is achieved via nonlinear partitioned iterative procedure. Comparison of results between the standard linear stabilized finite element method and the present variational formulation shows a remarkable reduction of oscillations in the solution while retaining the boundedness of the phase-indicator field. We perform a standalone test to verify the accuracy and stability of the Allen-Cahn two-phase solver. We examine the convergence and accuracy properties of the coupled phase-field solver through the standard benchmarks of the Laplace-Young law and a sloshing tank problem. Two- and three-dimensional dam break problems are simulated to assess the capability of the phase-field solver for complex air-water interfaces involving topological changes on unstructured meshes. Finally, we demonstrate the phase-field solver for a practical offshore engineering application of wave-structure interaction.

Design of Capillary Flows with Spatially Graded Porous Films

NASA Astrophysics Data System (ADS)

Joung, Young Soo; Figliuzzi, Bruno Michel; Buie, Cullen

2013-11-01

We have developed a new capillary tube model, consisting of multi-layered capillary tubes oriented in the direction of flow, to predict capillary speeds on spatially graded porous films. Capillary flows through thin porous media have been widely utilized for small size liquid transport systems. However, for most media it is challenging to realize arbitrary shapes and spatially functionalized micro-structures with variable flow properties. Therefore, conventional media can only be used for capillary flows obeying Washburn's equation and the modifications thereof. Given this background, we recently developed a method called breakdown anodization (BDA) to produce highly wetting porous films. The resulting surfaces show nearly zero contact angles and fast water spreading speed. Furthermore, capillary pressure and spreading diffusivity can be expressed as functions of capillary height when customized electric fields are used in BDA. From the capillary tube model, we derived a general capillary flow equation of motion in terms of capillary pressure and spreading diffusivity. The theoretical model shows good agreement with experimental capillary flows. The study will provide novel design methodologies for paper-based microfluidic devices.

TRUMP. Transient & S-State Temperature Distribution

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

Elrod, D.C.; Turner, W.D.

1992-03-03

TRUMP solves a general nonlinear parabolic partial differential equation describing flow in various kinds of potential fields, such as fields of temperature, pressure, or electricity and magnetism; simultaneously, it will solve two additional equations representing, in thermal problems, heat production by decomposition of two reactants having rate constants with a general Arrhenius temperature dependence. Steady-state and transient flow in one, two, or three dimensions are considered in geometrical configurations having simple or complex shapes and structures. Problem parameters may vary with spatial position, time, or primary dependent variables, temperature, pressure, or field strength. Initial conditions may vary with spatial position,more » and among the criteria that may be specified for ending a problem are upper and lower limits on the size of the primary dependent variable, upper limits on the problem time or on the number of time-steps or on the computer time, and attainment of steady state.« less

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

Elrod, D.C.; Turner, W.D.

TRUMP solves a general nonlinear parabolic partial differential equation describing flow in various kinds of potential fields, such as fields of temperature, pressure, or electricity and magnetism; simultaneously, it will solve two additional equations representing, in thermal problems, heat production by decomposition of two reactants having rate constants with a general Arrhenius temperature dependence. Steady-state and transient flow in one, two, or three dimensions are considered in geometrical configurations having simple or complex shapes and structures. Problem parameters may vary with spatial position, time, or primary dependent variables, temperature, pressure, or field strength. Initial conditions may vary with spatial position,more » and among the criteria that may be specified for ending a problem are upper and lower limits on the size of the primary dependent variable, upper limits on the problem time or on the number of time-steps or on the computer time, and attainment of steady state.« less

Spectral methods for the spin-2 equation near the cylinder at spatial infinity

NASA Astrophysics Data System (ADS)

Macedo, Rodrigo P.; Valiente Kroon, Juan A.

2018-06-01

We solve, numerically, the massless spin-2 equations, written in terms of a gauge based on the properties of conformal geodesics, in a neighbourhood of spatial infinity using spectral methods in both space and time. This strategy allows us to compute the solutions to these equations up to the critical sets where null infinity intersects with spatial infinity. Moreover, we use the convergence rates of the numerical solutions to read-off their regularity properties.

Visualization of Dynamic Vortex Structures in Magnetic Films with Uniaxial Anisotropy (Micromagnetic Simulation)

NASA Astrophysics Data System (ADS)

Zverev, V. V.; Izmozherov, I. M.; Filippov, B. N.

2018-02-01

Three-dimensional computer simulation of dynamic processes in a moving domain boundary separating domains in a soft magnetic uniaxial film with planar anisotropy is performed by numerical solution of Landau-Lifshitz-Gilbert equations. The developed visualization methods are used to establish the connection between the motion of surface vortices and antivortices, singular (Bloch) points, and core lines of intrafilm vortex structures. A relation between the character of magnetization dynamics and the film thickness is found. The analytical models of spatial vortex structures for imitation of topological properties of the structures observed in micromagnetic simulation are constructed.

Extended generalized recurrence plot quantification of complex circular patterns

NASA Astrophysics Data System (ADS)

Riedl, Maik; Marwan, Norbert; Kurths, Jürgen

2017-03-01

The generalized recurrence plot is a modern tool for quantification of complex spatial patterns. Its application spans the analysis of trabecular bone structures, Turing patterns, turbulent spatial plankton patterns, and fractals. Determinism is a central measure in this framework quantifying the level of regularity of spatial structures. We show by basic examples of fully regular patterns of different symmetries that this measure underestimates the orderliness of circular patterns resulting from rotational symmetries. We overcome this crucial problem by checking additional structural elements of the generalized recurrence plot which is demonstrated with the examples. Furthermore, we show the potential of the extended quantity of determinism applying it to more irregular circular patterns which are generated by the complex Ginzburg-Landau-equation and which can be often observed in real spatially extended dynamical systems. So, we are able to reconstruct the main separations of the system's parameter space analyzing single snapshots of the real part only, in contrast to the use of the original quantity. This ability of the proposed method promises also an improved description of other systems with complicated spatio-temporal dynamics typically occurring in fluid dynamics, climatology, biology, ecology, social sciences, etc.

Exact travelling wave solutions for a diffusion-convection equation in two and three spatial dimensions

NASA Astrophysics Data System (ADS)

Elwakil, S. A.; El-Labany, S. K.; Zahran, M. A.; Sabry, R.

2004-04-01

The modified extended tanh-function method were applied to the general class of nonlinear diffusion-convection equations where the concentration-dependent diffusivity, D( u), was taken to be a constant while the concentration-dependent hydraulic conductivity, K( u) were taken to be in a power law. The obtained solutions include rational-type, triangular-type, singular-type, and solitary wave solutions. In fact, the profile of the obtained solitary wave solutions resemble the characteristics of a shock-wave like structure for an arbitrary m (where m>1 is the power of the nonlinear convection term).

Quasi-static evolution of coronal magnetic fields

NASA Technical Reports Server (NTRS)

Longcope, D. W.; Sudan, R. N.

1992-01-01

A formalism is developed to describe the purely quasi-static part of the evolution of a coronal loop driven by its footpoints. This is accomplished under assumptions of a long, thin loop. The quasi-static equations reveal the possibility for sudden 'loss of equilibrium' at which time the system evolves dynamically rather than quasi-statically. Such quasi-static crises produce high-frequency Alfven waves and, in conjunction with Alfven wave dissipation models, form a viable coronal heating mechanism. Furthermore, an approximate solution to the quasi-static equations by perturbation method verifies the development of small-scale spatial current structure.

Can we understand structural and tectonic processes and their products without appeal to a complete mechanics?

NASA Astrophysics Data System (ADS)

Fletcher, Raymond C.; Pollard, David D.

1999-08-01

Our answer is `no'. Throughout the 20th century, the majority of structural geologists have worked with a conceptual basis that includes only isolated fragments of continuum mechanics (e.g. strain analysis, constitutive laws, force balance, Mohr's circles, or conservation of volume), and this has resulted in the proliferation of ad hoc models of structural and tectonic processes and their products. Furthermore, at a more abstract level, the possibility that mechanical quantities of interest (e.g. displacement, velocity, stress, or temperature) vary continuously in the spatial coordinates and time is largely ignored. These two conceptual oversights are related: without the mathematical concept of partial differentiation (as in the biharmonic equation of elasticity theory that brings strain compatability, Hooke's law, and stress equilibrium together) these spatial and temporal variations cannot be accounted for explicitly. Thus, the mechanical concept of boundary- and initial-value problems, formulated in terms of partial differential equations, has not been adopted as a necessary tool by most practitioners of structural geology and tectonics. We illustrate our case with two examples: the development of chevron folds and of échelon veins. We show how the ad hoc approach, while successful at one level, lacks predictive capability and possesses a low degree of refutability. Further progress in understanding these (and other) products of structural and tectonic processes can be made through an integrative approach using a complete and self-consistent mechanics.

Improving Student Understanding of Spatial Ecology Statistics

ERIC Educational Resources Information Center

Hopkins, Robert, II; Alberts, Halley

2015-01-01

This activity is designed as a primer to teaching population dispersion analysis. The aim is to help improve students' spatial thinking and their understanding of how spatial statistic equations work. Students use simulated data to develop their own statistic and apply that equation to experimental behavioral data for Gambusia affinis (western…

Helmholtz Natural Modes: the universal and discrete spatial fabric of electromagnetic wavefields

NASA Astrophysics Data System (ADS)

El Gawhary, Omar

2017-01-01

The interaction of electromagnetic waves with matter is at the foundation of the way we perceive and explore the world around us. In fact, when a field interacts with an object, signatures on the object’s geometry and physical properties are recorded in the resulting scattered field and are transported away from the object, where they can eventually be detected and processed. An optical field can transport information through its spectral content, its polarization state, and its spatial distribution. Generally speaking, the field’s spatial structure is typically subjected to changes under free-space propagation and any information therein encoded gets reshuffled by the propagation process. We must ascribe to this fundamental reason the fact that spectroscopy was known to the ancient civilizations already, and founded as modern science in the middle of seventeenth century, while to date we do not have an established scientific of field of ‘spatial spectroscopy’ yet. In this work we tackle this issue and we show how any field, whose evolution is dictated by Helmholtz equation, contains a universal and invariant spatial structure. When expressed in the framework of this spatial fabric, the spatial information content carried by any field reveals its invariant nature. This opens the way to novel paradigms in optical digital communications, inverse scattering, materials inspection, nanometrology and quantum optics.

Spatial Prediction of Coxiella burnetii Outbreak Exposure via Notified Case Counts in a Dose-Response Model.

PubMed

Brooke, Russell J; Kretzschmar, Mirjam E E; Hackert, Volker; Hoebe, Christian J P A; Teunis, Peter F M; Waller, Lance A

2017-01-01

We develop a novel approach to study an outbreak of Q fever in 2009 in the Netherlands by combining a human dose-response model with geostatistics prediction to relate probability of infection and associated probability of illness to an effective dose of Coxiella burnetii. The spatial distribution of the 220 notified cases in the at-risk population are translated into a smooth spatial field of dose. Based on these symptomatic cases, the dose-response model predicts a median of 611 asymptomatic infections (95% range: 410, 1,084) for the 220 reported symptomatic cases in the at-risk population; 2.78 (95% range: 1.86, 4.93) asymptomatic infections for each reported case. The low attack rates observed during the outbreak range from (Equation is included in full-text article.)to (Equation is included in full-text article.). The estimated peak levels of exposure extend to the north-east from the point source with an increasing proportion of asymptomatic infections further from the source. Our work combines established methodology from model-based geostatistics and dose-response modeling allowing for a novel approach to study outbreaks. Unobserved infections and the spatially varying effective dose can be predicted using the flexible framework without assuming any underlying spatial structure of the outbreak process. Such predictions are important for targeting interventions during an outbreak, estimating future disease burden, and determining acceptable risk levels.

Spatial complexity of solutions of higher order partial differential equations

NASA Astrophysics Data System (ADS)

Kukavica, Igor

2004-03-01

We address spatial oscillation properties of solutions of higher order parabolic partial differential equations. In the case of the Kuramoto-Sivashinsky equation ut + uxxxx + uxx + u ux = 0, we prove that for solutions u on the global attractor, the quantity card {x epsi [0, L]:u(x, t) = lgr}, where L > 0 is the spatial period, can be bounded by a polynomial function of L for all \\lambda\\in{\\Bbb R} . A similar property is proven for a general higher order partial differential equation u_t+(-1)^{s}\\partial_x^{2s}u+ \\sum_{k=0}^{2s-1}v_k(x,t)\\partial_x^k u =0 .

Multiscaling for systems with a broad continuum of characteristic lengths and times: Structural transitions in nanocomposites.

PubMed

Pankavich, S; Ortoleva, P

2010-06-01

The multiscale approach to N-body systems is generalized to address the broad continuum of long time and length scales associated with collective behaviors. A technique is developed based on the concept of an uncountable set of time variables and of order parameters (OPs) specifying major features of the system. We adopt this perspective as a natural extension of the commonly used discrete set of time scales and OPs which is practical when only a few, widely separated scales exist. The existence of a gap in the spectrum of time scales for such a system (under quasiequilibrium conditions) is used to introduce a continuous scaling and perform a multiscale analysis of the Liouville equation. A functional-differential Smoluchowski equation is derived for the stochastic dynamics of the continuum of Fourier component OPs. A continuum of spatially nonlocal Langevin equations for the OPs is also derived. The theory is demonstrated via the analysis of structural transitions in a composite material, as occurs for viral capsids and molecular circuits.

Control volume analyses of glottal flow using a fully-coupled numerical fluid-structure interaction model

NASA Astrophysics Data System (ADS)

Yang, Jubiao; Krane, Michael; Zhang, Lucy

2013-11-01

Vocal fold vibrations and the glottal jet are successfully simulated using the modified Immersed Finite Element method (mIFEM), a fully coupled dynamics approach to model fluid-structure interactions. A self-sustained and steady vocal fold vibration is captured given a constant pressure input at the glottal entrance. The flow rates at different axial locations in the glottis are calculated, showing small variations among them due to the vocal fold motion and deformation. To further facilitate the understanding of the phonation process, two control volume analyses, specifically with Bernoulli's equation and Newton's 2nd law, are carried out for the glottal flow based on the simulation results. A generalized Bernoulli's equation is derived to interpret the correlations between the velocity and pressure temporally and spatially along the center line which is a streamline using a half-space model with symmetry boundary condition. A specialized Newton's 2nd law equation is developed and divided into terms to help understand the driving mechanism of the glottal flow.

A composite likelihood approach for spatially correlated survival data

PubMed Central

Paik, Jane; Ying, Zhiliang

2013-01-01

The aim of this paper is to provide a composite likelihood approach to handle spatially correlated survival data using pairwise joint distributions. With e-commerce data, a recent question of interest in marketing research has been to describe spatially clustered purchasing behavior and to assess whether geographic distance is the appropriate metric to describe purchasing dependence. We present a model for the dependence structure of time-to-event data subject to spatial dependence to characterize purchasing behavior from the motivating example from e-commerce data. We assume the Farlie-Gumbel-Morgenstern (FGM) distribution and then model the dependence parameter as a function of geographic and demographic pairwise distances. For estimation of the dependence parameters, we present pairwise composite likelihood equations. We prove that the resulting estimators exhibit key properties of consistency and asymptotic normality under certain regularity conditions in the increasing-domain framework of spatial asymptotic theory. PMID:24223450

The spatial pattern of suicide in the US in relation to deprivation, fragmentation and rurality.

PubMed

Congdon, Peter

2011-01-01

Analysis of geographical patterns of suicide and psychiatric morbidity has demonstrated the impact of latent ecological variables (such as deprivation, rurality). Such latent variables may be derived by conventional multivariate techniques from sets of observed indices (for example, by principal components), by composite variable methods or by methods which explicitly consider the spatial framework of areas and, in particular, the spatial clustering of latent risks and outcomes. This article considers a latent random variable approach to explaining geographical contrasts in suicide in the US; and it develops a spatial structural equation model incorporating deprivation, social fragmentation and rurality. The approach allows for such latent spatial constructs to be correlated both within and between areas. Potential effects of area ethnic mix are also included. The model is applied to male and female suicide deaths over 2002–06 in 3142 US counties.

A composite likelihood approach for spatially correlated survival data.

PubMed

Paik, Jane; Ying, Zhiliang

2013-01-01

The aim of this paper is to provide a composite likelihood approach to handle spatially correlated survival data using pairwise joint distributions. With e-commerce data, a recent question of interest in marketing research has been to describe spatially clustered purchasing behavior and to assess whether geographic distance is the appropriate metric to describe purchasing dependence. We present a model for the dependence structure of time-to-event data subject to spatial dependence to characterize purchasing behavior from the motivating example from e-commerce data. We assume the Farlie-Gumbel-Morgenstern (FGM) distribution and then model the dependence parameter as a function of geographic and demographic pairwise distances. For estimation of the dependence parameters, we present pairwise composite likelihood equations. We prove that the resulting estimators exhibit key properties of consistency and asymptotic normality under certain regularity conditions in the increasing-domain framework of spatial asymptotic theory.

Determining Selection across Heterogeneous Landscapes: A Perturbation-Based Method and Its Application to Modeling Evolution in Space.

PubMed

Wickman, Jonas; Diehl, Sebastian; Blasius, Bernd; Klausmeier, Christopher A; Ryabov, Alexey B; Brännström, Åke

2017-04-01

Spatial structure can decisively influence the way evolutionary processes unfold. To date, several methods have been used to study evolution in spatial systems, including population genetics, quantitative genetics, moment-closure approximations, and individual-based models. Here we extend the study of spatial evolutionary dynamics to eco-evolutionary models based on reaction-diffusion equations and adaptive dynamics. Specifically, we derive expressions for the strength of directional and stabilizing/disruptive selection that apply both in continuous space and to metacommunities with symmetrical dispersal between patches. For directional selection on a quantitative trait, this yields a way to integrate local directional selection across space and determine whether the trait value will increase or decrease. The robustness of this prediction is validated against quantitative genetics. For stabilizing/disruptive selection, we show that spatial heterogeneity always contributes to disruptive selection and hence always promotes evolutionary branching. The expression for directional selection is numerically very efficient and hence lends itself to simulation studies of evolutionary community assembly. We illustrate the application and utility of the expressions for this purpose with two examples of the evolution of resource utilization. Finally, we outline the domain of applicability of reaction-diffusion equations as a modeling framework and discuss their limitations.

A deterministic model of electron transport for electron probe microanalysis

NASA Astrophysics Data System (ADS)

Bünger, J.; Richter, S.; Torrilhon, M.

2018-01-01

Within the last decades significant improvements in the spatial resolution of electron probe microanalysis (EPMA) were obtained by instrumental enhancements. In contrast, the quantification procedures essentially remained unchanged. As the classical procedures assume either homogeneity or a multi-layered structure of the material, they limit the spatial resolution of EPMA. The possibilities of improving the spatial resolution through more sophisticated quantification procedures are therefore almost untouched. We investigate a new analytical model (M 1-model) for the quantification procedure based on fast and accurate modelling of electron-X-ray-matter interactions in complex materials using a deterministic approach to solve the electron transport equations. We outline the derivation of the model from the Boltzmann equation for electron transport using the method of moments with a minimum entropy closure and present first numerical results for three different test cases (homogeneous, thin film and interface). Taking Monte Carlo as a reference, the results for the three test cases show that the M 1-model is able to reproduce the electron dynamics in EPMA applications very well. Compared to classical analytical models like XPP and PAP, the M 1-model is more accurate and far more flexible, which indicates the potential of deterministic models of electron transport to further increase the spatial resolution of EPMA.

Alternative stable qP wave equations in TTI media with their applications for reverse time migration

NASA Astrophysics Data System (ADS)

Zhou, Yang; Wang, Huazhong; Liu, Wenqing

2015-10-01

Numerical instabilities may arise if the spatial variation of symmetry axis is handled improperly when implementing P-wave modeling and reverse time migration in heterogeneous tilted transversely isotropic (TTI) media, especially in the cases where fast changes exist in TTI symmetry axis’ directions. Based on the pseudo-acoustic approximation to anisotropic elastic wave equations in Cartesian coordinates, alternative second order qP (quasi-P) wave equations in TTI media are derived in this paper. Compared with conventional stable qP wave equations, the proposed equations written in stress components contain only spatial derivatives of wavefield variables (stress components) and are free from spatial derivatives involving media parameters. These lead to an easy and efficient implementation for stable P-wave modeling and imaging. Numerical experiments demonstrate the stability and computational efficiency of the presented equations in complex TTI media.

Sound Radiated by a Wave-Like Structure in a Compressible Jet

NASA Technical Reports Server (NTRS)

Golubev, V. V.; Prieto, A. F.; Mankbadi, R. R.; Dahl, M. D.; Hixon, R.

2003-01-01

This paper extends the analysis of acoustic radiation from the source model representing spatially-growing instability waves in a round jet at high speeds. Compared to previous work, a modified approach to the sound source modeling is examined that employs a set of solutions to linearized Euler equations. The sound radiation is then calculated using an integral surface method.

Nonlinear amplification of coherent waves in media with soliton-type refractive index pattern.

PubMed

Bugaychuk, S; Conte, R

2012-08-01

We derive the complex Ginzburg-Landau equation for the dynamical self-diffraction of optical waves in a nonlinear cavity. The case of the reflection geometry of wave interaction as well as a medium that possesses the cubic nonlinearity (including a local and a nonlocal nonlinear responses) and the relaxation is considered. A stable localized spatial structure in the form of a "dark" dissipative soliton is formed in the cavity in the steady state. The envelope of the intensity pattern, as well as of the dynamical grating amplitude, takes the shape of a tanh function. The obtained complex Ginzburg-Landau equation describes the dynamics of this envelope; at the same time, the evolution of this spatial structure changes the parameters of the output waves. New effects are predicted in this system due to the transformation of the dissipative soliton which takes place during the interaction of a pulse with a continuous wave, such as retention of the pulse shape during the transmission of impulses in a long nonlinear cavity, and giant amplification of a seed pulse, which takes energy due to redistribution of the pump continuous energy into the signal.

Bayesian estimation of the transmissivity spatial structure from pumping test data

NASA Astrophysics Data System (ADS)

Demir, Mehmet Taner; Copty, Nadim K.; Trinchero, Paolo; Sanchez-Vila, Xavier

2017-06-01

Estimating the statistical parameters (mean, variance, and integral scale) that define the spatial structure of the transmissivity or hydraulic conductivity fields is a fundamental step for the accurate prediction of subsurface flow and contaminant transport. In practice, the determination of the spatial structure is a challenge because of spatial heterogeneity and data scarcity. In this paper, we describe a novel approach that uses time drawdown data from multiple pumping tests to determine the transmissivity statistical spatial structure. The method builds on the pumping test interpretation procedure of Copty et al. (2011) (Continuous Derivation method, CD), which uses the time-drawdown data and its time derivative to estimate apparent transmissivity values as a function of radial distance from the pumping well. A Bayesian approach is then used to infer the statistical parameters of the transmissivity field by combining prior information about the parameters and the likelihood function expressed in terms of radially-dependent apparent transmissivities determined from pumping tests. A major advantage of the proposed Bayesian approach is that the likelihood function is readily determined from randomly generated multiple realizations of the transmissivity field, without the need to solve the groundwater flow equation. Applying the method to synthetically-generated pumping test data, we demonstrate that, through a relatively simple procedure, information on the spatial structure of the transmissivity may be inferred from pumping tests data. It is also shown that the prior parameter distribution has a significant influence on the estimation procedure, given the non-uniqueness of the estimation procedure. Results also indicate that the reliability of the estimated transmissivity statistical parameters increases with the number of available pumping tests.

Application of the Modified Compaction Material Model to the Analysis of Landmine Detonation in Soil with Various Degrees of Water Saturation

DTIC Science & Technology

2007-01-01

Equation of State R2 – Constant in JWL Equation of State σ – Yield Stress T – Temperature...v – Specific volume w – Constant in JWL Equation of State x – Spatial coordinate y – Spatial coordinate Y – Yield stress Subscripts Comp – Value at...Constant in JWL Equation of State α – Porosity B – Compaction Modulus B1 – Strain Hardening Constant B2 – Constant in JWL Equation of State

Two-peak structure in the K-edge RIXS spectra of a spatially frustrated Heisenberg antiferromagnet

NASA Astrophysics Data System (ADS)

Datta, Trinanjan; Luo, Cheng; Yao, Dao-Xin

2014-03-01

Quantum fluctuations due to spatial anisotropy and strong magnetic frustration lead to the formation of a two-peak structure in the K-edge bimagnon RIXS intensity spectra of a Jx-Jy-J2 Heisenberg model on a square lattice. We compute the RIXS intensity, including up to first order 1/S spin wave expansion correction, using the Bethe-Salpeter equation within the ladder approximation scheme. The two-peak feature occurs in both the antiferromagnetic phase and the collinear antiferromagnetic phase. A knowledge of the peak splitting energy from both magnetically ordered regime can provide experimentalists with an alternative means to measure and study the effects of local microscopic exchange constants. Cottrell Research Corporation, NSFC-11074310, NSFC-11275279, Specialized Research Fund for the Doctoral Program of Higher Education.

Simulation of Pellet Ablation

NASA Astrophysics Data System (ADS)

Parks, P. B.; Ishizaki, Ryuichi

2000-10-01

In order to clarify the structure of the ablation flow, 2D simulation is carried out with a fluid code solving temporal evolution of MHD equations. The code includes electrostatic sheath effect at the cloud interface.(P.B. Parks et al.), Plasma Phys. Contr. Fusion 38, 571 (1996). An Eulerian cylindrical coordinate system (r,z) is used with z in a spherical pellet. The code uses the Cubic-Interpolated Psudoparticle (CIP) method(H. Takewaki and T. Yabe, J. Comput. Phys. 70), 355 (1987). that divides the fluid equations into non-advection and advection phases. The most essential element of the CIP method is in calculation of the advection phase. In this phase, a cubic interpolated spatial profile is shifted in space according to the total derivative equations, similarly to a particle scheme. Since the profile is interpolated by using the value and the spatial derivative value at each grid point, there is no numerical oscillation in space, that often appears in conventional spline interpolation. A free boundary condition is used in the code. The possibility of a stationary shock will also be shown in the presentation because the supersonic ablation flow across the magnetic field is impeded.

Chirped or time modulated excitation compared to short pulses for photoacoustic imaging in acoustic attenuating media

NASA Astrophysics Data System (ADS)

Burgholzer, P.; Motz, C.; Lang, O.; Berer, T.; Huemer, M.

2018-02-01

In photoacoustic imaging, optically generated acoustic waves transport the information about embedded structures to the sample surface. Usually, short laser pulses are used for the acoustic excitation. Acoustic attenuation increases for higher frequencies, which reduces the bandwidth and limits the spatial resolution. One could think of more efficient waveforms than single short pulses, such as pseudo noise codes, chirped, or harmonic excitation, which could enable a higher information-transfer from the samples interior to its surface by acoustic waves. We used a linear state space model to discretize the wave equation, such as the Stoke's equation, but this method could be used for any other linear wave equation. Linear estimators and a non-linear function inversion were applied to the measured surface data, for onedimensional image reconstruction. The proposed estimation method allows optimizing the temporal modulation of the excitation laser such that the accuracy and spatial resolution of the reconstructed image is maximized. We have restricted ourselves to one-dimensional models, as for higher dimensions the one-dimensional reconstruction, which corresponds to the acoustic wave without attenuation, can be used as input for any ultrasound imaging method, such as back-projection or time-reversal method.

Microscopic theory of linear light scattering from mesoscopic media and in near-field optics.

PubMed

Keller, Ole

2005-08-01

On the basis of quantum mechanical response theory a microscopic propagator theory of linear light scattering from mesoscopic systems is presented. The central integral equation problem is transferred to a matrix equation problem by discretization in transitions between pairs of (many-body) energy eigenstates. The local-field calculation which appears from this approach is valid down to the microscopic region. Previous theories based on the (macroscopic) dielectric constant concept make use of spatial (geometrical) discretization and cannot in general be trusted on the mesoscopic length scale. The present theory can be applied to light scattering studies in near-field optics. After a brief discussion of the macroscopic integral equation problem a microscopic potential description of the scattering process is established. In combination with the use of microscopic electromagnetic propagators the formalism allows one to make contact to the macroscopic theory of light scattering and to the spatial photon localization problem. The quantum structure of the microscopic conductivity response tensor enables one to establish a clear physical picture of the origin of local-field phenomena in mesoscopic and near-field optics. The Huygens scalar propagator formalism is revisited and its generality in microscopic physics pointed out.

A theory for the retrieval of virtual temperature from winds, radiances and the equations of fluid dynamics

NASA Technical Reports Server (NTRS)

Tzvi, G. C.

1986-01-01

A technique to deduce the virtual temperature from the combined use of the equations of fluid dynamics, observed wind and observed radiances is described. The wind information could come from ground-based sensitivity very high frequency (VHF) Doppler radars and/or from space-borne Doppler lidars. The radiometers are also assumed to be either space-borne and/or ground-based. From traditional radiometric techniques the vertical structure of the temperature can be estimated only crudely. While it has been known for quite some time that the virtual temperature could be deduced from wind information only, such techniques had to assume the infallibility of certain diagnostic relations. The proposed technique is an extension of the Gal-Chen technique. It is assumed that due to modeling uncertainties the equations of fluid dynamics are satisfied only in the least square sense. The retrieved temperature, however, is constrained to reproduce the observed radiances. It is shown that the combined use of the three sources of information (wind, radiances and fluid dynamical equations) can result in a unique determination of the vertical temperature structure with spatial and temporal resolution comparable to that of the observed wind.

The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs.

PubMed

Sorokin, Sergey V

2011-03-01

Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 2011 Acoustical Society of America

Biomechanically based simulation of brain deformations for intraoperative image correction: coupling of elastic and fluid models

NASA Astrophysics Data System (ADS)

Hagemann, Alexander; Rohr, Karl; Stiehl, H. Siegfried

2000-06-01

In order to improve the accuracy of image-guided neurosurgery, different biomechanical models have been developed to correct preoperative images w.r.t. intraoperative changes like brain shift or tumor resection. All existing biomechanical models simulate different anatomical structures by using either appropriate boundary conditions or by spatially varying material parameter values, while assuming the same physical model for all anatomical structures. In general, this leads to physically implausible results, especially in the case of adjacent elastic and fluid structures. Therefore, we propose a new approach which allows to couple different physical models. In our case, we simulate rigid, elastic, and fluid regions by using the appropriate physical description for each material, namely either the Navier equation or the Stokes equation. To solve the resulting differential equations, we derive a linear matrix system for each region by applying the finite element method (FEM). Thereafter, the linear matrix systems are linked together, ending up with one overall linear matrix system. Our approach has been tested using synthetic as well as tomographic images. It turns out from experiments, that the integrated treatment of rigid, elastic, and fluid regions significantly improves the prediction results in comparison to a pure linear elastic model.

von Kármán-Howarth equation for three-dimensional two-fluid plasmas.

PubMed

Andrés, N; Mininni, P D; Dmitruk, P; Gómez, D O

2016-06-01

We derive the von Kármán-Howarth equation for a full three-dimensional incompressible two-fluid plasma. In the long-time limit and for very large Reynolds numbers we obtain the equivalent of the hydrodynamic "four-fifths" law. This exact law predicts the scaling of the third-order two-point correlation functions, and puts a strong constraint on the plasma turbulent dynamics. Finally, we derive a simple expression for the 4/5 law in terms of third-order structure functions, which is appropriate for comparison with in situ measurements in the solar wind at different spatial ranges.

Causal modelling applied to the risk assessment of a wastewater discharge.

PubMed

Paul, Warren L; Rokahr, Pat A; Webb, Jeff M; Rees, Gavin N; Clune, Tim S

2016-03-01

Bayesian networks (BNs), or causal Bayesian networks, have become quite popular in ecological risk assessment and natural resource management because of their utility as a communication and decision-support tool. Since their development in the field of artificial intelligence in the 1980s, however, Bayesian networks have evolved and merged with structural equation modelling (SEM). Unlike BNs, which are constrained to encode causal knowledge in conditional probability tables, SEMs encode this knowledge in structural equations, which is thought to be a more natural language for expressing causal information. This merger has clarified the causal content of SEMs and generalised the method such that it can now be performed using standard statistical techniques. As it was with BNs, the utility of this new generation of SEM in ecological risk assessment will need to be demonstrated with examples to foster an understanding and acceptance of the method. Here, we applied SEM to the risk assessment of a wastewater discharge to a stream, with a particular focus on the process of translating a causal diagram (conceptual model) into a statistical model which might then be used in the decision-making and evaluation stages of the risk assessment. The process of building and testing a spatial causal model is demonstrated using data from a spatial sampling design, and the implications of the resulting model are discussed in terms of the risk assessment. It is argued that a spatiotemporal causal model would have greater external validity than the spatial model, enabling broader generalisations to be made regarding the impact of a discharge, and greater value as a tool for evaluating the effects of potential treatment plant upgrades. Suggestions are made on how the causal model could be augmented to include temporal as well as spatial information, including suggestions for appropriate statistical models and analyses.

Modeling TAE Response To Nonlinear Drives

NASA Astrophysics Data System (ADS)

Zhang, Bo; Berk, Herbert; Breizman, Boris; Zheng, Linjin

2012-10-01

Experiment has detected the Toroidal Alfven Eigenmodes (TAE) with signals at twice the eigenfrequency.These harmonic modes arise from the second order perturbation in amplitude of the MHD equation for the linear modes that are driven the energetic particle free energy. The structure of TAE in realistic geometry can be calculated by generalizing the linear numerical solver (AEGIS package). We have have inserted all the nonlinear MHD source terms, where are quadratic in the linear amplitudes, into AEGIS code. We then invert the linear MHD equation at the second harmonic frequency. The ratio of amplitudes of the first and second harmonic terms are used to determine the internal field amplitude. The spatial structure of energy and density distribution are investigated. The results can be directly employed to compare with experiments and determine the Alfven wave amplitude in the plasma region.

Modeling Global Spatial-Temporal Evolution of Society: Hyperbolic Growth and Historical Cycles

NASA Astrophysics Data System (ADS)

Kurkina, E. S.

2011-09-01

The global historical processes are under consideration; and laws of global evolution of the world community are studied. The world community is considered as a united complex self-developing and self-organizing system. It supposed that the main driving force of social-economical evolution was the positive feedback between the population size and the level of technological development, which was a cause of growth in blow-up regime both of population and of global economic indexes. The study is supported by the results of mathematical modeling founded on a nonlinear heat equation with a source. Every social-economical epoch characterizes by own specific spatial distributed structures. So the global dynamics of world community during the whole history is investigated throughout the prism of the developing of spatial-temporal structures. The model parameters have been chosen so that 1) total population follows stable hyperbolic growth, consistently with the demographic data; 2) the evolution of the World-System goes through 11 stages corresponding to the main historical epochs.

Road displacement model based on structural mechanics

NASA Astrophysics Data System (ADS)

Lu, Xiuqin; Guo, Qingsheng; Zhang, Yi

2006-10-01

Spatial conflict resolution is an important part of cartographic generalization, and it can deal with the problems of having too much information competing for too little space, while feature displacement is a primary operator of map generalization, which aims at resolving the spatial conflicts between neighbor objects especially road features. Considering the road object, this paper explains an idea of displacement based on structural mechanics. In view of spatial conflict problem after road symbolization, it is the buffer zones that are used to detect conflicts, then we focus on each conflicting region, with the finite element method, taking every triangular element for analysis, listing stiffness matrix, gathering system equations and calculating with iteration strategy, and we give the solution to road symbol conflicts. Being like this until all the conflicts in conflicting regions are solved, then we take the whole map into consideration again, conflicts are detected by reusing the buffer zones and solved by displacement operator, so as to all of them are handled.

New exact perfect fluid solutions of Einstein's equations. II

NASA Astrophysics Data System (ADS)

Uggla, Claes; Rosquist, Kjell

1990-12-01

A family of new spatially homogeneous Bianchi type VIh perfect fluid solutions of the Einstein equations is presented. The fluid flow is orthogonal to the spatially homogeneous hypersurfaces, and the pressure is proportional to the energy density.

Fast Magnetotail Reconnection: Challenge to Global MHD Modeling

NASA Astrophysics Data System (ADS)

Kuznetsova, M. M.; Hesse, M.; Rastaetter, L.; Toth, G.; de Zeeuw, D.; Gombosi, T.

2005-05-01

Representation of fast magnetotail reconnection rates during substorm onset is one of the major challenges to global MHD modeling. Our previous comparative study of collisionless magnetic reconnection in GEM Challenge geometry demonstrated that the reconnection rate is controlled by ion nongyrotropic behavior near the reconnection site and that it can be described in terms of nongyrotropic corrections to the magnetic induction equation. To further test the approach we performed MHD simulations with nongyrotropic corrections of forced reconnection for the Newton Challenge setup. As a next step we employ the global MHD code BATSRUS and test different methods to model fast magnetotail reconnection rates by introducing non-ideal corrections to the induction equation in terms of nongyrotropic corrections, spatially localized resistivity, or current dependent resistivity. The BATSRUS adaptive grid structure allows to perform global simulations with spatial resolution near the reconnection site comparable with spatial resolution of local MHD simulations for the Newton Challenge. We select solar wind conditions which drive the accumulation of magnetic field in the tail lobes and subsequent magnetic reconnection and energy release. Testing the ability of global MHD models to describe magnetotail evolution during substroms is one of the elements of science based validation efforts at the Community Coordinated Modeling Center.

Improved Simulation of Electrodiffusion in the Node of Ranvier by Mesh Adaptation.

PubMed

Dione, Ibrahima; Deteix, Jean; Briffard, Thomas; Chamberland, Eric; Doyon, Nicolas

2016-01-01

In neural structures with complex geometries, numerical resolution of the Poisson-Nernst-Planck (PNP) equations is necessary to accurately model electrodiffusion. This formalism allows one to describe ionic concentrations and the electric field (even away from the membrane) with arbitrary spatial and temporal resolution which is impossible to achieve with models relying on cable theory. However, solving the PNP equations on complex geometries involves handling intricate numerical difficulties related either to the spatial discretization, temporal discretization or the resolution of the linearized systems, often requiring large computational resources which have limited the use of this approach. In the present paper, we investigate the best ways to use the finite elements method (FEM) to solve the PNP equations on domains with discontinuous properties (such as occur at the membrane-cytoplasm interface). 1) Using a simple 2D geometry to allow comparison with analytical solution, we show that mesh adaptation is a very (if not the most) efficient way to obtain accurate solutions while limiting the computational efforts, 2) We use mesh adaptation in a 3D model of a node of Ranvier to reveal details of the solution which are nearly impossible to resolve with other modelling techniques. For instance, we exhibit a non linear distribution of the electric potential within the membrane due to the non uniform width of the myelin and investigate its impact on the spatial profile of the electric field in the Debye layer.

A structural equation model relating impaired sensorimotor function, fear of falling and gait patterns in older people.

PubMed

Menz, Hylton B; Lord, Stephen R; Fitzpatrick, Richard C

2007-02-01

Many falls in older people occur while walking, however the mechanisms responsible for gait instability are poorly understood. Therefore, the aim of this study was to develop a plausible model describing the relationships between impaired sensorimotor function, fear of falling and gait patterns in older people. Temporo-spatial gait parameters and acceleration patterns of the head and pelvis were obtained from 100 community-dwelling older people aged between 75 and 93 years while walking on an irregular walkway. A theoretical model was developed to explain the relationships between these variables, assuming that head stability is a primary output of the postural control system when walking. This model was then tested using structural equation modeling, a statistical technique which enables the testing of a set of regression equations simultaneously. The structural equation model indicated that: (i) reduced step length has a significant direct and indirect association with reduced head stability; (ii) impaired sensorimotor function is significantly associated with reduced head stability, but this effect is largely indirect, mediated by reduced step length, and; (iii) fear of falling is significantly associated with reduced step length, but has little direct influence on head stability. These findings provide useful insights into the possible mechanisms underlying gait characteristics and risk of falling in older people. Particularly important is the indication that fear-related step length shortening may be maladaptive.

Direct numerical solution of the Ornstein-Zernike integral equation and spatial distribution of water around hydrophobic molecules

NASA Astrophysics Data System (ADS)

Ikeguchi, Mitsunori; Doi, Junta

1995-09-01

The Ornstein-Zernike integral equation (OZ equation) has been used to evaluate the distribution function of solvents around solutes, but its numerical solution is difficult for molecules with a complicated shape. This paper proposes a numerical method to directly solve the OZ equation by introducing the 3D lattice. The method employs no approximation the reference interaction site model (RISM) equation employed. The method enables one to obtain the spatial distribution of spherical solvents around solutes with an arbitrary shape. Numerical accuracy is sufficient when the grid-spacing is less than 0.5 Å for solvent water. The spatial water distribution around a propane molecule is demonstrated as an example of a nonspherical hydrophobic molecule using iso-value surfaces. The water model proposed by Pratt and Chandler is used. The distribution agrees with the molecular dynamics simulation. The distribution increases offshore molecular concavities. The spatial distribution of water around 5α-cholest-2-ene (C27H46) is visualized using computer graphics techniques and a similar trend is observed.

Toward a muon-specific electronic structure theory: effective electronic Hartree-Fock equations for muonic molecules.

PubMed

Rayka, Milad; Goli, Mohammad; Shahbazian, Shant

2018-02-07

An effective set of Hartree-Fock (HF) equations are derived for electrons of muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator, which are completely equivalent to the usual two-component HF equations used to derive stationary states of the muonic molecules. In these effective equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and the electrons effectively and is optimized during the self-consistent field cycles. While in the two-component HF equations a muon is treated as a quantum particle, in the effective HF equations it is absorbed into the effective potential and practically transformed into an effective potential field experienced by electrons. The explicit form of the effective potential depends on the nature of muon's vibrations and is derivable from the basis set used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in a series of muonic molecules containing all atoms from the second and third rows of the Periodic Table. To solve the algebraic version of the equations muon-specific Gaussian basis sets are designed for both muon and surrounding electrons and it is demonstrated that the optimized exponents are quite distinct from those derived for the hydrogen isotopes. The developed effective HF theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure theory that incorporates various types of quantum correlations into the muonic systems beyond the HF equations.

Spatial averaging of a dissipative particle dynamics model for active suspensions

NASA Astrophysics Data System (ADS)

Panchenko, Alexander; Hinz, Denis F.; Fried, Eliot

2018-03-01

Starting from a fine-scale dissipative particle dynamics (DPD) model of self-motile point particles, we derive meso-scale continuum equations by applying a spatial averaging version of the Irving-Kirkwood-Noll procedure. Since the method does not rely on kinetic theory, the derivation is valid for highly concentrated particle systems. Spatial averaging yields stochastic continuum equations similar to those of Toner and Tu. However, our theory also involves a constitutive equation for the average fluctuation force. According to this equation, both the strength and the probability distribution vary with time and position through the effective mass density. The statistics of the fluctuation force also depend on the fine scale dissipative force equation, the physical temperature, and two additional parameters which characterize fluctuation strengths. Although the self-propulsion force entering our DPD model contains no explicit mechanism for aligning the velocities of neighboring particles, our averaged coarse-scale equations include the commonly encountered cubically nonlinear (internal) body force density.

Stabilization and control of distributed systems with time-dependent spatial domains

NASA Technical Reports Server (NTRS)

Wang, P. K. C.

1990-01-01

This paper considers the problem of the stabilization and control of distributed systems with time-dependent spatial domains. The evolution of the spatial domains with time is described by a finite-dimensional system of ordinary differential equations, while the distributed systems are described by first-order or second-order linear evolution equations defined on appropriate Hilbert spaces. First, results pertaining to the existence and uniqueness of solutions of the system equations are presented. Then, various optimal control and stabilization problems are considered. The paper concludes with some examples which illustrate the application of the main results.

A three-dimensional model of corotating streams in the solar wind. 1: Theoretical foundations

NASA Technical Reports Server (NTRS)

Pizzo, V. J.

1978-01-01

The theoretical and mathematical background pertinent to the study of steady, corotating solar wind structure in all three spatial dimensions (3-D) is discussed. The dynamical evolution of the plasma in interplanetary space (defined as the region beyond roughly 35 solar radii where the flow is supersonic) is approximately described by the nonlinear, single fluid, polytropic (magneto-) hydrodynamic equations. Efficient numerical techniques for solving this complex system of coupled, hyperbolic partial differential equations are outlined. The formulation is inviscid and nonmagnetic, but methods allow for the potential inclusion of both features with only modest modifications. One simple, highly idealized, hydrodynamic model stream is examined to illustrate the fundamental processes involved in the 3-D dynamics of stream evolution. Spatial variations in the rotational stream interaction mechanism were found to produce small nonradial flows on a global scale that lead to the transport of mass, energy, and momentum away from regions of relative compression and into regions of relative rarefaction.

Derivation of the Effective Nonlinear Schrodinger Equations for Dark and Power Law Spatial Plasmon-Polariton Solitons Using Nano Self-Focusing

DTIC Science & Technology

2011-03-01

An e?ective Nonlinear Schr?dinger Equation for propagation is derived for optical dark and power law spatial solitons at the subwavelength with a... soliton amplitude profiles are displayed as a hyperbolic secant function and hold there profile at short distances on the order of centimeters. Dark ...spatial solitons are similar but have hyperbolic tangent type profiles. Dark spatial solitons were first observed by Jerominek in 1985 and Belanger and

Static Einstein-Maxwell Black Holes with No Spatial Isometries in AdS Space.

PubMed

Herdeiro, Carlos A R; Radu, Eugen

2016-11-25

We explicitly construct static black hole solutions to the fully nonlinear, D=4, Einstein-Maxwell-anti-de Sitter (AdS) equations that have no continuous spatial symmetries. These black holes have a smooth, topologically spherical horizon (section), but without isometries, and approach, asymptotically, global AdS spacetime. They are interpreted as bound states of a horizon with the Einstein-Maxwell-AdS solitons recently discovered, for appropriate boundary data. In sharp contrast to the uniqueness results for a Minkowski electrovacuum, the existence of these black holes shows that single, equilibrium, black hole solutions in an AdS electrovacuum admit an arbitrary multipole structure.

Experimental investigation and numerical modelling of positive corona discharge: ozone generation

NASA Astrophysics Data System (ADS)

Yanallah, K; Pontiga, F; Fernández-Rueda, A; Castellanos, A

2009-03-01

The spatial distribution of the species generated in a wire-cylinder positive corona discharge in pure oxygen has been computed using a plasma chemistry model that includes the most significant reactions between electrons, ions, atoms and molecules. The plasma chemistry model is included in the continuity equations of each species, which are coupled with Poisson's equation for the electric field and the energy conservation equation for the gas temperature. The current-voltage characteristic measured in the experiments has been used as an input data to the numerical simulation. The numerical model is able to reproduce the basic structure of the positive corona discharge and highlights the importance of Joule heating on ozone generation. The average ozone density has been computed as a function of current intensity and compared with the experimental measurements of ozone concentration determined by UV absorption spectroscopy.

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.

Observations of discrete magnetosonic waves off the magnetic equator

DOE PAGES

Zhima, Zeren; Chen, Lunjin; Fu, Huishan; ...

2015-11-23

Fast mode magnetosonic waves are typically confined close to the magnetic equator and exhibit harmonic structures at multiples of the local, equatorial proton cyclotron frequency. Here, we report observations of magnetosonic waves well off the equator at geomagnetic latitudes from -16.5°to -17.9° and L shell ~2.7–4.6. The observed waves exhibit discrete spectral structures with multiple frequency spacings. The predominant frequency spacings are ~6 and 9 Hz, neither of which is equal to the local proton cyclotron frequency. Backward ray tracing simulations show that the feature of multiple frequency spacings is caused by propagation from two spatially narrow equatorial source regionsmore » located at L ≈ 4.2 and 3.7. The equatorial proton cyclotron frequencies at those two locations match the two observed frequency spacings. Finally, our analysis provides the first observations of the harmonic nature of magnetosonic waves well away from the equatorial region and suggests that the propagation from multiple equatorial sources contributes to these off-equatorial magnetosonic emissions with varying frequency spacings.« less

Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation

NASA Astrophysics Data System (ADS)

Su, Bo; Tuo, Xianguo; Xu, Ling

2017-08-01

Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.

Structure-preserving spectral element method in attenuating seismic wave modeling

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai

2016-04-01

This work describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems which has superior behaviors in long-time stability and dissipation preservation. To construct the conformal symplectic method, we first reformulate the damped acoustic wave equation and the elastic wave equations in their equivalent conformal multi-symplectic structures, which naturally reveal the intrinsic properties of the original systems, especially, the dissipation laws. We thereafter separate each structures into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed numerical scheme, which is conformal symplectic and can therefore guarantee the numerical stability and dissipation preservation after a large time modeling. Additionally, a relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh-wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic method in both the attenuating homogeneous and heterogeneous mediums.

Simple determinant representation for rogue waves of the nonlinear Schrödinger equation.

PubMed

Ling, Liming; Zhao, Li-Chen

2013-10-01

We present a simple representation for arbitrary-order rogue wave solution and a study on the trajectories of them explicitly. We find that the trajectories of two valleys on whole temporal-spatial distribution all look "X" -shaped for rogue waves. Additionally, we present different types of high-order rogue wave structures, which could be helpful towards realizing the complex dynamics of rogue waves.

The role of environmental variables in structuring landscape-scale species distributions in seafloor habitats.

PubMed

Kraan, Casper; Aarts, Geert; Van der Meer, Jaap; Piersma, Theunis

2010-06-01

Ongoing statistical sophistication allows a shift from describing species' spatial distributions toward statistically disentangling the possible roles of environmental variables in shaping species distributions. Based on a landscape-scale benthic survey in the Dutch Wadden Sea, we show the merits of spatially explicit generalized estimating equations (GEE). The intertidal macrozoobenthic species, Macoma balthica, Cerastoderma edule, Marenzelleria viridis, Scoloplos armiger, Corophium volutator, and Urothoe poseidonis served as test cases, with median grain-size and inundation time as typical environmental explanatory variables. GEEs outperformed spatially naive generalized linear models (GLMs), and removed much residual spatial structure, indicating the importance of median grain-size and inundation time in shaping landscape-scale species distributions in the intertidal. GEE regression coefficients were smaller than those attained with GLM, and GEE standard errors were larger. The best fitting GEE for each species was used to predict species' density in relation to median grain-size and inundation time. Although no drastic changes were noted compared to previous work that described habitat suitability for benthic fauna in the Wadden Sea, our predictions provided more detailed and unbiased estimates of the determinants of species-environment relationships. We conclude that spatial GEEs offer the necessary methodological advances to further steps toward linking pattern to process.

Corrections to the Eckhaus' stability criterion for one-dimensional stationary structures

NASA Astrophysics Data System (ADS)

Malomed, B. A.; Staroselsky, I. E.; Konstantinov, A. B.

1989-01-01

Two amendments to the well-known Eckhaus' stability criterion for small-amplitude non-linear structures generated by weak instability of a spatially uniform state of a non-equilibrium one-dimensional system against small perturbations with finite wavelengths are obtained. Firstly, we evaluate small corrections to the main Eckhaus' term which, on the contrary so that term, do not have a universal form. Comparison of those non-universal corrections with experimental or numerical results gives a possibility to select a more relevant form of an effective nonlinear evolution equation. In particular, the comparison with such results for convective rolls and Taylor vortices gives arguments in favor of the Swift-Hohenberg equation. Secondly, we derive an analog of the Eckhaus criterion for systems degenerate in the sense that in an expansion of their non-linear parts in powers of dynamical variables, the second and third degree terms are absent.

Space-time modeling of soil moisture

NASA Astrophysics Data System (ADS)

Chen, Zijuan; Mohanty, Binayak P.; Rodriguez-Iturbe, Ignacio

2017-11-01

A physically derived space-time mathematical representation of the soil moisture field is carried out via the soil moisture balance equation driven by stochastic rainfall forcing. The model incorporates spatial diffusion and in its original version, it is shown to be unable to reproduce the relative fast decay in the spatial correlation functions observed in empirical data. This decay resulting from variations in local topography as well as in local soil and vegetation conditions is well reproduced via a jitter process acting multiplicatively over the space-time soil moisture field. The jitter is a multiplicative noise acting on the soil moisture dynamics with the objective to deflate its correlation structure at small spatial scales which are not embedded in the probabilistic structure of the rainfall process that drives the dynamics. These scales of order of several meters to several hundred meters are of great importance in ecohydrologic dynamics. Properties of space-time correlation functions and spectral densities of the model with jitter are explored analytically, and the influence of the jitter parameters, reflecting variabilities of soil moisture at different spatial and temporal scales, is investigated. A case study fitting the derived model to a soil moisture dataset is presented in detail.

Non-local Second Order Closure Scheme for Boundary Layer Turbulence and Convection

NASA Astrophysics Data System (ADS)

Meyer, Bettina; Schneider, Tapio

2017-04-01

There has been scientific consensus that the uncertainty in the cloud feedback remains the largest source of uncertainty in the prediction of climate parameters like climate sensitivity. To narrow down this uncertainty, not only a better physical understanding of cloud and boundary layer processes is required, but specifically the representation of boundary layer processes in models has to be improved. General climate models use separate parameterisation schemes to model the different boundary layer processes like small-scale turbulence, shallow and deep convection. Small scale turbulence is usually modelled by local diffusive parameterisation schemes, which truncate the hierarchy of moment equations at first order and use second-order equations only to estimate closure parameters. In contrast, the representation of convection requires higher order statistical moments to capture their more complex structure, such as narrow updrafts in a quasi-steady environment. Truncations of moment equations at second order may lead to more accurate parameterizations. At the same time, they offer an opportunity to take spatially correlated structures (e.g., plumes) into account, which are known to be important for convective dynamics. In this project, we study the potential and limits of local and non-local second order closure schemes. A truncation of the momentum equations at second order represents the same dynamics as a quasi-linear version of the equations of motion. We study the three-dimensional quasi-linear dynamics in dry and moist convection by implementing it in a LES model (PyCLES) and compare it to a fully non-linear LES. In the quasi-linear LES, interactions among turbulent eddies are suppressed but nonlinear eddy—mean flow interactions are retained, as they are in the second order closure. In physical terms, suppressing eddy—eddy interactions amounts to suppressing, e.g., interactions among convective plumes, while retaining interactions between plumes and the environment (e.g., entrainment and detrainment). In a second part, we employ the possibility to include non-local statistical correlations in a second-order closure scheme. Such non-local correlations allow to directly incorporate the spatially coherent structures that occur in the form of convective updrafts penetrating the boundary layer. This allows us to extend the work that has been done using assumed-PDF schemes for parameterising boundary layer turbulence and shallow convection in a non-local sense.

A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis.

PubMed

Herschlag, Gregory J; Mitran, Sorin; Lin, Guang

2015-06-21

We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finite-range spatial correlation. Each approximation within the hierarchy is a set of ordinary differential equations that considers spatial correlations of varying lattice distance; the assumption is that the full system will have finite spatial correlations and thus the behavior of the models within the hierarchy will approach that of the full system. We provide evidence of this convergence in the context of one- and two-dimensional numerical examples. Lower levels within the hierarchy that consider shorter spatial correlations are shown to be up to three orders of magnitude faster than traditional kinetic Monte Carlo methods (KMC) for one-dimensional systems, while predicting similar system dynamics and steady states as KMC methods. We then test the hierarchy on a two-dimensional model for the oxidation of CO on RuO2(110), showing that low-order truncations of the hierarchy efficiently capture the essential system dynamics. By considering sequences of models in the hierarchy that account for longer spatial correlations, successive model predictions may be used to establish empirical approximation of error estimates. The hierarchy may be thought of as a class of generalized phenomenological kinetic models since each element of the hierarchy approximates the master equation and the lowest level in the hierarchy is identical to a simple existing phenomenological kinetic models.

Gaussian theory for spatially distributed self-propelled particles

NASA Astrophysics Data System (ADS)

Seyed-Allaei, Hamid; Schimansky-Geier, Lutz; Ejtehadi, Mohammad Reza

2016-12-01

Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier modes of the orientation distribution starting from a given number. Here we propose another method to derive continuum equations for interacting self-propelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. First, by means of simulation of the microscopic model, we justify that the distribution of individual directions fits well to a wrapped Gaussian distribution. Second, we numerically integrate the continuum equations derived in the GA in order to compare with results of simulations. We obtain that the global polarization in the GA exhibits a hysteresis in dependence on the noise intensity. It shows qualitatively the same behavior as we find in particles simulations. Moreover, both global polarizations agree perfectly for low noise intensities. The spatiotemporal structures of the GA are also in agreement with simulations. We conclude that the GA shows qualitative agreement for a wide range of noise intensities. In particular, for low noise intensities the agreement with simulations is better as other approximations, making the GA to an acceptable candidates of describing spatially distributed self-propelled particles.

Spatial evolutionary games with weak selection.

PubMed

Nanda, Mridu; Durrett, Richard

2017-06-06

Recently, a rigorous mathematical theory has been developed for spatial games with weak selection, i.e., when the payoff differences between strategies are small. The key to the analysis is that when space and time are suitably rescaled, the spatial model converges to the solution of a partial differential equation (PDE). This approach can be used to analyze all [Formula: see text] games, but there are a number of [Formula: see text] games for which the behavior of the limiting PDE is not known. In this paper, we give rules for determining the behavior of a large class of [Formula: see text] games and check their validity using simulation. In words, the effect of space is equivalent to making changes in the payoff matrix, and once this is done, the behavior of the spatial game can be predicted from the behavior of the replicator equation for the modified game. We say predicted here because in some cases the behavior of the spatial game is different from that of the replicator equation for the modified game. For example, if a rock-paper-scissors game has a replicator equation that spirals out to the boundary, space stabilizes the system and produces an equilibrium.

Spatial evolutionary games with weak selection

PubMed Central

Nanda, Mridu; Durrett, Richard

2017-01-01

Recently, a rigorous mathematical theory has been developed for spatial games with weak selection, i.e., when the payoff differences between strategies are small. The key to the analysis is that when space and time are suitably rescaled, the spatial model converges to the solution of a partial differential equation (PDE). This approach can be used to analyze all 2×2 games, but there are a number of 3×3 games for which the behavior of the limiting PDE is not known. In this paper, we give rules for determining the behavior of a large class of 3×3 games and check their validity using simulation. In words, the effect of space is equivalent to making changes in the payoff matrix, and once this is done, the behavior of the spatial game can be predicted from the behavior of the replicator equation for the modified game. We say predicted here because in some cases the behavior of the spatial game is different from that of the replicator equation for the modified game. For example, if a rock–paper–scissors game has a replicator equation that spirals out to the boundary, space stabilizes the system and produces an equilibrium. PMID:28533405

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Visuo-spatial abilities are key for young children's verbal number skills.

PubMed

Cornu, Véronique; Schiltz, Christine; Martin, Romain; Hornung, Caroline

2018-02-01

Children's development of verbal number skills (i.e., counting abilities and knowledge of the number names) presents a milestone in mathematical development. Different factors such as visuo-spatial and verbal abilities have been discussed as contributing to the development of these foundational skills. To understand the cognitive nature of verbal number skills in young children, the current study assessed the relation of preschoolers' verbal and visuo-spatial abilities to their verbal number skills. In total, 141 children aged 5 or 6 years participated in the current study. Verbal number skills were regressed on vocabulary, phonological awareness and visuo-spatial abilities, and verbal and visuo-spatial working memory in a structural equation model. Only visuo-spatial abilities emerged as a significant predictor of verbal number skills in the estimated model. Our results suggest that visuo-spatial abilities contribute to a larger extent to children's verbal number skills than verbal abilities. From a theoretical point of view, these results suggest a visuo-spatial, rather than a verbal, grounding of verbal number skills. These results are potentially informative for the conception of early mathematics assessments and interventions. Copyright © 2017 Elsevier Inc. All rights reserved.

Off-equilibrium infrared structure of self-interacting scalar fields: Universal scaling, vortex-antivortex superfluid dynamics, and Bose-Einstein condensation

NASA Astrophysics Data System (ADS)

Deng, Jian; Schlichting, Soeren; Venugopalan, Raju; Wang, Qun

2018-05-01

We map the infrared dynamics of a relativistic single-component (N =1 ) interacting scalar field theory to that of nonrelativistic complex scalar fields. The Gross-Pitaevskii (GP) equation, describing the real-time dynamics of single-component ultracold Bose gases, is obtained at first nontrivial order in an expansion proportional to the powers of λ ϕ2/m2 where λ , ϕ , and m are the coupling constant, the scalar field, and the particle mass respectively. Our analytical studies are corroborated by numerical simulations of the spatial and momentum structure of overoccupied scalar fields in (2+1)-dimensions. Universal scaling of infrared modes, vortex-antivortex superfluid dynamics, and the off-equilibrium formation of a Bose-Einstein condensate are observed. Our results for the universal scaling exponents are in agreement with those extracted in the numerical simulations of the GP equation. As in these simulations, we observe coarsening phase kinetics in the Bose superfluid with strongly anomalous scaling exponents relative to that of vertex resummed kinetic theory. Our relativistic field theory framework further allows one to study more closely the coupling between superfluid and normal fluid modes, specifically the turbulent momentum and spatial structure of the coupling between a quasiparticle cascade to the infrared and an energy cascade to the ultraviolet. We outline possible applications of the formalism to the dynamics of vortex-antivortex formation and to the off-equilibrium dynamics of the strongly interacting matter formed in heavy-ion collisions.

Nonlinear ring resonator: spatial pattern generation

NASA Astrophysics Data System (ADS)

Ivanov, Vladimir Y.; Lachinova, Svetlana L.; Irochnikov, Nikita G.

2000-03-01

We consider theoretically spatial pattern formation processes in a unidirectional ring cavity with thin layer of Kerr-type nonlinear medium. Our method is based on studying of two coupled equations. The first is a partial differential equation for temporal dynamics of phase modulation of light wave in the medium. It describes nonlinear interaction in the Kerr-type lice. The second is a free propagation equation for the intracavity field complex amplitude. It involves diffraction effects of light wave in the cavity.

A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems

PubMed Central

Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing

2012-01-01

An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849

Developing a generalized allometric equation for aboveground biomass estimation

NASA Astrophysics Data System (ADS)

Xu, Q.; Balamuta, J. J.; Greenberg, J. A.; Li, B.; Man, A.; Xu, Z.

2015-12-01

A key potential uncertainty in estimating carbon stocks across multiple scales stems from the use of empirically calibrated allometric equations, which estimate aboveground biomass (AGB) from plant characteristics such as diameter at breast height (DBH) and/or height (H). The equations themselves contain significant and, at times, poorly characterized errors. Species-specific equations may be missing. Plant responses to their local biophysical environment may lead to spatially varying allometric relationships. The structural predictor may be difficult or impossible to measure accurately, particularly when derived from remote sensing data. All of these issues may lead to significant and spatially varying uncertainties in the estimation of AGB that are unexplored in the literature. We sought to quantify the errors in predicting AGB at the tree and plot level for vegetation plots in California. To accomplish this, we derived a generalized allometric equation (GAE) which we used to model the AGB on a full set of tree information such as DBH, H, taxonomy, and biophysical environment. The GAE was derived using published allometric equations in the GlobAllomeTree database. The equations were sparse in details about the error since authors provide the coefficient of determination (R2) and the sample size. A more realistic simulation of tree AGB should also contain the noise that was not captured by the allometric equation. We derived an empirically corrected variance estimate for the amount of noise to represent the errors in the real biomass. Also, we accounted for the hierarchical relationship between different species by treating each taxonomic level as a covariate nested within a higher taxonomic level (e.g. species < genus). This approach provides estimation under incomplete tree information (e.g. missing species) or blurred information (e.g. conjecture of species), plus the biophysical environment. The GAE allowed us to quantify contribution of each different covariate in estimating the AGB of trees. Lastly, we applied the GAE to an existing vegetation plot database - Forest Inventory and Analysis database - to derive per-tree and per-plot AGB estimations, their errors, and how much the error could be contributed to the original equations, the plant's taxonomy, and their biophysical environment.

Front propagation in one-dimensional spatially periodic bistable media

NASA Astrophysics Data System (ADS)

Löber, Jakob; Bär, Markus; Engel, Harald

2012-12-01

Front propagation in heterogeneous bistable media is studied using the Schlögl model as a representative example. Spatially periodic modulations in the parameters of the bistable kinetics are taken into account perturbatively. Depending on the ratio L/l (L is the spatial period of the heterogeneity, l is the front width), appropriate singular perturbation techniques are applied to derive an ordinary differential equation for the position of the front in the presence of the heterogeneities. From this equation, the dependence of the average propagation speed on L/l as well as on the modulation amplitude is calculated. The analytical results obtained predict velocity overshoot, different cases of propagation failure, and the propagation speed for very large spatial periods in quantitative agreement with the results of direct numerical simulations of the underlying reaction-diffusion equation.

Discrete conservation laws and the convergence of long time simulations of the mkdv equation

NASA Astrophysics Data System (ADS)

Gorria, C.; Alejo, M. A.; Vega, L.

2013-02-01

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

Transport velocity transformation - A convenient method for performance analysis of multilayer solar cell structure

NASA Technical Reports Server (NTRS)

Wolf, M.

1981-01-01

It is noted that in the case of low-level injection, space-charge quasi-neutrality, and spatially constant material parameters (including an electrostatic field), the individual layer can be treated analytically and the basic solar cell performance parameters can be evaluated from three equations. The first equation represents the transformation of the transport velocity across the layer from the other layer boundary. The second establishes the light-generated current output from the layer interface, under the influence of the transport velocities and minority-carrier density at both layer boundaries and of bulk recombination. The third equation describes the flow of these carriers across other layers. The power of the approach is considered to lie in its facility for analysis of the solar cell's performance layer by layer, giving a clear picture of the individual layer's influence on cell efficiency.

Vorticity equation for MHD fast waves in geospace environment

NASA Technical Reports Server (NTRS)

Yamauchi, M.; Lundin, R.; Lui, A. T. Y.

1993-01-01

The MHD vorticity equation is modified in order to apply it to nonlinear MHD fast waves or shocks when their extent along the magnetic field is limited. Field-aligned current (FAC) generation is also discussed on the basis of this modified vorticity equation. When the wave normal is not aligned to the finite velocity convection and the source region is spatially limited, a longitudinal polarization causes a pair of plus and minus charges inside the compressional plane waves or shocks, generating a pair of FACs. This polarization is not related to the separation between the electrons and ions caused by their difference in mass, a separation which is inherent to compressional waves. The resultant double field-aligned current structure exists both with and without the contributions from curvature drift, which is questionable in terms of its contribution to vorticity change from the viewpoint of single-particle motion.

Thermal maps of Jupiter - Spatial organization and time dependence of stratospheric temperatures, 1980 to 1990

NASA Technical Reports Server (NTRS)

Orton, Glenn S.; Friedson, A. James; Baines, Kevin H.; Martin, Terry Z.; West, Robert A.; Caldwell, John; Hammel, Heidi B.; Bergstralh, Jay T.; Malcolm, Michael E.

1991-01-01

The spatial organization and time dependence of Jupiter's stratospheric temperatures have been measured by observing thermal emission from the 7.8-micrometer CH4 band. These temperatures, observed through the greater part of a Jovian year, exhibit the influence of seasonal radiative forcing. Distinct bands of high temperature are located at the poles and midlatitudes, while the equator alternates between warm and cold with a period of approximately 4 years. Substantial longitudinal variability is often observed within the warm midlatitude bands, and occasionally elsewhere on the planet. This variability includes small, localized structures, as well as large-scale waves with wavelengths longer than about 30,000 kilometers. The amplitudes of the waves vary on a time scale of about 1 month; structures on a smaller scale may have lifetimes of only days. Waves observed in 1985, 1987, and 1988 propagated with group velocities less than + or - 30 meters/sec.

An investigation of chaotic Kolmogorov flows

NASA Technical Reports Server (NTRS)

Platt, N.; Sirovich, L.; Fitzmaurice, N.

1990-01-01

A two dimensional flow governed by the incompressible Navier-Stokes equations with a steady spatially periodic forcing (known as the Kolmogorov flow) is numerically simulated. The behavior of the flow and its transition states as the Reynolds number (Re) varies is investigated in detail, as well as a number of the flow features. A sequence of bifurcations is shown to take place in the flow as Re varied. Two main regimes of the flow were observed: small and large scale structure regimes corresponding to different ranges of Re. Each of the regimes includes a number of quasiperiodic, chaotic, and relaminarization windows. In addition, each range contains a chaotic window with non-ergodic chaotic attractors. Spatially disordered, but temporally steady states were discovered in large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincare sections and, where possible, Lyapunov exponents and Kaplan-Yorke dimension.

The spatial structure of magnetospheric plasma disturbance estimated by using magnetic data obtained by SWARM satellites.

NASA Astrophysics Data System (ADS)

Yokoyama, Y.; Iyemori, T.; Aoyama, T.

2017-12-01

Field-aligned currents with various spatial scales flow into and out from high-latitude ionosphere. The magnetic fluctuations observed by LEO satellites along their orbits having period longer than a few seconds can be regarded as the manifestations of spatial structure of field aligned currents.This has been confirmed by using the initial orbital characteristics of 3 SWARM-satellites. From spectral analysis, we evaluated the spectral indices of these magnetic fluctuations and investigated their dependence on regions, such as magnetic latitude and MLT and so on. We found that the spectral indices take quite different values between the regions lower than the equatorward boundary of the auroral oval (around 63 degrees' in magnetic latitude) and the regions higher than that. On the other hands, we could not find the clear MLT dependence. In general, the FACs are believed to be generated in the magnetiospheric plasma sheet and boundary layer, and they flow along the field lines conserving their currents.The theory of FAC generation [e.g., Hasegawa and Sato ,1978] indicates that the FACs are strongly connected with magnetospheric plasma disturbances. Although the spectral indices above are these of spatial structures of the FACs over the ionosphere, by using the theoretical equation of FAC generation, we evaluate the spectral indices of magnetospheric plasma disturbance in FAC's generation regions. Furthermore, by projecting the area of fluctuations on the equatorial plane of magnetosphere (i.e. plasma sheet), we can estimate the spatial structure of magnetospheric plasma disturbance. In this presentation, we focus on the characteristics of disturbance in midnight region and discuss the relations to the substorm.

Still searching for the Holy Grail: on the use of effective soil parameters for Parflow-CLM.

NASA Astrophysics Data System (ADS)

Baroni, Gabriele; Schalge, Bernd; Rihani, Jehan; Attinger, Sabine

2015-04-01

In the last decades the advances in computer science have led to a growing number of coupled and distributed hydrological models based on Richards' equation. Several studies were conducted for understanding hydrological processes at different spatial and temporal scales and they showed promising uses of these types of models also in practical applications. However, these models are generally applied to scales different from that at which the equation is deduced and validated. For this reason, the models are implemented with effective soil parameters that, in principle, should preserve the water fluxes that would have been estimated assuming the finer resolution scale. In this context, the reduction in spatial discretization becomes a trade-off between complexity and performance of the model. The aim of the present contribution is to assess the performance of Parflow-CLM implemented at different spatial scales. A virtual experiment based on data available for the Neckar catchment (Germany) is used as reference at 100x100m resolution. Different upscaling rules for the soil hydraulic parameters are used for coarsening the model up to 1x1km. The analysis is carried out based on different model output e.g., river discharge, evapotranspiration, soil moisture and groundwater recharge. The effects of soil variability, correlation length and spatial distribution over the water flow direction on the simulation results are discussed. Further researches aim to quantify the related uncertainty in model output and the possibility to fill in the model structure inadequacy with data assimilation techniques.

Asymmetry of light absorption upon propagation of focused femtosecond laser pulses with spatiotemporal coupling through glass materials

NASA Astrophysics Data System (ADS)

Zhukov, Vladimir P.; Bulgakova, Nadezhda M.

2017-05-01

Ultrashort laser pulses are usually described in terms of temporal and spatial dependences of their electric field, assuming that the spatial dependence is separable from time dependence. However, in most situations this assumption is incorrect as generation of ultrashort pulses and their manipulation lead to couplings between spatial and temporal coordinates resulting in various effects such as pulse front tilt and spatial chirp. One of the most intriguing spatiotemporal coupling effects is the so-called "lighthouse effect", the phase front rotation with the beam propagation distance [Akturk et al., Opt. Express 13, 8642 (2005)]. The interaction of spatiotemporally coupled laser pulses with transparent materials have interesting peculiarities, such as the effect of nonreciprocal writing, which can be used to facilitate microfabrication of photonic structures inside optical glasses. In this work, we make an attempt to numerically investigate the influence of the pulse front tilt and the lighthouse effect on the absorption of laser energy inside fused silica glass. The model, which is based on nonlinear Maxwell's equations supplemented by the hydrodynamic equations for free electron plasma, is applied. As three-dimensional solution of such a problem would require huge computational resources, a simplified two-dimensional model has been proposed. It has enabled to gain a qualitative insight into the features of propagation of ultrashort laser pulses with the tilted front in the regimes of volumetric laser modification of transparent materials, including directional asymmetry upon direct laser writing in glass materials.

Maintenance of Austral Summertime Upper-Tropospheric Circulation over Tropical South America: The Bolivian High-Nordeste Low System.

NASA Astrophysics Data System (ADS)

Chen, Tsing-Chang; Weng, Shu-Ping; Schubert, Siegfried

1999-07-01

Using the NASA/GEOS reanalysis data for 1980-95, the austral-summer stationary eddies in the tropical-subtropical Southern Hemisphere are examined in two wave regimes: long and short wave (wave 1 and waves 2-6, respectively). The basic structure of the Bolivian high-Nordeste low (BH-NL) system is formed by a short-wave train across South America but modulated by the long-wave regime. The short-wave train exhibits a monsoonlike vertical phase reversal in the midtroposphere and a quarter-wave phase shift relative to the divergent circulation. As inferred from (a) the spatial relationship between the streamfunction and velocity potential and (b) the structure of the divergent circulation, the short-wave train forming the BH-NL system is maintained by South American local heating and remote African heating, while the long-wave regime is maintained by western tropical Pacific heating.The maintenance of the stationary waves in the two wave regimes is further illustrated by a simple diagnostic scheme that includes the velocity-potential maintenance equation (which links velocity potential and diabatic heating) and the streamfunction budget (which is the inverse Laplacian transform of the vorticity equation). Some simple relationships between streamfunction and velocity potential for both wave regimes are established to substantiate the links between diabatic heating and streamfunction; of particular interest is a Sverdrup balance in the short-wave regime. This simplified vorticity equation explains the vertical structure of the short-wave train associated with the BH-NL system and its spatial relationship with the divergent circulation.Based upon the diagnostic analysis of its maintenance a simple forced barotropic model is adopted to simulate the BH-NL system with idealized forcings, which imitates the real 200-mb divergence centers over South America, Africa, and the tropical Pacific. Numerical simulations demonstrate that the formation of the BH-NL system is affected not only by the African remote forcing, but also by the tropical Pacific forcing.

Stochastic Evolution of Augmented Born-Infeld Equations

NASA Astrophysics Data System (ADS)

Holm, Darryl D.

2018-06-01

This paper compares the results of applying a recently developed method of stochastic uncertainty quantification designed for fluid dynamics to the Born-Infeld model of nonlinear electromagnetism. The similarities in the results are striking. Namely, the introduction of Stratonovich cylindrical noise into each of their Hamiltonian formulations introduces stochastic Lie transport into their dynamics in the same form for both theories. Moreover, the resulting stochastic partial differential equations retain their unperturbed form, except for an additional term representing induced Lie transport by the set of divergence-free vector fields associated with the spatial correlations of the cylindrical noise. The explanation for this remarkable similarity lies in the method of construction of the Hamiltonian for the Stratonovich stochastic contribution to the motion in both cases, which is done via pairing spatial correlation eigenvectors for cylindrical noise with the momentum map for the deterministic motion. This momentum map is responsible for the well-known analogy between hydrodynamics and electromagnetism. The momentum map for the Maxwell and Born-Infeld theories of electromagnetism treated here is the 1-form density known as the Poynting vector. Two appendices treat the Hamiltonian structures underlying these results.

Comparison of cell centered and cell vertex scheme in the calculation of high speed compressible flows

NASA Astrophysics Data System (ADS)

Rahman, Syazila; Yusoff, Mohd. Zamri; Hasini, Hasril

2012-06-01

This paper describes the comparison between the cell centered scheme and cell vertex scheme in the calculation of high speed compressible flow properties. The calculation is carried out using Computational Fluid Dynamic (CFD) in which the mass, momentum and energy equations are solved simultaneously over the flow domain. The geometry under investigation consists of a Binnie and Green convergent-divergent nozzle and structured mesh scheme is implemented throughout the flow domain. The finite volume CFD solver employs second-order accurate central differencing scheme for spatial discretization. In addition, the second-order accurate cell-vertex finite volume spatial discretization is also introduced in this case for comparison. The multi-stage Runge-Kutta time integration is implemented for solving a set of non-linear governing equations with variables stored at the vertices. Artificial dissipations used second and fourth order terms with pressure switch to detect changes in pressure gradient. This is important to control the solution stability and capture shock discontinuity. The result is compared with experimental measurement and good agreement is obtained for both cases.

Modified symplectic schemes with nearly-analytic discrete operators for acoustic wave simulations

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Lang, Chao; Wang, Wenshuai; Pan, Zhide

2017-04-01

Using a structure-preserving algorithm significantly increases the computational efficiency of solving wave equations. However, only a few explicit symplectic schemes are available in the literature, and the capabilities of these symplectic schemes have not been sufficiently exploited. Here, we propose a modified strategy to construct explicit symplectic schemes for time advance. The acoustic wave equation is transformed into a Hamiltonian system. The classical symplectic partitioned Runge-Kutta (PRK) method is used for the temporal discretization. Additional spatial differential terms are added to the PRK schemes to form the modified symplectic methods and then two modified time-advancing symplectic methods with all of positive symplectic coefficients are then constructed. The spatial differential operators are approximated by nearly-analytic discrete (NAD) operators, and we call the fully discretized scheme modified symplectic nearly analytic discrete (MSNAD) method. Theoretical analyses show that the MSNAD methods exhibit less numerical dispersion and higher stability limits than conventional methods. Three numerical experiments are conducted to verify the advantages of the MSNAD methods, such as their numerical accuracy, computational cost, stability, and long-term calculation capability.

Uniqueness of solutions for a mathematical model for magneto-viscoelastic flows

NASA Astrophysics Data System (ADS)

Schlömerkemper, A.; Žabenský, J.

2018-06-01

We investigate uniqueness of weak solutions for a system of partial differential equations capturing behavior of magnetoelastic materials. This system couples the Navier–Stokes equations with evolutionary equations for the deformation gradient and for the magnetization obtained from a special case of the micromagnetic energy. It turns out that the conditions on uniqueness coincide with those for the well-known Navier–Stokes equations in bounded domains: weak solutions are unique in two spatial dimensions, and weak solutions satisfying the Prodi–Serrin conditions are unique among all weak solutions in three dimensions. That is, we obtain the so-called weak-strong uniqueness result in three spatial dimensions.

Existence and Stability of Spatial Plane Waves for the Incompressible Navier-Stokes in R^3

NASA Astrophysics Data System (ADS)

Correia, Simão; Figueira, Mário

2018-03-01

We consider the three-dimensional incompressible Navier-Stokes equation on the whole space. We observe that this system admits a L^∞ family of global spatial plane wave solutions, which are connected with the two-dimensional equation. We then proceed to prove local well-posedness over a space which includes L^3(R^3) and these solutions. Finally, we prove L^3-stability of spatial plane waves, with no condition on their size.

Sonic black holes in a one-dimensional relativistic flow

NASA Astrophysics Data System (ADS)

Carbonaro, P.

2015-09-01

The analogy between sound propagation in a fluid background and light propagation in a curved spacetime, discovered by Unruh in 1981, does not work in general when considering the motion of a fluid which is confined in one spatial dimension being unable in (1+1) dimensions to introduce in a coherent manner an effective acoustic metric, barring some exceptional cases. In this paper a relativistic fluid is considered and the general condition for the existence of an acoustic metric in strictly one-dimensional systems is found. Attention is also paid to the physical meaning of the equations of state characterizing such systems and to the remarkable symmetry of structure taken by the basic equations. Finally the Hawking temperature is calculated in an artificial de Laval nozzle.

Reconstruction of explicit structural properties at the nanoscale via spectroscopic microscopy

NASA Astrophysics Data System (ADS)

Cherkezyan, Lusik; Zhang, Di; Subramanian, Hariharan; Taflove, Allen; Backman, Vadim

2016-02-01

The spectrum registered by a reflected-light bright-field spectroscopic microscope (SM) can quantify the microscopically indiscernible, deeply subdiffractional length scales within samples such as biological cells and tissues. Nevertheless, quantification of biological specimens via any optical measures most often reveals ambiguous information about the specific structural properties within the studied samples. Thus, optical quantification remains nonintuitive to users from the diverse fields of technique application. In this work, we demonstrate that the SM signal can be analyzed to reconstruct explicit physical measures of internal structure within label-free, weakly scattering samples: characteristic length scale and the amplitude of spatial refractive-index (RI) fluctuations. We present and validate the reconstruction algorithm via finite-difference time-domain solutions of Maxwell's equations on an example of exponential spatial correlation of RI. We apply the validated algorithm to experimentally measure structural properties within isolated cells from two genetic variants of HT29 colon cancer cell line as well as within a prostate tissue biopsy section. The presented methodology can lead to the development of novel biophotonics techniques that create two-dimensional maps of explicit structural properties within biomaterials: the characteristic size of macromolecular complexes and the variance of local mass density.

New insights into the endophenotypic status of cognition in bipolar disorder: genetic modelling study of twins and siblings.

PubMed

Georgiades, Anna; Rijsdijk, Fruhling; Kane, Fergus; Rebollo-Mesa, Irene; Kalidindi, Sridevi; Schulze, Katja K; Stahl, Daniel; Walshe, Muriel; Sahakian, Barbara J; McDonald, Colm; Hall, Mei-Hua; Murray, Robin M; Kravariti, Eugenia

2016-06-01

Twin studies have lacked statistical power to apply advanced genetic modelling techniques to the search for cognitive endophenotypes for bipolar disorder. To quantify the shared genetic variability between bipolar disorder and cognitive measures. Structural equation modelling was performed on cognitive data collected from 331 twins/siblings of varying genetic relatedness, disease status and concordance for bipolar disorder. Using a parsimonious AE model, verbal episodic and spatial working memory showed statistically significant genetic correlations with bipolar disorder (rg = |0.23|-|0.27|), which lost statistical significance after covarying for affective symptoms. Using an ACE model, IQ and visual-spatial learning showed statistically significant genetic correlations with bipolar disorder (rg = |0.51|-|1.00|), which remained significant after covarying for affective symptoms. Verbal episodic and spatial working memory capture a modest fraction of the bipolar diathesis. IQ and visual-spatial learning may tap into genetic substrates of non-affective symptomatology in bipolar disorder. © The Royal College of Psychiatrists 2016.

Scalable Preconditioners for Structure Preserving Discretizations of Maxwell Equations in First Order Form

DOE PAGES

Phillips, Edward Geoffrey; Shadid, John N.; Cyr, Eric C.

2018-05-01

Here, we report multiple physical time-scales can arise in electromagnetic simulations when dissipative effects are introduced through boundary conditions, when currents follow external time-scales, and when material parameters vary spatially. In such scenarios, the time-scales of interest may be much slower than the fastest time-scales supported by the Maxwell equations, therefore making implicit time integration an efficient approach. The use of implicit temporal discretizations results in linear systems in which fast time-scales, which severely constrain the stability of an explicit method, can manifest as so-called stiff modes. This study proposes a new block preconditioner for structure preserving (also termed physicsmore » compatible) discretizations of the Maxwell equations in first order form. The intent of the preconditioner is to enable the efficient solution of multiple-time-scale Maxwell type systems. An additional benefit of the developed preconditioner is that it requires only a traditional multigrid method for its subsolves and compares well against alternative approaches that rely on specialized edge-based multigrid routines that may not be readily available. Lastly, results demonstrate parallel scalability at large electromagnetic wave CFL numbers on a variety of test problems.« less

Scalable Preconditioners for Structure Preserving Discretizations of Maxwell Equations in First Order Form

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

Phillips, Edward Geoffrey; Shadid, John N.; Cyr, Eric C.

Here, we report multiple physical time-scales can arise in electromagnetic simulations when dissipative effects are introduced through boundary conditions, when currents follow external time-scales, and when material parameters vary spatially. In such scenarios, the time-scales of interest may be much slower than the fastest time-scales supported by the Maxwell equations, therefore making implicit time integration an efficient approach. The use of implicit temporal discretizations results in linear systems in which fast time-scales, which severely constrain the stability of an explicit method, can manifest as so-called stiff modes. This study proposes a new block preconditioner for structure preserving (also termed physicsmore » compatible) discretizations of the Maxwell equations in first order form. The intent of the preconditioner is to enable the efficient solution of multiple-time-scale Maxwell type systems. An additional benefit of the developed preconditioner is that it requires only a traditional multigrid method for its subsolves and compares well against alternative approaches that rely on specialized edge-based multigrid routines that may not be readily available. Lastly, results demonstrate parallel scalability at large electromagnetic wave CFL numbers on a variety of test problems.« less

Local dynamics and spatiotemporal chaos. The Kuramoto- Sivashinsky equation: A case study

NASA Astrophysics Data System (ADS)

Wittenberg, Ralf Werner

The nature of spatiotemporal chaos in extended continuous systems is not yet well-understood. In this thesis, a model partial differential equation, the Kuramoto- Sivashinsky (KS) equation ut+uxxxx+uxx+uux =0 on a large one-dimensional periodic domain, is studied analytically, numerically, and through modeling to obtain a more detailed understanding of the observed spatiotemporally complex dynamics. In particular, with the aid of a wavelet decomposition, the relevant dynamical interactions are shown to be localized in space and scale. Motivated by these results, and by the idea that the attractor on a large domain may be understood via attractors on smaller domains, a spatially localized low- dimensional model for a minimal chaotic box is proposed. A (de)stabilized extension of the KS equation has recently attracted increased interest; for this situation, dissipativity and analyticity areproven, and an explicit shock-like solution is constructed which sheds light on the difficulties in obtaining optimal bounds for the KS equation. For the usual KS equation, the spatiotemporally chaotic state is carefully characterized in real, Fourier and wavelet space. The wavelet decomposition provides good scale separation which isolates the three characteristic regions of the dynamics: large scales of slow Gaussian fluctuations, active scales containing localized interactions of coherent structures, and small scales. Space localization is shown through a comparison of various correlation lengths and a numerical experiment in which different modes are uncoupled to estimate a dynamic interaction length. A detailed picture of the contributions of different scales to the spatiotemporally complex dynamics is obtained via a Galerkin projection of the KS equation onto the wavelet basis, and an extensive series of numerical experiments in which different combinations of wavelet levels are eliminated or forced. These results, and a formalism to derive an effective equation for periodized subsystems externally forced from a larger system, motivate various models for spatially localized forced systems. There is convincing evidence that short periodized systems, internally forced at the largest scales, form a minimal model for the observed extensively chaotic dynamics in larger domains.

Research into the influence of spatial variability and scale on the parameterization of hydrological processes

NASA Technical Reports Server (NTRS)

Wood, Eric F.

1993-01-01

The objectives of the research were as follows: (1) Extend the Representative Elementary Area (RE) concept, first proposed and developed in Wood et al, (1988), to the water balance fluxes of the interstorm period (redistribution, evapotranspiration and baseflow) necessary for the analysis of long-term water balance processes. (2) Derive spatially averaged water balance model equations for spatially variable soil, topography and vegetation, over A RANGE OF CLIMATES. This is a necessary step in our goal to derive consistent hydrologic results up to GCM grid scales necessary for global climate modeling. (3) Apply the above macroscale water balance equations with remotely sensed data and begin to explore the feasibility of parameterizing the water balance constitutive equations at GCM grid scale.

Modeling spatial competition for light in plant populations with the porous medium equation.

PubMed

Beyer, Robert; Etard, Octave; Cournède, Paul-Henry; Laurent-Gengoux, Pascal

2015-02-01

We consider a plant's local leaf area index as a spatially continuous variable, subject to particular reaction-diffusion dynamics of allocation, senescence and spatial propagation. The latter notably incorporates the plant's tendency to form new leaves in bright rather than shaded locations. Applying a generalized Beer-Lambert law allows to link existing foliage to production dynamics. The approach allows for inter-individual variability and competition for light while maintaining robustness-a key weakness of comparable existing models. The analysis of the single plant case leads to a significant simplification of the system's key equation when transforming it into the well studied porous medium equation. Confronting the theoretical model to experimental data of sugar beet populations, differing in configuration density, demonstrates its accuracy.

Enhanced numerical analysis of three-color HgCdTe detectors

NASA Astrophysics Data System (ADS)

Jóźwikowski, K.; Rogalski, A.

2007-04-01

The performance of three-color HgCdTe photovoltaic heterostructure detector is examined theoretically. In comparison with two-color detectors with two back-to-back junctions, three-color structure contain an absorber of intermediate wavelength placed between two junctions, and electronic barriers are used to isolate this intermediate region. This structure was first proposed by British workers. Enhanced original computer programs are applied to solve the system of non-linear continuity equations for carriers and Poisson equations. In addition, the numerical analysis includes the dependence of absorption coefficient on Burstein effect as well as interference effects in heterostructure with metallic electrical contacts. Three detector structures with different localizations of separating barriers are analyzed. The calculations results are presented in the form of spatial distributions of bandgap energy and quantum efficiency. It is shown that the performance of the detector is critically dependent on the barrier's doping level and position in relation to the junction. This behavior is serious disadvantage of the considered three color detector. A small shift of the barrier location and doping level causes serious changes in spectral responsivity.

Numerical analysis of three-colour HgCdTe detectors

NASA Astrophysics Data System (ADS)

Jóźwikowski, K.; Rogalski, A.

2007-12-01

The performance of three-colour HgCdTe photovoltaic heterostructure detector is examined theoretically. In comparison with two-colour detectors with two back-to-back junctions, three-colour structure contains an absorber of intermediate wavelength placed between two junctions and electronic barriers are used to isolate this intermediate region. This structure was first proposed by British workers. Three-detector structures with different localizations of separating barriers are analyzed. The calculation results are presented in the form of spatial distributions of bandgap energy and quantum efficiency. Enhanced original computer programs are applied to solve the system of non-linear continuity equations for carriers and Poisson equations. In addition, the numerical analysis includes the dependence of absorption coefficient on Burstein effect as well as interference effects in heterostructure with metallic electrical contacts. It is shown that the performance of the detector is critically dependent on the barrier’s doping level and position in relation to the junction. This behaviour is serious disadvantage of the considered three-colour detector. A small shift of the barrier location and doping level causes serious changes in spectral responsivity.

A generalized reaction diffusion model for spatial structure formed by motile cells.

PubMed

Ochoa, F L

1984-01-01

A non-linear stability analysis using a multi-scale perturbation procedure is carried out on a model of a generalized reaction diffusion mechanism which involves only a single equation but which nevertheless exhibits bifurcation to non-uniform states. The patterns generated by this model by variation in a parameter related to the scalar dimensions of domain of definition, indicate its capacity to represent certain key morphogenetic features of multicellular systems formed by motile cells.

A spline-based parameter estimation technique for static models of elastic structures

NASA Technical Reports Server (NTRS)

Dutt, P.; Taasan, S.

1986-01-01

The problem of identifying the spatially varying coefficient of elasticity using an observed solution to the forward problem is considered. Under appropriate conditions this problem can be treated as a first order hyperbolic equation in the unknown coefficient. Some continuous dependence results are developed for this problem and a spline-based technique is proposed for approximating the unknown coefficient, based on these results. The convergence of the numerical scheme is established and error estimates obtained.

Eastern Mediterranean Sea Spatial and Temporal Variability of Thermohaline Structure and Circulation Identified from Observational (T, S) Profiles

DTIC Science & Technology

2015-12-01

effect of Etesian winds between the late May and early October. Although they are generally dry, cool and moderate; they may turn into a windstorm...very significant to provide the realization of ocean modeling and prediction. The Optimal Spectral Decomposition (OSD) method is an effective ...represents the potential density, by differentiating this equation with respect to z and multiplying with the coriolis parameter f, conservation of

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

Bag, Satadru; Sahni, Varun; Viznyuk, Alexander

We obtain a closed system of equations for scalar perturbations in a multi-component braneworld. Our braneworld possesses a phantom-like equation of state at late times, w {sub eff} < −1, but no big-rip future singularity. In addition to matter and radiation, the braneworld possesses a new effective degree of freedom—the 'Weyl fluid' or 'dark radiation'. Setting initial conditions on super-Hubble spatial scales at the epoch of radiation domination, we evolve perturbations of radiation, pressureless matter and the Weyl fluid until the present epoch. We observe a gradual decrease in the amplitude of the Weyl-fluid perturbations after Hubble-radius crossing, which resultsmore » in a negligible effect of the Weyl fluid on the evolution of matter perturbations on spatial scales relevant for structure formation. Consequently, the quasi-static approximation of Koyama and Maartens provides a good fit to the exact results during the matter-dominated epoch. We find that the late-time growth of density perturbations on the brane proceeds at a faster rate than in ΛCDM. Additionally, the gravitational potentials Φ and Ψ evolve differently on the brane than in ΛCDM, for which Φ = Ψ. On the brane, by contrast, the ratio Φ/Ψ exceeds unity during the late matter-dominated epoch ( z ∼< 50). These features emerge as smoking gun tests of phantom brane cosmology and allow predictions of this scenario to be tested against observations of galaxy clustering and large-scale structure.« less

Regional and local species richness in an insular environment: Serpentine plants in California

USGS Publications Warehouse

Harrison, S.; Safford, H.D.; Grace, J.B.; Viers, J.H.; Davies, K.F.

2006-01-01

We asked how the richness of the specialized (endemic) flora of serpentine rock outcrops in California varies at both the regional and local scales. Our study had two goals: first, to test whether endemic richness is affected by spatial habitat structure (e.g., regional serpentine area, local serpentine outcrop area, regional and local measures of outcrop isolation), and second, to conduct this test in the context of a broader assessment of environmental influences (e.g., climate, soils, vegetation, disturbance) and historical influences (e.g., geologic age, geographic province) on local and regional species richness. We measured endemic and total richness and environmental variables in 109 serpentine sites (1000-m2 paired plots) in 78 serpentine-containing regions of the state. We used structural equation modeling (SEM) to simultaneously relate regional richness to regionalscale predictors, and local richness to both local-scale and regional-scale predictors. Our model for serpentine endemics explained 66% of the variation in local endemic richness based on local environment (vegetation, soils, rock cover) and on regional endemic richness. It explained 73% of the variation in regional endemic richness based on regional environment (climate and productivity), historical factors (geologic age and geographic province), and spatial structure (regional total area of serpentine, the only significant spatial variable in our analysis). We did not find a strong influence of spatial structure on species richness. However, we were able to distinguish local vs. regional influences on species richness to a novel extent, despite the existence of correlations between local and regional conditions. ?? 2006 by the Ecological Society of America.

Spatially averaged flow over a wavy boundary revisited

USGS Publications Warehouse

McLean, S.R.; Wolfe, S.R.; Nelson, J.M.

1999-01-01

Vertical profiles of streamwise velocity measured over bed forms are commonly used to deduce boundary shear stress for the purpose of estimating sediment transport. These profiles may be derived locally or from some sort of spatial average. Arguments for using the latter procedure are based on the assumption that spatial averaging of the momentum equation effectively removes local accelerations from the problem. Using analogies based on steady, uniform flows, it has been argued that the spatially averaged velocity profiles are approximately logarithmic and can be used to infer values of boundary shear stress. This technique of using logarithmic profiles is investigated using detailed laboratory measurements of flow structure and boundary shear stress over fixed two-dimensional bed forms. Spatial averages over the length of the bed form of mean velocity measurements at constant distances from the mean bed elevation yield vertical profiles that are highly logarithmic even though the effect of the bottom topography is observed throughout the water column. However, logarithmic fits of these averaged profiles do not yield accurate estimates of the measured total boundary shear stress. Copyright 1999 by the American Geophysical Union.

Free-space propagation of high-dimensional structured optical fields in an urban environment

PubMed Central

Lavery, Martin P. J.; Peuntinger, Christian; Günthner, Kevin; Banzer, Peter; Elser, Dominique; Boyd, Robert W.; Padgett, Miles J.; Marquardt, Christoph; Leuchs, Gerd

2017-01-01

Spatially structured optical fields have been used to enhance the functionality of a wide variety of systems that use light for sensing or information transfer. As higher-dimensional modes become a solution of choice in optical systems, it is important to develop channel models that suitably predict the effect of atmospheric turbulence on these modes. We investigate the propagation of a set of orthogonal spatial modes across a free-space channel between two buildings separated by 1.6 km. Given the circular geometry of a common optical lens, the orthogonal mode set we choose to implement is that described by the Laguerre-Gaussian (LG) field equations. Our study focuses on the preservation of phase purity, which is vital for spatial multiplexing and any system requiring full quantum-state tomography. We present experimental data for the modal degradation in a real urban environment and draw a comparison to recognized theoretical predictions of the link. Our findings indicate that adaptations to channel models are required to simulate the effects of atmospheric turbulence placed on high-dimensional structured modes that propagate over a long distance. Our study indicates that with mitigation of vortex splitting, potentially through precorrection techniques, one could overcome the challenges in a real point-to-point free-space channel in an urban environment. PMID:29075663

Free-space propagation of high-dimensional structured optical fields in an urban environment.

PubMed

Lavery, Martin P J; Peuntinger, Christian; Günthner, Kevin; Banzer, Peter; Elser, Dominique; Boyd, Robert W; Padgett, Miles J; Marquardt, Christoph; Leuchs, Gerd

2017-10-01

Spatially structured optical fields have been used to enhance the functionality of a wide variety of systems that use light for sensing or information transfer. As higher-dimensional modes become a solution of choice in optical systems, it is important to develop channel models that suitably predict the effect of atmospheric turbulence on these modes. We investigate the propagation of a set of orthogonal spatial modes across a free-space channel between two buildings separated by 1.6 km. Given the circular geometry of a common optical lens, the orthogonal mode set we choose to implement is that described by the Laguerre-Gaussian (LG) field equations. Our study focuses on the preservation of phase purity, which is vital for spatial multiplexing and any system requiring full quantum-state tomography. We present experimental data for the modal degradation in a real urban environment and draw a comparison to recognized theoretical predictions of the link. Our findings indicate that adaptations to channel models are required to simulate the effects of atmospheric turbulence placed on high-dimensional structured modes that propagate over a long distance. Our study indicates that with mitigation of vortex splitting, potentially through precorrection techniques, one could overcome the challenges in a real point-to-point free-space channel in an urban environment.

Ionic wave propagation and collision in an excitable circuit model of microtubules

NASA Astrophysics Data System (ADS)

Guemkam Ghomsi, P.; Tameh Berinyoh, J. T.; Moukam Kakmeni, F. M.

2018-02-01

In this paper, we report the propensity to excitability of the internal structure of cellular microtubules, modelled as a relatively large one-dimensional spatial array of electrical units with nonlinear resistive features. We propose a model mimicking the dynamics of a large set of such intracellular dynamical entities as an excitable medium. We show that the behavior of such lattices can be described by a complex Ginzburg-Landau equation, which admits several wave solutions, including the plane waves paradigm. A stability analysis of the plane waves solutions of our dynamical system is conducted both analytically and numerically. It is observed that perturbed plane waves will always evolve toward promoting the generation of localized periodic waves trains. These modes include both stationary and travelling spatial excitations. They encompass, on one hand, localized structures such as solitary waves embracing bright solitons, dark solitons, and bisolitonic impulses with head-on collisions phenomena, and on the other hand, the appearance of both spatially homogeneous and spatially inhomogeneous stationary patterns. This ability exhibited by our array of proteinic elements to display several states of excitability exposes their stunning biological and physical complexity and is of high relevance in the description of the developmental and informative processes occurring on the subcellular scale.

Ionic wave propagation and collision in an excitable circuit model of microtubules.

PubMed

Guemkam Ghomsi, P; Tameh Berinyoh, J T; Moukam Kakmeni, F M

2018-02-01

In this paper, we report the propensity to excitability of the internal structure of cellular microtubules, modelled as a relatively large one-dimensional spatial array of electrical units with nonlinear resistive features. We propose a model mimicking the dynamics of a large set of such intracellular dynamical entities as an excitable medium. We show that the behavior of such lattices can be described by a complex Ginzburg-Landau equation, which admits several wave solutions, including the plane waves paradigm. A stability analysis of the plane waves solutions of our dynamical system is conducted both analytically and numerically. It is observed that perturbed plane waves will always evolve toward promoting the generation of localized periodic waves trains. These modes include both stationary and travelling spatial excitations. They encompass, on one hand, localized structures such as solitary waves embracing bright solitons, dark solitons, and bisolitonic impulses with head-on collisions phenomena, and on the other hand, the appearance of both spatially homogeneous and spatially inhomogeneous stationary patterns. This ability exhibited by our array of proteinic elements to display several states of excitability exposes their stunning biological and physical complexity and is of high relevance in the description of the developmental and informative processes occurring on the subcellular scale.

Decoupled ARX and RBF Neural Network Modeling Using PCA and GA Optimization for Nonlinear Distributed Parameter Systems.

PubMed

Zhang, Ridong; Tao, Jili; Lu, Renquan; Jin, Qibing

2018-02-01

Modeling of distributed parameter systems is difficult because of their nonlinearity and infinite-dimensional characteristics. Based on principal component analysis (PCA), a hybrid modeling strategy that consists of a decoupled linear autoregressive exogenous (ARX) model and a nonlinear radial basis function (RBF) neural network model are proposed. The spatial-temporal output is first divided into a few dominant spatial basis functions and finite-dimensional temporal series by PCA. Then, a decoupled ARX model is designed to model the linear dynamics of the dominant modes of the time series. The nonlinear residual part is subsequently parameterized by RBFs, where genetic algorithm is utilized to optimize their hidden layer structure and the parameters. Finally, the nonlinear spatial-temporal dynamic system is obtained after the time/space reconstruction. Simulation results of a catalytic rod and a heat conduction equation demonstrate the effectiveness of the proposed strategy compared to several other methods.

Comptonization of X-rays by low-temperature electrons. [photon wavelength redistribution in cosmic sources

NASA Technical Reports Server (NTRS)

Illarionov, A.; Kallman, T.; Mccray, R.; Ross, R.

1979-01-01

A method is described for calculating the spectrum that results from the Compton scattering of a monochromatic source of X-rays by low-temperature electrons, both for initial-value relaxation problems and for steady-state spatial diffusion problems. The method gives an exact solution of the inital-value problem for evolution of the spectrum in an infinite homogeneous medium if Klein-Nishina corrections to the Thomson cross section are neglected. This, together with approximate solutions for problems in which Klein-Nishina corrections are significant and/or spatial diffusion occurs, shows spectral structure near the original photon wavelength that may be used to infer physical conditions in cosmic X-ray sources. Explicit results, shown for examples of time relaxation in an infinite medium and spatial diffusion through a uniform sphere, are compared with results obtained by Monte Carlo calculations and by solving the appropriate Fokker-Planck equation.

Spatial distribution on high-order-harmonic generation of an H2+ molecule in intense laser fields

NASA Astrophysics Data System (ADS)

Zhang, Jun; Ge, Xin-Lei; Wang, Tian; Xu, Tong-Tong; Guo, Jing; Liu, Xue-Shen

2015-07-01

High-order-harmonic generation (HHG) for the H2 + molecule in a 3-fs, 800-nm few-cycle Gaussian laser pulse combined with a static field is investigated by solving the one-dimensional electronic and one-dimensional nuclear time-dependent Schrödinger equation within the non-Born-Oppenheimer approximation. The spatial distribution in HHG is demonstrated and the results present the recombination process of the electron with the two nuclei, respectively. The spatial distribution of the HHG spectra shows that there is little possibility of the recombination of the electron with the nuclei around the origin z =0 a.u. and equilibrium internuclear positions z =±1.3 a.u. This characteristic is irrelevant to laser parameters and is only attributed to the molecular structure. Furthermore, we investigate the time-dependent electron-nuclear wave packet and ionization probability to further explain the underlying physical mechanism.

Radiation reabsorption in a laser-produced plasma

NASA Astrophysics Data System (ADS)

Brunner, W.; John, R. W.; Paul, H.; Steudel, H.

1988-11-01

Taking into account the emission and absorption of resonance radiation in a recombining laser-produced plasma of intermediate density, the system of rate equations for the population densities coupled with the radiative transfer equation is approximately treated. In the case of spatially varying absorption, an approximate form of the rate equation determining the population density of the upper resonance level is derived. By applying this relation to an axially symmetric plasma, a simple formula that describes the effect of radiation reabsorption on the spatial behavior of the population density is obtained.

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules

1999-01-01

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

An algebraic multigrid method for Q2-Q1 mixed discretizations of the Navier-Stokes equations

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

Prokopenko, Andrey; Tuminaro, Raymond S.

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily co-located at mesh points. Speci cally, we investigate a Q 2-Q 1 mixed finite element discretization of the incompressible Navier-Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees-of-freedom (dofs) are defined at spatial locations where there are no corresponding pressure dofs. Thus, AMG approaches lever- aging this co-located structure are not applicable. This paper instead proposes an automatic AMG coarsening that mimics certain pressure/velocitymore » dof relationships of the Q 2-Q 1 discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity dofs resembles that on the nest grid. To define coefficients within the inter-grid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier-Stokes problems.« less

Newtonian self-gravitating system in a relativistic huge void universe model

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

Nishikawa, Ryusuke; Nakao, Ken-ichi; Yoo, Chul-Moon, E-mail: ryusuke@sci.osaka-cu.ac.jp, E-mail: knakao@sci.osaka-cu.ac.jp, E-mail: yoo@gravity.phys.nagoya-u.ac.jp

We consider a test of the Copernican Principle through observations of the large-scale structures, and for this purpose we study the self-gravitating system in a relativistic huge void universe model which does not invoke the Copernican Principle. If we focus on the the weakly self-gravitating and slowly evolving system whose spatial extent is much smaller than the scale of the cosmological horizon in the homogeneous and isotropic background universe model, the cosmological Newtonian approximation is available. Also in the huge void universe model, the same kind of approximation as the cosmological Newtonian approximation is available for the analysis of themore » perturbations contained in a region whose spatial size is much smaller than the scale of the huge void: the effects of the huge void are taken into account in a perturbative manner by using the Fermi-normal coordinates. By using this approximation, we derive the equations of motion for the weakly self-gravitating perturbations whose elements have relative velocities much smaller than the speed of light, and show the derived equations can be significantly different from those in the homogeneous and isotropic universe model, due to the anisotropic volume expansion in the huge void. We linearize the derived equations of motion and solve them. The solutions show that the behaviors of linear density perturbations are very different from those in the homogeneous and isotropic universe model.« less

An algebraic multigrid method for Q2-Q1 mixed discretizations of the Navier-Stokes equations

DOE PAGES

Prokopenko, Andrey; Tuminaro, Raymond S.

2016-07-01

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily co-located at mesh points. Speci cally, we investigate a Q 2-Q 1 mixed finite element discretization of the incompressible Navier-Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees-of-freedom (dofs) are defined at spatial locations where there are no corresponding pressure dofs. Thus, AMG approaches lever- aging this co-located structure are not applicable. This paper instead proposes an automatic AMG coarsening that mimics certain pressure/velocitymore » dof relationships of the Q 2-Q 1 discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity dofs resembles that on the nest grid. To define coefficients within the inter-grid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier-Stokes problems.« less

State-of-charge estimation in lithium-ion batteries: A particle filter approach

NASA Astrophysics Data System (ADS)

Tulsyan, Aditya; Tsai, Yiting; Gopaluni, R. Bhushan; Braatz, Richard D.

2016-11-01

The dynamics of lithium-ion batteries are complex and are often approximated by models consisting of partial differential equations (PDEs) relating the internal ionic concentrations and potentials. The Pseudo two-dimensional model (P2D) is one model that performs sufficiently accurately under various operating conditions and battery chemistries. Despite its widespread use for prediction, this model is too complex for standard estimation and control applications. This article presents an original algorithm for state-of-charge estimation using the P2D model. Partial differential equations are discretized using implicit stable algorithms and reformulated into a nonlinear state-space model. This discrete, high-dimensional model (consisting of tens to hundreds of states) contains implicit, nonlinear algebraic equations. The uncertainty in the model is characterized by additive Gaussian noise. By exploiting the special structure of the pseudo two-dimensional model, a novel particle filter algorithm that sweeps in time and spatial coordinates independently is developed. This algorithm circumvents the degeneracy problems associated with high-dimensional state estimation and avoids the repetitive solution of implicit equations by defining a 'tether' particle. The approach is illustrated through extensive simulations.

Description of waves in inhomogeneous domains using Heun's equation

NASA Astrophysics Data System (ADS)

Bednarik, M.; Cervenka, M.

2018-04-01

There are a number of model equations describing electromagnetic, acoustic or quantum waves in inhomogeneous domains and some of them are of the same type from the mathematical point of view. This isomorphism enables us to use a unified approach to solving the corresponding equations. In this paper, the inhomogeneity is represented by a trigonometric spatial distribution of a parameter determining the properties of an inhomogeneous domain. From the point of view of modeling, this trigonometric parameter function can be smoothly connected to neighboring constant-parameter regions. For this type of distribution, exact local solutions of the model equations are represented by the local Heun functions. As the interval for which the solution is sought includes two regular singular points. For this reason, a method is proposed which resolves this problem only based on the local Heun functions. Further, the transfer matrix for the considered inhomogeneous domain is determined by means of the proposed method. As an example of the applicability of the presented solutions the transmission coefficient is calculated for the locally periodic structure which is given by an array of asymmetric barriers.

A Chebyshev matrix method for spatial modes of the Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Danabasoglu, G.; Biringen, S.

1989-01-01

The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blausius boundary layer. The problem is linearized by the companion matrix technique for semi-infinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.

Relaxation in two dimensions and the 'sinh-Poisson' equation

NASA Technical Reports Server (NTRS)

Montgomery, D.; Matthaeus, W. H.; Stribling, W. T.; Martinez, D.; Oughton, S.

1992-01-01

Long-time states of a turbulent, decaying, two-dimensional, Navier-Stokes flow are shown numerically to relax toward maximum-entropy configurations, as defined by the "sinh-Poisson" equation. The large-scale Reynolds number is about 14,000, the spatial resolution is (512)-squared, the boundary conditions are spatially periodic, and the evolution takes place over nearly 400 large-scale eddy-turnover times.

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

Wu, Wei; Wang, Jin, E-mail: jin.wang.1@stonybrook.edu; State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, 130022 Changchun, China and College of Physics, Jilin University, 130021 Changchun

We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic andmore » thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series.« less

Lagrangian averaging, nonlinear waves, and shock regularization

NASA Astrophysics Data System (ADS)

Bhat, Harish S.

In this thesis, we explore various models for the flow of a compressible fluid as well as model equations for shock formation, one of the main features of compressible fluid flows. We begin by reviewing the variational structure of compressible fluid mechanics. We derive the barotropic compressible Euler equations from a variational principle in both material and spatial frames. Writing the resulting equations of motion requires certain Lie-algebraic calculations that we carry out in detail for expository purposes. Next, we extend the derivation of the Lagrangian averaged Euler (LAE-alpha) equations to the case of barotropic compressible flows. The derivation in this thesis involves averaging over a tube of trajectories etaepsilon centered around a given Lagrangian flow eta. With this tube framework, the LAE-alpha equations are derived by following a simple procedure: start with a given action, expand via Taylor series in terms of small-scale fluid fluctuations xi, truncate, average, and then model those terms that are nonlinear functions of xi. We then analyze a one-dimensional subcase of the general models derived above. We prove the existence of a large family of traveling wave solutions. Computing the dispersion relation for this model, we find it is nonlinear, implying that the equation is dispersive. We carry out numerical experiments that show that the model possesses smooth, bounded solutions that display interesting pattern formation. Finally, we examine a Hamiltonian partial differential equation (PDE) that regularizes the inviscid Burgers equation without the addition of standard viscosity. Here alpha is a small parameter that controls a nonlinear smoothing term that we have added to the inviscid Burgers equation. We show the existence of a large family of traveling front solutions. We analyze the initial-value problem and prove well-posedness for a certain class of initial data. We prove that in the zero-alpha limit, without any standard viscosity, solutions of the PDE converge strongly to weak solutions of the inviscid Burgers equation. We provide numerical evidence that this limit satisfies an entropy inequality for the inviscid Burgers equation. We demonstrate a Hamiltonian structure for the PDE.

Dark gap solitons in exciton-polariton condensates in a periodic potential.

PubMed

Cheng, Szu-Cheng; Chen, Ting-Wei

2018-03-01

We show that dark spatial gap solitons can occur inside the band gap of an exciton-polariton condensate (EPC) in a one-dimensional periodic potential. The energy dispersions of an EPC loaded into a periodic potential show a band-gap structure. Using the effective-mass model of the complex Gross-Pitaevskii equation with pump and dissipation in an EPC in a periodic potential, dark gap solitons are demonstrated near the minimum energy points of the band center and band edge of the first and second bands, respectively. The excitation energies of dark gap solitons are below these minimum points and fall into the band gap. The spatial width of a dark gap soliton becomes smaller as the pump power is increased.

Dark gap solitons in exciton-polariton condensates in a periodic potential

NASA Astrophysics Data System (ADS)

Cheng, Szu-Cheng; Chen, Ting-Wei

2018-03-01

We show that dark spatial gap solitons can occur inside the band gap of an exciton-polariton condensate (EPC) in a one-dimensional periodic potential. The energy dispersions of an EPC loaded into a periodic potential show a band-gap structure. Using the effective-mass model of the complex Gross-Pitaevskii equation with pump and dissipation in an EPC in a periodic potential, dark gap solitons are demonstrated near the minimum energy points of the band center and band edge of the first and second bands, respectively. The excitation energies of dark gap solitons are below these minimum points and fall into the band gap. The spatial width of a dark gap soliton becomes smaller as the pump power is increased.

Stochastic Analysis of Reaction–Diffusion Processes

PubMed Central

Hu, Jifeng; Kang, Hye-Won

2013-01-01

Reaction and diffusion processes are used to model chemical and biological processes over a wide range of spatial and temporal scales. Several routes to the diffusion process at various levels of description in time and space are discussed and the master equation for spatially discretized systems involving reaction and diffusion is developed. We discuss an estimator for the appropriate compartment size for simulating reaction–diffusion systems and introduce a measure of fluctuations in a discretized system. We then describe a new computational algorithm for implementing a modified Gillespie method for compartmental systems in which reactions are aggregated into equivalence classes and computational cells are searched via an optimized tree structure. Finally, we discuss several examples that illustrate the issues that have to be addressed in general systems. PMID:23719732

Lump waves and breather waves for a (3+1)-dimensional generalized Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation for an offshore structure

NASA Astrophysics Data System (ADS)

Yin, Ying; Tian, Bo; Wu, Xiao-Yu; Yin, Hui-Min; Zhang, Chen-Rong

2018-04-01

In this paper, we investigate a (3+1)-dimensional generalized Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation, which describes the fluid flow in the case of an offshore structure. By virtue of the Hirota method and symbolic computation, bilinear forms, the lump-wave and breather-wave solutions are derived. Propagation characteristics and interaction of lump waves and breather waves are graphically discussed. Amplitudes and locations of the lump waves, amplitudes and periods of the breather waves all vary with the wavelengths in the three spatial directions, ratio of the wave amplitude to the depth of water, or product of the depth of water and the relative wavelength along the main direction of propagation. Of the interactions between the lump waves and solitons, there exist two different cases: (i) the energy is transferred from the lump wave to the soliton; (ii) the energy is transferred from the soliton to the lump wave.

The latitudinal structure of Pc 5 waves in space - Magnetic and electric field observations

NASA Technical Reports Server (NTRS)

Singer, H. J.; Kivelson, M. G.

1979-01-01

The occurrence frequency and spatial structure of Pc 5 magnetic pulsations in the dawnside of the plasma trough have been studied using data from the Ogo 5 satellite. The wave magnetic fields were obtained from the University of California, Los Angeles, flux-gate magnetometer measurements, and one component of the wave electric field was inferred from oscillations of the ion flux measured by the Lockheed light ion mass spectrometer. During portions of seven of the 19 passes comprising the survey, Pc 5 oscillations were observed in the ion flux but not in the magnetic field, and in each case the satellite was within 10 deg of the geomagnetic equator. Above 10 deg latitude, transverse magnetic and electric oscillations were both observed. The results are consistent with the model of a standing Alfven wave along a resonant field line with the geomagnetic equator as a node of the magnetic perturbation, that is, an odd mode.

Dissipation-preserving spectral element method for damped seismic wave equations

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai; Wang, Yushun

2017-12-01

This article describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems, which has superior behaviors in long-time stability and dissipation preservation. To reveal the intrinsic dissipative properties of the model equations, we first reformulate the original systems in their equivalent conformal multi-symplectic structures and derive the corresponding conformal symplectic conservation laws. We thereafter separate each system into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed conformal symplectic method. A relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh wave in elastic wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic methods in both the attenuating homogeneous and heterogeneous media.

Uranus - Disk structure within the 7300-A methane band

NASA Technical Reports Server (NTRS)

Price, M. J.; Franz, O. G.

1979-01-01

Orthogonal narrow-band (100 A) photoelectric slit scan photometry of Uranus has been used to infer the basic two-dimensional structure of the disk within the 7300-A methane band. Numerical image reconstruction and restoration techniques have been applied to quantitatively estimate the degrees of polar and limb brightening on the planet. Through partial removal of atmospheric smearing, an effective spatial resolution of approximately 0.9 arcsec has been achieved. Peak polar, limb, and central intensities on the disk are in the respective proportions 3:2:1. In addition, the bright polar feature is displaced from the geometric pole towards the equator of the planet.

Controlling the motion of solitons in 1-D magnonic crystal

NASA Astrophysics Data System (ADS)

Giridharan, D.; Sabareesan, P.; Daniel, M.

2018-04-01

We investigate nonlinear localized magnetic excitations in a simple form of one dimensional magnonic crystal by considering a ferromagnetic medium under periodic applied magnetic field of spatially varying strength. The governing Landau-Lifshitz equation is transformed into nonlinear evolution equation of a complex function through stereographic projection technique. The associated evolution equation numerically solved by using split-step Fourier method (SSFM). From the obtained results it is observed that the excitations appear in the form of solitons and the periodic magnetic field of spatially varying strength perturbs the soliton propagation. Bright and dark soliton solutions are constructed and studied the effect of tuning the strength of spatially periodic applied magnetic field on the nonlinear excitation of magnetization. The results show that the amplitude and velocity of the soliton can be effectively managed by varying the strength of spatially periodic applied magnetic field and it act as periodic potential which provides an additional degree of freedom to control the nature of soliton propagation in a ferromagnetic medium.

Vibration of a spatial elastica constrained inside a straight tube

NASA Astrophysics Data System (ADS)

Chen, Jen-San; Fang, Joyce

2014-04-01

In this paper we study the dynamic behavior of a clamped-clamped spatial elastica under edge thrust constrained inside a straight cylindrical tube. Attention is focused on the calculation of the natural frequencies and mode shapes of the planar and spatial one-point-contact deformations. The main issue in determining the natural frequencies of a constrained rod is the movement of the contact point during vibration. In order to capture the physical essence of the contact-point movement, an Eulerian description of the equations of motion based on director theory is formulated. After proper linearization of the equations of motion, boundary conditions, and contact conditions, the natural frequencies and mode shapes of the elastica can be obtained by solving a system of eighteen first-order differential equations with shooting method. It is concluded that the planar one-point-contact deformation becomes unstable and evolves to a spatial deformation at a bifurcation point in both displacement and force control procedures.

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

NASA Astrophysics Data System (ADS)

Želi, Velibor; Zorica, Dušan

2018-02-01

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

Topics in strong Langmuir turbulence

NASA Technical Reports Server (NTRS)

Nicholson, D. R.

1983-01-01

Progress in two approaches to the study of strong Langmuir turbulence is reported. In two spatial dimensions, numerical solution of the Zakharov equations yields a steady state involving linear growth, linear damping, and a collection of coherent, long-lived entities which might loosely be called solitons. In one spatial dimension, a statistical theory is applied to the cubically nonlinear Schroedinger equation and is solved analytically in a special case.

Topics in strong Langmuir turbulence

NASA Technical Reports Server (NTRS)

Nicholson, D. R.

1982-01-01

Progress in two approaches to the study of strong Langmuir turbulence is reported. In two spatial dimensions, numerical solution of the Zakharov equations yields a steady state involving linear growth, linear damping, and a collection of coherent, long-lived entities which might loosely be called solitons. In one spatial dimension, a statistical theory is applied to the cubically nonlinear Schroedinger equation and is solved analytically in a special case.

Simulation of Vortex Structure in Supersonic Free Shear Layer Using Pse Method

NASA Astrophysics Data System (ADS)

Guo, Xin; Wang, Qiang

The method of parabolized stability equations (PSE) are applied in the analysis of nonlinear stability and the simulation of flow structure in supersonic free shear layer. High accuracy numerical techniques including self-similar basic flow, high order differential method, appropriate transformation and decomposition of nonlinear terms are adopted and developed to solve the PSE effectively for free shear layer. The spatial evolving unstable waves which dominate the flow structure are investigated through nonlinear coupling spatial marching methods. The nonlinear interactions between harmonic waves are further analyzed and instantaneous flow field are obtained by adding the harmonic waves into basic flow. Relevant data agree well with that of DNS. The results demonstrate that T-S wave does not keeping growing exponential as the linear evolution, the energy transfer to high order harmonic modes and finally all harmonic modes get saturation due to the nonlinear interaction; Mean flow distortion is produced by the nonlinear interaction between the harmonic and its conjugate harmonic, makes great change to the average flow and increases the thickness of shear layer; PSE methods can well capture the large scale nonlinear flow structure in the supersonic free shear layer such as vortex roll-up, vortex pairing and nonlinear saturation.

Species richness and biomass explain spatial turnover in ecosystem functioning across tropical and temperate ecosystems.

PubMed

Barnes, Andrew D; Weigelt, Patrick; Jochum, Malte; Ott, David; Hodapp, Dorothee; Haneda, Noor Farikhah; Brose, Ulrich

2016-05-19

Predicting ecosystem functioning at large spatial scales rests on our ability to scale up from local plots to landscapes, but this is highly contingent on our understanding of how functioning varies through space. Such an understanding has been hampered by a strong experimental focus of biodiversity-ecosystem functioning research restricted to small spatial scales. To address this limitation, we investigate the drivers of spatial variation in multitrophic energy flux-a measure of ecosystem functioning in complex communities-at the landscape scale. We use a structural equation modelling framework based on distance matrices to test how spatial and environmental distances drive variation in community energy flux via four mechanisms: species composition, species richness, niche complementarity and biomass. We found that in both a tropical and a temperate study region, geographical and environmental distance indirectly influence species richness and biomass, with clear evidence that these are the dominant mechanisms explaining variability in community energy flux over spatial and environmental gradients. Our results reveal that species composition and trait variability may become redundant in predicting ecosystem functioning at the landscape scale. Instead, we demonstrate that species richness and total biomass may best predict rates of ecosystem functioning at larger spatial scales. © 2016 The Author(s).

A low noise discrete velocity method for the Boltzmann equation with quantized rotational and vibrational energy

NASA Astrophysics Data System (ADS)

Clarke, Peter; Varghese, Philip; Goldstein, David

2018-01-01

A discrete velocity method is developed for gas mixtures of diatomic molecules with both rotational and vibrational energy states. A full quantized model is described, and rotation-translation and vibration-translation energy exchanges are simulated using a Larsen-Borgnakke exchange model. Elastic and inelastic molecular interactions are modeled during every simulated collision to help produce smooth internal energy distributions. The method is verified by comparing simulations of homogeneous relaxation by our discrete velocity method to numerical solutions of the Jeans and Landau-Teller equations, and to direct simulation Monte Carlo. We compute the structure of a 1D shock using this method, and determine how the rotational energy distribution varies with spatial location in the shock and with position in velocity space.

Phase-resolved fluid dynamic forces of a flapping foil energy harvester based on PIV measurements

NASA Astrophysics Data System (ADS)

Liburdy, James

2017-11-01

Two-dimensional particle image velocimetry measurements are performed in a wind tunnel to evaluate the spatial and temporal fluid dynamic forces acting on a flapping foil operating in the energy harvesting regime. Experiments are conducted at reduced frequencies (k = fc/U) of 0.05 - 0.2, pitching angle of, and heaving amplitude of A / c = 0.6. The phase-averaged pressure field is obtained by integrating the pressure Poisson equation. Fluid dynamic forces are then obtained through the integral momentum equation. Results are compared with a simple force model based on the concept of flow impulse. These results help to show the detailed force distributions, their transient nature and aide in understanding the impact of the fluid flow structures that contribute to the power production.

Fully-coupled analysis of jet mixing problems. Part 1. Shock-capturing model, SCIPVIS

NASA Technical Reports Server (NTRS)

Dash, S. M.; Wolf, D. E.

1984-01-01

A computational model, SCIPVIS, is described which predicts the multiple cell shock structure in imperfectly expanded, turbulent, axisymmetric jets. The model spatially integrates the parabolized Navier-Stokes jet mixing equations using a shock-capturing approach in supersonic flow regions and a pressure-split approximation in subsonic flow regions. The regions are coupled using a viscous-characteristic procedure. Turbulence processes are represented via the solution of compressibility-corrected two-equation turbulence models. The formation of Mach discs in the jet and the interactive analysis of the wake-like mixing process occurring behind Mach discs is handled in a rigorous manner. Calculations are presented exhibiting the fundamental interactive processes occurring in supersonic jets and the model is assessed via comparisons with detailed laboratory data for a variety of under- and overexpanded jets.

Developing Vs30 site-condition maps by combining observations with geologic and topographic constraints

USGS Publications Warehouse

Thompson, E.M.; Wald, D.J.

2012-01-01

Despite obvious limitations as a proxy for site amplification, the use of time-averaged shear-wave velocity over the top 30 m (VS30) remains widely practiced, most notably through its use as an explanatory variable in ground motion prediction equations (and thus hazard maps and ShakeMaps, among other applications). As such, we are developing an improved strategy for producing VS30 maps given the common observational constraints. Using the abundant VS30 measurements in Taiwan, we compare alternative mapping methods that combine topographic slope, surface geology, and spatial correlation structure. The different VS30 mapping algorithms are distinguished by the way that slope and geology are combined to define a spatial model of VS30. We consider the globally applicable slope-only model as a baseline to which we compare two methods of combining both slope and geology. For both hybrid approaches, we model spatial correlation structure of the residuals using the kriging-with-a-trend technique, which brings the map into closer agreement with the observations. Cross validation indicates that we can reduce the uncertainty of the VS30 map by up to 16% relative to the slope-only approach.

Exhaustive Classification of the Invariant Solutions for a Specific Nonlinear Model Describing Near Planar and Marginally Long-Wave Unstable Interfaces for Phase Transition

NASA Astrophysics Data System (ADS)

Ahangari, Fatemeh

2018-05-01

Problems of thermodynamic phase transition originate inherently in solidification, combustion and various other significant fields. If the transition region among two locally stable phases is adequately narrow, the dynamics can be modeled by an interface motion. This paper is devoted to exhaustive analysis of the invariant solutions for a modified Kuramoto-Sivashinsky equation in two spatial and one temporal dimensions is presented. This nonlinear partial differential equation asymptotically characterizes near planar interfaces, which are marginally long-wave unstable. For this purpose, by applying the classical symmetry method for this model the classical symmetry operators are attained. Moreover, the structure of the Lie algebra of symmetries is discussed and the optimal system of subalgebras, which yields the preliminary classification of group invariant solutions is constructed. Mainly, the Lie invariants corresponding to the infinitesimal symmetry generators as well as associated similarity reduced equations are also pointed out. Furthermore, the nonclassical symmetries of this nonlinear PDE are also comprehensively investigated.

Congruence Approximations for Entrophy Endowed Hyperbolic Systems

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Saini, Subhash (Technical Monitor)

1998-01-01

Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.

The Fundamental Solution of the Linearized Navier Stokes Equations for Spinning Bodies in Three Spatial Dimensions Time Dependent Case

NASA Astrophysics Data System (ADS)

Thomann, Enrique A.; Guenther, Ronald B.

2006-02-01

Explicit formulae for the fundamental solution of the linearized time dependent Navier Stokes equations in three spatial dimensions are obtained. The linear equations considered in this paper include those used to model rigid bodies that are translating and rotating at a constant velocity. Estimates extending those obtained by Solonnikov in [23] for the fundamental solution of the time dependent Stokes equations, corresponding to zero translational and angular velocity, are established. Existence and uniqueness of solutions of these linearized problems is obtained for a class of functions that includes the classical Lebesgue spaces L p (R 3), 1 < p < ∞. Finally, the asymptotic behavior and semigroup properties of the fundamental solution are established.

Nonlinear Waves.

DTIC Science & Technology

1986-05-27

purposes will be the Korteweg-deVries (KdV) equation u, 6uu, u. , =0 (1) in one spatial dimension, and the Kadomtsev - Petviashvili (KP) equation (u, - 6uu...one temporal dimen- sion: the Modified Kadomtsev - Petviashvili II (MKPII), and Davey-Stewartson I (OSII) equation . The hyperoolic analogs of (1), (2...by introducing ’Ś an intermediate version of the equations associated with (1), an infinite family of conserva- Kadomtsev - Petviashvili equation

From individual spiking neurons to population behavior: Systematic elimination of short-wavelength spatial modes

NASA Astrophysics Data System (ADS)

Steyn-Ross, Moira L.; Steyn-Ross, D. A.

2016-02-01

Mean-field models of the brain approximate spiking dynamics by assuming that each neuron responds to its neighbors via a naive spatial average that neglects local fluctuations and correlations in firing activity. In this paper we address this issue by introducing a rigorous formalism to enable spatial coarse-graining of spiking dynamics, scaling from the microscopic level of a single type 1 (integrator) neuron to a macroscopic assembly of spiking neurons that are interconnected by chemical synapses and nearest-neighbor gap junctions. Spiking behavior at the single-neuron scale ℓ ≈10 μ m is described by Wilson's two-variable conductance-based equations [H. R. Wilson, J. Theor. Biol. 200, 375 (1999), 10.1006/jtbi.1999.1002], driven by fields of incoming neural activity from neighboring neurons. We map these equations to a coarser spatial resolution of grid length B ℓ , with B ≫1 being the blocking ratio linking micro and macro scales. Our method systematically eliminates high-frequency (short-wavelength) spatial modes q ⃗ in favor of low-frequency spatial modes Q ⃗ using an adiabatic elimination procedure that has been shown to be equivalent to the path-integral coarse graining applied to renormalization group theory of critical phenomena. This bottom-up neural regridding allows us to track the percolation of synaptic and ion-channel noise from the single neuron up to the scale of macroscopic population-average variables. Anticipated applications of neural regridding include extraction of the current-to-firing-rate transfer function, investigation of fluctuation criticality near phase-transition tipping points, determination of spatial scaling laws for avalanche events, and prediction of the spatial extent of self-organized macrocolumnar structures. As a first-order exemplar of the method, we recover nonlinear corrections for a coarse-grained Wilson spiking neuron embedded in a network of identical diffusively coupled neurons whose chemical synapses have been disabled. Intriguingly, we find that reblocking transforms the original type 1 Wilson integrator into a type 2 resonator whose spike-rate transfer function exhibits abrupt spiking onset with near-vertical takeoff and chaotic dynamics just above threshold.

Effect of space structures against development of transport infrastructure in Banda Aceh by using the concept of transit oriented development

NASA Astrophysics Data System (ADS)

Noer, Fadhly; Matondang, A. Rahim; Sirojuzilam, Saleh, Sofyan M.

2017-11-01

Due to the shifting of city urban development causing the shift of city services center, so there is a change in space pattern and space structure in Banda Aceh, then resulting urban sprawl which can lead to congestion problem occurs on the arterial road in Banda Aceh, it can be seen from the increasing number of vehicles per year by 6%. Another issue occurs by urban sprawl is not well organized of settlement due to the uncontrolled use of space so that caused grouping or the differences in socioeconomic strata that can impact to the complexity of population mobility problem. From this background problem considered to be solved by a concept that is Transit Oriented Development (TOD), that is a concept of transportation development in co-operation with spatial. This research will get the model of transportation infrastructure development with TOD concept that can handle transportation problem in Banda Aceh, due to change of spatial structure, and to find whether TOD concept can use for the area that has a population in medium density range. The result that is obtained equation so the space structure is: Space Structure = 0.520 + 0.206X3 + 0.264X6 + 0.100X7 and Transportation Infrastructure Development = -1.457 + 0.652X1 + 0.388X5 + 0.235X6 + 0.222X7 + 0.327X8, So results obtained with path analysis method obtained variable influences, node ratio, network connectivity, travel frequency, travel destination, travel cost, and travel time, it has a lower value when direct effect with transportation infrastructure development, but if the indirect effect through the structure of space has a greater influence, can be seen from spatial structure path scheme - transportation infrastructure development.

Generalized Landau Equation for a System with a Self-Consistent Mean Field - Derivation from an N-Particle Liouville Equation

NASA Astrophysics Data System (ADS)

Kandrup, H.

1981-02-01

Assume that the evolution of a system is determined by an N-particle Liouville equation. Suppose, moreover, that the particles which compose the system interact via a long range force like gravity so that the system will be spatially inhomogeneous. In this case, the mean force acting upon a test particle does not vanish, so that one wishes to isolate a self-consistent mean field and distinguish its "systematic" effects from the effects of "fluctuations." This is done here. The time-dependent projection operator formalism of Willis and Picard is used to obtain an exact equation for the time evolution of an appropriately defined one-particle probability density. If one implements the assumption that the "fluctuation" time scale is much shorter than both the relaxation and dynamical time scales, this exact equation can be approximated as a closed Markovian equation. In the limiting case of spatial homogeneity, one recovers precisely the standard Landau equation, which is customarily derived by a stochastic binary-encounter argument. This equation is contrasted with the standard heuristic equation for a mean field theory, as formulated for a Newtonian r-1 gravitational potential in stellar dynamics.

Spatio-temporal dynamics of turbulence trapped in geodesic acoustic modes

NASA Astrophysics Data System (ADS)

Sasaki, M.; Kobayashi, T.; Itoh, K.; Kasuya, N.; Kosuga, Y.; Fujisawa, A.; Itoh, S.-I.

2018-01-01

The spatio-temporal dynamics of turbulence with the interaction of geodesic acoustic modes (GAMs) are investigated, focusing on the phase-space structure of turbulence, where the phase-space consists of real-space and wavenumber-space. Based on the wave-kinetic framework, the coupling equation between the GAM and the turbulence is numerically solved. The turbulence trapped by the GAM velocity field is obtained. Due to the trapping effect, the turbulence intensity increases where the second derivative of the GAM velocity (curvature of the GAM) is negative. While, in the positive-curvature region, the turbulence is suppressed. Since the trapped turbulence propagates with the GAMs, this relationship is sustained spatially and temporally. The dynamics of the turbulence in the wavenumber spectrum are converted in the evolution of the frequency spectrum, and the simulation result is compared with the experimental observation in JFT-2M tokamak, where the similar patterns are obtained. The turbulence trapping effect is a key to understand the spatial structure of the turbulence in the presence of sheared flows.

The Davey-Stewartson Equation on the Half-Plane

NASA Astrophysics Data System (ADS)

Fokas, A. S.

2009-08-01

The Davey-Stewartson (DS) equation is a nonlinear integrable evolution equation in two spatial dimensions. It provides a multidimensional generalisation of the celebrated nonlinear Schrödinger (NLS) equation and it appears in several physical situations. The implementation of the Inverse Scattering Transform (IST) to the solution of the initial-value problem of the NLS was presented in 1972, whereas the analogous problem for the DS equation was solved in 1983. These results are based on the formulation and solution of certain classical problems in complex analysis, namely of a Riemann Hilbert problem (RH) and of either a d-bar or a non-local RH problem respectively. A method for solving the mathematically more complicated but physically more relevant case of boundary-value problems for evolution equations in one spatial dimension, like the NLS, was finally presented in 1997, after interjecting several novel ideas to the panoply of the IST methodology. Here, this method is further extended so that it can be applied to evolution equations in two spatial dimensions, like the DS equation. This novel extension involves several new steps, including the formulation of a d-bar problem for a sectionally non-analytic function, i.e. for a function which has different non-analytic representations in different domains of the complex plane. This, in addition to the computation of a d-bar derivative, also requires the computation of the relevant jumps across the different domains. This latter step has certain similarities (but is more complicated) with the corresponding step for those initial-value problems in two dimensions which can be solved via a non-local RH problem, like KPI.

Global Well-posedness of the Spatially Homogeneous Kolmogorov-Vicsek Model as a Gradient Flow

NASA Astrophysics Data System (ADS)

Figalli, Alessio; Kang, Moon-Jin; Morales, Javier

2018-03-01

We consider the so-called spatially homogenous Kolmogorov-Vicsek model, a non-linear Fokker-Planck equation of self-driven stochastic particles with orientation interaction under the space-homogeneity. We prove the global existence and uniqueness of weak solutions to the equation. We also show that weak solutions exponentially converge to a steady state, which has the form of the Fisher-von Mises distribution.

Linear instability of supersonic plane wakes

NASA Technical Reports Server (NTRS)

Papageorgiou, D. T.

1989-01-01

In this paper we present a theoretical and numerical study of the growth of linear disturbances in the high-Reynolds-number and laminar compressible wake behind a flat plate which is aligned with a uniform stream. No ad hoc assumptions are made as to the nature of the undisturbed flow (in contrast to previous investigations) but instead the theory is developed rationally by use of proper wake-profiles which satisfy the steady equations of motion. The initial growth of near wake perturbation is governed by the compressible Rayleigh equation which is studied analytically for long- and short-waves. These solutions emphasize the asymptotic structures involved and provide a rational basis for a nonlinear development. The evolution of arbitrary wavelength perturbations is addressed numerically and spatial stability solutions are presented that account for the relative importance of the different physical mechanisms present, such as three-dimensionality, increasing Mach numbers enough (subsonic) Mach numbers, there exists a region of absolute instability very close to the trailing-edge with the majority of the wake being convectively unstable. At higher Mach numbers (but still not large-hypersonic) the absolute instability region seems to disappear and the maximum available growth-rates decrease considerably. Three-dimensional perturbations provide the highest spatial growth-rates.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Numerical study on the incompressible Euler equations as a Hamiltonian system: Sectional curvature and Jacobi field

NASA Astrophysics Data System (ADS)

Ohkitani, K.

2010-05-01

We study some of the key quantities arising in the theory of [Arnold "Sur la geometrie differentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluides parfaits," Annales de l'institut Fourier 16, 319 (1966)] of the incompressible Euler equations both in two and three dimensions. The sectional curvatures for the Taylor-Green vortex and the ABC flow initial conditions are calculated exactly in three dimensions. We trace the time evolution of the Jacobi fields by direct numerical simulations and, in particular, see how the sectional curvatures get more and more negative in time. The spatial structure of the Jacobi fields is compared to the vorticity fields by visualizations. The Jacobi fields are found to grow exponentially in time for the flows with negative sectional curvatures. In two dimensions, a family of initial data proposed by Arnold (1966) is considered. The sectional curvature is observed to change its sign quickly even if it starts from a positive value. The Jacobi field is shown to be correlated with the passive scalar gradient in spatial structure. On the basis of Rouchon's physical-space based expression for the sectional curvature (1984), the origin of negative curvature is investigated. It is found that a "potential" αξ appearing in the definition of covariant time derivative plays an important role, in that a rapid growth in its gradient makes a major contribution to the negative curvature.

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

McHugh, P.R.; Ramshaw, J.D.

MAGMA is a FORTRAN computer code designed to viscous flow in in situ vitrification melt pools. It models three-dimensional, incompressible, viscous flow and heat transfer. The momentum equation is coupled to the temperature field through the buoyancy force terms arising from the Boussinesq approximation. All fluid properties, except density, are assumed variable. Density is assumed constant except in the buoyancy force terms in the momentum equation. A simple melting model based on the enthalpy method allows the study of the melt front progression and latent heat effects. An indirect addressing scheme used in the numerical solution of the momentum equationmore » voids unnecessary calculations in cells devoid of liquid. Two-dimensional calculations can be performed using either rectangular or cylindrical coordinates, while three-dimensional calculations use rectangular coordinates. All derivatives are approximated by finite differences. The incompressible Navier-Stokes equations are solved using a new fully implicit iterative technique, while the energy equation is differenced explicitly in time. Spatial derivatives are written in conservative form using a uniform, rectangular, staggered mesh based on the marker and cell placement of variables. Convective terms are differenced using a weighted average of centered and donor cell differencing to ensure numerical stability. Complete descriptions of MAGMA governing equations, numerics, code structure, and code verification are provided. 14 refs.« less

Laws of Large Numbers and Langevin Approximations for Stochastic Neural Field Equations

PubMed Central

2013-01-01

In this study, we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson–Cowan equation can be obtained as the limit in uniform convergence on compacts in probability for a sequence of microscopic models when the number of neuron populations distributed in space and the number of neurons per population tend to infinity. This result also allows to obtain limits for qualitatively different stochastic convergence concepts, e.g., convergence in the mean. Further, we present a central limit theorem for the martingale part of the microscopic models which, suitably re-scaled, converges to a centred Gaussian process with independent increments. These two results provide the basis for presenting the neural field Langevin equation, a stochastic differential equation taking values in a Hilbert space, which is the infinite-dimensional analogue of the chemical Langevin equation in the present setting. On a technical level, we apply recently developed law of large numbers and central limit theorems for piecewise deterministic processes taking values in Hilbert spaces to a master equation formulation of stochastic neuronal network models. These theorems are valid for processes taking values in Hilbert spaces, and by this are able to incorporate spatial structures of the underlying model. Mathematics Subject Classification (2000): 60F05, 60J25, 60J75, 92C20. PMID:23343328

D GIS for Flood Modelling in River Valleys

NASA Astrophysics Data System (ADS)

Tymkow, P.; Karpina, M.; Borkowski, A.

2016-06-01

The objective of this study is implementation of system architecture for collecting and analysing data as well as visualizing results for hydrodynamic modelling of flood flows in river valleys using remote sensing methods, tree-dimensional geometry of spatial objects and GPU multithread processing. The proposed solution includes: spatial data acquisition segment, data processing and transformation, mathematical modelling of flow phenomena and results visualization. Data acquisition segment was based on aerial laser scanning supplemented by images in visible range. Vector data creation was based on automatic and semiautomatic algorithms of DTM and 3D spatial features modelling. Algorithms for buildings and vegetation geometry modelling were proposed or adopted from literature. The implementation of the framework was designed as modular software using open specifications and partially reusing open source projects. The database structure for gathering and sharing vector data, including flood modelling results, was created using PostgreSQL. For the internal structure of feature classes of spatial objects in a database, the CityGML standard was used. For the hydrodynamic modelling the solutions of Navier-Stokes equations in two-dimensional version was implemented. Visualization of geospatial data and flow model results was transferred to the client side application. This gave the independence from server hardware platform. A real-world case in Poland, which is a part of Widawa River valley near Wroclaw city, was selected to demonstrate the applicability of proposed system.

A single spacecraft method to study the spatial profiles inside the magnetopause

NASA Astrophysics Data System (ADS)

Dorville, Nicolas; Belmont, Gerard; Rezeau, Laurence; Aunai, Nicolas; Retino, Alessandro

2013-04-01

Previous magnetopause observations have revealed that the tangential magnetic field often rotates over C-shaped hodograms during the boundary crossing. Using observations of magnetopause crossings by the ESA Cluster mission and a simulation developed at LPP by Nicolas Aunai, we developed a single spacecraft method using the temporal information on the magnetic field in such crossings, complemented by the ion data. We can so obtain a 1D spatial parameter to characterize the depth in the layer and study the structure of the magnetopause as a function of this parameter. This allows using one single spacecraft magnetic data, completed by ion data at large temporal scales, to study the spatial structure of the boundary, and access scales that the particle temporal measurements of the four spacecraft do not permit. To obtain the normal direction and position, we first initialize our computations thanks to the standard MVABC method. Then we use the magnetic field data in the current layer, and suppose it is 1D, rotating in the tangential plane along an ellipse, with an angle variation essentially linear in space, with small sinusoidal perturbations. Making the assumption that the normal velocity of ions is dominated by the motion of the boundary and that the internal structure of the magnetopause is stationary over the duration of a crossing, we can compute the best normal direction and parameters of the model with CIS velocity and FGM magnetic field data, and so derive the spatial position of the spacecraft in the boundary. This method, which has been tested on the simulation data, could be applied successfully on several magnetopause crossings observed by Cluster. It directly gives a thickness and a normal direction, and permits to establish spatial profiles of all the physical quantities inside the boundary. It can be used to better understand the internal structure of the boundary, its physical properties and behavior regarding the flux conservation equations. The obtained results are compared with the results of other methods.

A Least-Squares Transport Equation Compatible with Voids

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

Hansen, Jon; Peterson, Jacob; Morel, Jim

Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transportmore » equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares S n formulation represents an excellent alternative to existing second-order S n transport formulations« less

Dissipative structures induced by spin-transfer torques in nanopillars

NASA Astrophysics Data System (ADS)

León, Alejandro O.; Clerc, Marcel G.; Coulibaly, Saliya

2014-02-01

Macroscopic magnetic systems subjected to external forcing exhibit complex spatiotemporal behaviors as result of dissipative self-organization. Pattern formation from a uniform magnetization state, induced by the combination of a spin-polarized current and an external magnetic field, is studied for spin-transfer nano-oscillator devices. The system is described in the continuous limit by the Landau-Lifshitz-Gilbert equation. The bifurcation diagram of the quintessence parallel state, as a function of the external field and current, is elucidated. We have shown analytically that this state exhibits a spatial supercritical quintic bifurcation, which generates in two spatial dimensions a family of stationary stripes, squares, and superlattice states. Analytically, we have characterized their respective stabilities and bifurcations, which are controlled by a single dimensionless parameter. This scenario is confirmed numerically.

Relativistic numerical cosmology with silent universes

NASA Astrophysics Data System (ADS)

Bolejko, Krzysztof

2018-01-01

Relativistic numerical cosmology is most often based either on the exact solutions of the Einstein equations, or perturbation theory, or weak-field limit, or the BSSN formalism. The silent universe provides an alternative approach to investigate relativistic evolution of cosmological systems. The silent universe is based on the solution of the Einstein equations in 1  +  3 comoving coordinates with additional constraints imposed. These constraints include: the gravitational field is sourced by dust and cosmological constant only, both rotation and magnetic part of the Weyl tensor vanish, and the shear is diagnosable. This paper describes the code simsilun (free software distributed under the terms of the reposi General Public License), which implements the equations of the silent universe. The paper also discusses applications of the silent universe and it uses the Millennium simulation to set up the initial conditions for the code simsilun. The simulation obtained this way consists of 16 777 216 worldlines, which are evolved from z  =  80 to z  =  0. Initially, the mean evolution (averaged over the whole domain) follows the evolution of the background ΛCDM model. However, once the evolution of cosmic structures becomes nonlinear, the spatial curvature evolves from ΩK =0 to ΩK ≈ 0.1 at the present day. The emergence of the spatial curvature is associated with ΩM and Ω_Λ being smaller by approximately 0.05 compared to the ΛCDM.

A Discrete Probability Function Method for the Equation of Radiative Transfer

NASA Technical Reports Server (NTRS)

Sivathanu, Y. R.; Gore, J. P.

1993-01-01

A discrete probability function (DPF) method for the equation of radiative transfer is derived. The DPF is defined as the integral of the probability density function (PDF) over a discrete interval. The derivation allows the evaluation of the PDF of intensities leaving desired radiation paths including turbulence-radiation interactions without the use of computer intensive stochastic methods. The DPF method has a distinct advantage over conventional PDF methods since the creation of a partial differential equation from the equation of transfer is avoided. Further, convergence of all moments of intensity is guaranteed at the basic level of simulation unlike the stochastic method where the number of realizations for convergence of higher order moments increases rapidly. The DPF method is described for a representative path with approximately integral-length scale-sized spatial discretization. The results show good agreement with measurements in a propylene/air flame except for the effects of intermittency resulting from highly correlated realizations. The method can be extended to the treatment of spatial correlations as described in the Appendix. However, information regarding spatial correlations in turbulent flames is needed prior to the execution of this extension.

The effect of the electric wind on the spatial distribution of chemical species in the positive corona discharge

NASA Astrophysics Data System (ADS)

Yanallah, K.; Pontiga, F.; Bouazza, M. R.; Chen, J. H.

2017-08-01

The electrohydrodynamic air flow generated by a positive corona discharge, and its effect on the spatial distribution of chemical species within a wire-plate corona reactor, have been numerically simulated. The computational model is based on the solutions of the Navier-Stokes equation and the continuity equation of each chemical species generated by the electrical discharge. A simplified analytical expression of the electric force density, which only requires the current density as the input parameter, has been used in the Navier-Stokes equation to obtain the velocity field. For the solution of the continuity equations, a plasma chemistry model that includes the most important reactions between electrons, atoms and molecules in air has been used. Similar to the electric force, the electron density distribution has been approximated by using a semi-analytical expression appropriate for the electrode geometry. The results of the study show that the spatial distribution of chemical species can be very different, and depends on the interplay between the electrohydrodynamic flow, the chemical kinetics of the species and its characteristic lifetime.

Modeling animal movements using stochastic differential equations

Treesearch

Haiganoush K. Preisler; Alan A. Ager; Bruce K. Johnson; John G. Kie

2004-01-01

We describe the use of bivariate stochastic differential equations (SDE) for modeling movements of 216 radiocollared female Rocky Mountain elk at the Starkey Experimental Forest and Range in northeastern Oregon. Spatially and temporally explicit vector fields were estimated using approximating difference equations and nonparametric regression techniques. Estimated...

Multidimensional indexing structure for use with linear optimization queries

NASA Technical Reports Server (NTRS)

Bergman, Lawrence David (Inventor); Castelli, Vittorio (Inventor); Chang, Yuan-Chi (Inventor); Li, Chung-Sheng (Inventor); Smith, John Richard (Inventor)

2002-01-01

Linear optimization queries, which usually arise in various decision support and resource planning applications, are queries that retrieve top N data records (where N is an integer greater than zero) which satisfy a specific optimization criterion. The optimization criterion is to either maximize or minimize a linear equation. The coefficients of the linear equation are given at query time. Methods and apparatus are disclosed for constructing, maintaining and utilizing a multidimensional indexing structure of database records to improve the execution speed of linear optimization queries. Database records with numerical attributes are organized into a number of layers and each layer represents a geometric structure called convex hull. Such linear optimization queries are processed by searching from the outer-most layer of this multi-layer indexing structure inwards. At least one record per layer will satisfy the query criterion and the number of layers needed to be searched depends on the spatial distribution of records, the query-issued linear coefficients, and N, the number of records to be returned. When N is small compared to the total size of the database, answering the query typically requires searching only a small fraction of all relevant records, resulting in a tremendous speedup as compared to linearly scanning the entire dataset.

Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis.

PubMed

Faye, Grégory; Rankin, James; Chossat, Pascal

2013-05-01

The existence of spatially localized solutions in neural networks is an important topic in neuroscience as these solutions are considered to characterize working (short-term) memory. We work with an unbounded neural network represented by the neural field equation with smooth firing rate function and a wizard hat spatial connectivity. Noting that stationary solutions of our neural field equation are equivalent to homoclinic orbits in a related fourth order ordinary differential equation, we apply normal form theory for a reversible Hopf bifurcation to prove the existence of localized solutions; further, we present results concerning their stability. Numerical continuation is used to compute branches of localized solution that exhibit snaking-type behaviour. We describe in terms of three parameters the exact regions for which localized solutions persist.

Benchmark solutions for the galactic ion transport equations: Energy and spatially dependent problems

NASA Technical Reports Server (NTRS)

Ganapol, Barry D.; Townsend, Lawrence W.; Wilson, John W.

1989-01-01

Nontrivial benchmark solutions are developed for the galactic ion transport (GIT) equations in the straight-ahead approximation. These equations are used to predict potential radiation hazards in the upper atmosphere and in space. Two levels of difficulty are considered: (1) energy independent, and (2) spatially independent. The analysis emphasizes analytical methods never before applied to the GIT equations. Most of the representations derived have been numerically implemented and compared to more approximate calculations. Accurate ion fluxes are obtained (3 to 5 digits) for nontrivial sources. For monoenergetic beams, both accurate doses and fluxes are found. The benchmarks presented are useful in assessing the accuracy of transport algorithms designed to accommodate more complex radiation protection problems. In addition, these solutions can provide fast and accurate assessments of relatively simple shield configurations.

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

PubMed

Biala, T A; Jator, S N

2015-01-01

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

Data-driven discovery of partial differential equations.

PubMed

Rudy, Samuel H; Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

2017-04-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

Uni-directional optical pulses, temporal propagation, and spatial and temporal dispersion

NASA Astrophysics Data System (ADS)

Kinsler, P.

2018-02-01

I derive a temporally propagated uni-directional optical pulse equation valid in the few cycle limit. Temporal propagation is advantageous because it naturally preserves causality, unlike the competing spatially propagated models. The exact coupled bi-directional equations that this approach generates can be efficiently approximated down to a uni-directional form in cases where an optical pulse changes little over one optical cycle. They also permit a direct term-to-term comparison of the exact bi-directional theory with its corresponding approximate uni-directional theory. Notably, temporal propagation handles dispersion in a different way, and this difference serves to highlight existing approximations inherent in spatially propagated treatments of dispersion. Accordingly, I emphasise the need for future work in clarifying the limitations of the dispersion conversion required by these types of approaches; since the only alternative in the few cycle limit may be to resort to the much more computationally intensive full Maxwell equation solvers.

Simulation of light in-coupling through an aperture probe to investigate light propagation in a thin layer for opto-electronic application

NASA Astrophysics Data System (ADS)

Ermes, Markus; Lehnen, Stephan; Cao, Zhao; Bittkau, Karsten; Carius, Reinhard

2015-06-01

In thin optoelectronic devices, like organic light emitting diodes (OLED) or thin-film solar cells (TFSC), light propagation, which is initiated by a local point source, is of particular importance. In OLEDs, light is generated in the layer by the luminescence of single molecules, whereas in TFSCs, light is coupled into the devices by scattering at small surface features. In both applications, light propagation within the active layers has a significant impact on the optical device performance. Scanning near-field optical microscopy (SNOM) using aperture probes is a powerful tool to investigate this propagation with a high spatial resolution. Dual-probe SNOM allows simulating the local light generation by an illumination probe as well as the detection of the light propagated through the layer. In our work, we focus on the light propagation in thin silicon films as used in thin-film silicon solar cells. We investigate the light-in-coupling from an illuminating probe via rigorous solution of Maxwell's equations using a Finite-Difference Time-Domain approach, especially to gain insight into the light distribution inside a thin layer, which is not accessible in the experiment. The structures investigated include at and structured surfaces with varying illumination positions and wavelengths. From the performed simulations, we define a "spatial sensitivity" which is characteristic for the local structure and illumination position. This quantity can help to identify structures which are beneficial as well as detrimental to absorption inside the investigated layer. We find a strong dependence of the spatial sensitivity on the surface structure as well as both the absorption coefficient and the probe position. Furthermore, we investigate inhomogeneity in local light propagation resulting from different surface structures and illumination positions.

Dynamics of focused femtosecond laser pulse during photodisruption of crystalline lens

NASA Astrophysics Data System (ADS)

Gupta, Pradeep Kumar; Singh, Ram Kishor; Sharma, R. P.

2018-04-01

Propagation of laser pulses of femtosecond time duration (focused through a focusing lens inside the crystalline lens) has been investigated in this paper. Transverse beam diffraction, group velocity dispersion, graded refractive index structure of the crystalline lens, self-focusing, and photodisruption in which plasma is formed due to the high intensity of laser pulses through multiphoton ionization have been taken into account. The model equations are the modified nonlinear Schrödinger equation along with a rate equation that takes care of plasma generation. A close analysis of model equations suggests that the femtosecond laser pulse duration is critical to the breakdown in the lens. Our numerical simulations reveal that the combined effect of self-focusing and multiphoton ionization provides the breakdown threshold. During the focusing of femtosecond laser pulses, additional spatial pulse splitting arises along with temporal splitting. This splitting of laser pulses arises on account of self-focusing, laser induced breakdown, and group velocity distribution, which modifies the shape of laser pulses. The importance of the present study in cavitation bubble generation to improve the elasticity of the eye lens has also been discussed in this paper.

Numerical Study of Nonlinear Structures of Locally Excited Marangoni Convection in the Long-Wave Approximation

NASA Astrophysics Data System (ADS)

Wertgeim, Igor I.

2018-02-01

We investigate stationary and non-stationary solutions of nonlinear equations of the long-wave approximation for the Marangoni convection caused by a localized source of heat or a surface active impurity (surfactant) in a thin horizontal layer of a viscous incompressible fluid with a free surface. The distribution of heat or concentration flux is determined by the uniform vertical gradient of temperature or impurity concentration, distorted by the imposition of a slightly inhomogeneous heating or of surfactant, localized in the horizontal plane. The lower boundary of the layer is considered thermally insulated or impermeable, whereas the upper boundary is free and deformable. The equations obtained in the long-wave approximation are formulated in terms of the amplitudes of the temperature distribution or impurity concentration, deformation of the surface, and vorticity. For a simplification of the problem, a sequence of nonlinear equations is obtained, which in the simplest form leads to a nonlinear Schrödinger equation with a localized potential. The basic state of the system, its dependence on the parameters and stability are investigated. For stationary solutions localized in the region of the surface tension inhomogeneity, domains of parameters corresponding to different spatial patterns are delineated.

Influence of magnetic pressure on stellar structure: A Mechanism for solar variability

NASA Technical Reports Server (NTRS)

Schatten, K. H.; Endal, A. S.

1980-01-01

A physical mechanism is proposed that couples the Sun's dynamo magnetic field to its gravitational potential energy. The mechanism involves the isotropic field pressure resulting in a lifting force on the convective envelope, thereby raising its potential energy. Decay of the field due to solar activity allows the envelop to subside and releases this energy, which can augment the otherwise steady solar luminosity. Equations are developed and applied to the Sun for several field configurations. The best estimate model suggests that uniform luminosity variations as large as 0.02% for half a sunspot cycle may occur. Brief temporal variations or the rotation of spatial structures could allow larger excursions in the energy released.

Theory of Metastable State Relaxation for Non-Critical Binary Systems with Non-Conserved Order Parameter

NASA Technical Reports Server (NTRS)

Izmailov, Alexander; Myerson, Allan S.

1993-01-01

A new mathematical ansatz for a solution of the time-dependent Ginzburg-Landau non-linear partial differential equation is developed for non-critical systems such as non-critical binary solutions (solute + solvent) described by the non-conserved scalar order parameter. It is demonstrated that in such systems metastability initiates heterogeneous solute redistribution which results in formation of the non-equilibrium singly-periodic spatial solute structure. It is found how the time-dependent period of this structure evolves in time. In addition, the critical radius r(sub c) for solute embryo of the new solute rich phase together with the metastable state lifetime t(sub c) are determined analytically and analyzed.

Poisson structure on a space with linear SU(2) fuzziness

NASA Astrophysics Data System (ADS)

Khorrami, Mohammad; Fatollahi, Amir H.; Shariati, Ahmad

2009-07-01

The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which the counterpart of the angular momentum as well as the Euler parametrization of the phase space are introduced. SU(2)-invariant classical systems are discussed, and it is observed that the path of particle can be obtained by the solution of a first-order equation, as the case with such models on commutative spaces. The examples of free particle, rotationally invariant potentials, and specially the isotropic harmonic oscillator are investigated in more detail.

Accelerated orbits in black hole fields: the static case

NASA Astrophysics Data System (ADS)

Bini, Donato; de Felice, Fernando; Geralico, Andrea

2011-11-01

We study non-geodesic orbits of test particles endowed with a structure, assuming the Schwarzschild spacetime as background. We develop a formalism which allows one to recognize the geometrical characterization of those orbits in terms of their Frenet-Serret parameters and apply it to explicit cases as those of spatially circular orbits which witness the equilibrium under conflicting types of interactions. In our general analysis, we solve the equations of motion offering a detailed picture of the dynamics having in mind a check with a possible astronomical setup. We focus on certain ambiguities which plague the interpretation of the measurements preventing one from identifying the particular structure carried by the particle.

Shock-capturing parabolized Navier-Stokes model /SCIPVIS/ for the analysis of turbulent underexpanded jets

NASA Technical Reports Server (NTRS)

Dash, S. M.; Wolf, D. E.

1983-01-01

A new computational model, SCIPVIS, has been developed to predict the multiple-cell wave/shock structure in under or over-expanded turbulent jets. SCIPVIS solves the parabolized Navier-Stokes jet mixing equations utilizing a shock-capturing approach in supersonic regions of the jet and a pressure-split approach in subsonic regions. Turbulence processes are represented by the solution of compressibility corrected two-equation turbulence models. The formation of Mach discs in the jet and the interactive turbulent mixing process occurring behind the disc are handled in a detailed fashion. SCIPVIS presently analyzes jets exhausting into a quiescent or supersonic external stream for which a single-pass spatial marching solution can be obtained. The iterative coupling of SCIPVIS with a potential flow solver for the analysis of subsonic/transonic external streams is under development.

Treatment of late time instabilities in finite-difference EMP scattering codes

NASA Astrophysics Data System (ADS)

Simpson, L. T.; Holland, R.; Arman, S.

1982-12-01

Constraints applicable to a finite difference mesh for solution of Maxwell's equations are defined. The equations are applied in the time domain for computing electromagnetic coupling to complex structures, e.g., rectangular, cylindrical, or spherical. In a spatially varying grid, the amplitude growth of high frequency waves becomes exponential through multiple reflections from the outer boundary in cases of late-time solution. The exponential growth of the numerical noise exceeds the value of the real signal. The correction technique employs an absorbing surface and a radiating boundary, along with tailored selection of the grid mesh size. High frequency noise is removed through use of a low-pass digital filter, a linear least squares fit is made to thy low frequency filtered response, and the original, filtered, and fitted data are merged to preserve the high frequency early-time response.

OpenCMISS: a multi-physics & multi-scale computational infrastructure for the VPH/Physiome project.

PubMed

Bradley, Chris; Bowery, Andy; Britten, Randall; Budelmann, Vincent; Camara, Oscar; Christie, Richard; Cookson, Andrew; Frangi, Alejandro F; Gamage, Thiranja Babarenda; Heidlauf, Thomas; Krittian, Sebastian; Ladd, David; Little, Caton; Mithraratne, Kumar; Nash, Martyn; Nickerson, David; Nielsen, Poul; Nordbø, Oyvind; Omholt, Stig; Pashaei, Ali; Paterson, David; Rajagopal, Vijayaraghavan; Reeve, Adam; Röhrle, Oliver; Safaei, Soroush; Sebastián, Rafael; Steghöfer, Martin; Wu, Tim; Yu, Ting; Zhang, Heye; Hunter, Peter

2011-10-01

The VPH/Physiome Project is developing the model encoding standards CellML (cellml.org) and FieldML (fieldml.org) as well as web-accessible model repositories based on these standards (models.physiome.org). Freely available open source computational modelling software is also being developed to solve the partial differential equations described by the models and to visualise results. The OpenCMISS code (opencmiss.org), described here, has been developed by the authors over the last six years to replace the CMISS code that has supported a number of organ system Physiome projects. OpenCMISS is designed to encompass multiple sets of physical equations and to link subcellular and tissue-level biophysical processes into organ-level processes. In the Heart Physiome project, for example, the large deformation mechanics of the myocardial wall need to be coupled to both ventricular flow and embedded coronary flow, and the reaction-diffusion equations that govern the propagation of electrical waves through myocardial tissue need to be coupled with equations that describe the ion channel currents that flow through the cardiac cell membranes. In this paper we discuss the design principles and distributed memory architecture behind the OpenCMISS code. We also discuss the design of the interfaces that link the sets of physical equations across common boundaries (such as fluid-structure coupling), or between spatial fields over the same domain (such as coupled electromechanics), and the concepts behind CellML and FieldML that are embodied in the OpenCMISS data structures. We show how all of these provide a flexible infrastructure for combining models developed across the VPH/Physiome community. Copyright © 2011 Elsevier Ltd. All rights reserved.

Solving the Vlasov equation in two spatial dimensions with the Schrödinger method

NASA Astrophysics Data System (ADS)

Kopp, Michael; Vattis, Kyriakos; Skordis, Constantinos

2017-12-01

We demonstrate that the Vlasov equation describing collisionless self-gravitating matter may be solved with the so-called Schrödinger method (ScM). With the ScM, one solves the Schrödinger-Poisson system of equations for a complex wave function in d dimensions, rather than the Vlasov equation for a 2 d -dimensional phase space density. The ScM also allows calculating the d -dimensional cumulants directly through quasilocal manipulations of the wave function, avoiding the complexity of 2 d -dimensional phase space. We perform for the first time a quantitative comparison of the ScM and a conventional Vlasov solver in d =2 dimensions. Our numerical tests were carried out using two types of cold cosmological initial conditions: the classic collapse of a sine wave and those of a Gaussian random field as commonly used in cosmological cold dark matter N-body simulations. We compare the first three cumulants, that is, the density, velocity and velocity dispersion, to those obtained by solving the Vlasov equation using the publicly available code ColDICE. We find excellent qualitative and quantitative agreement between these codes, demonstrating the feasibility and advantages of the ScM as an alternative to N-body simulations. We discuss, the emergence of effective vorticity in the ScM through the winding number around the points where the wave function vanishes. As an application we evaluate the background pressure induced by the non-linearity of large scale structure formation, thereby estimating the magnitude of cosmological backreaction. We find that it is negligibly small and has time dependence and magnitude compatible with expectations from the effective field theory of large scale structure.

Simulations of spray autoignition and flame establishment with two-dimensional CMC

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

Wright, Y.M.; Boulouchos, K.; De Paola, G.

2005-12-01

The unsteady two-dimensional conditional moment closure (CMC) model with first-order closure of the chemistry and supplied with standard models for the conditional convection and turbulent diffusion terms has been interfaced with a commercial engine CFD code and analyzed with two numerical methods, an 'exact' calculation with the method of lines and a faster fractional-step method. The aim was to examine the sensitivity of the predictions to the operator splitting errors and to identify the extent to which spatial transport terms are important for spray autoignition problems. Despite the underlying simplifications, solution of the full CMC equations allows a single modelmore » to be used for the autoignition, flame propagation ('premixed mode'), and diffusion flame mode of diesel combustion, which makes CMC a good candidate model for practical engine calculations. It was found that (i) the conditional averages have significant spatial gradients before ignition and during the premixed mode and (ii) that the inclusion of physical-space transport affects the calculation of the autoignition delay time, both of which suggest that volume-averaged CMC approaches may be inappropriate for diesel-like problems. A balance of terms in the CMC equation before and after autoignition shows the relative magnitude of spatial transport and allows conjectures on the structure of the premixed phase of diesel combustion. Very good agreement with available experimental data is found concerning ignition delays and the effect of background air turbulence on them.« less

Two types of nonlinear wave equations for diffractive beams in bubbly liquids with nonuniform bubble number density.

PubMed

Kanagawa, Tetsuya

2015-05-01

This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set.

Simultaneous reconstruction of 3D refractive index, temperature, and intensity distribution of combustion flame by double computed tomography technologies based on spatial phase-shifting method

NASA Astrophysics Data System (ADS)

Guo, Zhenyan; Song, Yang; Yuan, Qun; Wulan, Tuya; Chen, Lei

2017-06-01

In this paper, a transient multi-parameter three-dimensional (3D) reconstruction method is proposed to diagnose and visualize a combustion flow field. Emission and transmission tomography based on spatial phase-shifted technology are combined to reconstruct, simultaneously, the various physical parameter distributions of a propane flame. Two cameras triggered by the internal trigger mode capture the projection information of the emission and moiré tomography, respectively. A two-step spatial phase-shifting method is applied to extract the phase distribution in the moiré fringes. By using the filtered back-projection algorithm, we reconstruct the 3D refractive-index distribution of the combustion flow field. Finally, the 3D temperature distribution of the flame is obtained from the refractive index distribution using the Gladstone-Dale equation. Meanwhile, the 3D intensity distribution is reconstructed based on the radiation projections from the emission tomography. Therefore, the structure and edge information of the propane flame are well visualized.

Spatial operator algebra framework for multibody system dynamics

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Jain, Abhinandan; Kreutz, K.

1989-01-01

The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.

Spatial Operator Algebra for multibody system dynamics

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Jain, A.; Kreutz-Delgado, K.

1992-01-01

The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.

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.

Fractional power-law spatial dispersion in electrodynamics

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

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru; Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife; Trujillo, Juan J., E-mail: jtrujill@ullmat.es

2013-07-15

Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb’s law and Debye’s screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type. -- Highlights: •Plasma-like non-local media with power-law spatial dispersion. •Fractional differential equations for electric fields in the media. •The generalizations of Coulomb’s lawmore » and Debye’s screening for the media.« less

The impact of forest structure and spatial scale on the relationship between ground plot above ground biomass and GEDI lidar waveforms

NASA Astrophysics Data System (ADS)

Armston, J.; Marselis, S.; Hancock, S.; Duncanson, L.; Tang, H.; Kellner, J. R.; Calders, K.; Disney, M.; Dubayah, R.

2017-12-01

The NASA Global Ecosystem Dynamics Investigation (GEDI) will place a multi-beam waveform lidar instrument on the International Space Station (ISS) to provide measurements of forest vertical structure globally. These measurements of structure will underpin empirical modelling of above ground biomass density (AGBD) at the scale of individual GEDI lidar footprints (25m diameter). The GEDI pre-launch calibration strategy for footprint level models relies on linking AGBD estimates from ground plots with GEDI lidar waveforms simulated from coincident discrete return airborne laser scanning data. Currently available ground plot data have variable and often large uncertainty at the spatial resolution of GEDI footprints due to poor colocation, allometric model error, sample size and plot edge effects. The relative importance of these sources of uncertainty partly depends on the quality of ground measurements and region. It is usually difficult to know the magnitude of these uncertainties a priori so a common approach to mitigate their influence on model training is to aggregate ground plot and waveform lidar data to a coarser spatial scale (0.25-1ha). Here we examine the impacts of these principal sources of uncertainty using a 3D simulation approach. Sets of realistic tree models generated from terrestrial laser scanning (TLS) data or parametric modelling matched to tree inventory data were assembled from four contrasting forest plots across tropical rainforest, deciduous temperate forest, and sclerophyll eucalypt woodland sites. These tree models were used to simulate geometrically explicit 3D scenes with variable tree density, size class and spatial distribution. GEDI lidar waveforms are simulated over ground plots within these scenes using monte carlo ray tracing, allowing the impact of varying ground plot and waveform colocation error, forest structure and edge effects on the relationship between ground plot AGBD and GEDI lidar waveforms to be directly assessed. We quantify the sensitivity of calibration equations relating GEDI lidar structure measurements and AGBD to these factors at a range of spatial scales (0.0625-1ha) and discuss the implications for the expanding use of existing in situ ground plot data by GEDI.

Theoretical aspects of tidal and planetary wave propagation at thermospheric heights

NASA Technical Reports Server (NTRS)

Volland, H.; Mayr, H. G.

1977-01-01

A simple semiquantitative model is presented which allows analytic solutions of tidal and planetary wave propagation at thermospheric heights. This model is based on perturbation approximation and mode separation. The effects of viscosity and heat conduction are parameterized by Rayleigh friction and Newtonian cooling. Because of this simplicity, one gains a clear physical insight into basic features of atmospheric wave propagation. In particular, we discuss the meridional structures of pressure and horizontal wind (the solutions of Laplace's equation) and their modification due to dissipative effects at thermospheric heights. Furthermore, we solve the equations governing the height structure of the wave modes and arrive at a very simple asymptotic solution valid in the upper part of the thermosphere. That 'system transfer function' of the thermosphere allows one to estimate immediately the reaction of the thermospheric wave mode parameters such as pressure, temperature, and winds to an external heat source of arbitrary temporal and spatial distribution. Finally, the diffusion effects of the minor constituents due to the global wind circulation are discussed, and some results of numerical calculations are presented.

MPI parallelization of Vlasov codes for the simulation of nonlinear laser-plasma interactions

NASA Astrophysics Data System (ADS)

Savchenko, V.; Won, K.; Afeyan, B.; Decyk, V.; Albrecht-Marc, M.; Ghizzo, A.; Bertrand, P.

2003-10-01

The simulation of optical mixing driven KEEN waves [1] and electron plasma waves [1] in laser-produced plasmas require nonlinear kinetic models and massive parallelization. We use Massage Passing Interface (MPI) libraries and Appleseed [2] to solve the Vlasov Poisson system of equations on an 8 node dual processor MAC G4 cluster. We use the semi-Lagrangian time splitting method [3]. It requires only row-column exchanges in the global data redistribution, minimizing the total number of communications between processors. Recurrent communication patterns for 2D FFTs involves global transposition. In the Vlasov-Maxwell case, we use splitting into two 1D spatial advections and a 2D momentum advection [4]. Discretized momentum advection equations have a double loop structure with the outer index being assigned to different processors. We adhere to a code structure with separate routines for calculations and data management for parallel computations. [1] B. Afeyan et al., IFSA 2003 Conference Proceedings, Monterey, CA [2] V. K. Decyk, Computers in Physics, 7, 418 (1993) [3] Sonnendrucker et al., JCP 149, 201 (1998) [4] Begue et al., JCP 151, 458 (1999)

Reynolds number and settling velocity influence for finite-release particle-laden gravity currents in a basin

NASA Astrophysics Data System (ADS)

Francisco, E. P.; Espath, L. F. R.; Laizet, S.; Silvestrini, J. H.

2018-01-01

Three-dimensional highly resolved Direct Numerical Simulations (DNS) of particle-laden gravity currents are presented for the lock-exchange problem in an original basin configuration, similar to delta formation in lakes. For this numerical study, we focus on gravity currents over a flat bed for which density differences are small enough for the Boussinesq approximation to be valid. The concentration of particles is described in an Eulerian fashion by using a transport equation combined with the incompressible Navier-Stokes equations, with the possibility of particles deposition but no erosion nor re-suspension. The focus of this study is on the influence of the Reynolds number and settling velocity on the development of the current which can freely evolve in the streamwise and spanwise direction. It is shown that the settling velocity has a strong influence on the spatial extent of the current, the sedimentation rate, the suspended mass and the shape of the lobe-and-cleft structures while the Reynolds number is mainly affecting the size and number of vortical structures at the front of the current, and the energy budget.

Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system

NASA Astrophysics Data System (ADS)

Avitabile, D.; Desroches, M.; Knobloch, E.; Krupa, M.

2017-11-01

A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of solutions describing the possible location of stationary fronts are identified, whose origin is traced to the onset of convective and absolute instability when the system is unbounded. The former are present only for non-zero upstream boundary conditions and provide a quantitative understanding of noise-sustained structures in systems of this type. The latter correspond to the onset of a global mode and are present even with zero upstream boundary conditions. The role of canard trajectories in the nonlinear transition between these states is clarified and the stability properties of the resulting spatial structures are determined. Front location in the convective regime is highly sensitive to the upstream boundary condition, and its dependence on this boundary condition is studied using a combination of numerical continuation and Monte Carlo simulations of the partial differential equation. Statistical properties of the system subjected to random or stochastic boundary conditions at the inlet are interpreted using the deterministic slow-fast spatial dynamical system.

Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system.

PubMed

Avitabile, D; Desroches, M; Knobloch, E; Krupa, M

2017-11-01

A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of solutions describing the possible location of stationary fronts are identified, whose origin is traced to the onset of convective and absolute instability when the system is unbounded. The former are present only for non-zero upstream boundary conditions and provide a quantitative understanding of noise-sustained structures in systems of this type. The latter correspond to the onset of a global mode and are present even with zero upstream boundary conditions. The role of canard trajectories in the nonlinear transition between these states is clarified and the stability properties of the resulting spatial structures are determined. Front location in the convective regime is highly sensitive to the upstream boundary condition, and its dependence on this boundary condition is studied using a combination of numerical continuation and Monte Carlo simulations of the partial differential equation. Statistical properties of the system subjected to random or stochastic boundary conditions at the inlet are interpreted using the deterministic slow-fast spatial dynamical system.

A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohammed A.

2014-09-01

In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach

Fast wavelet based algorithms for linear evolution equations

NASA Technical Reports Server (NTRS)

Engquist, Bjorn; Osher, Stanley; Zhong, Sifen

1992-01-01

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

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

Rofouie, P.; Rey, A. D., E-mail: alejandro.rey@mail.mcgill.ca; Pasini, D.

Periodic surface nano-wrinkling is found throughout biological liquid crystalline materials, such as collagen films, spider silk gland ducts, exoskeleton of beetles, and flower petals. These surface ultrastructures are responsible for structural colors observed in some beetles and plants that can dynamically respond to external conditions, such as humidity and temperature. In this paper, the formation of the surface undulations is investigated through the interaction of anisotropic interfacial tension, swelling through hydration, and capillarity at free surfaces. Focusing on the cellulosic cholesteric liquid crystal (CCLC) material model, the generalized shape equation for anisotropic interfaces using the Cahn-Hoffman capillarity vector and themore » Rapini-Papoular anchoring energy are applied to analyze periodic nano-wrinkling in plant-based plywood free surfaces with water-induced cholesteric pitch gradients. Scaling is used to derive the explicit relations between the undulations’ amplitude expressed as a function of the anchoring strength and the spatially varying pitch. The optical responses of the periodic nano-structured surfaces are studied through finite difference time domain simulations indicating that CCLC surfaces with spatially varying pitch reflect light in a wavelength higher than that of a CCLC’s surface with constant pitch. This structural color change is controlled by the pitch gradient through hydration. All these findings provide a foundation to understand structural color phenomena in nature and for the design of optical sensor devices.« less

Potential and flux field landscape theory. I. Global stability and dynamics of spatially dependent non-equilibrium systems.

PubMed

Wu, Wei; Wang, Jin

2013-09-28

We established a potential and flux field landscape theory to quantify the global stability and dynamics of general spatially dependent non-equilibrium deterministic and stochastic systems. We extended our potential and flux landscape theory for spatially independent non-equilibrium stochastic systems described by Fokker-Planck equations to spatially dependent stochastic systems governed by general functional Fokker-Planck equations as well as functional Kramers-Moyal equations derived from master equations. Our general theory is applied to reaction-diffusion systems. For equilibrium spatially dependent systems with detailed balance, the potential field landscape alone, defined in terms of the steady state probability distribution functional, determines the global stability and dynamics of the system. The global stability of the system is closely related to the topography of the potential field landscape in terms of the basins of attraction and barrier heights in the field configuration state space. The effective driving force of the system is generated by the functional gradient of the potential field alone. For non-equilibrium spatially dependent systems, the curl probability flux field is indispensable in breaking detailed balance and creating non-equilibrium condition for the system. A complete characterization of the non-equilibrium dynamics of the spatially dependent system requires both the potential field and the curl probability flux field. While the non-equilibrium potential field landscape attracts the system down along the functional gradient similar to an electron moving in an electric field, the non-equilibrium flux field drives the system in a curly way similar to an electron moving in a magnetic field. In the small fluctuation limit, the intrinsic potential field as the small fluctuation limit of the potential field for spatially dependent non-equilibrium systems, which is closely related to the steady state probability distribution functional, is found to be a Lyapunov functional of the deterministic spatially dependent system. Therefore, the intrinsic potential landscape can characterize the global stability of the deterministic system. The relative entropy functional of the stochastic spatially dependent non-equilibrium system is found to be the Lyapunov functional of the stochastic dynamics of the system. Therefore, the relative entropy functional quantifies the global stability of the stochastic system with finite fluctuations. Our theory offers an alternative general approach to other field-theoretic techniques, to study the global stability and dynamics of spatially dependent non-equilibrium field systems. It can be applied to many physical, chemical, and biological spatially dependent non-equilibrium systems.

Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations

NASA Astrophysics Data System (ADS)

Zlotnik, A. A.

2017-04-01

The multidimensional quasi-gasdynamic system written in the form of mass, momentum, and total energy balance equations for a perfect polytropic gas with allowance for a body force and a heat source is considered. A new conservative symmetric spatial discretization of these equations on a nonuniform rectangular grid is constructed (with the basic unknown functions—density, velocity, and temperature—defined on a common grid and with fluxes and viscous stresses defined on staggered grids). Primary attention is given to the analysis of entropy behavior: the discretization is specially constructed so that the total entropy does not decrease. This is achieved via a substantial revision of the standard discretization and applying numerous original features. A simplification of the constructed discretization serves as a conservative discretization with nondecreasing total entropy for the simpler quasi-hydrodynamic system of equations. In the absence of regularizing terms, the results also hold for the Navier-Stokes equations of a viscous compressible heat-conducting gas.

Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma

DOE PAGES

Scullard, Christian R.; Belt, Andrew P.; Fennell, Susan C.; ...

2016-09-01

We present a numerical solution of the quantum Lenard-Balescu equation using a spectral method, namely an expansion in Laguerre polynomials. This method exactly conserves both particles and kinetic energy and facilitates the integration over the dielectric function. To demonstrate the method, we solve the equilibration problem for a spatially homogeneous one-component plasma with various initial conditions. Unlike the more usual Landau/Fokker-Planck system, this method requires no input Coulomb logarithm; the logarithmic terms in the collision integral arise naturally from the equation along with the non-logarithmic order-unity terms. The spectral method can also be used to solve the Landau equation andmore » a quantum version of the Landau equation in which the integration over the wavenumber requires only a lower cutoff. We solve these problems as well and compare them with the full Lenard-Balescu solution in the weak-coupling limit. Finally, we discuss the possible generalization of this method to include spatial inhomogeneity and velocity anisotropy.« less

Boundary-driven anomalous spirals in oscillatory media

NASA Astrophysics Data System (ADS)

Kessler, David A.; Levine, Herbert

2017-06-01

We study a heretofore ignored class of spiral patterns in oscillatory media as characterized by the complex Landau-Ginzburg model. These spirals emerge from modulating the growth rate as a function of r, thereby turning off the instability at large r. They are uniquely determined by matching to this outer condition, lifting a degeneracy in the set of steady-state solutions of the original equations. Unlike the well-studied spiral which acts as a wave source, has a simple core structure and is insensitive to the details of the boundary on which no-flux conditions are imposed, these new spirals are wave sinks, have non-monotonic wavefront curvature near the core, and can be patterned by the form of the spatial boundary. We predict that these anomalous spirals could be produced in nonlinear optics experiments via spatially modulating the gain of the medium.

Large Spatial and Temporal Separations of Cause and Effect in Policy Making - Dealing with Non-linear Effects

NASA Astrophysics Data System (ADS)

McCaskill, John

There can be large spatial and temporal separation of cause and effect in policy making. Determining the correct linkage between policy inputs and outcomes can be highly impractical in the complex environments faced by policy makers. In attempting to see and plan for the probable outcomes, standard linear models often overlook, ignore, or are unable to predict catastrophic events that only seem improbable due to the issue of multiple feedback loops. There are several issues with the makeup and behaviors of complex systems that explain the difficulty many mathematical models (factor analysis/structural equation modeling) have in dealing with non-linear effects in complex systems. This chapter highlights those problem issues and offers insights to the usefulness of ABM in dealing with non-linear effects in complex policy making environments.

A Tour Through Shape Dynamic Black Holes

NASA Astrophysics Data System (ADS)

Herczeg, Gabriel

Shape dynamics is a classical theory of gravity which agrees with general relativity in many important cases, but possesses different gauge symmetries and constraints. Rather than spacetime diffeomorphism invariance, shape dynamics takes spatial diffeomorphism invariance and spatial Weyl invariance as the fundamental gauge symmetries associated with the gravitational field. Despite these differences, shape dynamics and general relativity generically predict the same dynamics--there exist gauge-fixings of each theory that ensure agreement with the other. However, these gauge-fixing conditions are not necessarily globally well-defined and it is therefore possible to find solutions of the shape dynamics equations of motion that agree with general relativity on some open neighborhoods, but which have different global structures. In particular, the black hole solutions of the two theories disagree globally. Understanding these novel "shape dynamic black holes" is the primary goal of this thesis.

Pair correlation function and nonlinear kinetic equation for a spatially uniform polarizable nonideal plasma

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

Belyi, V.V.; Kukharenko, Y.A.; Wallenborn, J.

Taking into account the first non-Markovian correction to the Balescu-Lenard equation, we have derived an expression for the pair correlation function and a nonlinear kinetic equation valid for a nonideal polarized classical plasma. This last equation allows for the description of the correlational energy evolution and shows the global conservation of energy with dynamical polarization. {copyright} {ital 1996 The American Physical Society.}

Data-driven discovery of partial differential equations

PubMed Central

Rudy, Samuel H.; Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

2017-01-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg–de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable. PMID:28508044

Stochasticity in numerical solutions of the nonlinear Schroedinger equation

NASA Technical Reports Server (NTRS)

Shen, Mei-Mei; Nicholson, D. R.

1987-01-01

The cubically nonlinear Schroedinger equation is an important model of nonlinear phenomena in fluids and plasmas. Numerical solutions in a spatially periodic system commonly involve truncation to a finite number of Fourier modes. These solutions are found to be stochastic in the sense that the largest Liapunov exponent is positive. As the number of modes is increased, the size of this exponent appears to converge to zero, in agreement with the recent demonstration of the integrability of the spatially periodic case.

A double expansion method for the frequency response of finite-length beams with periodic parameters

NASA Astrophysics Data System (ADS)

Ying, Z. G.; Ni, Y. Q.

2017-03-01

A double expansion method for the frequency response of finite-length beams with periodic distribution parameters is proposed. The vibration response of the beam with spatial periodic parameters under harmonic excitations is studied. The frequency response of the periodic beam is the function of parametric period and then can be expressed by the series with the product of periodic and non-periodic functions. The procedure of the double expansion method includes the following two main steps: first, the frequency response function and periodic parameters are expanded by using identical periodic functions based on the extension of the Floquet-Bloch theorem, and the period-parametric differential equation for the frequency response is converted into a series of linear differential equations with constant coefficients; second, the solutions to the linear differential equations are expanded by using modal functions which satisfy the boundary conditions, and the linear differential equations are converted into algebraic equations according to the Galerkin method. The expansion coefficients are obtained by solving the algebraic equations and then the frequency response function is finally determined. The proposed double expansion method can uncouple the effects of the periodic expansion and modal expansion so that the expansion terms are determined respectively. The modal number considered in the second expansion can be reduced remarkably in comparison with the direct expansion method. The proposed double expansion method can be extended and applied to the other structures with periodic distribution parameters for dynamics analysis. Numerical results on the frequency response of the finite-length periodic beam with various parametric wave numbers and wave amplitude ratios are given to illustrate the effective application of the proposed method and the new frequency response characteristics, including the parameter-excited modal resonance, doubling-peak frequency response and remarkable reduction of the maximum frequency response for certain parametric wave number and wave amplitude. The results have the potential application to structural vibration control.

Spatial solitons and stability in the one-dimensional and the two-dimensional generalized nonlinear Schrödinger equation with fourth-order diffraction and parity-time-symmetric potentials

NASA Astrophysics Data System (ADS)

Tiofack, C. G. L.; Ndzana, F., II; Mohamadou, A.; Kofane, T. C.

2018-03-01

We investigate the existence and stability of solitons in parity-time (PT )-symmetric optical media characterized by a generic complex hyperbolic refractive index distribution and fourth-order diffraction (FOD). For the linear case, we demonstrate numerically that the FOD parameter can alter the PT -breaking points. For nonlinear cases, the exact analytical expressions of the localized modes are obtained both in one- and two-dimensional nonlinear Schrödinger equations with self-focusing and self-defocusing Kerr nonlinearity. The effect of FOD on the stability structure of these localized modes is discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. Examples of stable and unstable solutions are given. The transverse power flow density associated with these localized modes is also discussed. It is found that the relative strength of the FOD coefficient can utterly change the direction of the power flow, which may be used to control the energy exchange among gain or loss regions.

A coupling method for a cardiovascular simulation model which includes the Kalman filter.

PubMed

Hasegawa, Yuki; Shimayoshi, Takao; Amano, Akira; Matsuda, Tetsuya

2012-01-01

Multi-scale models of the cardiovascular system provide new insight that was unavailable with in vivo and in vitro experiments. For the cardiovascular system, multi-scale simulations provide a valuable perspective in analyzing the interaction of three phenomenons occurring at different spatial scales: circulatory hemodynamics, ventricular structural dynamics, and myocardial excitation-contraction. In order to simulate these interactions, multiscale cardiovascular simulation systems couple models that simulate different phenomena. However, coupling methods require a significant amount of calculation, since a system of non-linear equations must be solved for each timestep. Therefore, we proposed a coupling method which decreases the amount of calculation by using the Kalman filter. In our method, the Kalman filter calculates approximations for the solution to the system of non-linear equations at each timestep. The approximations are then used as initial values for solving the system of non-linear equations. The proposed method decreases the number of iterations required by 94.0% compared to the conventional strong coupling method. When compared with a smoothing spline predictor, the proposed method required 49.4% fewer iterations.

A Second Order Semi-Discrete Cosserat Rod Model Suitable for Dynamic Simulations in Real Time

NASA Astrophysics Data System (ADS)

Lang, Holger; Linn, Joachim

2009-09-01

We present an alternative approach for a semi-discrete viscoelastic Cosserat rod model that allows both fast dynamic computations within milliseconds and accurate results compared to detailed finite element solutions. The model is able to represent extension, shearing, bending and torsion. For inner dissipation, a consistent damping potential from Antman is chosen. The continuous equations of motion, which consist a system of nonlinear hyperbolic partial differential algebraic equations, are derived from a two dimensional variational principle. The semi-discrete balance equations are obtained by spatial finite difference schemes on a staggered grid and standard index reduction techniques. The right-hand side of the model and its Jacobian can be chosen free of higher algebraic (e.g. root) or transcendent (e.g. trigonometric or exponential) functions and is therefore extremely cheap to evaluate numerically. For the time integration of the system, we use well established stiff solvers. As our model yields computational times within milliseconds, it is suitable for interactive manipulation. It reflects structural mechanics solutions sufficiently correct, as comparison with detailed finite element results shows.

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady

1990-01-01

A new computer code was developed to solve the 2-D or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating-direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 3 is the Programmer's Reference, and describes the program structure, the FORTRAN variables stored in common blocks, and the details of each subprogram.

2.5-D poroelastic wave modelling in double porosity media

NASA Astrophysics Data System (ADS)

Liu, Xu; Greenhalgh, Stewart; Wang, Yanghua

2011-09-01

To approximate seismic wave propagation in double porosity media, the 2.5-D governing equations of poroelastic waves are developed and numerically solved. The equations are obtained by taking a Fourier transform in the strike or medium-invariant direction over all of the field quantities in the 3-D governing equations. The new memory variables from the Zener model are suggested as a way to represent the sum of the convolution integrals for both the solid particle velocity and the macroscopic fluid flux in the governing equations. By application of the memory equations, the field quantities at every time step need not be stored. However, this approximation allows just two Zener relaxation times to represent the very complex double porosity and dual permeability attenuation mechanism, and thus reduce the difficulty. The 2.5-D governing equations are numerically solved by a time-splitting method for the non-stiff parts and an explicit fourth-order Runge-Kutta method for the time integration and a Fourier pseudospectral staggered-grid for handling the spatial derivative terms. The 2.5-D solution has the advantage of producing a 3-D wavefield (point source) for a 2-D model but is much more computationally efficient than the full 3-D solution. As an illustrative example, we firstly show the computed 2.5-D wavefields in a homogeneous single porosity model for which we reformulated an analytic solution. Results for a two-layer, water-saturated double porosity model and a laterally heterogeneous double porosity structure are also presented.

Tunable nano-wrinkling of chiral surfaces: Structure and diffraction optics

NASA Astrophysics Data System (ADS)

Rofouie, P.; Pasini, D.; Rey, A. D.

2015-09-01

Periodic surface nano-wrinkling is found throughout biological liquid crystalline materials, such as collagen films, spider silk gland ducts, exoskeleton of beetles, and flower petals. These surface ultrastructures are responsible for structural colors observed in some beetles and plants that can dynamically respond to external conditions, such as humidity and temperature. In this paper, the formation of the surface undulations is investigated through the interaction of anisotropic interfacial tension, swelling through hydration, and capillarity at free surfaces. Focusing on the cellulosic cholesteric liquid crystal (CCLC) material model, the generalized shape equation for anisotropic interfaces using the Cahn-Hoffman capillarity vector and the Rapini-Papoular anchoring energy are applied to analyze periodic nano-wrinkling in plant-based plywood free surfaces with water-induced cholesteric pitch gradients. Scaling is used to derive the explicit relations between the undulations' amplitude expressed as a function of the anchoring strength and the spatially varying pitch. The optical responses of the periodic nano-structured surfaces are studied through finite difference time domain simulations indicating that CCLC surfaces with spatially varying pitch reflect light in a wavelength higher than that of a CCLC's surface with constant pitch. This structural color change is controlled by the pitch gradient through hydration. All these findings provide a foundation to understand structural color phenomena in nature and for the design of optical sensor devices.

Interaction of spatially separated oscillating solitons in biased two-photon photorefractive materials

NASA Astrophysics Data System (ADS)

Asif, Noushin; Biswas, Anjan; Jovanoski, Z.; Konar, S.

2015-01-01

This paper presents the dynamics of two spatially separated optical solitons in two-photon photorefractive materials. The variational formalism has been employed to derive evolution equations of different parameters which characterize the dynamics of two interacting solitons. This approach yields a system of coupled ordinary differential equations for evolution of different parameters characterizing solitons such as amplitude, spatial width, chirp, center of gravity, etc., which have been subsequently solved adopting numerical method to extract information on their dynamics. Depending on their initial separation and power, solitons are shown to either disperse or compresses individually and attract each other. Dragging and trapping of a probe soliton by another pump have been discussed.

Macroscopic momentum and mechanical energy equations for incompressible single-phase flow in porous media.

PubMed

Paéz-García, Catherine Teresa; Valdés-Parada, Francisco J; Lasseux, Didier

2017-02-01

Modeling flow in porous media is usually focused on the governing equations for mass and momentum transport, which yield the velocity and pressure at the pore or Darcy scales. However, in many applications, it is important to determine the work (or power) needed to induce flow in porous media, and this can be achieved when the mechanical energy equation is taken into account. At the macroscopic scale, this equation may be postulated to be the result of the inner product of Darcy's law and the seepage velocity. However, near the porous medium boundaries, this postulate seems questionable due to the spatial variations of the effective properties (velocity, permeability, porosity, etc.). In this work we derive the macroscopic mechanical energy equation using the method of volume averaging for the simple case of incompressible single-phase flow in porous media. Our analysis shows that the result of averaging the pore-scale version of the mechanical energy equation at the Darcy scale is not, in general, the expected product of Darcy's law and the seepage velocity. As a matter of fact, this result is only applicable in the bulk region of the porous medium and, in the derivation of this result, the properties of the permeability tensor are determinant. Furthermore, near the porous medium boundaries, a more novel version of the mechanical energy equation is obtained, which incorporates additional terms that take into account the rapid variations of structural properties taking place in this particular portion of the system. This analysis can be applied to multiphase and compressible flows in porous media and in many other multiscale systems.

Long-time asymptotic solution structure of Camassa-Holm equation subject to an initial condition with non-zero reflection coefficient of the scattering data

NASA Astrophysics Data System (ADS)

Chang, Chueh-Hsin; Yu, Ching-Hao; Sheu, Tony Wen-Hann

2016-10-01

In this article, we numerically revisit the long-time solution behavior of the Camassa-Holm equation ut - uxxt + 2ux + 3uux = 2uxuxx + uuxxx. The finite difference solution of this integrable equation is sought subject to the newly derived initial condition with Delta-function potential. Our underlying strategy of deriving a numerical phase accurate finite difference scheme in time domain is to reduce the numerical dispersion error through minimization of the derived discrepancy between the numerical and exact modified wavenumbers. Additionally, to achieve the goal of conserving Hamiltonians in the completely integrable equation of current interest, a symplecticity-preserving time-stepping scheme is developed. Based on the solutions computed from the temporally symplecticity-preserving and the spatially wavenumber-preserving schemes, the long-time asymptotic CH solution characters can be accurately depicted in distinct regions of the space-time domain featuring with their own quantitatively very different solution behaviors. We also aim to numerically confirm that in the two transition zones their long-time asymptotics can indeed be described in terms of the theoretically derived Painlevé transcendents. Another attempt of this study is to numerically exhibit a close connection between the presently predicted finite-difference solution and the solution of the Painlevé ordinary differential equation of type II in two different transition zones.

Plasma bubble monitoring by TEC map and 630 nm airglow image

NASA Astrophysics Data System (ADS)

Takahashi, H.; Wrasse, C. M.; Otsuka, Y.; Ivo, A.; Gomes, V.; Paulino, I.; Medeiros, A. F.; Denardini, C. M.; Sant'Anna, N.; Shiokawa, K.

2015-08-01

Equatorial ionosphere plasma bubbles over the South American continent were successfully observed by mapping the total electron content (TECMAP) using data provided by ground-based GNSS receiver networks. The TECMAP could cover almost all of the continent within ~4000 km distance in longitude and latitude, monitoring TEC variability continuously with a time resolution of 10 min. Simultaneous observations of OI 630 nm all-sky image at Cachoeira Paulista (22.7°S, 45.0°W) and Cariri (7.4°S, 36.5°W) were used to compare the bubble structures. The spatial resolution of the TECMAP varied from 50 km to 1000 km, depending on the density of the observation sites. On the other hand, optical imaging has a spatial resolution better than 15 km, depicting the fine structure of the bubbles but covering a limited area (~1600 km diameter). TECMAP has an advantage in its spatial coverage and the continuous monitoring (day and night) form. The initial phase of plasma depletion in the post-sunset equatorial ionization anomaly (PS-EIA) trough region, followed by development of plasma bubbles in the crest region, could be monitored in a progressive way over the magnetic equator. In December 2013 to January 2014, periodically spaced bubble structures were frequently observed. The longitudinal spacing between the bubbles was around 600-800 km depending on the day. The periodic form of plasma bubbles may suggest a seeding process related to the solar terminator passage in the ionosphere.

Stability and Interaction of Coherent Structure in Supersonic Reactive Wakes

NASA Technical Reports Server (NTRS)

Menon, Suresh

1983-01-01

A theoretical formulation and analysis is presented for a study of the stability and interaction of coherent structure in reacting free shear layers. The physical problem under investigation is a premixed hydrogen-oxygen reacting shear layer in the wake of a thin flat plate. The coherent structure is modeled as a periodic disturbance and its stability is determined by the application of linearized hydrodynamic stability theory which results in a generalized eigenvalue problem for reactive flows. Detailed stability analysis of the reactive wake for neutral, symmetrical and antisymmetrical disturbance is presented. Reactive stability criteria is shown to be quite different from classical non-reactive stability. The interaction between the mean flow, coherent structure and fine-scale turbulence is theoretically formulated using the von-Kaman integral technique. Both time-averaging and conditional phase averaging are necessary to separate the three types of motion. The resulting integro-differential equations can then be solved subject to initial conditions with appropriate shape functions. In the laminar flow transition region of interest, the spatial interaction between the mean motion and coherent structure is calculated for both non-reactive and reactive conditions and compared with experimental data wherever available. The fine-scale turbulent motion determined by the application of integral analysis to the fluctuation equations. Since at present this turbulence model is still untested, turbulence is modeled in the interaction problem by a simple algebraic eddy viscosity model. The applicability of the integral turbulence model formulated here is studied parametrically by integrating these equations for the simple case of self-similar mean motion with assumed shape functions. The effect of the motion of the coherent structure is studied and very good agreement is obtained with previous experimental and theoretical works for non-reactive flow. For the reactive case, lack of experimental data made direct comparison difficult. It was determined that the growth rate of the disturbance amplitude is lower for reactive case. The results indicate that the reactive flow stability is in qualitative agreement with experimental observation.

Time Parallel Solution of Linear Partial Differential Equations on the Intel Touchstone Delta Supercomputer

NASA Technical Reports Server (NTRS)

Toomarian, N.; Fijany, A.; Barhen, J.

1993-01-01

Evolutionary partial differential equations are usually solved by decretization in time and space, and by applying a marching in time procedure to data and algorithms potentially parallelized in the spatial domain.

Turbulent solutions of equations of fluid motion

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1985-01-01

Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence, such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations the initially nonrandom flow develops into an apparently random turbulence. The cases considered include turbulence that is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.

Filtering of non-linear instabilities. [from finite difference solution of fluid dynamics equations

NASA Technical Reports Server (NTRS)

Khosla, P. K.; Rubin, S. G.

1979-01-01

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown here that these problems can in fact be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate 'filtering' can reduce the intensity of these oscillations and in some cases possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and non-conservation differencing. The entire spectrum of filtered equations retains a three-point character as well as second-order spatial accuracy. Burgers equation has been considered as a model. Several filters are examined in detail, and smooth solutions have been obtained for extremely large cell Reynolds numbers.

Random scalar fields and hyperuniformity

NASA Astrophysics Data System (ADS)

Ma, Zheng; Torquato, Salvatore

2017-06-01

Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystals and liquids. Hyperuniform systems have attracted recent attention because they are endowed with novel transport and optical properties. Recently, the hyperuniformity concept has been generalized to characterize two-phase media, scalar fields, and random vector fields. In this paper, we devise methods to explicitly construct hyperuniform scalar fields. Specifically, we analyze spatial patterns generated from Gaussian random fields, which have been used to model the microwave background radiation and heterogeneous materials, the Cahn-Hilliard equation for spinodal decomposition, and Swift-Hohenberg equations that have been used to model emergent pattern formation, including Rayleigh-Bénard convection. We show that the Gaussian random scalar fields can be constructed to be hyperuniform. We also numerically study the time evolution of spinodal decomposition patterns and demonstrate that they are hyperuniform in the scaling regime. Moreover, we find that labyrinth-like patterns generated by the Swift-Hohenberg equation are effectively hyperuniform. We show that thresholding (level-cutting) a hyperuniform Gaussian random field to produce a two-phase random medium tends to destroy the hyperuniformity of the progenitor scalar field. We then propose guidelines to achieve effectively hyperuniform two-phase media derived from thresholded non-Gaussian fields. Our investigation paves the way for new research directions to characterize the large-structure spatial patterns that arise in physics, chemistry, biology, and ecology. Moreover, our theoretical results are expected to guide experimentalists to synthesize new classes of hyperuniform materials with novel physical properties via coarsening processes and using state-of-the-art techniques, such as stereolithography and 3D printing.

Computing aerodynamic sound using advanced statistical turbulence theories

NASA Technical Reports Server (NTRS)

Hecht, A. M.; Teske, M. E.; Bilanin, A. J.

1981-01-01

It is noted that the calculation of turbulence-generated aerodynamic sound requires knowledge of the spatial and temporal variation of Q sub ij (xi sub k, tau), the two-point, two-time turbulent velocity correlations. A technique is presented to obtain an approximate form of these correlations based on closure of the Reynolds stress equations by modeling of higher order terms. The governing equations for Q sub ij are first developed for a general flow. The case of homogeneous, stationary turbulence in a unidirectional constant shear mean flow is then assumed. The required closure form for Q sub ij is selected which is capable of qualitatively reproducing experimentally observed behavior. This form contains separation time dependent scale factors as parameters and depends explicitly on spatial separation. The approximate forms of Q sub ij are used in the differential equations and integral moments are taken over the spatial domain. The velocity correlations are used in the Lighthill theory of aerodynamic sound by assuming normal joint probability.

Discrete Variational Approach for Modeling Laser-Plasma Interactions

NASA Astrophysics Data System (ADS)

Reyes, J. Paxon; Shadwick, B. A.

2014-10-01

The traditional approach for fluid models of laser-plasma interactions begins by approximating fields and derivatives on a grid in space and time, leading to difference equations that are manipulated to create a time-advance algorithm. In contrast, by introducing the spatial discretization at the level of the action, the resulting Euler-Lagrange equations have particular differencing approximations that will exactly satisfy discrete versions of the relevant conservation laws. For example, applying a spatial discretization in the Lagrangian density leads to continuous-time, discrete-space equations and exact energy conservation regardless of the spatial grid resolution. We compare the results of two discrete variational methods using the variational principles from Chen and Sudan and Brizard. Since the fluid system conserves energy and momentum, the relative errors in these conserved quantities are well-motivated physically as figures of merit for a particular method. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY-1104683.

An Efficient Solution Method for Multibody Systems with Loops Using Multiple Processors

NASA Technical Reports Server (NTRS)

Ghosh, Tushar K.; Nguyen, Luong A.; Quiocho, Leslie J.

2015-01-01

This paper describes a multibody dynamics algorithm formulated for parallel implementation on multiprocessor computing platforms using the divide-and-conquer approach. The system of interest is a general topology of rigid and elastic articulated bodies with or without loops. The algorithm divides the multibody system into a number of smaller sets of bodies in chain or tree structures, called "branches" at convenient joints called "connection points", and uses an Order-N (O (N)) approach to formulate the dynamics of each branch in terms of the unknown spatial connection forces. The equations of motion for the branches, leaving the connection forces as unknowns, are implemented in separate processors in parallel for computational efficiency, and the equations for all the unknown connection forces are synthesized and solved in one or several processors. The performances of two implementations of this divide-and-conquer algorithm in multiple processors are compared with an existing method implemented on a single processor.

A stochastic-dynamic model for global atmospheric mass field statistics

NASA Technical Reports Server (NTRS)

Ghil, M.; Balgovind, R.; Kalnay-Rivas, E.

1981-01-01

A model that yields the spatial correlation structure of atmospheric mass field forecast errors was developed. The model is governed by the potential vorticity equation forced by random noise. Expansion in spherical harmonics and correlation function was computed analytically using the expansion coefficients. The finite difference equivalent was solved using a fast Poisson solver and the correlation function was computed using stratified sampling of the individual realization of F(omega) and hence of phi(omega). A higher order equation for gamma was derived and solved directly in finite differences by two successive applications of the fast Poisson solver. The methods were compared for accuracy and efficiency and the third method was chosen as clearly superior. The results agree well with the latitude dependence of observed atmospheric correlation data. The value of the parameter c sub o which gives the best fit to the data is close to the value expected from dynamical considerations.

Numerical simulation of turbulence in the presence of shear

NASA Technical Reports Server (NTRS)

Shaanan, S.; Ferziger, J. H.; Reynolds, W. C.

1975-01-01

The numerical calculations are presented of the large eddy structure of turbulent flows, by use of the averaged Navier-Stokes equations, where averages are taken over spatial regions small compared to the size of the computational grid. The subgrid components of motion are modeled by a local eddy-viscosity model. A new finite-difference scheme is proposed to represent the nonlinear average advective term which has fourth-order accuracy. This scheme exhibits several advantages over existing schemes with regard to the following: (1) the scheme is compact as it extends only one point away in each direction from the point to which it is applied; (2) it gives better resolution for high wave-number waves in the solution of Poisson equation, and (3) it reduces programming complexity and computation time. Examples worked out in detail are the decay of isotropic turbulence, homogeneous turbulent shear flow, and homogeneous turbulent shear flow with system rotation.

Inhomogeneous cosmology and backreaction: Current status and future prospects

NASA Astrophysics Data System (ADS)

Bolejko, Krzysztof; Korzyński, Mikołaj

Astronomical observations reveal hierarchical structures in the universe, from galaxies, groups of galaxies, clusters and superclusters, to filaments and voids. On the largest scales, it seems that some kind of statistical homogeneity can be observed. As a result, modern cosmological models are based on spatially homogeneous and isotropic solutions of the Einstein equations, and the evolution of the universe is approximated by the Friedmann equations. In parallel to standard homogeneous cosmology, the field of inhomogeneous cosmology and backreaction is being developed. This field investigates whether small scale inhomogeneities via nonlinear effects can backreact and alter the properties of the universe on its largest scales, leading to a non-Friedmannian evolution. This paper presents the current status of inhomogeneous cosmology and backreaction. It also discusses future prospects of the field of inhomogeneous cosmology, which is based on a survey of 50 academics working in the field of inhomogeneous cosmology.

Patterns induced by super cross-diffusion in a predator-prey system with Michaelis-Menten type harvesting.

PubMed

Liu, Biao; Wu, Ranchao; Chen, Liping

2018-04-01

Turing instability and pattern formation in a super cross-diffusion predator-prey system with Michaelis-Menten type predator harvesting are investigated. Stability of equilibrium points is first explored with or without super cross-diffusion. It is found that cross-diffusion could induce instability of equilibria. To further derive the conditions of Turing instability, the linear stability analysis is carried out. From theoretical analysis, note that cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, we derive amplitude equations near the Turing bifurcation point for the excited modes by means of weakly nonlinear theory. Dynamical analysis of the amplitude equations interprets the structural transitions and stability of various forms of Turing patterns. Furthermore, the theoretical results are illustrated via numerical simulations. Copyright © 2018. Published by Elsevier Inc.

Multiscale Analysis of Rapidly Rotating Dynamo Simulations

NASA Astrophysics Data System (ADS)

Orvedahl, R.; Calkins, M. A.; Featherstone, N. A.

2017-12-01

The magnetic field of the planets and stars are generated by dynamo action in their electrically conducting fluid interiors. Numerical models of this process solve the fundamental equations of magnetohydrodynamics driven by convection in a rotating spherical shell. Rotation plays an important role in modifying the resulting convective flows and the self-generated magnetic field. We present results of simulating rapidly rotating systems that are unstable to dynamo action. We use the pseudo-spectral code Rayleigh to generate a suite of direct numerical simulations. Each simulation uses the Boussinesq approximation and is characterized by an Ekman number (Ek=ν /Ω L2) of 10-5. We vary the degree of convective forcing to obtain a range of convective Rossby numbers. The resulting flows and magnetic structures are analyzed using a Reynolds decomposition. We determine the relative importance of each term in the scale-separated governing equations and estimate the relevant spatial scales responsible for generating the mean magnetic field.

Probability and Cumulative Density Function Methods for the Stochastic Advection-Reaction Equation

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

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

We present a cumulative density function (CDF) method for the probabilistic analysis of $d$-dimensional advection-dominated reactive transport in heterogeneous media. We employ a probabilistic approach in which epistemic uncertainty on the spatial heterogeneity of Darcy-scale transport coefficients is modeled in terms of random fields with given correlation structures. Our proposed CDF method employs a modified Large-Eddy-Diffusivity (LED) approach to close and localize the nonlocal equations governing the one-point PDF and CDF of the concentration field, resulting in a $(d + 1)$ dimensional PDE. Compared to the classsical LED localization, the proposed modified LED localization explicitly accounts for the mean-field advectivemore » dynamics over the phase space of the PDF and CDF. To illustrate the accuracy of the proposed closure, we apply our CDF method to one-dimensional single-species reactive transport with uncertain, heterogeneous advection velocities and reaction rates modeled as random fields.« less

Mean-field approach to evolving spatial networks, with an application to osteocyte network formation

NASA Astrophysics Data System (ADS)

Taylor-King, Jake P.; Basanta, David; Chapman, S. Jonathan; Porter, Mason A.

2017-07-01

We consider evolving networks in which each node can have various associated properties (a state) in addition to those that arise from network structure. For example, each node can have a spatial location and a velocity, or it can have some more abstract internal property that describes something like a social trait. Edges between nodes are created and destroyed, and new nodes enter the system. We introduce a "local state degree distribution" (LSDD) as the degree distribution at a particular point in state space. We then make a mean-field assumption and thereby derive an integro-partial differential equation that is satisfied by the LSDD. We perform numerical experiments and find good agreement between solutions of the integro-differential equation and the LSDD from stochastic simulations of the full model. To illustrate our theory, we apply it to a simple model for osteocyte network formation within bones, with a view to understanding changes that may take place during cancer. Our results suggest that increased rates of differentiation lead to higher densities of osteocytes, but with a smaller number of dendrites. To help provide biological context, we also include an introduction to osteocytes, the formation of osteocyte networks, and the role of osteocytes in bone metastasis.

TRUMP; transient and steady state temperature distribution. [IBM360,370; CDC7600; FORTRAN IV (95%) and BAL (5%) (IBM); FORTRAN IV (CDC)

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

Elrod, D.C.; Turner, W.D.

TRUMP solves a general nonlinear parabolic partial differential equation describing flow in various kinds of potential fields, such as fields of temperature, pressure, or electricity and magnetism; simultaneously, it will solve two additional equations representing, in thermal problems, heat production by decomposition of two reactants having rate constants with a general Arrhenius temperature dependence. Steady-state and transient flow in one, two, or three dimensions are considered in geometrical configurations having simple or complex shapes and structures. Problem parameters may vary with spatial position, time, or primary dependent variables--temperature, pressure, or field strength. Initial conditions may vary with spatial position, andmore » among the criteria that may be specified for ending a problem are upper and lower limits on the size of the primary dependent variable, upper limits on the problem time or on the number of time-steps or on the computer time, and attainment of steady state.IBM360,370;CDC7600; FORTRAN IV (95%) and BAL (5%) (IBM); FORTRAN IV (CDC); OS/360 (IBM360), OS/370 (IBM370), SCOPE 2.1.5 (CDC7600); As dimensioned, the program requires 400K bytes of storage on an IBM370 and 145,100 (octal) words on a CDC7600.« less

Propagation characteristics of optical fiber structures with arbitrary shape and index variation

NASA Technical Reports Server (NTRS)

Manshadi, F.

1990-01-01

The application of the scalar wave-fast Fourier transform (SW-FFT) technique to the computation of the propagation characteristics of some complex optical fiber structures is presented. The SW-FFT technique is based on the numerical solution of the scalar wave equation by a forward-marching fast Fourier transform method. This solution yields the spatial configuration of the fields as well as its modal characteristics in and around the guiding structure. The following are treated by the SW-FFT method: analysis of coupled optical fibers and computation of their odd and even modes and coupling length; the solution of tapered optical waveguides (transitions) and the study of the effect of the slope of the taper on mode conversion; and the analysis of branching optical fibers and demonstration of their mode-filtering and/or power-dividing properties.

Nonlinear Wave Propagation.

DTIC Science & Technology

1987-11-23

e.g. the Kadomtsev - Petviashvili . Davey-Stewartson, and three-wave interaction equations -see for example the review [11]). little progress has been made... equations for our purposes will be the Korteweg-deVries (KdV) equation u, - 6uu., + u, =0 ( ) in one spatial dimension, and the Kadomtsev - Petviashvili (KP...similarities with KP [4] than with u, =sin u, (2) KdV (the IST for (5) has been recently considered and the Kadomtsev - Petviashvili (KP) equation in ref. [ 5

Symplectic partitioned Runge-Kutta scheme for Maxwell's equations

NASA Astrophysics Data System (ADS)

Huang, Zhi-Xiang; Wu, Xian-Liang

Using the symplectic partitioned Runge-Kutta (PRK) method, we construct a new scheme for approximating the solution to infinite dimensional nonseparable Hamiltonian systems of Maxwell's equations for the first time. The scheme is obtained by discretizing the Maxwell's equations in the time direction based on symplectic PRK method, and then evaluating the equation in the spatial direction with a suitable finite difference approximation. Several numerical examples are presented to verify the efficiency of the scheme.

Spectral refractive index assessment of turbid samples by combining spatial frequency near-infrared spectroscopy with Kramers-Kronig analysis

NASA Astrophysics Data System (ADS)

Meitav, Omri; Shaul, Oren; Abookasis, David

2018-03-01

A practical algorithm for estimating the wavelength-dependent refractive index (RI) of a turbid sample in the spatial frequency domain with the aid of Kramers-Kronig (KK) relations is presented. In it, phase-shifted sinusoidal patterns (structured illumination) are serially projected at a high spatial frequency onto the sample surface (mouse scalp) at different near-infrared wavelengths while a camera mounted normally to the sample surface captures the reflected diffuse light. In the offline analysis pipeline, recorded images at each wavelength are converted to spatial absorption maps by logarithmic function, and once the absorption coefficient information is obtained, the imaginary part (k) of the complex RI (CRI), based on Maxell's equations, can be calculated. Using the data represented by k, the real part of the CRI (n) is then resolved by KK analysis. The wavelength dependence of n ( λ ) is then fitted separately using four standard dispersion models: Cornu, Cauchy, Conrady, and Sellmeier. In addition, three-dimensional surface-profile distribution of n is provided based on phase profilometry principles and a phase-unwrapping-based phase-derivative-variance algorithm. Experimental results demonstrate the capability of the proposed idea for sample's determination of a biological sample's RI value.

Eigenvectors phase correction in inverse modal problem

NASA Astrophysics Data System (ADS)

Qiao, Guandong; Rahmatalla, Salam

2017-12-01

The solution of the inverse modal problem for the spatial parameters of mechanical and structural systems is heavily dependent on the quality of the modal parameters obtained from the experiments. While experimental and environmental noises will always exist during modal testing, the resulting modal parameters are expected to be corrupted with different levels of noise. A novel methodology is presented in this work to mitigate the errors in the eigenvectors when solving the inverse modal problem for the spatial parameters. The phases of the eigenvector component were utilized as design variables within an optimization problem that minimizes the difference between the calculated and experimental transfer functions. The equation of motion in terms of the modal and spatial parameters was used as a constraint in the optimization problem. Constraints that reserve the positive and semi-positive definiteness and the inter-connectivity of the spatial matrices were implemented using semi-definite programming. Numerical examples utilizing noisy eigenvectors with augmented Gaussian white noise of 1%, 5%, and 10% were used to demonstrate the efficacy of the proposed method. The results showed that the proposed method is superior when compared with a known method in the literature.

Filtering of non-linear instabilities

NASA Technical Reports Server (NTRS)

Khosla, P. K.; Rubin, S. G.

1978-01-01

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown that these problems can be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate filtering can reduce the intensity of these oscillations and possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and nonconservation differencing. The entire spectrum of filtered equations retains a three point character as well as second order spatial accuracy. Burgers equation was considered as a model.

Imaging of turbulent structures and tomographic reconstruction of TORPEX plasma emissivity

NASA Astrophysics Data System (ADS)

Iraji, D.; Furno, I.; Fasoli, A.; Theiler, C.

2010-12-01

In the TORPEX [A. Fasoli et al., Phys. Plasmas 13, 055902 (2006)], a simple magnetized plasma device, low frequency electrostatic fluctuations associated with interchange waves, are routinely measured by means of extensive sets of Langmuir probes. To complement the electrostatic probe measurements of plasma turbulence and study of plasma structures smaller than the spatial resolution of probes array, a nonperturbative direct imaging system has been developed on TORPEX, including a fast framing Photron-APX-RS camera and an image intensifier unit. From the line-integrated camera images, we compute the poloidal emissivity profile of the plasma by applying a tomographic reconstruction technique using a pixel method and solving an overdetermined set of equations by singular value decomposition. This allows comparing statistical, spectral, and spatial properties of visible light radiation with electrostatic fluctuations. The shape and position of the time-averaged reconstructed plasma emissivity are observed to be similar to those of the ion saturation current profile. In the core plasma, excluding the electron cyclotron and upper hybrid resonant layers, the mean value of the plasma emissivity is observed to vary with (Te)α(ne)β, in which α =0.25-0.7 and β =0.8-1.4, in agreement with collisional radiative model. The tomographic reconstruction is applied to the fast camera movie acquired with 50 kframes/s rate and 2 μs of exposure time to obtain the temporal evolutions of the emissivity fluctuations. Conditional average sampling is also applied to visualize and measure sizes of structures associated with the interchange mode. The ω-time and the two-dimensional k-space Fourier analysis of the reconstructed emissivity fluctuations show the same interchange mode that is detected in the ω and k spectra of the ion saturation current fluctuations measured by probes. Small scale turbulent plasma structures can be detected and tracked in the reconstructed emissivity movies with the spatial resolution down to 2 cm, well beyond the spatial resolution of the probe array.

Sex Differences in Using Spatial and Verbal Abilities Influence Route Learning Performance in a Virtual Environment: A Comparison of 6- to 12-Year Old Boys and Girls.

PubMed

Merrill, Edward C; Yang, Yingying; Roskos, Beverly; Steele, Sara

2016-01-01

Previous studies have reported sex differences in wayfinding performance among adults. Men are typically better at using Euclidean information and survey strategies while women are better at using landmark information and route strategies. However, relatively few studies have examined sex differences in wayfinding in children. This research investigated relationships between route learning performance and two general abilities: spatial ability and verbal memory in 153 boys and girls between 6- to 12-years-old. Children completed a battery of spatial ability tasks (a two-dimension mental rotation task, a paper folding task, a visuo-spatial working memory task, and a Piagetian water level task) and a verbal memory task. In the route learning task, they had to learn a route through a series of hallways presented via computer. Boys had better overall route learning performance than did girls. In fact, the difference between boys and girls was constant across the age range tested. Structural equation modeling of the children's performance revealed that spatial abilities and verbal memory were significant contributors to route learning performance. However, there were different patterns of correlates for boys and girls. For boys, spatial abilities contributed to route learning while verbal memory did not. In contrast, for girls both spatial abilities and verbal memory contributed to their route learning performance. This difference may reflect the precursor of a strategic difference between boys and girls in wayfinding that is commonly observed in adults.

Strategic Resource Allocation in the Human Brain Supports Cognitive Coordination of Object and Spatial Working Memory

PubMed Central

Jackson, Margaret C; Morgan, Helen M; Shapiro, Kimron L; Mohr, Harald; Linden, David EJ

2011-01-01

The ability to integrate different types of information (e.g., object identity and spatial orientation) and maintain or manipulate them concurrently in working memory (WM) facilitates the flow of ongoing tasks and is essential for normal human cognition. Research shows that object and spatial information is maintained and manipulated in WM via separate pathways in the brain (object/ventral versus spatial/dorsal). How does the human brain coordinate the activity of different specialized systems to conjoin different types of information? Here we used functional magnetic resonance imaging to investigate conjunction- versus single-task manipulation of object (compute average color blend) and spatial (compute intermediate angle) information in WM. Object WM was associated with ventral (inferior frontal gyrus, occipital cortex), and spatial WM with dorsal (parietal cortex, superior frontal, and temporal sulci) regions. Conjoined object/spatial WM resulted in intermediate activity in these specialized areas, but greater activity in different prefrontal and parietal areas. Unique to our study, we found lower temporo-occipital activity and greater deactivation in temporal and medial prefrontal cortices for conjunction- versus single-tasks. Using structural equation modeling, we derived a conjunction-task connectivity model that comprises a frontoparietal network with a bidirectional DLPFC-VLPFC connection, and a direct parietal-extrastriate pathway. We suggest that these activation/deactivation patterns reflect efficient resource allocation throughout the brain and propose a new extended version of the biased competition model of WM. Hum Brain Mapp, 2011. © 2010 Wiley-Liss, Inc. PMID:20715083

Spatial pattern and heterogeneity of soil moisture along a transect in a small catchment on the Loess Plateau

NASA Astrophysics Data System (ADS)

Yang, Yang; Dou, Yanxing; Liu, Dong; An, Shaoshan

2017-07-01

Spatial pattern and heterogeneity of soil moisture is important for the hydrological process on the Loess Plateau. This study combined the classical and geospatial statistical techniques to examine the spatial pattern and heterogeneity of soil moisture along a transect scale (e.g. land use types and topographical attributes) on the Loess Plateau. The average values of soil moisture were on the order of farmland > orchard > grassland > abandoned land > shrubland > forestland. Vertical distribution characteristics of soil moisture (0-500 cm) were similar among land use types. Highly significant (p < 0.01) negative correlations were found between soil moisture and elevation (h) except for shrubland (p > 0.05), whereas no significant correlations were found between soil moisture and plan curvature (Kh), stream power index (SPI), compound topographic index (CTI) (p > 0.05), indicating that topographical attributes (mainly h) have a negative effect on the soil moisture spatial heterogeneity. Besides, soil moisture spatial heterogeneity decreased from forestland to grassland and farmland, accompanied by a decline from 15° to 1° alongside upper to lower slope position. This study highlights the importance of land use types and topographical attributes on the soil moisture spatial heterogeneity from a combined analysis of the structural equation model (SEM) and generalized additive models (GAMs), and the relative contribution of land use types to the soil moisture spatial heterogeneity was higher than that of topographical attributes, which provides insights for researches focusing on soil moisture varitions on the Loess Plateau.

Gravitational instantons, self-duality, and geometric flows

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

Bourliot, F.; Estes, J.; Petropoulos, P. M.

2010-05-15

We discuss four-dimensional 'spatially homogeneous' gravitational instantons. These are self-dual solutions of Euclidean vacuum Einstein equations. They are endowed with a product structure RxM{sub 3} leading to a foliation into three-dimensional subspaces evolving in Euclidean time. For a large class of homogeneous subspaces, the dynamics coincides with a geometric flow on the three-dimensional slice, driven by the Ricci tensor plus an so(3) gauge connection. The flowing metric is related to the vielbein of the subspace, while the gauge field is inherited from the anti-self-dual component of the four-dimensional Levi-Civita connection.

Electrostatic energy and screened charge interaction near the surface of metals with different Fermi surface shape

NASA Astrophysics Data System (ADS)

Gabovich, A. M.; Il'chenko, L. G.; Pashitskii, E. A.; Romanov, Yu. A.

1980-04-01

Using the Poisson equation Green function for a self-consistent field in a spatially inhomogeneous system, expressions for the electrostatic energy and screened charge interaction near the surface of a semi-infinite metal and a thin quantizing film are derived. It is shown that the decrease law and Friedel oscillation amplitude of adsorbed atom indirect interaction are determined by the electron spectrum character and the Fermi surface shape. The results obtained enable us to explain, in particular, the submonolayer adsorbed film structure on the W and Mo surfaces.

Turbulence, flow and transport: hints from reversed field pinch

NASA Astrophysics Data System (ADS)

Vianello, N.; Antoni, V.; Spada, E.; Spolaore, M.; Serianni, G.; Cavazzana, R.; Bergsåker, H.; Cecconello, M.; Drake, J. R.

2006-04-01

The interplay between sheared E × B flows and turbulence has been experimentally investigated in the edge region of the Extrap-T2R reversed field pinch experiment. Electrostatic fluctuations are found to rule the momentum balance equation representing the main driving term for sheared flows which counterbalances anomalous viscous damping. The driving role of electrostatic fluctuations is proved by the spatial structure of the Reynolds stress and by the time behaviour of the mean energy production term which supports the existence of an energy exchange from the small scales of turbulence to the larger scales of the mean flow.

Spatial optimal disturbances in swept-wing boundary layers

NASA Astrophysics Data System (ADS)

Chen, Cheng

2018-04-01

With the use of the adjoint-based optimization method proposed by Tempelmann et al. (J. Fluid Mech., vol. 704, 2012, pp. 251-279), in which the parabolized stability equation (PSE) and so-called adjoint parabolized stability equation (APSE) are solved iteratively, we obtain the spatial optimal disturbance shape and investigate its dependence on the parameters of disturbance wave and wall condition, such as radial frequency ω and wall temperature Twall, in a swept-wing boundary layer flow. Further, the non-modal growth mechanism of this optimal disturbance has been also discussed, regarding its spatial evolution way in the streamwise direction. The results imply that the spanwise wavenumber, disturbance frequency and wall cooling do not change the physical mechanism of perturbation growth, just with a substantial effect on the magnitude of perturbation growth. Further, wall cooling may have enhancing or suppressing effect on spatial optimal disturbance growth, depending on the streamwise location.

Exact solutions and low-frequency instability of the adiabatic auroral arc model

NASA Technical Reports Server (NTRS)

Cornwall, John M.

1988-01-01

The adiabatic auroral arc model couples a kinetic theory parallel current driven by mirror forces to horizontal ionospheric currents; the resulting equations are nonlinear. Some exact stationary solutions to these equations, some of them based on the Liouville equation, are developed, with both latitudinal and longitudinal spatial variations. These Liouville equation exact solutions are related to stability boundaries of low-frequency instabilities such as Kelvin-Helmholtz, as shown by a study of a simplified model.

Benchmark solutions for the galactic heavy-ion transport equations with energy and spatial coupling

NASA Technical Reports Server (NTRS)

Ganapol, Barry D.; Townsend, Lawrence W.; Lamkin, Stanley L.; Wilson, John W.

1991-01-01

Nontrivial benchmark solutions are developed for the galactic heavy ion transport equations in the straightahead approximation with energy and spatial coupling. Analytical representations of the ion fluxes are obtained for a variety of sources with the assumption that the nuclear interaction parameters are energy independent. The method utilizes an analytical LaPlace transform inversion to yield a closed form representation that is computationally efficient. The flux profiles are then used to predict ion dose profiles, which are important for shield design studies.

Optical properties of electrohydrodynamic convection patterns: rigorous and approximate methods.

PubMed

Bohley, Christian; Heuer, Jana; Stannarius, Ralf

2005-12-01

We analyze the optical behavior of two-dimensionally periodic structures that occur in electrohydrodynamic convection (EHC) patterns in nematic sandwich cells. These structures are anisotropic, locally uniaxial, and periodic on the scale of micrometers. For the first time, the optics of these structures is investigated with a rigorous method. The method used for the description of the electromagnetic waves interacting with EHC director patterns is a numerical approach that discretizes directly the Maxwell equations. It works as a space-grid-time-domain method and computes electric and magnetic fields in time steps. This so-called finite-difference-time-domain (FDTD) method is able to generate the fields with arbitrary accuracy. We compare this rigorous method with earlier attempts based on ray-tracing and analytical approximations. Results of optical studies of EHC structures made earlier based on ray-tracing methods are confirmed for thin cells, when the spatial periods of the pattern are sufficiently large. For the treatment of small-scale convection structures, the FDTD method is without alternatives.

A Spatially Continuous Model of Carbohydrate Digestion and Transport Processes in the Colon

PubMed Central

Moorthy, Arun S.; Brooks, Stephen P. J.; Kalmokoff, Martin; Eberl, Hermann J.

2015-01-01

A spatially continuous mathematical model of transport processes, anaerobic digestion and microbial complexity as would be expected in the human colon is presented. The model is a system of first-order partial differential equations with context determined number of dependent variables, and stiff, non-linear source terms. Numerical simulation of the model is used to elucidate information about the colon-microbiota complex. It is found that the composition of materials on outflow of the model does not well-describe the composition of material in other model locations, and inferences using outflow data varies according to model reactor representation. Additionally, increased microbial complexity allows the total microbial community to withstand major system perturbations in diet and community structure. However, distribution of strains and functional groups within the microbial community can be modified depending on perturbation length and microbial kinetic parameters. Preliminary model extensions and potential investigative opportunities using the computational model are discussed. PMID:26680208

Analysis of the Cape Cod tracer data

USGS Publications Warehouse

Ezzedine, Souheil; Rubin, Yoram

1997-01-01

An analysis of the Cape Cod test was performed using several first- and higher-order theoretical models. We compare conditional and unconditional solutions of the transport equation and employ them for analysis of the experimental data. We consider spatial moments, mass breakthrough curves, and the distribution of the solute mass in space. The concentration measurements were also analyzed using theoretical models for the expected value and variance of concentration. The theoretical models we employed are based on the spatial correlation structure of the conductivity field, without any fitting of parameters to the tracer data, and hence we can test the predictive power of the theories tested. The effects of recharge on macrodispersion are investigated, and it is shown that recharge provides a reasonable explanation for the enhanced lateral spread of the Cape Cod plume. The compendium of the experimental results presented here is useful for testing of theoretical and numerical models.

Exact states in waveguides with periodically modulated nonlinearity

NASA Astrophysics Data System (ADS)

Ding, E.; Chan, H. N.; Chow, K. W.; Nakkeeran, K.; Malomed, B. A.

2017-09-01

We introduce a one-dimensional model based on the nonlinear Schrödinger/Gross-Pitaevskii equation where the local nonlinearity is subject to spatially periodic modulation in terms of the Jacobi {dn} function, with three free parameters including the period, amplitude, and internal form-factor. An exact periodic solution is found for each set of parameters and, which is more important for physical realizations, we solve the inverse problem and predict the period and amplitude of the modulation that yields a particular exact spatially periodic state. A numerical stability analysis demonstrates that the periodic states become modulationally unstable for large periods, and regain stability in the limit of an infinite period, which corresponds to a bright soliton pinned to a localized nonlinearity-modulation pattern. The exact dark-bright soliton complex in a coupled system with a localized modulation structure is also briefly considered. The system can be realized in planar optical waveguides and cigar-shaped atomic Bose-Einstein condensates.

The application of the constants of motion to nonlinear stationary waves in complex plasmas: a unified fluid dynamic viewpoint

NASA Astrophysics Data System (ADS)

McKenzie, J. F.; Dubinin, E.; Sauer, K.; Doyle, T. B.

2004-08-01

Perturbation reductive procedures, as used to analyse various weakly nonlinear plasma waves (solitons and periodic waves), normally lead to the dynamical system being described by KdV, Burgers' or a nonlinear Schrödinger-type equation, with properties that can be deduced from an array of mathematical techniques. Here we develop a fully nonlinear theory of one-dimensional stationary plasma waves, which elucidates the common nature of various diverse wave phenomena. This is accomplished by adopting an essentially fluid dynamic viewpoint. In this unified treatment the constants of the motion (for mass, momentum and energy) lead naturally to the construction of the wave structure equations. It is shown, for example, that electrostatic, Hall magnetohydrodynamic and ion cyclotron acoustic nonlinear waves all obey first-order differential equations of the same generic type for the longitudinal flow field of the wave. The equilibrium points, which define the soliton amplitude, are given by the compressive and/or rarefactive roots of a total plasma ‘energy’ or ‘momentum’ function characterizing the wave type. This energy function, which is an algebraic combination of the Bernoulli momentum and energy functions for the longitudinal flow field, is the fluid dynamic counterpart of the pseudo-potentials, which are characteristic of system structure equations formulated in other than fluid variables. Another general feature of the structure equation is the phenomenon of choked flow, which occurs when the flow speed becomes sonic. It is this trans-sonic property that limits the soliton amplitudes and defines the critical collective Mach numbers of the waves. These features are also obtained in multi-component plasmas where, for example, in a bi-ion plasma, momentum exchanges between protons and heavier ions are mediated by the Maxwell magnetic stresses. With a suitable generalization of the concept of a sonic point in a bi-ion system and the corresponding choked flow feature, the wave structures, although now more complicated, can also be understood within this overall fluid framework. Particularly useful tools in this context are the momentum hodograph (an algebraic relation between the bi-ion speeds and the electron speed, or magnetic field, which follows from the conservation of mass, momentum and charge-neutrality) and a generalized Bernoulli energy density for each species. Analysis shows that the bi-ion solitons are essentially compressive, but contain the remarkable feature of the presence of a proton rarefactive core. A new type of soliton, called an ‘oscilliton’ because embedded spatial oscillations are superimposed on the classical soliton, is also described and discussed. A necessary condition for the existence of this type of wave is that the linear phase velocity must exhibit an extremum where the phase speed matches the group speed. The remarkable properties of this wave are illustrated for the case of both whistler waves and bi-ion waves where, for the latter, the requisite condition is met near the cross-over frequencies. In the case of the whistler oscilliton, which propagates at speeds in excess of one half of the Alfvén speed (based on the electrons), an analytic solution has been constructed through a phase-portrait integral of the system in which the proton and electron dynamics must be placed on the same footing. The relevance of the different wave structures to diverse space environments is briefly discussed in relation to recently available high-time and spatial resolution data from satellite observations.

Determining linear vibration frequencies of a ferromagnetic shell

NASA Astrophysics Data System (ADS)

Bagdoev, A. G.; Vardanyan, A. V.; Vardanyan, S. V.; Kukudzhanov, V. N.

2007-10-01

The problems of determining the roots of dispersion equations for free bending vibrations of thin magnetoelastic plates and shells are of both theoretical and practical interest, in particular, in studying vibrations of metallic structures used in controlled thermonuclear reactors. These problems were solved on the basis of the Kirchhoff hypothesis in [1-5]. In [6], an exact spatial approach to determining the vibration frequencies of thin plates was suggested, and it was shown that it completely agrees with the solution obtained according to the Kirchhoff hypothesis. In [7-9], this exact approach was used to solve the problem on vibrations of thin magnetoelastic plates, and it was shown by cumbersome calculations that the solutions obtained according to the exact theory and the Kirchhoff hypothesis differ substantially except in a single case. In [10], the equations of the dynamic theory of elasticity in the axisymmetric problem are given. In [11], the equations for the vibration frequencies of thin ferromagnetic plates with arbitrary conductivity were obtained in the exact statement. In [12], the Kirchhoff hypothesis was used to obtain dispersion relations for a magnetoelastic thin shell. In [5, 13-16], the relations for the Maxwell tensor and the ponderomotive force for magnetics were presented. In [17], the dispersion relations for thin ferromagnetic plates in the transverse field in the spatial statement were studied analytically and numerically. In the present paper, on the basis of the exact approach, we study free bending vibrations of a thin ferromagnetic cylindrical shell. We obtain the exact dispersion equation in the form of a sixth-order determinant, which can be solved numerically in the case of a magnetoelastic thin shell. The numerical results are presented in tables and compared with the results obtained by the Kirchhoff hypothesis. We show a large number of differences in the results, even for the least frequency.

On some control problems of dynamic of reactor

NASA Astrophysics Data System (ADS)

Baskakov, A. V.; Volkov, N. P.

2017-12-01

The paper analyzes controllability of the transient processes in some problems of nuclear reactor dynamics. In this case, the mathematical model of nuclear reactor dynamics is described by a system of integro-differential equations consisting of the non-stationary anisotropic multi-velocity kinetic equation of neutron transport and the balance equation of delayed neutrons. The paper defines the formulation of the linear problem on control of transient processes in nuclear reactors with application of spatially distributed actions on internal neutron sources, and the formulation of the nonlinear problems on control of transient processes with application of spatially distributed actions on the neutron absorption coefficient and the neutron scattering indicatrix. The required control actions depend on the spatial and velocity coordinates. The theorems on existence and uniqueness of these control actions are proved in the paper. To do this, the control problems mentioned above are reduced to equivalent systems of integral equations. Existence and uniqueness of the solution for this system of integral equations is proved by the method of successive approximations, which makes it possible to construct an iterative scheme for numerical analyses of transient processes in a given nuclear reactor with application of the developed mathematical model. Sufficient conditions for controllability of transient processes are also obtained. In conclusion, a connection is made between the control problems and the observation problems, which, by to the given information, allow us to reconstruct either the function of internal neutron sources, or the neutron absorption coefficient, or the neutron scattering indicatrix....

The Impact of Buoyancy and Flame Structure on Soot, Radiation and NOx Emissions from a Turbulent Diffusion Flame

NASA Technical Reports Server (NTRS)

Kennedy, I. M.; Kollman, W.; VanderWal, R. L.

1999-01-01

It is hypothesized that the spatial structure of a turbulent diffusion flame plays an important role in determining the emissions of radiative energy, soot and NO, from a combustor. This structure, manifested in the two point statistics, is influenced by buoyancy. Radiation, soot and NOx emissions are the cumulative result of processes that occur throughout a flame. For example, radiation fluxes along a line of sight can be found from summing up the contributions from sources in individual pockets of hot soot that emit, and from sinks in cold soot that absorb. Soot and NOx are both the results of slow chemistry and are not equilibrium products. The time that is available for production and burnout is crucial in determining the eventual emissions of these pollutants. Turbulence models generally rely on a single point closure of the appropriate time averaged equations. Hence, spatial information is lost and needs to be modeled using solution variables such as turbulence kinetic energy and dissipation rate, often with the assumption of isotropy. However, buoyancy can affect the physical structure of turbulent flames and can change the spatial extent of soot bearing regions. Theoretical comparisons with models are best done in the limit of infinite Froude number because the inclusion of buoyancy in flow models introduces significant uncertainties. Hence, LII measurements of soot, measurements of radiation fluxes from soot, Particle Imaging Velocimetry (PIV) of the flow field and measurements of post flame NOX will be carried out on the NASA Lewis 2.2 sec drop tower and eventually on the parabolic flight aircraft. The drop rig will be a modified version of a unit that has been successfully used at Lewis in the past.

Delay-induced depinning of localized structures in a spatially inhomogeneous Swift-Hohenberg model

NASA Astrophysics Data System (ADS)

Tabbert, Felix; Schelte, Christian; Tlidi, Mustapha; Gurevich, Svetlana V.

2017-03-01

We report on the dynamics of localized structures in an inhomogeneous Swift-Hohenberg model describing pattern formation in the transverse plane of an optical cavity. This real order parameter equation is valid close to the second-order critical point associated with bistability. The optical cavity is illuminated by an inhomogeneous spatial Gaussian pumping beam and subjected to time-delayed feedback. The Gaussian injection beam breaks the translational symmetry of the system by exerting an attracting force on the localized structure. We show that the localized structure can be pinned to the center of the inhomogeneity, suppressing the delay-induced drift bifurcation that has been reported in the particular case where the injection is homogeneous, assuming a continuous wave operation. Under an inhomogeneous spatial pumping beam, we perform the stability analysis of localized solutions to identify different instability regimes induced by time-delayed feedback. In particular, we predict the formation of two-arm spirals, as well as oscillating and depinning dynamics caused by the interplay of an attracting inhomogeneity and destabilizing time-delayed feedback. The transition from oscillating to depinning solutions is investigated by means of numerical continuation techniques. Analytically, we use an order parameter approach to derive a normal form of the delay-induced Hopf bifurcation leading to an oscillating solution. Additionally we model the interplay of an attracting inhomogeneity and destabilizing time delay by describing the localized solution as an overdamped particle in a potential well generated by the inhomogeneity. In this case, the time-delayed feedback acts as a driving force. Comparing results from the later approach with the full Swift-Hohenberg model, we show that the approach not only provides an instructive description of the depinning dynamics, but also is numerically accurate throughout most of the parameter regime.

Improved estimation of hydraulic conductivity by combining stochastically simulated hydrofacies with geophysical data.

PubMed

Zhu, Lin; Gong, Huili; Chen, Yun; Li, Xiaojuan; Chang, Xiang; Cui, Yijiao

2016-03-01

Hydraulic conductivity is a major parameter affecting the output accuracy of groundwater flow and transport models. The most commonly used semi-empirical formula for estimating conductivity is Kozeny-Carman equation. However, this method alone does not work well with heterogeneous strata. Two important parameters, grain size and porosity, often show spatial variations at different scales. This study proposes a method for estimating conductivity distributions by combining a stochastic hydrofacies model with geophysical methods. The Markov chain model with transition probability matrix was adopted to re-construct structures of hydrofacies for deriving spatial deposit information. The geophysical and hydro-chemical data were used to estimate the porosity distribution through the Archie's law. Results show that the stochastic simulated hydrofacies model reflects the sedimentary features with an average model accuracy of 78% in comparison with borehole log data in the Chaobai alluvial fan. The estimated conductivity is reasonable and of the same order of magnitude of the outcomes of the pumping tests. The conductivity distribution is consistent with the sedimentary distributions. This study provides more reliable spatial distributions of the hydraulic parameters for further numerical modeling.

Metamaterial devices for molding the flow of diffuse light (Conference Presentation)

NASA Astrophysics Data System (ADS)

Wegener, Martin

2016-09-01

Much of optics in the ballistic regime is about designing devices to mold the flow of light. This task is accomplished via specific spatial distributions of the refractive index or the refractive-index tensor. For light propagating in turbid media, a corresponding design approach has not been applied previously. Here, we review our corresponding recent work in which we design spatial distributions of the light diffusivity or the light-diffusivity tensor to accomplish specific tasks. As an application, we realize cloaking of metal contacts on large-area OLEDs, eliminating the contacts' shadows, thereby homogenizing the diffuse light emission. In more detail, metal contacts on large-area organic light-emitting diodes (OLEDs) are mandatory electrically, but they cast optical shadows, leading to unwanted spatially inhomogeneous diffuse light emission. We show that the contacts can be made invisible either by (i) laminate metamaterials designed by coordinate transformations of the diffusion equation or by (ii) triangular-shaped regions with piecewise constant diffusivity, hence constant concentration of scattering centers. These structures are post-optimized in regard to light throughput by Monte-Carlo ray-tracing simulations and successfully validated by model experiments.

Spatial and temporal compact equations for water waves

NASA Astrophysics Data System (ADS)

Dyachenko, Alexander; Kachulin, Dmitriy; Zakharov, Vladimir

2016-04-01

A one-dimensional potential flow of an ideal incompressible fluid with a free surface in a gravity field is the Hamiltonian system with the Hamiltonian: H = 1/2intdxint-∞^η |nablaφ|^2dz + g/2ont η^2dxŗφ(x,z,t) - is the potential of the fluid, g - gravity acceleration, η(x,t) - surface profile Hamiltonian can be expanded as infinite series of steepness: {Ham4} H &=& H2 + H3 + H4 + dotsŗH2 &=& 1/2int (gη2 + ψ hat kψ) dx, ŗH3 &=& -1/2int \\{(hat kψ)2 -(ψ_x)^2}η dx,ŗH4 &=&1/2int {ψxx η2 hat kψ + ψ hat k(η hat k(η hat kψ))} dx. where hat k corresponds to the multiplication by |k| in Fourier space, ψ(x,t)= φ(x,η(x,t),t). This truncated Hamiltonian is enough for gravity waves of moderate amplitudes and can not be reduced. We have derived self-consistent compact equations, both spatial and temporal, for unidirectional water waves. Equations are written for normal complex variable c(x,t), not for ψ(x,t) and η(x,t). Hamiltonian for temporal compact equation can be written in x-space as following: {SPACE_C} H = intc^*hat V c dx + 1/2int [ i/4(c2 partial/partial x {c^*}2 - {c^*}2 partial/partial x c2)- |c|2 hat K(|c|^2) ]dx Here operator hat V in K-space is so that Vk = ω_k/k. If along with this to introduce Gardner-Zakharov-Faddeev bracket (for the analytic in the upper half-plane function) {GZF} partial^+x Leftrightarrow ikθk Hamiltonian for spatial compact equation is the following: {H24} &&H=1/gint1/ω|cω|2 dω +ŗ&+&1/2g^3int|c|^2(ddot c^*c + ddot c c^*)dt + i/g^2int |c|^2hatω(dot c c* - cdot c^*)dt. equation of motion is: {t-space} &&partial /partial xc +i/g partial^2/partial t^2c =ŗ&=& 1/2g^3partial^3/partial t3 [ partial^2/partial t^2(|c|^2c) +2 |c|^2ddot c +ddot c^*c2 ]+ŗ&+&i/g3 partial^3/partial t3 [ partial /partial t( chatω |c|^2) + dot c hatω |c|2 + c hatω(dot c c* - cdot c^*) ]. It solves the spatial Cauchy problem for surface gravity wave on the deep water. Main features of the equations are: Equations are written for complex normal variable c(x,t) which is analytic function in the upper half-planeHamiltonians both for temporal and spatial equations are very simple It can be easily implemented for numerical simulation The equations can be generalized for "almost" 2-D waves like KdV is generalized to KP. This work was supported by was Grant "Wave turbulence: theory, numerical simulation, experiment" #14-22-00174 of Russian Science Foundation.

An effective rate equation approach to reaction kinetics in small volumes: theory and application to biochemical reactions in nonequilibrium steady-state conditions.

PubMed

Grima, R

2010-07-21

Chemical master equations provide a mathematical description of stochastic reaction kinetics in well-mixed conditions. They are a valid description over length scales that are larger than the reactive mean free path and thus describe kinetics in compartments of mesoscopic and macroscopic dimensions. The trajectories of the stochastic chemical processes described by the master equation can be ensemble-averaged to obtain the average number density of chemical species, i.e., the true concentration, at any spatial scale of interest. For macroscopic volumes, the true concentration is very well approximated by the solution of the corresponding deterministic and macroscopic rate equations, i.e., the macroscopic concentration. However, this equivalence breaks down for mesoscopic volumes. These deviations are particularly significant for open systems and cannot be calculated via the Fokker-Planck or linear-noise approximations of the master equation. We utilize the system-size expansion including terms of the order of Omega(-1/2) to derive a set of differential equations whose solution approximates the true concentration as given by the master equation. These equations are valid in any open or closed chemical reaction network and at both the mesoscopic and macroscopic scales. In the limit of large volumes, the effective mesoscopic rate equations become precisely equal to the conventional macroscopic rate equations. We compare the three formalisms of effective mesoscopic rate equations, conventional rate equations, and chemical master equations by applying them to several biochemical reaction systems (homodimeric and heterodimeric protein-protein interactions, series of sequential enzyme reactions, and positive feedback loops) in nonequilibrium steady-state conditions. In all cases, we find that the effective mesoscopic rate equations can predict very well the true concentration of a chemical species. This provides a useful method by which one can quickly determine the regions of parameter space in which there are maximum differences between the solutions of the master equation and the corresponding rate equations. We show that these differences depend sensitively on the Fano factors and on the inherent structure and topology of the chemical network. The theory of effective mesoscopic rate equations generalizes the conventional rate equations of physical chemistry to describe kinetics in systems of mesoscopic size such as biological cells.

Modeling transport across the running-sandpile cellular automaton by means of fractional transport equations

NASA Astrophysics Data System (ADS)

Sánchez, R.; Newman, D. E.; Mier, J. A.

2018-05-01

Fractional transport equations are used to build an effective model for transport across the running sandpile cellular automaton [Hwa et al., Phys. Rev. A 45, 7002 (1992), 10.1103/PhysRevA.45.7002]. It is shown that both temporal and spatial fractional derivatives must be considered to properly reproduce the sandpile transport features, which are governed by self-organized criticality, at least over sufficiently long or large scales. In contrast to previous applications of fractional transport equations to other systems, the specifics of sand motion require in this case that the spatial fractional derivatives used for the running sandpile must be of the completely asymmetrical Riesz-Feller type. Appropriate values for the fractional exponents that define these derivatives in the case of the running sandpile are obtained numerically.

Model Comparison of Bayesian Semiparametric and Parametric Structural Equation Models

ERIC Educational Resources Information Center

Song, Xin-Yuan; Xia, Ye-Mao; Pan, Jun-Hao; Lee, Sik-Yum

2011-01-01

Structural equation models have wide applications. One of the most important issues in analyzing structural equation models is model comparison. This article proposes a Bayesian model comparison statistic, namely the "L[subscript nu]"-measure for both semiparametric and parametric structural equation models. For illustration purposes, we consider…

Applying Meta-Analysis to Structural Equation Modeling

ERIC Educational Resources Information Center

Hedges, Larry V.

2016-01-01

Structural equation models play an important role in the social sciences. Consequently, there is an increasing use of meta-analytic methods to combine evidence from studies that estimate the parameters of structural equation models. Two approaches are used to combine evidence from structural equation models: A direct approach that combines…

Wavelet and adaptive methods for time dependent problems and applications in aerosol dynamics

NASA Astrophysics Data System (ADS)

Guo, Qiang

Time dependent partial differential equations (PDEs) are widely used as mathematical models of environmental problems. Aerosols are now clearly identified as an important factor in many environmental aspects of climate and radiative forcing processes, as well as in the health effects of air quality. The mathematical models for the aerosol dynamics with respect to size distribution are nonlinear partial differential and integral equations, which describe processes of condensation, coagulation and deposition. Simulating the general aerosol dynamic equations on time, particle size and space exhibits serious difficulties because the size dimension ranges from a few nanometer to several micrometer while the spatial dimension is usually described with kilometers. Therefore, it is an important and challenging task to develop efficient techniques for solving time dependent dynamic equations. In this thesis, we develop and analyze efficient wavelet and adaptive methods for the time dependent dynamic equations on particle size and further apply them to the spatial aerosol dynamic systems. Wavelet Galerkin method is proposed to solve the aerosol dynamic equations on time and particle size due to the fact that aerosol distribution changes strongly along size direction and the wavelet technique can solve it very efficiently. Daubechies' wavelets are considered in the study due to the fact that they possess useful properties like orthogonality, compact support, exact representation of polynomials to a certain degree. Another problem encountered in the solution of the aerosol dynamic equations results from the hyperbolic form due to the condensation growth term. We propose a new characteristic-based fully adaptive multiresolution numerical scheme for solving the aerosol dynamic equation, which combines the attractive advantages of adaptive multiresolution technique and the characteristics method. On the aspect of theoretical analysis, the global existence and uniqueness of solutions of continuous time wavelet numerical methods for the nonlinear aerosol dynamics are proved by using Schauder's fixed point theorem and the variational technique. Optimal error estimates are derived for both continuous and discrete time wavelet Galerkin schemes. We further derive reliable and efficient a posteriori error estimate which is based on stable multiresolution wavelet bases and an adaptive space-time algorithm for efficient solution of linear parabolic differential equations. The adaptive space refinement strategies based on the locality of corresponding multiresolution processes are proved to converge. At last, we develop efficient numerical methods by combining the wavelet methods proposed in previous parts and the splitting technique to solve the spatial aerosol dynamic equations. Wavelet methods along the particle size direction and the upstream finite difference method along the spatial direction are alternately used in each time interval. Numerical experiments are taken to show the effectiveness of our developed methods.

Topics Associated with Nonlinear Evolution Equations and Inverse Scattering in Multidimensions,

DTIC Science & Technology

1987-03-01

significant that these concepts can be generalized to 2 spatial plus one time dimension. Here the prototype equation is the Kadomtsev - Petviashvili (K-P...O-193 32 ? T TOPICS ASSOCIATED WITH NONLINEAR E VOLUTION EQUATIONS / AND INVERSE SCATTER! .(U) CLARKSON UNIV POTSDAM NY INST...8217 - Evolution Equations and L Inverse Scattering in Multi- dimensions by _i A ,’I Mark J. Ablowi ClrsnUiest PosaNwYr/37 LaRMFOMON* .F-5 Anwo~~~d kr /ua

Simulation study on the spatial and temporal characteristics of focused microwave beam discharge in nitrogen

NASA Astrophysics Data System (ADS)

Yang, Wei; Zhou, Qianhong; Dong, Zhiwei

2018-01-01

This paper reports a simulation study on a focused microwave (frequency 9.4 GHz, pulse width 2.5 μs, and peak electric field 1.2 kV/cm) discharge in 200 Pa nitrogen. A one-dimensional (1D) fluid model is based on the wave equation for the microwave field propagating through the gas breakdown plasma, the continuity equations for electron, ion and neutral particle densities, and the energy balance equations for mean electron temperature, and nitrogen vibrational and translational temperatures. These equations are numerically solved in a self-consistent manner with a simplified plasma chemistry set, in which the reaction rates involving electrons are calculated from the electron energy distribution function (EEDF) using a two-term expansion method. The spatial and temporal characteristics of the focused microwave breakdown in nitrogen are demonstrated, which include the amplitude of the microwave electric field, and the densities and temperatures of the plasma components. The temporal evolution of the plasma electron density agrees reasonably well with that measured with a microwave interferometer. The spatial-temporal distributions of metastable states are discussed on the plasma chemistry and the character of mean electron temperature. The spatially integrated N2(C3) density shows similar trends with the measured temporal intensity of optical emission spectroscopy, except for a time delay of 100-300 ns. The quantitative discrepancies are explained in light of limitations of the 1D model with a two-term expansion of EEDF. The theoretical model is found to describe the gas breakdown plasma generated by focused microwave beams at least qualitatively.

Acceleration of stable TTI P-wave reverse-time migration with GPUs

NASA Astrophysics Data System (ADS)

Kim, Youngseo; Cho, Yongchae; Jang, Ugeun; Shin, Changsoo

2013-03-01

When a pseudo-acoustic TTI (tilted transversely isotropic) coupled wave equation is used to implement reverse-time migration (RTM), shear wave energy is significantly included in the migration image. Because anisotropy has intrinsic elastic characteristics, coupling P-wave and S-wave modes in the pseudo-acoustic wave equation is inevitable. In RTM with only primary energy or the P-wave mode in seismic data, the S-wave energy is regarded as noise for the migration image. To solve this problem, we derive a pure P-wave equation for TTI media that excludes the S-wave energy. Additionally, we apply the rapid expansion method (REM) based on a Chebyshev expansion and a pseudo-spectral method (PSM) to calculate spatial derivatives in the wave equation. When REM is incorporated with the PSM for the spatial derivatives, wavefields with high numerical accuracy can be obtained without grid dispersion when performing numerical wave modeling. Another problem in the implementation of TTI RTM is that wavefields in an area with high gradients of dip or azimuth angles can be blown up in the progression of the forward and backward algorithms of the RTM. We stabilize the wavefields by applying a spatial-frequency domain high-cut filter when calculating the spatial derivatives using the PSM. In addition, to increase performance speed, the graphic processing unit (GPU) architecture is used instead of traditional CPU architecture. To confirm the degree of acceleration compared to the CPU version on our RTM, we then analyze the performance measurements according to the number of GPUs employed.

Kinetics of Polydomain Ordering at Second-Order Phase Transitions (by the Example of the AuCu3 Alloy)

NASA Astrophysics Data System (ADS)

Feldman, E. P.; Stefanovich, L. I.; Gumennyk, K. V.

2008-08-01

Kinetics of polydomain spinodal ordering is studied in alloys of AuCu3 type. We introduce four non-conserved long-range order parameters whose sum, however, is conserved and, using the statistical approach, follow the temporal evolution of their random spatial distribution after a rapid temperature quench. A system of nonlinear differential equations for correlators of second and third order is derived. Asymptotical analysis of this system allows to investigate the scaling regime, which develops on the late stages of evolution and to extract additional information concerning the rate of decrease of the specific volume of disordered regions and the rate of decrease of the average thickness of antiphase boundaries. Comparison of these results to experimental data is given. The quench below the spinodal and the onset of long-range order may be separated by the incubation time, whose origin is different from that in first-order phase transitions. Numerical integration of equations for correlators shows also, that it is possible to prepare a sample in such a way that its further evolution will go with formation of transient kinetically slowed polydomain structures different from the final L12 structure.

A constitutive theory of reacting electrolyte mixtures

NASA Astrophysics Data System (ADS)

Costa Reis, Martina; Wang, Yongqi; Bono Maurizio Sacchi Bassi, Adalberto

2013-11-01

A constitutive theory of reacting electrolyte mixtures is formulated. The intermolecular interactions among the constituents of the mixture are accounted for through additional freedom degrees to each constituent of the mixture. Balance equations for polar reacting continuum mixtures are accordingly formulated and a proper set of constitutive equations is derived with basis in the Müller-Liu formulation of the second law of thermodynamics. Moreover, the non-equilibrium and equilibrium responses of the reacting mixture are investigated in detail by emphasizing the inner and reactive structures of the medium. From the balance laws and constitutive relations, the effects of molecular structure of constituents upon the fluid flow are studied. It is also demonstrated that the local thermodynamic equilibrium state can be reached without imposing that the set of independent constitutive variables is time independent, neither spatially homogeneous nor null. The resulting constitutive relations presented throughout this work are of relevance to many practical applications, such as swelling of clays, developing of bio and polymeric membranes, and use of electrorheological fluids in industrial processes. The first author acknowledges financial support from National Counsel of Technological and Scientific Development (CNPq) and German Academic Exchange Service (DAAD).

Low-pressure hydrogen discharge maintenance in a large-size plasma source with localized high radio-frequency power deposition

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

Todorov, D.; Shivarova, A., E-mail: ashiva@phys.uni-sofia.bg; Paunska, Ts.

2015-03-15

The development of the two-dimensional fluid-plasma model of a low-pressure hydrogen discharge, presented in the study, is regarding description of the plasma maintenance in a discharge vessel with the configuration of the SPIDER source. The SPIDER source, planned for the neutral-beam-injection plasma-heating system of ITER, is with localized high RF power deposition to its eight drivers (cylindrical-coil inductive discharges) and a large-area second chamber, common for all the drivers. The continuity equations for the charged particles (electrons and the three types of positive ions) and for the neutral species (atoms and molecules), their momentum equations, the energy balance equations formore » electrons, atoms and molecules and the Poisson equations are involved in the discharge description. In addition to the local processes in the plasma volume, the surface processes of particle reflection and conversion on the walls as well as for a heat exchange with the walls are included in the model. The analysis of the results stresses on the role of the fluxes (particle and energy fluxes) in the formation of the discharge structure. The conclusion is that the discharge behavior is completely obeyed to non-locality. The latter is displayed by: (i) maximum values of plasma parameters (charged particle densities and temperatures of the neutral species) outside the region of the RF power deposition, (ii) shifted maxima of the electron density and temperature, of the plasma potential and of the electron production, (iii) an electron flux, with a vortex structure, strongly exceeding the total ion flux which gives evidence of a discharge regime of non-ambipolarity and (iv) a spatial distribution of the densities of the neutral species resulting from their fluxes.« less

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

NASA Technical Reports Server (NTRS)

Tseng, K.

1984-01-01

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

To the theory of mechanisms subfamilies

NASA Astrophysics Data System (ADS)

Fomin, A.; Dvornikov, L.; Paramonov, M.; Jahr, A.

2016-04-01

The principles of formation of mechanisms subfamilies based on the usage of different kinds of kinematic pairs within the families of mechanisms are substantiated in the current paper. The division of mechanisms into subfamilies allows defining not only fundamental differences in the structure of mechanisms, but also provides the necessary foundation for the synthesis of new structures. 57 subfamilies of mechanisms have been totally distinguished. Among them, 31 subfamilies - within the zero family, 15 subfamilies - within the first family, 7 subfamilies - within the second family, 3 subfamilies - within the third family and 1 subfamily-within the fourth family. There were separately viewed planar mechanisms of the third family with three general imposed constraints and spatial mechanisms of the second family with two general imposed constraints in terms of their subfamilies. New methods of kinematical and dynamical investigations of mechanisms might be developed according to their analytical equations describing structural organization of different subfamilies of mechanisms.

Vibration characteristics of a steadily rotating slender ring

NASA Technical Reports Server (NTRS)

Lallman, F. J.

1980-01-01

Partial differential equations are derived to describe the structural vibrations of a uniform homogeneous ring which is very flexible because the radius is very large compared with the cross sectional dimensions. Elementary beam theory is used and small deflections are assumed in the derivation. Four sets of structural modes are examined: bending and compression modes in the plane of the ring; bending modes perpendicular to the plane of the ring; and twisting modes about the centroid of the ring cross section. Spatial and temporal characteristics of these modes, presented in terms of vibration frequencies and ratios between vibration amplitudes, are demonstrated in several figures. Given a sufficiently high rotational rate, the dynamics of the ring approach those of a vibrating string. In this case, the velocity of traveling wave in the material of the ring approaches in velocity of the material relative to inertial space, resulting in structural modes which are almost stationary in space.

Direct Numerical Simulation of a Coolant Jet in a Periodic Crossflow

NASA Technical Reports Server (NTRS)

Sharma, Chirdeep; Acharya, Sumanta

1998-01-01

A Direct Numerical Simulation of a coolant jet injected normally into a periodic crossflow is presented. The physical situation simulated represents a periodic module in a coolant hole array with a heated crossflow. A collocated finite difference scheme is used which is fifth-order accurate spatially and second-order accurate temporally. The scheme is based on a fractional step approach and requires the solution of a pressure-Poisson equation. The simulations are obtained for a blowing ratio of 0.25 and a channel Reynolds number of 5600. The simulations reveal the dynamics of several large scale structures including the Counter-rotating Vortex Pair (CVP), the horse-shoe vortex, the shear layer vortex, the wall vortex and the wake vortex. The origins and the interactions of these vortical structures are identified and explored. Also presented are the turbulence statistics and how they relate to the flow structures.

Stable diffraction-management soliton in a periodic structure with alternating left-handed and right-handed media

NASA Astrophysics Data System (ADS)

Zhang, Jinggui

2017-09-01

In this paper, we first derive a modified two-dimensional non-linear Schrödinger equation including high-order diffraction (HOD) suitable for the propagation of optical beam near the low-diffraction regime in Kerr non-linear media with spatial dispersion. Then, we apply our derived physical model to a designed two-dimensional configuration filled with alternate layers of a left-handed material (LHM) and a right-handed media by employing the mean-field theory. It is found that the periodic structure including LHM may experience diminished, cancelled, and even reversed diffraction behaviours through engineering the relative thickness between both media. In particular, the variational method analytically predicts that close to the zero-diffraction regime, such periodic structure can support stable diffraction-management solitons whose beamwidth and peak amplitude evolve periodically with the help of HOD effect. Numerical simulation based on the split-step Fourier method confirms the analytical results.

Effective modern methods of protecting metal road structures from corrosion

NASA Astrophysics Data System (ADS)

Panteleeva, Margarita

2017-10-01

In the article the ways of protection of barrier road constructions from various external influences which cause development of irreversible corrosion processes are considered. The author studied modern methods of action on metal for corrosion protection and chose the most effective of them: a method of directly affecting the metal structures themselves. This method was studied in more detail in the framework of the experiment. As a result, the article describes the experiment of using a three-layer polymer coating, which includes a thermally activated primer, an elastomeric thermoplastic layer with a spatial structure, and a strong outer polyolefin layer. As a result of the experiment, the ratios of the ingredients for obtaining samples of the treated metal having the best parameters of corrosion resistance, elasticity, and strength were revealed. The author constructed a regression equation describing the main properties of the protective polymer coating using the simplex-lattice planning method in the composition-property diagrams.

Multi-Hamiltonian structure of the Born-Infeld equation

NASA Astrophysics Data System (ADS)

Arik, Metin; Neyzi, Fahrünisa; Nutku, Yavuz; Olver, Peter J.; Verosky, John M.

1989-06-01

The multi-Hamiltonian structure, conservation laws, and higher order symmetries for the Born-Infeld equation are exhibited. A new transformation of the Born-Infeld equation to the equations of a Chaplygin gas is presented and explored. The Born-Infeld equation is distinguished among two-dimensional hyperbolic systems by its wealth of such multi-Hamiltonian structures.

Epidemic spreading in a hierarchical social network.

PubMed

Grabowski, A; Kosiński, R A

2004-09-01

A model of epidemic spreading in a population with a hierarchical structure of interpersonal interactions is described and investigated numerically. The structure of interpersonal connections is based on a scale-free network. Spatial localization of individuals belonging to different social groups, and the mobility of a contemporary community, as well as the effectiveness of different interpersonal interactions, are taken into account. Typical relations characterizing the spreading process, like a range of epidemic and epidemic curves, are discussed. The influence of preventive vaccinations on the spreading process is investigated. The critical value of preventively vaccinated individuals that is sufficient for the suppression of an epidemic is calculated. Our results are compared with solutions of the master equation for the spreading process and good agreement of the character of this process is found.

Projected quasiparticle theory for molecular electronic structure

NASA Astrophysics Data System (ADS)

Scuseria, Gustavo E.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Samanta, Kousik; Ellis, Jason K.

2011-09-01

We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately broken and restored in a self-consistent variation-after-projection approach. We show that the resulting method yields a comprehensive black-box treatment of static correlations with effective one-electron (mean-field) computational cost. The ensuing wave function is of multireference character and permeates the entire Hilbert space of the problem. The energy expression is different from regular HFB theory but remains a functional of an independent quasiparticle density matrix. All reduced density matrices are expressible as an integration of transition density matrices over a gauge grid. We present several proof-of-principle examples demonstrating the compelling power of projected quasiparticle theory for quantum chemistry.

Conjugate Compressible Fluid Flow and Heat Transfer in Ducts

NASA Technical Reports Server (NTRS)

Cross, M. F.

2011-01-01

A computational approach to modeling transient, compressible fluid flow with heat transfer in long, narrow ducts is presented. The primary application of the model is for analyzing fluid flow and heat transfer in solid propellant rocket motor nozzle joints during motor start-up, but the approach is relevant to a wide range of analyses involving rapid pressurization and filling of ducts. Fluid flow is modeled through solution of the spatially one-dimensional, transient Euler equations. Source terms are included in the governing equations to account for the effects of wall friction and heat transfer. The equation solver is fully-implicit, thus providing greater flexibility than an explicit solver. This approach allows for resolution of pressure wave effects on the flow as well as for fast calculation of the steady-state solution when a quasi-steady approach is sufficient. Solution of the one-dimensional Euler equations with source terms significantly reduces computational run times compared to general purpose computational fluid dynamics packages solving the Navier-Stokes equations with resolved boundary layers. In addition, conjugate heat transfer is more readily implemented using the approach described in this paper than with most general purpose computational fluid dynamics packages. The compressible flow code has been integrated with a transient heat transfer solver to analyze heat transfer between the fluid and surrounding structure. Conjugate fluid flow and heat transfer solutions are presented. The author is unaware of any previous work available in the open literature which uses the same approach described in this paper.

Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics

NASA Astrophysics Data System (ADS)

Roca, Carlos P.; Cuesta, José A.; Sánchez, Angel

2009-12-01

Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. While very many interesting results have been obtained with this equation in the three decades elapsed since it was first proposed, it is important to realize the limits of its applicability. One particularly relevant issue in this respect is that of non-mean-field effects, that may arise from temporal fluctuations or from spatial correlations, both neglected in the replicator equation. This review discusses these temporal and spatial effects focusing on the non-trivial modifications they induce when compared to the outcome of replicator dynamics. Alongside this question, the hypothesis of linearity and its relation to the choice of the rule for strategy update is also analyzed. The discussion is presented in terms of the emergence of cooperation, as one of the current key problems in Biology and in other disciplines.

Spatial solitons of desired intensity and width and their self-tapering/uptapering in cubic quintic nonlinear medium

NASA Astrophysics Data System (ADS)

Krishna Sarkar, Ram; Medhekar, S.

2007-12-01

In this paper, we have investigated the propagation behavior of a Gaussian beam in cubic quintic nonlinear medium with and without absorption or gain. A governing differential equation for the evolution of beam width with the distance of propagation has been derived using the standard parabolic equation approach. By solving the governing equation numerically for different sets of parameters, we have shown that spatial solitons of fixed width and desired intensity and of fixed intensity and desired width are possible. Such liberty does not exist in other saturable media. We have also investigated self-tapering and self-uptapering of spatial solitons in the presence of absorption or gain and showed that the rate of self-tapering/uptapering is not only controlled by the magnitude of absorption or gain but also by the values of cubic and quintic terms. It is revealed that by self-tapering, the smallest achievable soliton width decreases/increases by increasing the magnitude of the cubic/quintic term. It is also revealed that the smallest achievable soliton width by self-tapering, is smaller for a larger initial width.

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.…

Global dynamics of a delay differential equation with spatial non-locality in an unbounded domain

NASA Astrophysics Data System (ADS)

Yi, Taishan; Zou, Xingfu

In this paper, we study the global dynamics of a class of differential equations with temporal delay and spatial non-locality in an unbounded domain. Adopting the compact open topology, we describe the delicate asymptotic properties of the nonlocal delayed effect and establish some a priori estimate for nontrivial solutions which enables us to show the permanence of the equation. Combining these results with a dynamical systems approach, we determine the global dynamics of the equation under appropriate conditions. Applying the main results to the model with Ricker's birth function and Mackey-Glass's hematopoiesis function, we obtain threshold results for the global dynamics of these two models. We explain why our results on the global attractivity of the positive equilibrium in C∖{0} under the compact open topology becomes invalid in C∖{0} with respect to the usual supremum norm, and we identify a subset of C∖{0} in which the positive equilibrium remains attractive with respect to the supremum norm.

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

Naughton, M.J.; Bourke, W.; Browning, G.L.

The convergence of spectral model numerical solutions of the global shallow-water equations is examined as a function of the time step and the spectral truncation. The contributions to the errors due to the spatial and temporal discretizations are separately identified and compared. Numerical convergence experiments are performed with the inviscid equations from smooth (Rossby-Haurwitz wave) and observed (R45 atmospheric analysis) initial conditions, and also with the diffusive shallow-water equations. Results are compared with the forced inviscid shallow-water equations case studied by Browning et al. Reduction of the time discretization error by the removal of fast waves from the solution usingmore » initialization is shown. The effects of forcing and diffusion on the convergence are discussed. Time truncation errors are found to dominate when a feature is large scale and well resolved; spatial truncation errors dominate for small-scale features and also for large scale after the small scales have affected them. Possible implications of these results for global atmospheric modeling are discussed. 31 refs., 14 figs., 4 tabs.« less

Internal consistency and stability of the CANTAB neuropsychological test battery in children.

PubMed

Syväoja, Heidi J; Tammelin, Tuija H; Ahonen, Timo; Räsänen, Pekka; Tolvanen, Asko; Kankaanpää, Anna; Kantomaa, Marko T

2015-06-01

The Cambridge Neuropsychological Test Automated Battery (CANTAB) is a computer-assessed test battery widely use in different populations. The internal consistency and 1-year stability of CANTAB tests were examined in school-age children. Two hundred-thirty children (57% girls) from five schools in the Jyväskylä school district in Finland participated in the study in spring 2011. The children completed the following CANTAB tests: (a) visual memory (pattern recognition memory [PRM] and spatial recognition memory [SRM]), (b) executive function (spatial span [SSP], Stockings of Cambridge [SOC], and intra-extra dimensional set shift [IED]), and (c) attention (reaction time [RTI] and rapid visual information processing [RVP]). Seventy-four children participated in the follow-up measurements (64% girls) in spring 2012. Cronbach's alpha reliability coefficient was used to estimate the internal consistency of the nonhampering test, and structural equation models were applied to examine the stability of these tests. The reliability and the stability could not be determined for IED or SSP because of the nature of these tests. The internal consistency was acceptable only in the RTI task. The 1-year stability was moderate-to-good for the PRM, RTI, and RVP. The SSP and IED showed a moderate correlation between the two measurement points. The SRM and the SOC tasks were not reliable or stable measures in this study population. For research purposes, we recommend using structural equation modeling to improve reliability. The results suggest that the reliability and the stability of computer-based test batteries should be confirmed in the target population before using them for clinical or research purposes. (c) 2015 APA, all rights reserved).

Predicting boundary shear stress and sediment transport over bed forms

USGS Publications Warehouse

McLean, S.R.; Wolfe, S.R.; Nelson, J.M.

1999-01-01

To estimate bed-load sediment transport rates in flows over bed forms such as ripples and dunes, spatially averaged velocity profiles are frequently used to predict mean boundary shear stress. However, such averaging obscures the complex, nonlinear interaction of wake decay, boundary-layer development, and topographically induced acceleration downstream of flow separation and often leads to inaccurate estimates of boundary stress, particularly skin friction, which is critically important in predicting bed-load transport rates. This paper presents an alternative methodology for predicting skin friction over 2D bed forms. The approach is based on combining the equations describing the mechanics of the internal boundary layer with semiempirical structure functions to predict the velocity at the crest of a bedform, where the flow is most similar to a uniform boundary layer. Significantly, the methodology is directed toward making specific predictions only at the bed-form crest, and as a result it avoids the difficulty and questionable validity of spatial averaging. The model provides an accurate estimate of the skin friction at the crest where transport rates are highest. Simple geometric constraints can be used to derive the mean transport rates as long as bed load is dominant.To estimate bed-load sediment transport rates in flows over bed forms such as ripples and dunes, spatially averaged velocity profiles are frequently used to predict mean boundary shear stress. However, such averaging obscures the complex, nonlinear interaction of wake decay, boundary-layer development, and topographically induced acceleration downstream of flow separation and often leads to inaccurate estimates of boundary stress, particularly skin friction, which is critically important in predicting bed-load transport rates. This paper presents an alternative methodology for predicting skin friction over 2D bed forms. The approach is based on combining the equations describing the mechanics of the internal boundary layer with semiempirical structure functions to predict the velocity at the crest of a bedform, where the flow is most similar to a uniform boundary layer. Significantly, the methodology is directed toward making specific predictions only at the bed-form crest, and as a result it avoids the difficulty and questionable validity of spatial averaging. The model provides an accurate estimate of the skin friction at the crest where transport rates are highest. Simple geometric constraints can be used to derive the mean transport rates as long as bed load is dominant.

Soliton tunneling in the nonlinear Schrödinger equation with variable coefficients and an external harmonic potential.

PubMed

Zhong, Wei-Ping; Belić, Milivoj R

2010-05-01

We report on the nonlinear tunneling effects of spatial solitons of the generalized nonlinear Schrödinger equation with distributed coefficients in an external harmonic potential. By using the homogeneous balance principle and the F-expansion technique we find the spatial bright and dark soliton solutions. We then display tunneling effects of such solutions occurring under special conditions; specifically when the spatial solitons pass unchanged through the potential barriers and wells affected by special choices of the diffraction and/or the nonlinearity coefficients. Our results show that the solitons display tunneling effects not only when passing through the nonlinear potential barriers or wells but also when passing through the diffractive barriers or wells. During tunneling the solitons may also undergo a controllable compression.

Solving the Hamilton-Jacobi equation for general relativity

NASA Astrophysics Data System (ADS)

Parry, J.; Salopek, D. S.; Stewart, J. M.

1994-03-01

We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly invariant under reparametrizations of the spatial coordinates (``gauge invariant''). At each order we solve the Hamiltonian constraint using a conformal transformation of the three-metric as well as a line integral in superspace. This gives a recursion relation for the generating functional which then may be solved to arbitrary order simply by functionally differentiating previous orders. At fourth order in spatial gradients we demonstrate solutions for irrotational dust as well as for a scalar field. We explicitly evolve the three-metric to the same order. This method can be used to derive the Zel'dovich approximation for general relativity.

On oscillating flows in randomly heterogeneous porous media.

PubMed

Trefry, M G; McLaughlin, D; Metcalfe, G; Lester, D; Ord, A; Regenauer-Lieb, K; Hobbs, B E

2010-01-13

The emergence of structure in reactive geofluid systems is of current interest. In geofluid systems, the fluids are supported by a porous medium whose physical and chemical properties may vary in space and time, sometimes sharply, and which may also evolve in reaction with the local fluids. Geofluids may also experience pressure and temperature conditions within the porous medium that drive their momentum relations beyond the normal Darcy regime. Furthermore, natural geofluid systems may experience forcings that are periodic in nature, or at least episodic. The combination of transient forcing, near-critical fluid dynamics and heterogeneous porous media yields a rich array of emergent geofluid phenomena that are only now beginning to be understood. One of the barriers to forward analysis in these geofluid systems is the problem of data scarcity. It is most often the case that fluid properties are reasonably well known, but that data on porous medium properties are measured with much less precision and spatial density. It is common to seek to perform an estimation of the porous medium properties by an inverse approach, that is, by expressing porous medium properties in terms of observed fluid characteristics. In this paper, we move toward such an inversion for the case of a generalized geofluid momentum equation in the context of time-periodic boundary conditions. We show that the generalized momentum equation results in frequency-domain responses that are governed by a second-order equation which is amenable to numerical solution. A stochastic perturbation approach demonstrates that frequency-domain responses of the fluids migrating in heterogeneous domains have spatial spectral densities that can be expressed in terms of the spectral densities of porous media properties. This journal is © 2010 The Royal Society

A novel simulation theory and model system for multi-field coupling pipe-flow system

NASA Astrophysics Data System (ADS)

Chen, Yang; Jiang, Fan; Cai, Guobiao; Xu, Xu

2017-09-01

Due to the lack of a theoretical basis for multi-field coupling in many system-level models, a novel set of system-level basic equations for flow/heat transfer/combustion coupling is put forward. Then a finite volume model of quasi-1D transient flow field for multi-species compressible variable-cross-section pipe flow is established by discretising the basic equations on spatially staggered grids. Combining with the 2D axisymmetric model for pipe-wall temperature field and specific chemical reaction mechanisms, a finite volume model system is established; a set of specific calculation methods suitable for multi-field coupling system-level research is structured for various parameters in this model; specific modularisation simulation models can be further derived in accordance with specific structures of various typical components in a liquid propulsion system. This novel system can also be used to derive two sub-systems: a flow/heat transfer two-field coupling pipe-flow model system without chemical reaction and species diffusion; and a chemical equilibrium thermodynamic calculation-based multi-field coupling system. The applicability and accuracy of two sub-systems have been verified through a series of dynamic modelling and simulations in earlier studies. The validity of this system is verified in an air-hydrogen combustion sample system. The basic equations and the model system provide a unified universal theory and numerical system for modelling and simulation and even virtual testing of various pipeline systems.

One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.

2018-04-01

The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

Exotic singularities and spatially curved loop quantum cosmology

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

Singh, Parampreet; Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5; Vidotto, Francesca

2011-03-15

We investigate the occurrence of various exotic spacelike singularities in the past and the future evolution of k={+-}1 Friedmann-Robertson-Walker model and loop quantum cosmology using a sufficiently general phenomenological model for the equation of state. We highlight the nontrivial role played by the intrinsic curvature for these singularities and the new physics which emerges at the Planck scale. We show that quantum gravity effects generically resolve all strong curvature singularities including big rip and big freeze singularities. The weak singularities, which include sudden and big brake singularities, are ignored by quantum gravity when spatial curvature is negative, as was previouslymore » found for the spatially flat model. Interestingly, for the spatially closed model there exist cases where weak singularities may be resolved when they occur in the past evolution. The spatially closed model exhibits another novel feature. For a particular class of equation of state, this model also exhibits an additional physical branch in loop quantum cosmology, a baby universe separated from the parent branch. Our analysis generalizes previous results obtained on the resolution of strong curvature singularities in flat models to isotropic spacetimes with nonzero spatial curvature.« less

Inverse scattering transform analysis of rogue waves using local periodization procedure

NASA Astrophysics Data System (ADS)

Randoux, Stéphane; Suret, Pierre; El, Gennady

2016-07-01

The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra.

A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2017-12-01

In this manuscript, we consider an initial-boundary-value problem governed by a (1 + 1)-dimensional hyperbolic partial differential equation with constant damping that generalizes many nonlinear wave equations from mathematical physics. The model considers the presence of a spatial Laplacian of fractional order which is defined in terms of Riesz fractional derivatives, as well as the inclusion of a generic continuously differentiable potential. It is known that the undamped regime has an associated positive energy functional, and we show here that it is preserved throughout time under suitable boundary conditions. To approximate the solutions of this model, we propose a finite-difference discretization based on fractional centered differences. Some discrete quantities are proposed in this work to estimate the energy functional, and we show that the numerical method is capable of conserving the discrete energy under the same boundary conditions for which the continuous model is conservative. Moreover, we establish suitable computational constraints under which the discrete energy of the system is positive. The method is consistent of second order, and is both stable and convergent. The numerical simulations shown here illustrate the most important features of our numerical methodology.

Non-material finite element modelling of large vibrations of axially moving strings and beams

NASA Astrophysics Data System (ADS)

Vetyukov, Yury

2018-02-01

We present a new mathematical model for the dynamics of a beam or a string, which moves in a given axial direction across a particular domain. Large in-plane vibrations are coupled with the gross axial motion, and a Lagrangian (material) form of the equations of structural mechanics becomes inefficient. The proposed mixed Eulerian-Lagrangian description features mechanical fields as functions of a spatial coordinate in the axial direction. The material travels across a finite element mesh, and the boundary conditions are applied in fixed nodes. Beginning with the variational equation of virtual work in its material form, we analytically derive the Lagrange's equations of motion of the second kind for the considered case of a discretized non-material control domain and for geometrically exact kinematics. The dynamic analysis is straightforward as soon as the strain and the kinetic energies of the control domain are available. In numerical simulations we demonstrate the rapid mesh convergence of the model, the effect of the bending stiffness and the dynamic instability when the axial velocity gets high. We also show correspondence to the results of fully Lagrangian benchmark solutions.

Inverse scattering transform analysis of rogue waves using local periodization procedure

PubMed Central

Randoux, Stéphane; Suret, Pierre; El, Gennady

2016-01-01

The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra. PMID:27385164

Localized solutions of Lugiato-Lefever equations with focused pump.

PubMed

Cardoso, Wesley B; Salasnich, Luca; Malomed, Boris A

2017-12-04

Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too-in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump and loss. Then, a family of exact analytical solutions for spatially confined modes is produced for the pump focused in the form of a delta-function, with a nonlinear loss (two-photon absorption) added to the LL model. Numerical findings demonstrate that these exact solutions are stable, both dynamically and structurally (the latter means that stable numerical solutions close to the exact ones are found when a specific condition, necessary for the existence of the analytical solution, does not hold). In 2D, vast families of stable confined modes are produced by means of a variational approximation and full numerical simulations.

Cross-Diffusion Induced Turing Instability and Amplitude Equation for a Toxic-Phytoplankton-Zooplankton Model with Nonmonotonic Functional Response

NASA Astrophysics Data System (ADS)

Han, Renji; Dai, Binxiang

2017-06-01

The spatiotemporal pattern induced by cross-diffusion of a toxic-phytoplankton-zooplankton model with nonmonotonic functional response is investigated in this paper. The linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, we derive amplitude equations near the Turing bifurcation point for the excited modes in the framework of a weakly nonlinear theory, and the stability analysis of the amplitude equations interprets the structural transitions and stability of various forms of Turing patterns. Furthermore, we illustrate the theoretical results via numerical simulations. It is shown that the spatiotemporal distribution of the plankton is homogeneous in the absence of cross-diffusion. However, when the cross-diffusivity is greater than the critical value, the spatiotemporal distribution of all the plankton species becomes inhomogeneous in spaces and results in different kinds of patterns: spot, stripe, and the mixture of spot and stripe patterns depending on the cross-diffusivity. Simultaneously, the impact of toxin-producing rate of toxic-phytoplankton (TPP) species and natural death rate of zooplankton species on pattern selection is also explored.

The Green's function in a channel with a sound-absorbing cover in the case of a uniform flow

NASA Astrophysics Data System (ADS)

Sobolev, A. F.

2012-07-01

We study the modal structure of an acoustic field of a point source as function of channel wall admittance in the case of a two-dimensional channel. The characteristic equation for determining the eigen-values corresponding to the boundary problem is studied in the form of this equation's dependence on the admittance, which varies in the entire complex plane. All modes, without exception, existing in the channel and forming the source field are classified based on the obtained topography of the characteristic equation. The expressions that describe the amplitudes and spatial distribution of the hydrodynamic modes, attenuation rate (for stable modes), or increment (for unstable modes) were obtained as functions of the wall admittance and flow velocity. It is shown that in addition to the hydrodynamic unstable modes existing downstream from the source, hydrodynamic unstable modes exist upstream from the source at any admittance. They appear only when the admittance has an elastic character. It is shown that hydrodynamic modes are induced only in the case when the source is located close to the wall or on the wall. The amplitude of these modes decreases exponentially with distance from the wall.

Ensemble Averaged Probability Density Function (APDF) for Compressible Turbulent Reacting Flows

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2012-01-01

In this paper, we present a concept of the averaged probability density function (APDF) for studying compressible turbulent reacting flows. The APDF is defined as an ensemble average of the fine grained probability density function (FG-PDF) with a mass density weighting. It can be used to exactly deduce the mass density weighted, ensemble averaged turbulent mean variables. The transport equation for APDF can be derived in two ways. One is the traditional way that starts from the transport equation of FG-PDF, in which the compressible Navier- Stokes equations are embedded. The resulting transport equation of APDF is then in a traditional form that contains conditional means of all terms from the right hand side of the Navier-Stokes equations except for the chemical reaction term. These conditional means are new unknown quantities that need to be modeled. Another way of deriving the transport equation of APDF is to start directly from the ensemble averaged Navier-Stokes equations. The resulting transport equation of APDF derived from this approach appears in a closed form without any need for additional modeling. The methodology of ensemble averaging presented in this paper can be extended to other averaging procedures: for example, the Reynolds time averaging for statistically steady flow and the Reynolds spatial averaging for statistically homogeneous flow. It can also be extended to a time or spatial filtering procedure to construct the filtered density function (FDF) for the large eddy simulation (LES) of compressible turbulent reacting flows.

A New Method for 3D Radiative Transfer with Adaptive Grids

NASA Astrophysics Data System (ADS)

Folini, D.; Walder, R.; Psarros, M.; Desboeufs, A.

2003-01-01

We present a new method for 3D NLTE radiative transfer in moving media, including an adaptive grid, along with some test examples and first applications. The central features of our approach we briefly outline in the following. For the solution of the radiative transfer equation, we make use of a generalized mean intensity approach. In this approach, the transfer eqation is solved directly, instead of using the moments of the transfer equation, thus avoiding the associated closure problem. In a first step, a system of equations for the transfer of each directed intensity is set up, using short characteristics. Next, the entity of systems of equations for each directed intensity is re-formulated in the form of one system of equations for the angle-integrated mean intensity. This system then is solved by a modern, fast BiCGStab iterative solver. An additional advantage of this procedure is that convergence rates barely depend on the spatial discretization. For the solution of the rate equations we use Housholder transformations. Lines are treated by a 3D generalization of the well-known Sobolev-approximation. The two parts, solution of the transfer equation and solution of the rate equations, are iteratively coupled. We recently have implemented an adaptive grid, which allows for recursive refinement on a cell-by-cell basis. The spatial resolution, which is always a problematic issue in 3D simulations, we can thus locally reduce or augment, depending on the problem to be solved.

Nonnegative methods for bilinear discontinuous differencing of the S N equations on quadrilaterals

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-12-22

Historically, matrix lumping and ad hoc flux fixups have been the only methods used to eliminate or suppress negative angular flux solutions associated with the unlumped bilinear discontinuous (UBLD) finite element spatial discretization of the two-dimensional S N equations. Though matrix lumping inhibits negative angular flux solutions of the S N equations, it does not guarantee strictly positive solutions. In this paper, we develop and define a strictly nonnegative, nonlinear, Petrov-Galerkin finite element method that fully preserves the bilinear discontinuous spatial moments of the transport equation. Additionally, we define two ad hoc fixups that maintain particle balance and explicitly setmore » negative nodes of the UBLD finite element solution to zero but use different auxiliary equations to fully define their respective solutions. We assess the ability to inhibit negative angular flux solutions and the accuracy of every spatial discretization that we consider using a glancing void test problem with a discontinuous solution known to stress numerical methods. Though significantly more computationally intense, the nonlinear Petrov-Galerkin scheme results in a strictly nonnegative solution and is a more accurate solution than all the other methods considered. One fixup, based on shape preserving, results in a strictly nonnegative final solution but has increased numerical diffusion relative to the Petrov-Galerkin scheme and is less accurate than the UBLD solution. The second fixup, which preserves as many spatial moments as possible while setting negative values of the unlumped solution to zero, is less accurate than the Petrov-Galerkin scheme but is more accurate than the other fixup. However, it fails to guarantee a strictly nonnegative final solution. As a result, the fully lumped bilinear discontinuous finite element solution is the least accurate method, with significantly more numerical diffusion than the Petrov-Galerkin scheme and both fixups.« less

Nonnegative methods for bilinear discontinuous differencing of the S N equations on quadrilaterals

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

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

Historically, matrix lumping and ad hoc flux fixups have been the only methods used to eliminate or suppress negative angular flux solutions associated with the unlumped bilinear discontinuous (UBLD) finite element spatial discretization of the two-dimensional S N equations. Though matrix lumping inhibits negative angular flux solutions of the S N equations, it does not guarantee strictly positive solutions. In this paper, we develop and define a strictly nonnegative, nonlinear, Petrov-Galerkin finite element method that fully preserves the bilinear discontinuous spatial moments of the transport equation. Additionally, we define two ad hoc fixups that maintain particle balance and explicitly setmore » negative nodes of the UBLD finite element solution to zero but use different auxiliary equations to fully define their respective solutions. We assess the ability to inhibit negative angular flux solutions and the accuracy of every spatial discretization that we consider using a glancing void test problem with a discontinuous solution known to stress numerical methods. Though significantly more computationally intense, the nonlinear Petrov-Galerkin scheme results in a strictly nonnegative solution and is a more accurate solution than all the other methods considered. One fixup, based on shape preserving, results in a strictly nonnegative final solution but has increased numerical diffusion relative to the Petrov-Galerkin scheme and is less accurate than the UBLD solution. The second fixup, which preserves as many spatial moments as possible while setting negative values of the unlumped solution to zero, is less accurate than the Petrov-Galerkin scheme but is more accurate than the other fixup. However, it fails to guarantee a strictly nonnegative final solution. As a result, the fully lumped bilinear discontinuous finite element solution is the least accurate method, with significantly more numerical diffusion than the Petrov-Galerkin scheme and both fixups.« less

The Stabilizing Effect of Spacetime Expansion on Relativistic Fluids With Sharp Results for the Radiation Equation of State

NASA Astrophysics Data System (ADS)

Speck, Jared

2013-07-01

In this article, we study the 1 + 3-dimensional relativistic Euler equations on a pre-specified conformally flat expanding spacetime background with spatial slices that are diffeomorphic to {R}^3. We assume that the fluid verifies the equation of state {p = c2s ρ,} where {0 ≤ cs ≤ √{1/3}} is the speed of sound. We also assume that the reciprocal of the scale factor associated with the expanding spacetime metric verifies a c s -dependent time-integrability condition. Under these assumptions, we use the vector field energy method to prove that an explicit family of physically motivated, spatially homogeneous, and spatially isotropic fluid solutions are globally future-stable under small perturbations of their initial conditions. The explicit solutions corresponding to each scale factor are analogs of the well-known spatially flat Friedmann-Lemaître-Robertson-Walker family. Our nonlinear analysis, which exploits dissipative terms generated by the expansion, shows that the perturbed solutions exist for all future times and remain close to the explicit solutions. This work is an extension of previous results, which showed that an analogous stability result holds when the spacetime is exponentially expanding. In the case of the radiation equation of state p = (1/3)ρ, we also show that if the time-integrability condition for the reciprocal of the scale factor fails to hold, then the explicit fluid solutions are unstable. More precisely, we show the existence of an open family of initial data such that (i) it contains arbitrarily small smooth perturbations of the explicit solutions' data and (ii) the corresponding perturbed solutions necessarily form shocks in finite time. The shock formation proof is based on the conformal invariance of the relativistic Euler equations when {c2s = 1/3,} which allows for a reduction to a well-known result of Christodoulou.

Bright-type and dark-type vector solitons of the (2 + 1)-dimensional spatially modulated quintic nonlinear Schrödinger equation in nonlinear optics and Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Wu, Hong-Yu; Jiang, Li-Hong

2018-03-01

We study a (2 + 1) -dimensional N -coupled quintic nonlinear Schrödinger equation with spatially modulated nonlinearity and transverse modulation in nonlinear optics and Bose-Einstein condensate, and obtain bright-type and dark-type vector multipole as well as vortex soliton solutions. When the modulation depth q is fixed as 0 and 1, we can construct vector multipole and vortex solitons, respectively. Based on these solutions, we investigate the form and phase characteristics of vector multipole and vortex solitons.

The Dirac equation and the normalization of its solutions in a closed Friedmann- Robertson-Walker universe

NASA Astrophysics Data System (ADS)

Finster, Felix; Reintjes, Moritz

2009-05-01

We set up the Dirac equation in a Friedmann-Robertson-Walker geometry and separate the spatial and time variables. In the case of a closed universe, the spatial dependence is solved explicitly, giving rise to a discrete set of solutions. We compute the probability integral and analyze a spacetime normalization integral. This analysis allows us to introduce the fermionic projector in a closed Friedmann-Robertson-Walker geometry and to specify its global normalization as well as its local form. First author supported in part by the Deutsche Forschungsgemeinschaft.

Solidification of a binary mixture

NASA Technical Reports Server (NTRS)

Antar, B. N.

1982-01-01

The time dependent concentration and temperature profiles of a finite layer of a binary mixture are investigated during solidification. The coupled time dependent Stefan problem is solved numerically using an implicit finite differencing algorithm with the method of lines. Specifically, the temporal operator is approximated via an implicit finite difference operator resulting in a coupled set of ordinary differential equations for the spatial distribution of the temperature and concentration for each time. Since the resulting differential equations set form a boundary value problem with matching conditions at an unknown spatial point, the method of invariant imbedding is used for its solution.

Development of Spatially-Based Emission Factors from Real-Time Measurements of Gaseous Pollutants Using Cermet Sensors

DTIC Science & Technology

2005-03-01

produce a current-limited steady state output potential that follows the Nernst equation (Fraden 1993): E = Eo + ((RT)/nF)ln(CO/CR) (2) CO...temperature, EO: electrode potential at standard state. Nernst equation governs many half-cell reactions in electrochemical cells. The cell...voltammetric cell, the analytes react (oxidize or reduce) at very characteristic potentials according to the following simplified equation (Smyth

Coupling of Coastal Wave Transformation and Computational Fluid Dynamics Models for Seakeeping Analysis

DTIC Science & Technology

2017-04-03

setup in terms of temporal and spatial discretization . The second component was an extension of existing depth-integrated wave models to describe...equations (Abbott, 1976). Discretization schemes involve numerical dispersion and dissipation that distort the true character of the governing equations...represent a leading-order approximation of the Boussinesq-type equations. Tam and Webb (1993) proposed a wavenumber-based discretization scheme to preserve

Quantification of root water uptake in soil using X-ray computed tomography and image-based modelling.

PubMed

Daly, Keith R; Tracy, Saoirse R; Crout, Neil M J; Mairhofer, Stefan; Pridmore, Tony P; Mooney, Sacha J; Roose, Tiina

2018-01-01

Spatially averaged models of root-soil interactions are often used to calculate plant water uptake. Using a combination of X-ray computed tomography (CT) and image-based modelling, we tested the accuracy of this spatial averaging by directly calculating plant water uptake for young wheat plants in two soil types. The root system was imaged using X-ray CT at 2, 4, 6, 8 and 12 d after transplanting. The roots were segmented using semi-automated root tracking for speed and reproducibility. The segmented geometries were converted to a mesh suitable for the numerical solution of Richards' equation. Richards' equation was parameterized using existing pore scale studies of soil hydraulic properties in the rhizosphere of wheat plants. Image-based modelling allows the spatial distribution of water around the root to be visualized and the fluxes into the root to be calculated. By comparing the results obtained through image-based modelling to spatially averaged models, the impact of root architecture and geometry in water uptake was quantified. We observed that the spatially averaged models performed well in comparison to the image-based models with <2% difference in uptake. However, the spatial averaging loses important information regarding the spatial distribution of water near the root system. © 2017 John Wiley & Sons Ltd.

Spatial Moment Equations for a Groundwater Plume with Degradation and Rate-Limited Sorption

EPA Science Inventory

In this note, we analytically derive the solution for the spatial moments of groundwater solute concentration distributions simulated by a one-dimensional model that assumes advective-dispersive transport with first-order degradation and rate-limited sorption. Sorption kinetics...

A Process Model for the Comprehension of Organic Chemistry Notation

ERIC Educational Resources Information Center

Havanki, Katherine L.

2012-01-01

This dissertation examines the cognitive processes individuals use when reading organic chemistry equations and factors that affect these processes, namely, visual complexity of chemical equations and participant characteristics (expertise, spatial ability, and working memory capacity). A six stage process model for the comprehension of organic…

Novel Metamaterial Blueprints and Elements for Electromagnetic Applications

NASA Astrophysics Data System (ADS)

Odabasi, Hayrettin

In the first part of this dissertation, we explore the metric invariance of Maxwell's equations to design metamaterial blueprints for three novel electromagnetic devices. The metric invariance of Maxwell's equations here means that the effects of an (hypothetical) distortion of the background spatial domain on the electromagnetic fields can be mimicked by properly chosen material constitutive tensors. The exploitation of such feature of Maxwell's equations to derive metamaterial devices has been denoted as `transformation optics' (TO). The first device proposed here consists of metamaterial blueprints of waveguide claddings for (waveguide) miniaturization. These claddings provide a precise control of mode distribution and frequency cut-off. The proposed claddings are distinct from conventional dielectric loadings as the former do not support hybrid modes and are impedance-matched to free-space. We next derive a class of metamaterial blueprints designed for low-profile antenna applications, whereby a simple spatial transformation is used to yield uniaxial metamaterial substrate with electrical height higher than its physical height and surface waves are not supported, which is an advantage for patch antenna applications. We consider the radiation from horizontal wire and patch antennas in the presence of such substrates. Fundamental characteristics such as return loss and radiation pattern of the antennas are investigated in detail. Finally, transformation optics is also applied to design cylindrical impedance-matched absorbers. In this case, we employ a complex-valued transformation optics approach (in the Fourier domain) as opposed to the conventional real-valued approach. A connection of such structures with perfectly matched layers and recently proposed optical pseudo black-hole devices is made. In the second part of this dissertation, we move from the derivation of metamaterial blueprints to the application of pre-defined unit-cell metamaterial structures for miniaturization purposes. We first employ electric-field-coupled (ELC) resonators and complementary electric-field-coupled (CELC) resonators to design a new class of electrically small antennas. Since electric-field coupled resonators were recently proposed in the literature to obtain negative permittivity response, we next propose ELC resonators as a new type of waveguide loadings to provide mode control and waveguide miniaturization.

A Space-Time Conservation Element and Solution Element Method for Solving the Two- and Three-Dimensional Unsteady Euler Equations Using Quadrilateral and Hexahedral Meshes

NASA Technical Reports Server (NTRS)

Zhang, Zeng-Chan; Yu, S. T. John; Chang, Sin-Chung; Jorgenson, Philip (Technical Monitor)

2001-01-01

In this paper, we report a version of the Space-Time Conservation Element and Solution Element (CE/SE) Method in which the 2D and 3D unsteady Euler equations are simulated using structured or unstructured quadrilateral and hexahedral meshes, respectively. In the present method, mesh values of flow variables and their spatial derivatives are treated as independent unknowns to be solved for. At each mesh point, the value of a flow variable is obtained by imposing a flux conservation condition. On the other hand, the spatial derivatives are evaluated using a finite-difference/weighted-average procedure. Note that the present extension retains many key advantages of the original CE/SE method which uses triangular and tetrahedral meshes, respectively, for its 2D and 3D applications. These advantages include efficient parallel computing ease of implementing non-reflecting boundary conditions, high-fidelity resolution of shocks and waves, and a genuinely multidimensional formulation without using a dimensional-splitting approach. In particular, because Riemann solvers, the cornerstones of the Godunov-type upwind schemes, are not needed to capture shocks, the computational logic of the present method is considerably simpler. To demonstrate the capability of the present method, numerical results are presented for several benchmark problems including oblique shock reflection, supersonic flow over a wedge, and a 3D detonation flow.

Structural, mechanical and vibrational study of uranyl silicate mineral soddyite by DFT calculations

NASA Astrophysics Data System (ADS)

Colmenero, Francisco; Bonales, Laura J.; Cobos, Joaquín; Timón, Vicente

2017-09-01

Uranyl silicate mineral soddyite, (UO2)2(SiO4)·2(H2O), is a fundamental component of the paragenetic sequence of secondary phases that arises from the weathering of uraninite ore deposits and corrosion of spent nuclear fuel. In this work, soddyite was studied by first principle calculations based on the density functional theory. As far as we know, this is the first time that soddyite structure is determined theoretically. The computed structure of soddyite reproduces the one determined experimentally by X-Ray diffraction (orthorhombic symmetry, spatial group Fddd O2; lattice parameters a = 8.334 Å, b = 11.212 Å; c = 18.668 Å). Lattice parameters, bond lengths, bond angles and X-Ray powder pattern were found to be in very good agreement with their experimental counterparts. Furthermore, the mechanical properties were obtained and the satisfaction of the Born conditions for mechanical stability of the structure was demonstrated by means of calculations of the elasticity tensor. The equation of state of soddyite was obtained by fitting lattice volumes and pressures to a fourth order Birch-Murnahan equation of state. The Raman spectrum was also computed by means of density functional perturbation theory and compared with the experimental spectrum obtained from a natural soddyite sample. The results were also found in agreement with the experimental data. A normal mode analysis of the theoretical spectra was carried out and used in order to assign the main bands of the Raman spectrum.

Sex Differences in Using Spatial and Verbal Abilities Influence Route Learning Performance in a Virtual Environment: A Comparison of 6- to 12-Year Old Boys and Girls

PubMed Central

Merrill, Edward C.; Yang, Yingying; Roskos, Beverly; Steele, Sara

2016-01-01

Previous studies have reported sex differences in wayfinding performance among adults. Men are typically better at using Euclidean information and survey strategies while women are better at using landmark information and route strategies. However, relatively few studies have examined sex differences in wayfinding in children. This research investigated relationships between route learning performance and two general abilities: spatial ability and verbal memory in 153 boys and girls between 6- to 12-years-old. Children completed a battery of spatial ability tasks (a two-dimension mental rotation task, a paper folding task, a visuo-spatial working memory task, and a Piagetian water level task) and a verbal memory task. In the route learning task, they had to learn a route through a series of hallways presented via computer. Boys had better overall route learning performance than did girls. In fact, the difference between boys and girls was constant across the age range tested. Structural equation modeling of the children’s performance revealed that spatial abilities and verbal memory were significant contributors to route learning performance. However, there were different patterns of correlates for boys and girls. For boys, spatial abilities contributed to route learning while verbal memory did not. In contrast, for girls both spatial abilities and verbal memory contributed to their route learning performance. This difference may reflect the precursor of a strategic difference between boys and girls in wayfinding that is commonly observed in adults. PMID:26941701

Numerical simulation of electrophoresis separation processes

NASA Technical Reports Server (NTRS)

Ganjoo, D. K.; Tezduyar, T. E.

1986-01-01

A new Petrov-Galerkin finite element formulation has been proposed for transient convection-diffusion problems. Most Petrov-Galerkin formulations take into account the spatial discretization, and the weighting functions so developed give satisfactory solutions for steady state problems. Though these schemes can be used for transient problems, there is scope for improvement. The schemes proposed here, which consider temporal as well as spatial discretization, provide improved solutions. Electrophoresis, which involves the motion of charged entities under the influence of an applied electric field, is governed by equations similiar to those encountered in fluid flow problems, i.e., transient convection-diffusion equations. Test problems are solved in electrophoresis and fluid flow. The results obtained are satisfactory. It is also expected that these schemes, suitably adapted, will improve the numerical solutions of the compressible Euler and the Navier-Stokes equations.

Multi-Hamiltonian structure of equations of hydrodynamic type

NASA Astrophysics Data System (ADS)

Gümral, H.; Nutku, Y.

1990-11-01

The discussion of the Hamiltonian structure of two-component equations of hydrodynamic type is completed by presenting the Hamiltonian operators for Euler's equation governing the motion of plane sound waves of finite amplitude and another quasilinear second-order wave equation. There exists a doubly infinite family of conserved Hamiltonians for the equations of gas dynamics that degenerate into one, namely, the Benney sequence, for shallow-water waves. Infinite sequences of conserved quantities for these equations are also presented. In the case of multicomponent equations of hydrodynamic type, it is shown, that Kodama's generalization of the shallow-water equations admits bi-Hamiltonian structure.

Optimal Scaling of Aftershock Zones using Ground Motion Forecasts

NASA Astrophysics Data System (ADS)

Wilson, John Max; Yoder, Mark R.; Rundle, John B.

2018-02-01

The spatial distribution of aftershocks following major earthquakes has received significant attention due to the shaking hazard these events pose for structures and populations in the affected region. Forecasting the spatial distribution of aftershock events is an important part of the estimation of future seismic hazard. A simple spatial shape for the zone of activity has often been assumed in the form of an ellipse having semimajor axis to semiminor axis ratio of 2.0. However, since an important application of these calculations is the estimation of ground shaking hazard, an effective criterion for forecasting future aftershock impacts is to use ground motion prediction equations (GMPEs) in addition to the more usual approach of using epicentral or hypocentral locations. Based on these ideas, we present an aftershock model that uses self-similarity and scaling relations to constrain parameters as an option for such hazard assessment. We fit the spatial aspect ratio to previous earthquake sequences in the studied regions, and demonstrate the effect of the fitting on the likelihood of post-disaster ground motion forecasts for eighteen recent large earthquakes. We find that the forecasts in most geographic regions studied benefit from this optimization technique, while some are better suited to the use of the a priori aspect ratio.

On Relations Between the Ozonosphere and the General Atmospheric Circulation in Tropics

NASA Astrophysics Data System (ADS)

Kuznetsov, G. I.; Kramarova, N. A.

2006-05-01

The main features of temporal and spatial ozone distribution over tropics and their relations with peculiarities of the general atmospheric circulation are obtained using the total ozone data for the tropical region (Ozone Data for the World and TOMS (version 8)). Among the factors influencing ozone regime in tropics the properties of the region, like intertropical convergence zone and a structure of tropical tropopause, and processes such as stratosphere-troposphere exchange, migration of ozone equator, Quasi Biennial Oscillation are analyzed. To investigate the long term variability of tropical ozone detrended and de-seasonalized fields of TOMS observations are analyzed by means of EOF method. The first four EOFs explain about 75% of residual total ozone variability in tropical region. Spatial patterns of EOFs and corresponding time coefficients are closely connected with the Quasi-Biennial Oscillation (EOF-1), the 11-years Solar Cycle (EOF-2), the QBO-annual beat (EOF-3) and with the South Oscillation (EOF-4) correspondingly. The detailed analyses of temporal and spatial distribution of ozone EOF patterns reveals a distinct change of ozone fields to the both sides of equator at 10-15 latitude as well as at the zones of tropical tropopause break. A time delay of ozone QBO phase is observed while moving towards higher latitudes. Some features of the tropical ozone regime manifest themselves in the peculiarities of Antarctic Ozone Anomalies. A time variability of ozone QBO passes three months ahead of the Singapore 30 mbar zonal wind. Obtained relations let us to construct a linear regression model based on EOF decomposition to estimate total ozone monthly means over tropics. This model is successfully applied to predict 30 mbar zonal wind in dependence on tropical ozone behavior.

Accounting for spatial variation of trabecular anisotropy with subject-specific finite element modeling moderately improves predictions of local subchondral bone stiffness at the proximal tibia.

PubMed

Nazemi, S Majid; Kalajahi, S Mehrdad Hosseini; Cooper, David M L; Kontulainen, Saija A; Holdsworth, David W; Masri, Bassam A; Wilson, David R; Johnston, James D

2017-07-05

Previously, a finite element (FE) model of the proximal tibia was developed and validated against experimentally measured local subchondral stiffness. This model indicated modest predictions of stiffness (R 2 =0.77, normalized root mean squared error (RMSE%)=16.6%). Trabecular bone though was modeled with isotropic material properties despite its orthotropic anisotropy. The objective of this study was to identify the anisotropic FE modeling approach which best predicted (with largest explained variance and least amount of error) local subchondral bone stiffness at the proximal tibia. Local stiffness was measured at the subchondral surface of 13 medial/lateral tibial compartments using in situ macro indentation testing. An FE model of each specimen was generated assuming uniform anisotropy with 14 different combinations of cortical- and tibial-specific density-modulus relationships taken from the literature. Two FE models of each specimen were also generated which accounted for the spatial variation of trabecular bone anisotropy directly from clinical CT images using grey-level structure tensor and Cowin's fabric-elasticity equations. Stiffness was calculated using FE and compared to measured stiffness in terms of R 2 and RMSE%. The uniform anisotropic FE model explained 53-74% of the measured stiffness variance, with RMSE% ranging from 12.4 to 245.3%. The models which accounted for spatial variation of trabecular bone anisotropy predicted 76-79% of the variance in stiffness with RMSE% being 11.2-11.5%. Of the 16 evaluated finite element models in this study, the combination of Synder and Schneider (for cortical bone) and Cowin's fabric-elasticity equations (for trabecular bone) best predicted local subchondral bone stiffness. Copyright © 2017 Elsevier Ltd. All rights reserved.

Influence of mesh structure on 2D full shallow water equations and SCS Curve Number simulation of rainfall/runoff events

NASA Astrophysics Data System (ADS)

Caviedes-Voullième, Daniel; García-Navarro, Pilar; Murillo, Javier

2012-07-01

SummaryHydrological simulation of rain-runoff processes is often performed with lumped models which rely on calibration to generate storm hydrographs and study catchment response to rain. In this paper, a distributed, physically-based numerical model is used for runoff simulation in a mountain catchment. This approach offers two advantages. The first is that by using shallow-water equations for runoff flow, there is less freedom to calibrate routing parameters (as compared to, for example, synthetic hydrograph methods). The second, is that spatial distributions of water depth and velocity can be obtained. Furthermore, interactions among the various hydrological processes can be modeled in a physically-based approach which may depend on transient and spatially distributed factors. On the other hand, the undertaken numerical approach relies on accurate terrain representation and mesh selection, which also affects significantly the computational cost of the simulations. Hence, we investigate the response of a gauged catchment with this distributed approach. The methodology consists of analyzing the effects that the mesh has on the simulations by using a range of meshes. Next, friction is applied to the model and the response to variations and interaction with the mesh is studied. Finally, a first approach with the well-known SCS Curve Number method is studied to evaluate its behavior when coupled with a shallow-water model for runoff flow. The results show that mesh selection is of great importance, since it may affect the results in a magnitude as large as physical factors, such as friction. Furthermore, results proved to be less sensitive to roughness spatial distribution than to mesh properties. Finally, the results indicate that SCS-CN may not be suitable for simulating hydrological processes together with a shallow-water model.

Understanding the robustness of Hadley cell response to wide variations in ocean heat transport

NASA Astrophysics Data System (ADS)

Rencurrel, M. C.; Rose, B. E. J.

2017-12-01

One important aspect of our climate system is the relationship between surface climate and the poleward energy transport in the atmosphere and ocean. Previous studies have shown that increases in poleward ocean heat transport (OHT) tend to warm the midlatitudes without strongly affecting tropical SSTs, resulting in a reduction in the equator-to-pole temperature gradient. This "tropical thermostat" effect depends crucially on a slowdown of the Hadley circulation (HC), with consequent changes in surface evaporation, atmospheric water vapor, and cloudiness. Here we extend previous studies by considering a wide range of spatial patterns of OHT, which we impose in a suite of slab-ocean aquaplanet GCM simulations. The forcing patterns are idealized but sample a variety of ocean circulation features. We find that the tropical thermostat and HC slowdown effects are relatively robust across all forcing patterns. A 1 PW increase in the amplitude of the prescribed OHT spatial pattern results in a global mean warming and a roughly 5 x 1010 kg/s decrease in HC mass flux, regardless of the detailed spatial structure of the imposed OHT. While the rate of HC slowdown is relatively robust, the mechanisms driving it are less so. Smaller, equator-to-subtropical scale OHT patterns are associated with greater reduced Gross Moist Stability (GMS) than the larger-scale OHT patterns. As the imposed OHT is limited equatorward, the HC becomes less efficient at transporting energy out of the tropics, implying that GMS has a modulating effect on the dynamical response of the cell. These experiments offer some new insights on the interplay between atmospheric dynamics and the radiative and hydrological aspects of global climate.

On reinitializing level set functions

NASA Astrophysics Data System (ADS)

Min, Chohong

2010-04-01

In this paper, we consider reinitializing level functions through equation ϕt+sgn(ϕ0)(‖∇ϕ‖-1)=0[16]. The method of Russo and Smereka [11] is taken in the spatial discretization of the equation. The spatial discretization is, simply speaking, the second order ENO finite difference with subcell resolution near the interface. Our main interest is on the temporal discretization of the equation. We compare the three temporal discretizations: the second order Runge-Kutta method, the forward Euler method, and a Gauss-Seidel iteration of the forward Euler method. The fact that the time in the equation is fictitious makes a hypothesis that all the temporal discretizations result in the same result in their stationary states. The fact that the absolute stability region of the forward Euler method is not wide enough to include all the eigenvalues of the linearized semi-discrete system of the second order ENO spatial discretization makes another hypothesis that the forward Euler temporal discretization should invoke numerical instability. Our results in this paper contradict both the hypotheses. The Runge-Kutta and Gauss-Seidel methods obtain the second order accuracy, and the forward Euler method converges with order between one and two. Examining all their properties, we conclude that the Gauss-Seidel method is the best among the three. Compared to the Runge-Kutta, it is twice faster and requires memory two times less with the same accuracy.

Hydration effects on the electrostatic potential around tuftsin.

PubMed

Valdeavella, C V; Blatt, H D; Yang, L; Pettitt, B M

1999-08-01

The electrostatic potential and component dielectric constants from molecular dynamics (MD) trajectories of tuftsin, a tetrapeptide with the amino acid sequence Thr-Lys-Pro-Arg in water and in saline solution are presented. The results obtained from the analysis of the MD trajectories for the total electrostatic potential at points on a grid using the Ewald technique are compared with the solution to the Poisson-Boltzmann (PB) equation. The latter was solved using several sets of dielectric constant parameters. The effects of structural averaging on the PB results were also considered. Solute conformational mobility in simulations gives rise to an electrostatic potential map around the solute dominated by the solute monopole (or lowest order multipole). The detailed spatial variation of the electrostatic potential on the molecular surface brought about by the compounded effects of the distribution of water and ions close to the peptide, solvent mobility, and solute conformational mobility are not qualitatively reproducible from a reparametrization of the input solute and solvent dielectric constants to the PB equation for a single structure or for structurally averaged PB calculations. Nevertheless, by fitting the PB to the MD electrostatic potential surfaces with the dielectric constants as fitting parameters, we found that the values that give the best fit are the values calculated from the MD trajectories. Implications of using such field calculations on the design of tuftsin peptide analogues are discussed.

Sound production due to large-scale coherent structures

NASA Technical Reports Server (NTRS)

Gatski, T. B.

1979-01-01

The acoustic pressure fluctuations due to large-scale finite amplitude disturbances in a free turbulent shear flow are calculated. The flow is decomposed into three component scales; the mean motion, the large-scale wave-like disturbance, and the small-scale random turbulence. The effect of the large-scale structure on the flow is isolated by applying both a spatial and phase average on the governing differential equations and by initially taking the small-scale turbulence to be in energetic equilibrium with the mean flow. The subsequent temporal evolution of the flow is computed from global energetic rate equations for the different component scales. Lighthill's theory is then applied to the region with the flowfield as the source and an observer located outside the flowfield in a region of uniform velocity. Since the time history of all flow variables is known, a minimum of simplifying assumptions for the Lighthill stress tensor is required, including no far-field approximations. A phase average is used to isolate the pressure fluctuations due to the large-scale structure, and also to isolate the dynamic process responsible. Variation of mean square pressure with distance from the source is computed to determine the acoustic far-field location and decay rate, and, in addition, spectra at various acoustic field locations are computed and analyzed. Also included are the effects of varying the growth and decay of the large-scale disturbance on the sound produced.

Fully anisotropic 3-D EM modelling on a Lebedev grid with a multigrid pre-conditioner

NASA Astrophysics Data System (ADS)

Jaysaval, Piyoosh; Shantsev, Daniil V.; de la Kethulle de Ryhove, Sébastien; Bratteland, Tarjei

2016-12-01

We present a numerical algorithm for 3-D electromagnetic (EM) simulations in conducting media with general electric anisotropy. The algorithm is based on the finite-difference discretization of frequency-domain Maxwell's equations on a Lebedev grid, in which all components of the electric field are collocated but half a spatial step staggered with respect to the magnetic field components, which also are collocated. This leads to a system of linear equations that is solved using a stabilized biconjugate gradient method with a multigrid preconditioner. We validate the accuracy of the numerical results for layered and 3-D tilted transverse isotropic (TTI) earth models representing typical scenarios used in the marine controlled-source EM method. It is then demonstrated that not taking into account the full anisotropy of the conductivity tensor can lead to misleading inversion results. For synthetic data corresponding to a 3-D model with a TTI anticlinal structure, a standard vertical transverse isotropic (VTI) inversion is not able to image a resistor, while for a 3-D model with a TTI synclinal structure it produces a false resistive anomaly. However, if the VTI forward solver used in the inversion is replaced by the proposed TTI solver with perfect knowledge of the strike and dip of the dipping structures, the resulting resistivity images become consistent with the true models.

Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

NASA Astrophysics Data System (ADS)

Pipkins, Daniel Scott

Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially.

Estimation of peak discharge quantiles for selected annual exceedance probabilities in northeastern Illinois

USGS Publications Warehouse

Over, Thomas M.; Saito, Riki J.; Veilleux, Andrea G.; Sharpe, Jennifer B.; Soong, David T.; Ishii, Audrey L.

2016-06-28

This report provides two sets of equations for estimating peak discharge quantiles at annual exceedance probabilities (AEPs) of 0.50, 0.20, 0.10, 0.04, 0.02, 0.01, 0.005, and 0.002 (recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, respectively) for watersheds in Illinois based on annual maximum peak discharge data from 117 watersheds in and near northeastern Illinois. One set of equations was developed through a temporal analysis with a two-step least squares-quantile regression technique that measures the average effect of changes in the urbanization of the watersheds used in the study. The resulting equations can be used to adjust rural peak discharge quantiles for the effect of urbanization, and in this study the equations also were used to adjust the annual maximum peak discharges from the study watersheds to 2010 urbanization conditions.The other set of equations was developed by a spatial analysis. This analysis used generalized least-squares regression to fit the peak discharge quantiles computed from the urbanization-adjusted annual maximum peak discharges from the study watersheds to drainage-basin characteristics. The peak discharge quantiles were computed by using the Expected Moments Algorithm following the removal of potentially influential low floods defined by a multiple Grubbs-Beck test. To improve the quantile estimates, regional skew coefficients were obtained from a newly developed regional skew model in which the skew increases with the urbanized land use fraction. The drainage-basin characteristics used as explanatory variables in the spatial analysis include drainage area, the fraction of developed land, the fraction of land with poorly drained soils or likely water, and the basin slope estimated as the ratio of the basin relief to basin perimeter.This report also provides the following: (1) examples to illustrate the use of the spatial and urbanization-adjustment equations for estimating peak discharge quantiles at ungaged sites and to improve flood-quantile estimates at and near a gaged site; (2) the urbanization-adjusted annual maximum peak discharges and peak discharge quantile estimates at streamgages from 181 watersheds including the 117 study watersheds and 64 additional watersheds in the study region that were originally considered for use in the study but later deemed to be redundant.The urbanization-adjustment equations, spatial regression equations, and peak discharge quantile estimates developed in this study will be made available in the web application StreamStats, which provides automated regression-equation solutions for user-selected stream locations. Figures and tables comparing the observed and urbanization-adjusted annual maximum peak discharge records by streamgage are provided at https://doi.org/10.3133/sir20165050 for download.

Negative stiffness and modulated states in active nematics.

PubMed

Srivastava, Pragya; Mishra, Prashant; Marchetti, M Cristina

2016-10-04

We examine the dynamics of an active nematic liquid crystal on a frictional substrate. When frictional damping dominates over viscous dissipation, we eliminate flow in favor of active stresses to obtain a minimal dynamical model for the nematic order parameter, with elastic constants renormalized by activity. The renormalized elastic constants can become negative at large activity, leading to the selection of spatially inhomogeneous patterns via a mechanism analogous to that responsible for modulated phases arising at an equilibrium Lifshitz point. Tuning activity and the degree of nematic order in the passive system, we obtain a linear stability phase diagram that exhibits a nonequilibrium tricritical point where ordered, modulated and disordered phases meet. Numerical solution of the nonlinear equations yields a succession of spatial structures of increasing complexity with increasing activity, including kink walls and active turbulence, as observed in experiments on microtubule bundles confined at an oil-water interface. Our work provides a minimal model for an overdamped active nematic that reproduces all the nonequilibrium structures seen in simulations of the full active nematic hydrodynamics and provides a framework for understanding some of the mechanisms for selection of the nonequilibrium patterns in the language of equilibrium critical phenomena.

Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations

NASA Astrophysics Data System (ADS)

Liu, Changying; Iserles, Arieh; Wu, Xinyuan

2018-03-01

The Klein-Gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering. Its computation represents a major challenge. The main theme of this paper is the construction of symmetric and arbitrarily high-order time integrators for the nonlinear Klein-Gordon equation by integrating Birkhoff-Hermite interpolation polynomials. To this end, under the assumption of periodic boundary conditions, we begin with the formulation of the nonlinear Klein-Gordon equation as an abstract second-order ordinary differential equation (ODE) and its operator-variation-of-constants formula. We then derive a symmetric and arbitrarily high-order Birkhoff-Hermite time integration formula for the nonlinear abstract ODE. Accordingly, the stability, convergence and long-time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix, subject to suitable temporal and spatial smoothness. A remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for PDEs in the literature. Numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches.

A variational image-based approach to the correction of susceptibility artifacts in the alignment of diffusion weighted and structural MRI.

PubMed

Tao, Ran; Fletcher, P Thomas; Gerber, Samuel; Whitaker, Ross T

2009-01-01

This paper presents a method for correcting the geometric and greyscale distortions in diffusion-weighted MRI that result from inhomogeneities in the static magnetic field. These inhomogeneities may due to imperfections in the magnet or to spatial variations in the magnetic susceptibility of the object being imaged--so called susceptibility artifacts. Echo-planar imaging (EPI), used in virtually all diffusion weighted acquisition protocols, assumes a homogeneous static field, which generally does not hold for head MRI. The resulting distortions are significant, sometimes more than ten millimeters. These artifacts impede accurate alignment of diffusion images with structural MRI, and are generally considered an obstacle to the joint analysis of connectivity and structure in head MRI. In principle, susceptibility artifacts can be corrected by acquiring (and applying) a field map. However, as shown in the literature and demonstrated in this paper, field map corrections of susceptibility artifacts are not entirely accurate and reliable, and thus field maps do not produce reliable alignment of EPIs with corresponding structural images. This paper presents a new, image-based method for correcting susceptibility artifacts. The method relies on a variational formulation of the match between an EPI baseline image and a corresponding T2-weighted structural image but also specifically accounts for the physics of susceptibility artifacts. We derive a set of partial differential equations associated with the optimization, describe the numerical methods for solving these equations, and present results that demonstrate the effectiveness of the proposed method compared with field-map correction.

Spatial adaptive sampling in multiscale simulation

NASA Astrophysics Data System (ADS)

Rouet-Leduc, Bertrand; Barros, Kipton; Cieren, Emmanuel; Elango, Venmugil; Junghans, Christoph; Lookman, Turab; Mohd-Yusof, Jamaludin; Pavel, Robert S.; Rivera, Axel Y.; Roehm, Dominic; McPherson, Allen L.; Germann, Timothy C.

2014-07-01

In a common approach to multiscale simulation, an incomplete set of macroscale equations must be supplemented with constitutive data provided by fine-scale simulation. Collecting statistics from these fine-scale simulations is typically the overwhelming computational cost. We reduce this cost by interpolating the results of fine-scale simulation over the spatial domain of the macro-solver. Unlike previous adaptive sampling strategies, we do not interpolate on the potentially very high dimensional space of inputs to the fine-scale simulation. Our approach is local in space and time, avoids the need for a central database, and is designed to parallelize well on large computer clusters. To demonstrate our method, we simulate one-dimensional elastodynamic shock propagation using the Heterogeneous Multiscale Method (HMM); we find that spatial adaptive sampling requires only ≈ 50 ×N0.14 fine-scale simulations to reconstruct the stress field at all N grid points. Related multiscale approaches, such as Equation Free methods, may also benefit from spatial adaptive sampling.

Two-soliton interaction as an elementary act of soliton turbulence in integrable systems

NASA Astrophysics Data System (ADS)

Pelinovsky, E. N.; Shurgalina, E. G.; Sergeeva, A. V.; Talipova, T. G.; El, G. A.; Grimshaw, R. H. J.

2013-01-01

Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. To quantify the contribution of these interactions to the dynamical and statistical characteristics of the nonlinear wave field of soliton turbulence we study properties of the spatial moments of the two-soliton solution of the Korteweg-de Vries (KdV) equation. While the first two moments are integrals of the KdV evolution, the 3rd and 4th moments undergo significant variations in the dominant interaction region, which could have strong effect on the values of the skewness and kurtosis in soliton turbulence.

Response of moderately thick laminated cross-ply composite shells subjected to random excitation

NASA Technical Reports Server (NTRS)

Elishakoff, Isaak; Cederbaum, Gabriel; Librescu, Liviu

1989-01-01

This study deals with the dynamic response of transverse shear deformable laminated shells subjected to random excitation. The analysis encompasses the following problems: (1) the dynamic response of circular cylindrical shells of finite length excited by an axisymmetric uniform ring loading, stationary in time, and (2) the response of spherical and cylindrical panels subjected to stationary random loadings with uniform spatial distribution. The associated equations governing the structural theory of shells are derived upon discarding the classical Love-Kirchhoff (L-K) assumptions. In this sense, the theory is formulated in the framework of the first-order transverse shear deformation theory (FSDT).

A metrics for soil hydrological processes and their intrinsic dimensionality in heterogeneous systems

NASA Astrophysics Data System (ADS)

Lischeid, G.; Hohenbrink, T.; Schindler, U.

2012-04-01

Hydrology is based on the observation that catchments process input signals, e.g., precipitation, in a highly deterministic way. Thus, the Darcy or the Richards equation can be applied to model water fluxes in the saturated or vadose zone, respectively. Soils and aquifers usually exhibit substantial spatial heterogeneities at different scales that can, in principle, be represented by corresponding parameterisations of the models. In practice, however, data are hardly available at the required spatial resolution, and accounting for observed heterogeneities of soil and aquifer structure renders models very time and CPU consuming. We hypothesize that the intrinsic dimensionality of soil hydrological processes, which is induced by spatial heterogeneities, actually is very low and that soil hydrological processes in heterogeneous soils follow approximately the same trajectory. That means, the way how the soil transforms any hydrological input signals is the same for different soil textures and structures. Different soils differ only with respect to the extent of transformation of input signals. In a first step, we analysed the output of a soil hydrological model, based on the Richards equation, for homogeneous soils down to 5 m depth for different soil textures. A matrix of time series of soil matrix potential and soil water content at 10 cm depth intervals was set up. The intrinsic dimensionality of that matrix was assessed using the Correlation Dimension and a non-linear principal component approach. The latter provided a metrics for the extent of transformation ("damping") of the input signal. In a second step, model outputs for heterogeneous soils were analysed. In a last step, the same approaches were applied to 55 time series of observed soil water content from 15 sites and different depths. In all cases, the intrinsic dimensionality in fact was very close to unity, confirming our hypothesis. The metrics provided a very efficient tool to quantify the observed behaviour, depending on depth and soil heterogeneity: Different soils differed primarily with respect to the extent of damping per depth interval rather than to the kind of damping. We will show how that metrics can be used in a very efficient way for representing soil heterogeneities in simulation models.

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

Gong, Jinn-Ouk; Hwang, Jai-chan; Noh, Hyerim

We present a complete set of exact and fully non-linear equations describing all three types of cosmological perturbations—scalar, vector and tensor perturbations. We derive the equations in a thoroughly gauge-ready manner, so that any spatial and temporal gauge conditions can be employed. The equations are completely general without any physical restriction except that we assume a flat homogeneous and isotropic universe as a background. We also comment briefly on the application of our formulation to the non-expanding Minkowski background.

Numerical study of radiometric forces via the direct solution of the Boltzmann kinetic equation

NASA Astrophysics Data System (ADS)

Anikin, Yu. A.

2011-07-01

The two-dimensional rarefied gas motion in a Crookes radiometer and the resulting radiometric forces are studied by numerically solving the Boltzmann kinetic equation. The collision integral is directly evaluated using a projection method, and second-order accurate TVD schemes are used to solve the advection equation. The radiometric forces are found as functions of the Knudsen number and the temperatures, and their spatial distribution is analyzed.

Optical testing using the transport-of-intensity equation.

PubMed

Dorrer, C; Zuegel, J D

2007-06-11

The transport-of-intensity equation links the intensity and phase of an optical source to the longitudinal variation of its intensity in the presence of Fresnel diffraction. This equation can be used to provide a simple, accurate spatial-phase measurement for optical testing of flat surfaces. The properties of this approach are derived. The experimental demonstration is performed by quantifying the surface variations induced by the magnetorheological finishing process on laser rods.

2-Dimensional B-Spline Algorithms with Applications to Ray Tracing in Media of Spatially-Varying Refractive Index

DTIC Science & Technology

2007-08-01

In the approach, photon trajectories are computed using a solution of the Eikonal equation (ray-tracing methods) rather than linear trajectories. The...coupling the radiative transport solution into heat transfer and damage models. 15. SUBJECT TERMS: B-Splines, Ray-Tracing, Eikonal Equation...multi-layer biological tissue model. In the approach, photon trajectories are computed using a solution of the Eikonal equation (ray-tracing methods

Stability of spatially developing boundary layers

NASA Astrophysics Data System (ADS)

Govindarajan, Rama

1993-07-01

A new formulation of the stability of boundary-layer flows in pressure gradients is presented, taking into account the spatial development of the flow. The formulation assumes that disturbance wavelength and eigenfunction vary downstream no more rapidly than the boundary-layer thickness, and includes all terms of O(1) and O(R(exp -1)) in the boundary-layer Reynolds number R. Although containing the Orr-Sommerfeld operator, the present approach does not yield the Orr-Sommerfeld equation in any rational limit. In Blasius flow, the present stability equation is consistent with that of Bertolotti et al. (1992) to terms of O(R(exp -1)). For the Falkner-Skan similarity solutions neutral boundaries are computed without the necessity of having to march in space. Results show that the effects of spatial growth are striking in flows subjected to adverse pressure gradients.

Computationally efficient statistical differential equation modeling using homogenization

USGS Publications Warehouse

Hooten, Mevin B.; Garlick, Martha J.; Powell, James A.

2013-01-01

Statistical models using partial differential equations (PDEs) to describe dynamically evolving natural systems are appearing in the scientific literature with some regularity in recent years. Often such studies seek to characterize the dynamics of temporal or spatio-temporal phenomena such as invasive species, consumer-resource interactions, community evolution, and resource selection. Specifically, in the spatial setting, data are often available at varying spatial and temporal scales. Additionally, the necessary numerical integration of a PDE may be computationally infeasible over the spatial support of interest. We present an approach to impose computationally advantageous changes of support in statistical implementations of PDE models and demonstrate its utility through simulation using a form of PDE known as “ecological diffusion.” We also apply a statistical ecological diffusion model to a data set involving the spread of mountain pine beetle (Dendroctonus ponderosae) in Idaho, USA.

Spontaneous symmetry breaking, conformal anomaly and incompressible fluid turbulence

NASA Astrophysics Data System (ADS)

Oz, Yaron

2017-11-01

We propose an effective conformal field theory (CFT) description of steady state incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We derive a KPZ-type equation for the anomalous scaling of the longitudinal velocity structure functions and relate the intermittency parameter to the boundary Euler (A-type) conformal anomaly coefficient. The proposed theory consists of a mean field CFT that exhibits Kolmogorov linear scaling (K41 theory) coupled to a dilaton. The dilaton is a Nambu-Goldstone gapless mode that arises from a spontaneous breaking due to the energy flux of the separate scale and time symmetries of the inviscid Navier-Stokes equations to a K41 scaling with a dynamical exponent z=2/3 . The dilaton acts as a random measure that dresses the K41 theory and introduces intermittency. We discuss the two, three and large number of space dimensions cases and how entanglement entropy can be used to characterize the intermittency strength.

Numerical Investigation of Oxygenated and Deoxygenated Blood Flow through a Tapered Stenosed Arteries in Magnetic Field.

PubMed

Abdollahzadeh Jamalabadi, M Y; Akbari Bidokhti, Amin Ali; Khak Rah, Hamid; Vaezi, Siavash; Hooshmand, Payam

2016-01-01

Current paper is focused on transient modeling of blood flow through a tapered stenosed arteries surrounded a by solenoid under the presence of heat transfer. The oxygenated and deoxygenated blood are considered here by the Newtonian and Non-Newtonian fluid (power law and Carreau-Yasuda) models. The governing equations of bio magnetic fluid flow for an incompressible, laminar, homogeneous, non-Newtonian are solved by finite volume method with SIMPLE algorithm for structured grid. Both magnetization and electric current source terms are well thought-out in momentum and energy equations. The effects of fluid viscosity model, Hartmann number, and magnetic number on wall shear stress, shearing stress at the stenosis throat and maximum temperature of the system are investigated and are optimized. The current study results are in agreement with some of the existing findings in the literature and are useful in thermal and mechanical design of spatially varying magnets to control the drug delivery and biomagnetic fluid flows through tapered arteries.

Modulational instability, beak-shaped rogue waves, multi-dark-dark solitons and dynamics in pair-transition-coupled nonlinear Schrödinger equations.

PubMed

Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong

2017-07-01

The integrable coupled nonlinear Schrödinger equations with four-wave mixing are investigated. We first explore the conditions for modulational instability of continuous waves of this system. Secondly, based on the generalized N -fold Darboux transformation (DT), beak-shaped higher-order rogue waves (RWs) and beak-shaped higher-order rogue wave pairs are derived for the coupled model with attractive interaction in terms of simple determinants. Moreover, we derive the simple multi-dark-dark and kink-shaped multi-dark-dark solitons for the coupled model with repulsive interaction through the generalizing DT. We explore their dynamics and classifications by different kinds of spatial-temporal distribution structures including triangular, pentagonal, 'claw-like' and heptagonal patterns. Finally, we perform the numerical simulations to predict that some dark solitons and RWs are stable enough to develop within a short time. The results would enrich our understanding on nonlinear excitations in many coupled nonlinear wave systems with transition coupling effects.

A geometric measure of dark energy with pairs of galaxies.

PubMed

Marinoni, Christian; Buzzi, Adeline

2010-11-25

Observations indicate that the expansion of the Universe is accelerating, which is attributed to a ‘dark energy’ component that opposes gravity. There is a purely geometric test of the expansion of the Universe (the Alcock–Paczynski test), which would provide an independent way of investigating the abundance (Ω(X)) and equation of state (W(X)) of dark energy. It is based on an analysis of the geometrical distortions expected from comparing the real-space and redshift-space shape of distant cosmic structures, but it has proved difficult to implement. Here we report an analysis of the symmetry properties of distant pairs of galaxies from archival data. This allows us to determine that the Universe is flat. By alternately fixing its spatial geometry at Ω(k)≡0 and the dark energy equation-of-state parameter at W(X)≡-1, and using the results of baryon acoustic oscillations, we can establish at the 68.3% confidence level that and -0.85>W(X)>-1.12 and 0.60<Ω(X)<0.80.

Multiscale Analysis of Rapidly Rotating Dynamo Simulations

NASA Astrophysics Data System (ADS)

Orvedahl, Ryan; Calkins, Michael; Featherstone, Nicholas

2017-11-01

The magnetic field of the planets and stars are generated by dynamo action in their electrically conducting fluid interiors. Numerical models of this process solve the fundamental equations of magnetohydrodynamics driven by convection in a rotating spherical shell. Rotation plays an important role in modifying the resulting convective flows and the self-generated magnetic field. We present results of simulating rapidly rotating systems that are unstable to dynamo action. We use the pseudo-spectral code Rayleigh to generate a suite of direct numerical simulations. Each simulation uses the Boussinesq approximation and is characterized by an Ekman number (Ek = ν / ΩL2) of 10-5. We vary the degree of convective forcing to obtain a range of convective Rossby numbers. The resulting flows and magnetic structures are analyzed using a Reynolds decomposition. We determine the relative importance of each term in the scale-separated governing equations and estimate the relevant spatial scales responsible for generating the mean magnetic field.

Magnetic field diffusion and dissipation in reversed-field plasmas

NASA Technical Reports Server (NTRS)

Drake, J. F.; Gladd, N. T.; Huba, J. D.

1981-01-01

A diffusion equation is derived which describes the evolution of a magnetic field in a plasma of arbitrary beta and resistivity. The equation is valid for a one-dimensional slab geometry, assumes the plasma remains in quasi-equilibrium throughout its evolution and does not include thermal transport. Scaling laws governing the rate of change of the magnetic energy, particle drift energy, and magnetic flux are calculated. It is found that the magnetic free energy can be substantially larger than the particle drift energy and can be an important energy reservoir in driving plasma instabilities (e.g., the lower-hybrid-drift instability). In addition, the effect of a spatially varying resistivity on the evolution of a reversed-field plasma is studied. The resistivity model used is based upon the anomalous transport properties associated with the nonlocal mode structure of the lower-hybrid-drift instability. The relevance of this research to laboratory plasmas (e.g., theta pinches, reversed-field theta pinches) and space plasmas (e.g., the earth's magnetotail) is discussed.

Capsize of polarization in dilute photonic crystals.

PubMed

Gevorkian, Zhyrair; Hakhoumian, Arsen; Gasparian, Vladimir; Cuevas, Emilio

2017-11-29

We investigate, experimentally and theoretically, polarization rotation effects in dilute photonic crystals with transverse permittivity inhomogeneity perpendicular to the traveling direction of waves. A capsize, namely a drastic change of polarization to the perpendicular direction is observed in a one-dimensional photonic crystal in the frequency range 10 ÷ 140 GHz. To gain more insights into the rotational mechanism, we have developed a theoretical model of dilute photonic crystal, based on Maxwell's equations with a spatially dependent two dimensional inhomogeneous dielectric permittivity. We show that the polarization's rotation can be explained by an optical splitting parameter appearing naturally in Maxwell's equations for magnetic or electric fields components. This parameter is an optical analogous of Rashba like spin-orbit interaction parameter present in quantum waves, introduces a correction to the band structure of the two-dimensional Bloch states, creates the dynamical phase shift between the waves propagating in the orthogonal directions and finally leads to capsizing of the initial polarization. Excellent agreement between theory and experiment is found.

The Numerical Analysis of a Turbulent Compressible Jet. Degree awarded by Ohio State Univ., 2000

NASA Technical Reports Server (NTRS)

DeBonis, James R.

2001-01-01

A numerical method to simulate high Reynolds number jet flows was formulated and applied to gain a better understanding of the flow physics. Large-eddy simulation was chosen as the most promising approach to model the turbulent structures due to its compromise between accuracy and computational expense. The filtered Navier-Stokes equations were developed including a total energy form of the energy equation. Subgrid scale models for the momentum and energy equations were adapted from compressible forms of Smagorinsky's original model. The effect of using disparate temporal and spatial accuracy in a numerical scheme was discovered through one-dimensional model problems and a new uniformly fourth-order accurate numerical method was developed. Results from two- and three-dimensional validation exercises show that the code accurately reproduces both viscous and inviscid flows. Numerous axisymmetric jet simulations were performed to investigate the effect of grid resolution, numerical scheme, exit boundary conditions and subgrid scale modeling on the solution and the results were used to guide the three-dimensional calculations. Three-dimensional calculations of a Mach 1.4 jet showed that this LES simulation accurately captures the physics of the turbulent flow. The agreement with experimental data was relatively good and is much better than results in the current literature. Turbulent intensities indicate that the turbulent structures at this level of modeling are not isotropic and this information could lend itself to the development of improved subgrid scale models for LES and turbulence models for RANS simulations. A two point correlation technique was used to quantify the turbulent structures. Two point space correlations were used to obtain a measure of the integral length scale, which proved to be approximately 1/2 D(sub j). Two point space-time correlations were used to obtain the convection velocity for the turbulent structures. This velocity ranged from 0.57 to 0.71 U(sub j).

A variational treatment of material configurations with application to interface motion and microstructural evolution

NASA Astrophysics Data System (ADS)

Teichert, Gregory H.; Rudraraju, Shiva; Garikipati, Krishna

2017-02-01

We present a unified variational treatment of evolving configurations in crystalline solids with microstructure. The crux of our treatment lies in the introduction of a vector configurational field. This field lies in the material, or configurational, manifold, in contrast with the traditional displacement field, which we regard as lying in the spatial manifold. We identify two distinct cases which describe (a) problems in which the configurational field's evolution is localized to a mathematically sharp interface, and (b) those in which the configurational field's evolution can extend throughout the volume. The first case is suitable for describing incoherent phase interfaces in polycrystalline solids, and the latter is useful for describing smooth changes in crystal structure and naturally incorporates coherent (diffuse) phase interfaces. These descriptions also lead to parameterizations of the free energies for the two cases, from which variational treatments can be developed and equilibrium conditions obtained. For sharp interfaces that are out-of-equilibrium, the second law of thermodynamics furnishes restrictions on the kinetic law for the interface velocity. The class of problems in which the material undergoes configurational changes between distinct, stable crystal structures are characterized by free energy density functions that are non-convex with respect to configurational strain. For physically meaningful solutions and mathematical well-posedness, it becomes necessary to incorporate interfacial energy. This we have done by introducing a configurational strain gradient dependence in the free energy density function following ideas laid out by Toupin (1962, Elastic materials with couple-stresses. Arch. Ration. Mech. Anal., 11, 385-414). The variational treatment leads to a system of partial differential equations governing the configuration that is coupled with the traditional equations of nonlinear elasticity. The coupled system of equations governs the configurational change in crystal structure, and elastic deformation driven by elastic, Eshelbian, and configurational stresses. Numerical examples are presented to demonstrate interface motion as well as evolving microstructures of crystal structures.

A variational treatment of material configurations with application to interface motion and microstructural evolution

DOE PAGES

Teichert, Gregory H.; Rudraraju, Shiva; Garikipati, Krishna

2016-11-20

We present a unified variational treatment of evolving configurations in crystalline solids with microstructure. The crux of our treatment lies in the introduction of a vector configurational field. This field lies in the material, or configurational, manifold, in contrast with the traditional displacement field, which we regard as lying in the spatial manifold. We identify two distinct cases which describe (a) problems in which the configurational field's evolution is localized to a mathematically sharp interface, and (b) those in which the configurational field's evolution can extend throughout the volume. The first case is suitable for describing incoherent phase interfaces inmore » polycrystalline solids, and the latter is useful for describing smooth changes in crystal structure and naturally incorporates coherent (diffuse) phase interfaces. These descriptions also lead to parameterizations of the free energies for the two cases, from which variational treatments can be developed and equilibrium conditions obtained. For sharp interfaces that are out-of-equilibrium, the second law of thermodynamics furnishes restrictions on the kinetic law for the interface velocity. The class of problems in which the material undergoes configurational changes between distinct, stable crystal structures are characterized by free energy density functions that are non-convex with respect to configurational strain. For physically meaningful solutions and mathematical well-posedness, it becomes necessary to incorporate interfacial energy. This we have done by introducing a configurational strain gradient dependence in the free energy density function following ideas laid out by Toupin (Arch. Rat. Mech. Anal., 11, 1962, 385-414). The variational treatment leads to a system of partial differential equations governing the configuration that is coupled with the traditional equations of nonlinear elasticity. The coupled system of equations governs the configurational change in crystal structure, and elastic deformation driven by elastic, Eshelbian, and configurational stresses. As a result, numerical examples are presented to demonstrate interface motion as well as evolving microstructures of crystal structures.« less

Effective electrodiffusion equation for non-uniform nanochannels.

PubMed

Marini Bettolo Marconi, Umberto; Melchionna, Simone; Pagonabarraga, Ignacio

2013-06-28

We derive a one-dimensional formulation of the Planck-Nernst-Poisson equation to describe the dynamics of a symmetric binary electrolyte in channels whose section is nanometric and varies along the axial direction. The approach is in the spirit of the Fick-Jacobs diffusion equation and leads to a system of coupled equations for the partial densities which depends on the charge sitting at the walls in a non-trivial fashion. We consider two kinds of non-uniformities, those due to the spatial variation of charge distribution and those due to the shape variation of the pore and report one- and three-dimensional solutions of the electrokinetic equations.

Effect of Variable Spatial Scales on USLE-GIS Computations

NASA Astrophysics Data System (ADS)

Patil, R. J.; Sharma, S. K.

2017-12-01

Use of appropriate spatial scale is very important in Universal Soil Loss Equation (USLE) based spatially distributed soil erosion modelling. This study aimed at assessment of annual rates of soil erosion at different spatial scales/grid sizes and analysing how changes in spatial scales affect USLE-GIS computations using simulation and statistical variabilities. Efforts have been made in this study to recommend an optimum spatial scale for further USLE-GIS computations for management and planning in the study area. The present research study was conducted in Shakkar River watershed, situated in Narsinghpur and Chhindwara districts of Madhya Pradesh, India. Remote Sensing and GIS techniques were integrated with Universal Soil Loss Equation (USLE) to predict spatial distribution of soil erosion in the study area at four different spatial scales viz; 30 m, 50 m, 100 m, and 200 m. Rainfall data, soil map, digital elevation model (DEM) and an executable C++ program, and satellite image of the area were used for preparation of the thematic maps for various USLE factors. Annual rates of soil erosion were estimated for 15 years (1992 to 2006) at four different grid sizes. The statistical analysis of four estimated datasets showed that sediment loss dataset at 30 m spatial scale has a minimum standard deviation (2.16), variance (4.68), percent deviation from observed values (2.68 - 18.91 %), and highest coefficient of determination (R2 = 0.874) among all the four datasets. Thus, it is recommended to adopt this spatial scale for USLE-GIS computations in the study area due to its minimum statistical variability and better agreement with the observed sediment loss data. This study also indicates large scope for use of finer spatial scales in spatially distributed soil erosion modelling.

Bayesian Analysis of Structural Equation Models with Nonlinear Covariates and Latent Variables

ERIC Educational Resources Information Center

Song, Xin-Yuan; Lee, Sik-Yum

2006-01-01

In this article, we formulate a nonlinear structural equation model (SEM) that can accommodate covariates in the measurement equation and nonlinear terms of covariates and exogenous latent variables in the structural equation. The covariates can come from continuous or discrete distributions. A Bayesian approach is developed to analyze the…

Prolongation structures of nonlinear evolution equations

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.; Estabrook, F. B.

1975-01-01

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

Versatile application of indirect Fourier transformation to structure factor analysis: from X-ray diffraction of molecular liquids to small angle scattering of protein solutions.

PubMed

Fukasawa, Toshiko; Sato, Takaaki

2011-02-28

We highlight versatile applicability of a structure-factor indirect Fourier transformation (IFT) technique, hereafter called SQ-IFT. The original IFT aims at the pair distance distribution function, p(r), of colloidal particles from small angle scattering of X-rays (SAXS) and neutrons (SANS), allowing the conversion of the experimental form factor, P(q), into a more intuitive real-space spatial autocorrelation function. Instead, SQ-IFT is an interaction potential model-free approach to the 'effective' or 'experimental' structure factor to yield the pair correlation functions (PCFs), g(r), of colloidal dispersions like globular protein solutions for small-angle scattering data as well as the radial distribution functions (RDFs) of molecular liquids in liquid diffraction (LD) experiments. We show that SQ-IFT yields accurate RDFs of liquid H(2)O and monohydric alcohol reflecting their local intermolecular structures, in which q-weighted structure function, qH(q), conventionally utilized in many LD studies out of necessity of performing direct Fourier transformation, is no longer required. We also show that SQ-IFT applied to theoretically calculated structure factors for uncharged and charged colloidal dispersions almost perfectly reproduces g(r) obtained as a solution of the Ornstein-Zernike (OZ) equation. We further demonstrate the relevance of SQ-IFT in its practical applications, using SANS effective structure factors of lysozyme solutions reported in recent literatures which revealed the equilibrium cluster formation due to coexisting long range electrostatic repulsion and short range attraction between the proteins. Finally, we present SAXS experiments on human serum albumin (HSA) at different ionic strength and protein concentration, in which we discuss the real space picture of spatial distributions of the proteins via the interaction potential model-free route.

Toward a Time-Domain Fractal Lightning Simulation

NASA Astrophysics Data System (ADS)

Liang, C.; Carlson, B. E.; Lehtinen, N. G.; Cohen, M.; Lauben, D.; Inan, U. S.

2010-12-01

Electromagnetic simulations of lightning are useful for prediction of lightning properties and exploration of the underlying physical behavior. Fractal lightning models predict the spatial structure of the discharge, but thus far do not provide much information about discharge behavior in time and therefore cannot predict electromagnetic wave emissions or current characteristics. Here we develop a time-domain fractal lightning simulation from Maxwell's equations, the method of moments with the thin wire approximation, an adaptive time-stepping scheme, and a simplified electrical model of the lightning channel. The model predicts current pulse structure and electromagnetic wave emissions and can be used to simulate the entire duration of a lightning discharge. The model can be used to explore the electrical characteristics of the lightning channel, the temporal development of the discharge, and the effects of these characteristics on observable electromagnetic wave emissions.

Stochastic inflation lattice simulations - Ultra-large scale structure of the universe

NASA Technical Reports Server (NTRS)

Salopek, D. S.

1991-01-01

Non-Gaussian fluctuations for structure formation may arise in inflation from the nonlinear interaction of long wavelength gravitational and scalar fields. Long wavelength fields have spatial gradients, a (exp -1), small compared to the Hubble radius, and they are described in terms of classical random fields that are fed by short wavelength quantum noise. Lattice Langevin calculations are given for a toy model with a scalar field interacting with an exponential potential where one can obtain exact analytic solutions of the Fokker-Planck equation. For single scalar field models that are consistent with current microwave background fluctuations, the fluctuations are Gaussian. However, for scales much larger than our observable Universe, one expects large metric fluctuations that are non-Gaussian. This example illuminates non-Gaussian models involving multiple scalar fields which are consistent with current microwave background limits.

Intersubband Transitions in InAs/AlSb Quantum Wells

NASA Technical Reports Server (NTRS)

Li, J.; Koloklov, K.; Ning, C. Z.; Larraber, D. C.; Khodaparast, G. A.; Kono, J.; Ueda, K.; Nakajima, Y.; Sasa, S.; Inoue, M.

2003-01-01

We have studied intersubband transitions in InAs/AlSb quantum wells experimentally and theoretically. Experimentally, we performed polarization-resolved infrared absorption spectroscopy to measure intersubband absorption peak frequencies and linewidths as functions of temperature (from 4 K to room temperature) and quantum well width (from a few nm to 10 nm). To understand experimental results, we performed a self-consistent 8-band k-p band-structure calculation including spatial charge separation. Based on the calculated band structure, we developed a set of density matrix equations to compute TE and TM optical transitions self-consistently, including both interband and intersubband channels. This density matrix formalism is also ideal for the inclusion of various many-body effects, which are known to be important for intersubband transitions. Detailed comparison between experimental data and theoretical simulations is presented.

Quadratic Finite Element Method for 1D Deterministic Transport

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

Tolar, Jr., D R; Ferguson, J M

2004-01-06

In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r},{und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r},{und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.

Combination of oriented partial differential equation and shearlet transform for denoising in electronic speckle pattern interferometry fringe patterns.

PubMed

Xu, Wenjun; Tang, Chen; Gu, Fan; Cheng, Jiajia

2017-04-01

It is a key step to remove the massive speckle noise in electronic speckle pattern interferometry (ESPI) fringe patterns. In the spatial-domain filtering methods, oriented partial differential equations have been demonstrated to be a powerful tool. In the transform-domain filtering methods, the shearlet transform is a state-of-the-art method. In this paper, we propose a filtering method for ESPI fringe patterns denoising, which is a combination of second-order oriented partial differential equation (SOOPDE) and the shearlet transform, named SOOPDE-Shearlet. Here, the shearlet transform is introduced into the ESPI fringe patterns denoising for the first time. This combination takes advantage of the fact that the spatial-domain filtering method SOOPDE and the transform-domain filtering method shearlet transform benefit from each other. We test the proposed SOOPDE-Shearlet on five experimentally obtained ESPI fringe patterns with poor quality and compare our method with SOOPDE, shearlet transform, windowed Fourier filtering (WFF), and coherence-enhancing diffusion (CEDPDE). Among them, WFF and CEDPDE are the state-of-the-art methods for ESPI fringe patterns denoising in transform domain and spatial domain, respectively. The experimental results have demonstrated the good performance of the proposed SOOPDE-Shearlet.

Analyzing the equilibrium states of a quasi-neutral spatially inhomogeneous system of charges above a liquid dielectric film based on the first principles of quantum statistics

NASA Astrophysics Data System (ADS)

Lytvynenko, D. M.; Slyusarenko, Yu V.

2017-08-01

A theory of quasi-neutral equilibrium states of charges above a liquid dielectric surface is developed. This theory is based on the first principles of quantum statistics for systems comprising many identical particles. The proposed approach involves applying the variational principle, modified for the considered systems, and the Thomas-Fermi model. In the terms of the developed theory self-consistency equations are obtained. These equations provide the relation between the main parameters describing the system: the potential of the static electric field, the distribution function of charges and the surface profile of the liquid dielectric. The equations are used to study the phase transition in the system to a spatially periodic state. The proposed method can be applied in analyzing the properties of the phase transition in the system in relation to the spatially periodic states of wave type. Using the analytical and numerical methods, we perform a detailed study of the dependence of the critical parameters of such a phase transition on the thickness of the liquid dielectric film. Some stability criteria for the new asymmetric phase of the studied system are discussed.

Basis adaptation and domain decomposition for steady partial differential equations with random coefficients

DOE PAGES

Tipireddy, R.; Stinis, P.; Tartakovsky, A. M.

2017-09-04

In this paper, we present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support ourmore » construction with numerical experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Lastly, our results show that highly accurate global solutions can be obtained with significantly reduced computational costs.« less

Bouncing and emergent cosmologies from Arnowitt–Deser–Misner RG flows

NASA Astrophysics Data System (ADS)

Bonanno, Alfio; Gionti, S. J. Gabriele; Platania, Alessia

2018-03-01

Asymptotically safe gravity provides a framework for the description of gravity from the trans-Planckian regime to cosmological scales. According to this scenario, the cosmological constant and Newton’s coupling are functions of the energy scale whose evolution is dictated by the renormalization group (RG) equations. The formulation of the RG equations on foliated spacetimes, based on the Arnowitt–Deser–Misner (ADM) formalism, furnishes a natural way to construct the RG energy scale from the spectrum of the Laplacian operator on the spatial slices. Combining this idea with an RG improvement procedure, in this work we study quantum gravitational corrections to the Einstein–Hilbert action on Friedmann–Lemaître–Robertson–Walker backgrounds. The resulting quantum-corrected Friedmann equations can give rise to both bouncing cosmologies and emergent Universe solutions. Our bouncing models do not require the presence of exotic matter and emergent Universe solutions can be constructed for any allowed topology of the spatial slices.

Homogeneous quantum electrodynamic turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

Basis adaptation and domain decomposition for steady-state partial differential equations with random coefficients

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

Tipireddy, R.; Stinis, P.; Tartakovsky, A. M.

We present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support our construction with numericalmore » experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Our results show that highly accurate global solutions can be obtained with significantly reduced computational costs.« less

Fifth-order complex Korteweg-de Vries-type equations

NASA Astrophysics Data System (ADS)

Khanal, Netra; Wu, Jiahong; Yuan, Juan-Ming

2012-05-01

This paper studies spatially periodic complex-valued solutions of the fifth-order Korteweg-de Vries (KdV)-type equations. The aim is at several fundamental issues including the existence, uniqueness and finite-time blowup problems. Special attention is paid to the Kawahara equation, a fifth-order KdV-type equation. When a Burgers dissipation is attached to the Kawahara equation, we establish the existence and uniqueness of the Fourier series solution with the Fourier modes decaying algebraically in terms of the wave numbers. We also examine a special series solution to the Kawahara equation and prove the convergence and global regularity of such solutions associated with a single mode initial data. In addition, finite-time blowup results are discussed for the special series solution of the Kawahara equation.

Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.

PubMed

Das, Shankar P; Yoshimori, Akira

2013-10-01

Exact equations of motion for the microscopically defined collective density ρ(x,t) and the momentum density ĝ(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.

Vlasov-Maxwell and Vlasov-Poisson equations as models of a one-dimensional electron plasma

NASA Technical Reports Server (NTRS)

Klimas, A. J.; Cooper, J.

1983-01-01

The Vlasov-Maxwell and Vlasov-Poisson systems of equations for a one-dimensional electron plasma are defined and discussed. A method for transforming a solution of one system which is periodic over a bounded or unbounded spatial interval to a similar solution of the other is constructed.

The GEDI Strategy for Improved Mapping of Forest Biomass and Structure

NASA Astrophysics Data System (ADS)

Dubayah, R.

2017-12-01

In 2014 the Committee on Earth Observation Satellites (CEOS) published a comprehensive report on approaches to meet future requirements for space-based observations of carbon. Entitled the CEOS Strategy for Carbon Observations from Space and endorsed by its member space agencies, the report outlines carbon information needs for climate and other policy, and how these needs may be met through existing and planned satellite missions. The CEOS Strategymakes recommendations for new, high-priority measurements. Among these is that space-based measurements using lidar should have priority to provide information on height, structure and biomass, complementing the existing and planned suite of SAR missions, such as the NASA NISAR and ESA BIOMASS missions. NASA's Global Ecosystem Dynamics Investigation (GEDI) directly meets this challenge. Scheduled for launch in late 2018 for deployment on the International Space Station, GEDI will provide more than 12 billion observations of canopy height, vertical structure and topography using a 10-beam lidar optimized for ecosystem measurements. Central to the success of GEDI is the development of calibration equations that relate observed forest structure to biomass at a variety of spatial scales. GEDI creates these calibrations by combining a large data base of field plot measurements with coincident airborne lidar observations that are used to simulate GEDI lidar waveforms. GEDI uses these relatively sparse footprint estimates of structure and biomass to create lower resolution, but spatially continuous grids of structure and biomass. GEDI is also developing radar/lidar fusion algorithms to produce higher-resolution, spatially continuous estimates of canopy height and biomass in collaboration with the German Aerospace Center (DLR). In this talk we present the current status of the GEDI calibration and validation program, and its approach for fusing its observations with the next generation of SAR sensors for improved mapping of forest structure from space. As stressed by the CEOS Strategy, the success of these efforts will critically depend on enhanced intra- and inter-mission calibration and validation activities, underpinned by an expanding network of in situ field observations, such as being implemented by GEDI.

Gender, space, and the location changes of jobs and people: a spatial simultaneous equations analysis.

PubMed

Hoogstra, Gerke J

2012-01-01

This article summarizes a spatial econometric analysis of local population and employment growth in the Netherlands, with specific reference to impacts of gender and space. The simultaneous equations model used distinguishes between population- and gender-specific employment groups, and includes autoregressive and cross-regressive spatial lags to detect relations both within and among these groups. Spatial weights matrices reflecting different bands of travel times are used to calculate the spatial lags and to gauge the spatial nature of these relations. The empirical results show that although population–employment interaction is more localized for women's employment, no gender difference exists in the direction of interaction. Employment growth for both men and women is more influenced by population growth than vice versa. The interaction within employment groups is even more important than population growth. Women's, and especially men's, local employment growth mostly benefits from the same employment growth in neighboring locations. Finally, interaction between these groups is practically absent, although men's employment growth may have a negative impact on women's employment growth within small geographic areas. In summary, the results confirm the crucial roles of gender and space, and offer important insights into possible relations within and among subgroups of jobs and people.

Electrical and mechanical fully coupled theory and experimental verification of Rosen-type piezoelectric transformers.

PubMed

Hsu, Yu-Hsiang; Lee, Chih-Kung; Hsiao, Wen-Hsin

2005-10-01

A piezoelectric transformer is a power transfer device that converts its input and output voltage as well as current by effectively using electrical and mechanical coupling effects of piezoelectric materials. Equivalent-circuit models, which are traditionally used to analyze piezoelectric transformers, merge each mechanical resonance effect into a series of ordinary differential equations. Because of using ordinary differential equations, equivalent circuit models are insufficient to reflect the mechanical behavior of piezoelectric plates. Electromechanically, fully coupled governing equations of Rosen-type piezoelectric transformers, which are partial differential equations in nature, can be derived to address the deficiencies of the equivalent circuit models. It can be shown that the modal actuator concept can be adopted to optimize the electromechanical coupling effect of the driving section once the added spatial domain design parameters are taken into account, which are three-dimensional spatial dependencies of electromechanical properties. The maximum power transfer condition for a Rosen-type piezoelectric transformer is detailed. Experimental results, which lead us to a series of new design rules, also are presented to prove the validity and effectiveness of the theoretical predictions.

Dark Solitons for the Defocusing Cubic Nonlinear Schrödinger Equation with the Spatially Periodic Potential and Nonlinearity

NASA Astrophysics Data System (ADS)

Yan, Zhen-Ya; Yan, Fang-Chi

2015-09-01

We study the existence of dark solitons of the defocusing cubic nonlinear Schrödinger (NLS) eqaution with the spatially-periodic potential and nonlinearity. Firstly, we propose six families of upper and lower solutions of the dynamical systems arising from the stationary defocusing NLS equation. Secondly, by regarding a dark soliton as a heteroclinic orbit of the Poincaré map, we present some constraint conditions for the periodic potential and nonlinearity to show the existence of stationary dark solitons of the defocusing NLS equation for six different cases in terms of the theory of strict lower and upper solutions and the dynamics of planar homeomorphisms. Finally, we give the explicit dark solitons of the defocusing NLS equation with the chosen periodic potential and nonlinearity. Supported by the National Natural Science Foundation of China under Grant No. 61178091, the National Key Basic Research Program of China under Grant No. 2011CB302400, and the Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China under Grant No. Y4KF211CJ1

Solutions to Yang-Mills Equations on Four-Dimensional de Sitter Space

NASA Astrophysics Data System (ADS)

Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.

2017-08-01

We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter space dS4 and construct a smooth and spatially homogeneous magnetic solution to the Yang-Mills equations. Slicing dS4 as R ×S3, via an SU(2)-equivariant ansatz, we reduce the Yang-Mills equations to ordinary matrix differential equations and further to Newtonian dynamics in a double-well potential. Its local maximum yields a Yang-Mills solution whose color-magnetic field at time τ ∈R is given by B˜a=-1/2 Ia/(R2cosh2τ ), where Ia for a =1 , 2, 3 are the SU(2) generators and R is the de Sitter radius. At any moment, this spatially homogeneous configuration has finite energy, but its action is also finite and of the value -1/2 j (j +1 )(2 j +1 )π3 in a spin-j representation. Similarly, the double-well bounce produces a family of homogeneous finite-action electric-magnetic solutions with the same energy. There is a continuum of other solutions whose energy and action extend down to zero.

Nonlinear evolution equations for surface plasmons for nano-focusing at a Kerr/metallic interface and tapered waveguide

NASA Astrophysics Data System (ADS)

Crutcher, Sihon H.; Osei, Albert; Biswas, Anjan

2012-06-01

Maxwell's equations for a metallic and nonlinear Kerr interface waveguide at the nanoscale can be approximated to a (1+1) D Nonlinear Schrodinger type model equation (NLSE) with appropriate assumptions and approximations. Theoretically, without losses or perturbations spatial plasmon solitons profiles are easily produced. However, with losses, the amplitude or beam profile is no longer stationary and adiabatic parameters have to be considered to understand propagation. For this model, adiabatic parameters are calculated considering losses resulting in linear differential coupled integral equations with constant definite integral coefficients not dependent on the transverse and longitudinal coordinates. Furthermore, by considering another configuration, a waveguide that is an M-NL-M (metal-nonlinear Kerr-metal) that tapers, the tapering can balance the loss experienced at a non-tapered metal/nonlinear Kerr interface causing attenuation of the beam profile, so these spatial plasmon solitons can be produced. In this paper taking into consideration the (1+1)D NLSE model for a tapered waveguide, we derive a one soliton solution based on He's Semi-Inverse Variational Principle (HPV).

Structural Equation Modeling of Multivariate Time Series

ERIC Educational Resources Information Center

du Toit, Stephen H. C.; Browne, Michael W.

2007-01-01

The covariance structure of a vector autoregressive process with moving average residuals (VARMA) is derived. It differs from other available expressions for the covariance function of a stationary VARMA process and is compatible with current structural equation methodology. Structural equation modeling programs, such as LISREL, may therefore be…

Generalized Multilevel Structural Equation Modeling

ERIC Educational Resources Information Center

Rabe-Hesketh, Sophia; Skrondal, Anders; Pickles, Andrew

2004-01-01

A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent…

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

Remming, Ian S.; Khokhlov, Alexei M.

We present general equations for non-ideal, reactive flow magnetohydrodynamics (RFMHD) in the form best suited for describing thermonuclear combustion in high-density degenerate matter of SNe Ia. The relative importance of various non-ideal effects is analyzed as a function of characteristic spatial and temporal scales of the problem. From the general RFMHD equations, we derive the one-dimensional ordinary differential equations describing the steady-state propagation of a planar thermonuclear flame front in a magnetic field. The physics of the flame is first studied qualitatively using a simple case of one-step Arrhenius kinetics, a perfect gas equation of state (EOS), and constant thermalmore » conductivity coefficients. After that, the equations are solved, the internal flame front structure is calculated, and the flame velocity, S {sub l} , and flame thickness, δ {sub l} , are found for carbon–oxygen degenerate material of supernovae using a realistic EOS, transport properties, and detailed nuclear kinetics. The magnetic field changes the flame behavior significantly, both qualitatively and quantitatively, as compared to the non-magnetic case of classical combustion. (1) The magnetic field influences the evolutionarity of a flame front and makes it impossible for a flame to propagate steadily in a wide range of magnetic field strengths and orientations relative to the front. (2) When the flame moves steadily, it can propagate in several distinct modes, the most important being the slow C {sub S} and super-Alfvénic C {sub sup} modes. (3) The speed of the flame can be diminished or enhanced by up to several factors relative to the non-magnetic laminar flame speed.« less

On the preservation of cooperation in two-strategy games with nonlocal interactions.

PubMed

Aydogmus, Ozgur; Zhou, Wen; Kang, Yun

2017-03-01

Nonlocal interactions such as spatial interaction are ubiquitous in nature and may alter the equilibrium in evolutionary dynamics. Models including nonlocal spatial interactions can provide a further understanding on the preservation and emergence of cooperation in evolutionary dynamics. In this paper, we consider a variety of two-strategy evolutionary spatial games with nonlocal interactions based on an integro-differential replicator equation. By defining the invasion speed and minimal traveling wave speed for the derived model, we study the effects of the payoffs, the selection pressure and the spatial parameter on the preservation of cooperation. One of our most interesting findings is that, for the Prisoners Dilemma games in which the defection is the only evolutionary stable strategy for unstructured populations, analyses on its asymptotic speed of propagation suggest that, in contrast with spatially homogeneous games, the cooperators can invade the habitat under proper conditions. Other two-strategy evolutionary spatial games are also explored. Both our theoretical and numerical studies show that the nonlocal spatial interaction favors diversity in strategies in a population and is able to preserve cooperation in a competing environment. A real data application in a virus mutation study echoes our theoretical observations. In addition, we compare the results of our model to the partial differential equation approach to demonstrate the importance of including non-local interaction component in evolutionary game models. Copyright © 2016 Elsevier Inc. All rights reserved.

Alternative bi-Hamiltonian structures for WDVV equations of associativity

NASA Astrophysics Data System (ADS)

Kalayci, J.; Nutku, Y.

1998-01-01

The WDVV equations of associativity in two-dimensional topological field theory are completely integrable third-order Monge-Ampère equations which admit bi-Hamiltonian structure. The time variable plays a distinguished role in the discussion of Hamiltonian structure, whereas in the theory of WDVV equations none of the independent variables merits such a distinction. WDVV equations admit very different alternative Hamiltonian structures under different possible choices of the time variable, but all these various Hamiltonian formulations can be brought together in the framework of the covariant theory of symplectic structure. They can be identified as different components of the covariant Witten-Zuckerman symplectic 2-form current density where a variational formulation of the WDVV equation that leads to the Hamiltonian operator through the Dirac bracket is available.

A universal constraint-based formulation for freely moving immersed bodies in fluids

NASA Astrophysics Data System (ADS)

Patankar, Neelesh A.

2012-11-01

Numerical simulation of moving immersed bodies in fluids is now practiced routinely. A variety of variants of these approaches have been published, most of which rely on using a background mesh for the fluid equations and tracking the body using Lagrangian points. In this talk, generalized constraint-based governing equations will be presented that provide a unified framework for various immersed body techniques. The key idea that is common to these methods is to assume that the entire fluid-body domain is a ``fluid'' and then to constrain the body domain to move in accordance with its governing equations. The immersed body can be rigid or deforming. The governing equations are developed so that they are independent of the nature of temporal or spatial discretization schemes. Specific choices of time stepping and spatial discretization then lead to techniques developed in prior literature ranging from freely moving rigid to elastic self-propelling bodies. To simulate Brownian systems, thermal fluctuations can be included in the fluid equations via additional random stress terms. Solving the fluctuating hydrodynamic equations coupled with the immersed body results in the Brownian motion of that body. The constraint-based formulation leads to fractional time stepping algorithms a la Chorin-type schemes that are suitable for fast computations of rigid or self-propelling bodies whose deformation kinematics are known. Support from NSF is gratefully acknowledged.

The Effect of Velocity Correlation on the Spatial Evolution of Breakthrough Curves in Heterogeneous Media

NASA Astrophysics Data System (ADS)

Massoudieh, A.; Dentz, M.; Le Borgne, T.

2017-12-01

In heterogeneous media, the velocity distribution and the spatial correlation structure of velocity for solute particles determine the breakthrough curves and how they evolve as one moves away from the solute source. The ability to predict such evolution can help relating the spatio-statistical hydraulic properties of the media to the transport behavior and travel time distributions. While commonly used non-local transport models such as anomalous dispersion and classical continuous time random walk (CTRW) can reproduce breakthrough curve successfully by adjusting the model parameter values, they lack the ability to relate model parameters to the spatio-statistical properties of the media. This in turns limits the transferability of these models. In the research to be presented, we express concentration or flux of solutes as a distribution over their velocity. We then derive an integrodifferential equation that governs the evolution of the particle distribution over velocity at given times and locations for a particle ensemble, based on a presumed velocity correlation structure and an ergodic cross-sectional velocity distribution. This way, the spatial evolution of breakthrough curves away from the source is predicted based on cross-sectional velocity distribution and the connectivity, which is expressed by the velocity transition probability density. The transition probability is specified via a copula function that can help construct a joint distribution with a given correlation and given marginal velocities. Using this approach, we analyze the breakthrough curves depending on the velocity distribution and correlation properties. The model shows how the solute transport behavior evolves from ballistic transport at small spatial scales to Fickian dispersion at large length scales relative to the velocity correlation length.

Recovery of evolution of Grad-Shafranov equilibria from single-spacecraft data: Benchmarking and application to a flux transfer event

NASA Astrophysics Data System (ADS)

Sonnerup, B. U.; Hasegawa, H.; Nakamura, T.

2010-12-01

Even after the advent of multi-spacecraft missions such as Cluster and THEMIS, it has been difficult to distinguish between time evolution of, and spatial variation within, a space plasma structure on the basis of in situ measurements. We present a method for analyzing time evolution of two-dimensional (2D) and magnetohydrostatic, namely Grad-Shafranov equilibria, using data recorded by an observing probe as it traverses a quasi-static, 2D magnetic-field/plasma structure. The method recovers spatial initial values used in the classical Grad-Shafranov (GS) reconstruction [Sonnerup et al., JGR, 2006] for an interval before and after the time of actual measurements, by advancing them backward and forward in time based on a set of equation for an incompressible plasma; the consequence is generation of multiple GS maps or a movie of the 2D field structure. The method is successfully benchmarked by use of a 2D magnetohydrodynamic simulation of time-dependent magnetic reconnection, and then is applied to a magnetic flux transfer event (FTE) seen by Cluster at the dayside high-latitude magnetopause, which has been analyzed with the GS method [Hasegawa et al., Ann. Geophys., 2006]. The application shows that the field lines constituting the FTE flux rope were contracting toward its center as a result of modest convective flow in the region around the core of the flux rope.

Integrability of the coupled cubic-quintic complex Ginzburg-Landau equations and multiple-soliton solutions via mathematical methods

NASA Astrophysics Data System (ADS)

Selima, Ehab S.; Seadawy, Aly R.; Yao, Xiaohua; Essa, F. A.

2018-02-01

This paper is devoted to study the (1+1)-dimensional coupled cubic-quintic complex Ginzburg-Landau equations (cc-qcGLEs) with complex coefficients. This equation can be used to describe the nonlinear evolution of slowly varying envelopes of periodic spatial-temporal patterns in a convective binary fluid. Dispersion relation and properties of cc-qcGLEs are constructed. Painlevé analysis is used to check the integrability of cc-qcGLEs and to establish the Bäcklund transformation form. New traveling wave solutions and a general form of multiple-soliton solutions of cc-qcGLEs are obtained via the Bäcklund transformation and simplest equation method with Bernoulli, Riccati and Burgers’ equations as simplest equations.

A minimum entropy principle in the gas dynamics equations

NASA Technical Reports Server (NTRS)

Tadmor, E.

1986-01-01

Let u(x bar,t) be a weak solution of the Euler equations, governing the inviscid polytropic gas dynamics; in addition, u(x bar, t) is assumed to respect the usual entropy conditions connected with the conservative Euler equations. We show that such entropy solutions of the gas dynamics equations satisfy a minimum entropy principle, namely, that the spatial minimum of their specific entropy, (Ess inf s(u(x,t)))/x, is an increasing function of time. This principle equally applies to discrete approximations of the Euler equations such as the Godunov-type and Lax-Friedrichs schemes. Our derivation of this minimum principle makes use of the fact that there is a family of generalized entrophy functions connected with the conservative Euler equations.

Revisiting Temporal Markov Chains for Continuum modeling of Transport in Porous Media

NASA Astrophysics Data System (ADS)

Delgoshaie, A. H.; Jenny, P.; Tchelepi, H.

2017-12-01

The transport of fluids in porous media is dominated by flow­-field heterogeneity resulting from the underlying permeability field. Due to the high uncertainty in the permeability field, many realizations of the reference geological model are used to describe the statistics of the transport phenomena in a Monte Carlo (MC) framework. There has been strong interest in working with stochastic formulations of the transport that are different from the standard MC approach. Several stochastic models based on a velocity process for tracer particle trajectories have been proposed. Previous studies have shown that for high variances of the log-conductivity, the stochastic models need to account for correlations between consecutive velocity transitions to predict dispersion accurately. The correlated velocity models proposed in the literature can be divided into two general classes of temporal and spatial Markov models. Temporal Markov models have been applied successfully to tracer transport in both the longitudinal and transverse directions. These temporal models are Stochastic Differential Equations (SDEs) with very specific drift and diffusion terms tailored for a specific permeability correlation structure. The drift and diffusion functions devised for a certain setup would not necessarily be suitable for a different scenario, (e.g., a different permeability correlation structure). The spatial Markov models are simple discrete Markov chains that do not require case specific assumptions. However, transverse spreading of contaminant plumes has not been successfully modeled with the available correlated spatial models. Here, we propose a temporal discrete Markov chain to model both the longitudinal and transverse dispersion in a two-dimensional domain. We demonstrate that these temporal Markov models are valid for different correlation structures without modification. Similar to the temporal SDEs, the proposed model respects the limited asymptotic transverse spreading of the plume in two-dimensional problems.

Improved estimation of hydraulic conductivity by combining stochastically simulated hydrofacies with geophysical data

PubMed Central

Zhu, Lin; Gong, Huili; Chen, Yun; Li, Xiaojuan; Chang, Xiang; Cui, Yijiao

2016-01-01

Hydraulic conductivity is a major parameter affecting the output accuracy of groundwater flow and transport models. The most commonly used semi-empirical formula for estimating conductivity is Kozeny-Carman equation. However, this method alone does not work well with heterogeneous strata. Two important parameters, grain size and porosity, often show spatial variations at different scales. This study proposes a method for estimating conductivity distributions by combining a stochastic hydrofacies model with geophysical methods. The Markov chain model with transition probability matrix was adopted to re-construct structures of hydrofacies for deriving spatial deposit information. The geophysical and hydro-chemical data were used to estimate the porosity distribution through the Archie’s law. Results show that the stochastic simulated hydrofacies model reflects the sedimentary features with an average model accuracy of 78% in comparison with borehole log data in the Chaobai alluvial fan. The estimated conductivity is reasonable and of the same order of magnitude of the outcomes of the pumping tests. The conductivity distribution is consistent with the sedimentary distributions. This study provides more reliable spatial distributions of the hydraulic parameters for further numerical modeling. PMID:26927886

Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

NASA Astrophysics Data System (ADS)

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations.

Imaging of turbulent structures and tomographic reconstruction of TORPEX plasma emissivity

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

Iraji, D.; Furno, I.; Fasoli, A.

In the TORPEX [A. Fasoli et al., Phys. Plasmas 13, 055902 (2006)], a simple magnetized plasma device, low frequency electrostatic fluctuations associated with interchange waves, are routinely measured by means of extensive sets of Langmuir probes. To complement the electrostatic probe measurements of plasma turbulence and study of plasma structures smaller than the spatial resolution of probes array, a nonperturbative direct imaging system has been developed on TORPEX, including a fast framing Photron-APX-RS camera and an image intensifier unit. From the line-integrated camera images, we compute the poloidal emissivity profile of the plasma by applying a tomographic reconstruction technique usingmore » a pixel method and solving an overdetermined set of equations by singular value decomposition. This allows comparing statistical, spectral, and spatial properties of visible light radiation with electrostatic fluctuations. The shape and position of the time-averaged reconstructed plasma emissivity are observed to be similar to those of the ion saturation current profile. In the core plasma, excluding the electron cyclotron and upper hybrid resonant layers, the mean value of the plasma emissivity is observed to vary with (T{sub e}){sup {alpha}}(n{sub e}){sup {beta}}, in which {alpha}=0.25-0.7 and {beta}=0.8-1.4, in agreement with collisional radiative model. The tomographic reconstruction is applied to the fast camera movie acquired with 50 kframes/s rate and 2 {mu}s of exposure time to obtain the temporal evolutions of the emissivity fluctuations. Conditional average sampling is also applied to visualize and measure sizes of structures associated with the interchange mode. The {omega}-time and the two-dimensional k-space Fourier analysis of the reconstructed emissivity fluctuations show the same interchange mode that is detected in the {omega} and k spectra of the ion saturation current fluctuations measured by probes. Small scale turbulent plasma structures can be detected and tracked in the reconstructed emissivity movies with the spatial resolution down to 2 cm, well beyond the spatial resolution of the probe array.« less

On the large eddy simulation of turbulent flows in complex geometry

NASA Technical Reports Server (NTRS)

Ghosal, Sandip

1993-01-01

Application of the method of Large Eddy Simulation (LES) to a turbulent flow consists of three separate steps. First, a filtering operation is performed on the Navier-Stokes equations to remove the small spatial scales. The resulting equations that describe the space time evolution of the 'large eddies' contain the subgrid-scale (sgs) stress tensor that describes the effect of the unresolved small scales on the resolved scales. The second step is the replacement of the sgs stress tensor by some expression involving the large scales - this is the problem of 'subgrid-scale modeling'. The final step is the numerical simulation of the resulting 'closed' equations for the large scale fields on a grid small enough to resolve the smallest of the large eddies, but still much larger than the fine scale structures at the Kolmogorov length. In dividing a turbulent flow field into 'large' and 'small' eddies, one presumes that a cut-off length delta can be sensibly chosen such that all fluctuations on a scale larger than delta are 'large eddies' and the remainder constitute the 'small scale' fluctuations. Typically, delta would be a length scale characterizing the smallest structures of interest in the flow. In an inhomogeneous flow, the 'sensible choice' for delta may vary significantly over the flow domain. For example, in a wall bounded turbulent flow, most statistical averages of interest vary much more rapidly with position near the wall than far away from it. Further, there are dynamically important organized structures near the wall on a scale much smaller than the boundary layer thickness. Therefore, the minimum size of eddies that need to be resolved is smaller near the wall. In general, for the LES of inhomogeneous flows, the width of the filtering kernel delta must be considered to be a function of position. If a filtering operation with a nonuniform filter width is performed on the Navier-Stokes equations, one does not in general get the standard large eddy equations. The complication is caused by the fact that a filtering operation with a nonuniform filter width in general does not commute with the operation of differentiation. This is one of the issues that we have looked at in detail as it is basic to any attempt at applying LES to complex geometry flows. Our principal findings are summarized.

Transport lattice models of heat transport in skin with spatially heterogeneous, temperature-dependent perfusion.

PubMed

Gowrishankar, T R; Stewart, Donald A; Martin, Gregory T; Weaver, James C

2004-11-17

Investigation of bioheat transfer problems requires the evaluation of temporal and spatial distributions of temperature. This class of problems has been traditionally addressed using the Pennes bioheat equation. Transport of heat by conduction, and by temperature-dependent, spatially heterogeneous blood perfusion is modeled here using a transport lattice approach. We represent heat transport processes by using a lattice that represents the Pennes bioheat equation in perfused tissues, and diffusion in nonperfused regions. The three layer skin model has a nonperfused viable epidermis, and deeper regions of dermis and subcutaneous tissue with perfusion that is constant or temperature-dependent. Two cases are considered: (1) surface contact heating and (2) spatially distributed heating. The model is relevant to the prediction of the transient and steady state temperature rise for different methods of power deposition within the skin. Accumulated thermal damage is estimated by using an Arrhenius type rate equation at locations where viable tissue temperature exceeds 42 degrees C. Prediction of spatial temperature distributions is also illustrated with a two-dimensional model of skin created from a histological image. The transport lattice approach was validated by comparison with an analytical solution for a slab with homogeneous thermal properties and spatially distributed uniform sink held at constant temperatures at the ends. For typical transcutaneous blood gas sensing conditions the estimated damage is small, even with prolonged skin contact to a 45 degrees C surface. Spatial heterogeneity in skin thermal properties leads to a non-uniform temperature distribution during a 10 GHz electromagnetic field exposure. A realistic two-dimensional model of the skin shows that tissue heterogeneity does not lead to a significant local temperature increase when heated by a hot wire tip. The heat transport system model of the skin was solved by exploiting the mathematical analogy between local thermal models and local electrical (charge transport) models, thereby allowing robust, circuit simulation software to obtain solutions to Kirchhoff's laws for the system model. Transport lattices allow systematic introduction of realistic geometry and spatially heterogeneous heat transport mechanisms. Local representations for both simple, passive functions and more complex local models can be easily and intuitively included into the system model of a tissue.

Singularities of the Euler equation and hydrodynamic stability

NASA Technical Reports Server (NTRS)

Tanveer, S.; Speziale, Charles G.

1993-01-01

Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.

Singularities of the Euler equation and hydrodynamic stability

NASA Technical Reports Server (NTRS)

Tanveer, S.; Speziale, Charles G.

1992-01-01

Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.

Temporal and spatial foliations of spacetimes.

NASA Astrophysics Data System (ADS)

Herold, H.

For the solution of initial-value problems in numerical relativity usually the (3+1) splitting of Einstein's equations is employed. An important part of this splitting is the choice of the temporal gauge condition. In order to estimate the quality of time-evolution schemes, different time slicings of given well-known spherically symmetric spacetimes have been studied. Besides the maximal slicing condition the harmonic slicing prescription has been used to calculate temporal foliations of the Schwarzschild and the Oppenheimer-Snyder spacetime. Additionally, the author has studied a recently proposed, geometrically motivated spatial gauge condition, which is defined by considering the foliations of the three-dimensional space-like hypersurfaces by 2-surfaces of constant mean extrinsic curvature. Apart from the equations for the shift vector, which can be derived for this gauge condition, he has investigated such spatial foliations for well-known stationary axially symmetric spacetimes, namely for the Kerr metric and for numerically determined solutions for rapidly rotating neutron stars.

Spatial pattern dynamics due to the fitness gradient flux in evolutionary games.

PubMed

deForest, Russ; Belmonte, Andrew

2013-06-01

We introduce a nondiffusive spatial coupling term into the replicator equation of evolutionary game theory. The spatial flux is based on motion due to local gradients in the relative fitness of each strategy, providing a game-dependent alternative to diffusive coupling. We study numerically the development of patterns in one dimension (1D) for two-strategy games including the coordination game and the prisoner's dilemma, and in two dimensions (2D) for the rock-paper-scissors game. In 1D we observe modified traveling wave solutions in the presence of diffusion, and asymptotic attracting states under a frozen-strategy assumption without diffusion. In 2D we observe spiral formation and breakup in the frozen-strategy rock-paper-scissors game without diffusion. A change of variables appropriate to replicator dynamics is shown to correctly capture the 1D asymptotic steady state via a nonlinear diffusion equation.

Optimal estimation of spatially variable recharge and transmissivity fields under steady-state groundwater flow. Part 1. Theory

NASA Astrophysics Data System (ADS)

Graham, Wendy D.; Tankersley, Claude D.

1994-05-01

Stochastic methods are used to analyze two-dimensional steady groundwater flow subject to spatially variable recharge and transmissivity. Approximate partial differential equations are developed for the covariances and cross-covariances between the random head, transmissivity and recharge fields. Closed-form solutions of these equations are obtained using Fourier transform techniques. The resulting covariances and cross-covariances can be incorporated into a Bayesian conditioning procedure which provides optimal estimates of the recharge, transmissivity and head fields given available measurements of any or all of these random fields. Results show that head measurements contain valuable information for estimating the random recharge field. However, when recharge is treated as a spatially variable random field, the value of head measurements for estimating the transmissivity field can be reduced considerably. In a companion paper, the method is applied to a case study of the Upper Floridan Aquifer in NE Florida.

Spatial pattern dynamics due to the fitness gradient flux in evolutionary games

NASA Astrophysics Data System (ADS)

deForest, Russ; Belmonte, Andrew

2013-06-01

We introduce a nondiffusive spatial coupling term into the replicator equation of evolutionary game theory. The spatial flux is based on motion due to local gradients in the relative fitness of each strategy, providing a game-dependent alternative to diffusive coupling. We study numerically the development of patterns in one dimension (1D) for two-strategy games including the coordination game and the prisoner's dilemma, and in two dimensions (2D) for the rock-paper-scissors game. In 1D we observe modified traveling wave solutions in the presence of diffusion, and asymptotic attracting states under a frozen-strategy assumption without diffusion. In 2D we observe spiral formation and breakup in the frozen-strategy rock-paper-scissors game without diffusion. A change of variables appropriate to replicator dynamics is shown to correctly capture the 1D asymptotic steady state via a nonlinear diffusion equation.

Nonlinear spatial evolution of inviscid instabilities on hypersonic boundary layers

NASA Technical Reports Server (NTRS)

Wundrow, David W.

1996-01-01

The spatial development of an initially linear vorticity-mode instability on a compressible flat-plate boundary layer is considered. The analysis is done in the framework of the hypersonic limit where the free-stream Mach number M approaches infinity. Nonlinearity is shown to become important locally, in a thin critical layer, when sigma, the deviation of the phase speed from unity, becomes o(M(exp -8/7)) and the magnitude of the pressure fluctuations becomes 0(sigma(exp 5/2)M(exp 2)). The unsteady flow outside the critical layer takes the form of a linear instability wave but with its amplitude completely determined by the nonlinear flow within the critical layer. The coupled set of equations which govern the critical-layer dynamics reflect a balance between spatial-evolution, (linear and nonlinear) convection and nonlinear vorticity-generation terms. The numerical solution to these equations shows that nonlinear effects produce a dramatic reduction in the instability-wave amplitude.

Efficient electronic structure theory via hierarchical scale-adaptive coupled-cluster formalism: I. Theory and computational complexity analysis

NASA Astrophysics Data System (ADS)

Lyakh, Dmitry I.

2018-03-01

A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the hierarchical techniques from the renormalisation group approach, H/H2-matrix algebra and fast multipole method, the computational scaling reduction in our formalism is achieved via coarsening of quantum many-body interactions at larger interaction scales, thus imposing a hierarchical structure on many-body tensors of coupled-cluster theory. In our approach, the interaction scale can be defined on any appropriate Euclidean domain (spatial domain, momentum-space domain, energy domain, etc.). We show that the hierarchically resolved many-body tensors can reduce the storage requirements to O(N), where N is the number of simulated quantum particles. Subsequently, we prove that any connected many-body diagram consisting of a finite number of arbitrary-order tensors, e.g. an arbitrary coupled-cluster diagram, can be evaluated in O(NlogN) floating-point operations. On top of that, we suggest an additional approximation to further reduce the computational complexity of higher order coupled-cluster equations, i.e. equations involving higher than double excitations, which otherwise would introduce a large prefactor into formal O(NlogN) scaling.

3D electromagnetic modelling of a TTI medium and TTI effects in inversion

NASA Astrophysics Data System (ADS)

Jaysaval, Piyoosh; Shantsev, Daniil; de la Kethulle de Ryhove, Sébastien

2016-04-01

We present a numerical algorithm for 3D electromagnetic (EM) forward modelling in conducting media with general electric anisotropy. The algorithm is based on the finite-difference discretization of frequency-domain Maxwell's equations on a Lebedev grid, in which all components of the electric field are collocated but half a spatial step staggered with respect to the magnetic field components, which also are collocated. This leads to a system of linear equations that is solved using a stabilized biconjugate gradient method with a multigrid preconditioner. We validate the accuracy of the numerical results for layered and 3D tilted transverse isotropic (TTI) earth models representing typical scenarios used in the marine controlled-source EM method. It is then demonstrated that not taking into account the full anisotropy of the conductivity tensor can lead to misleading inversion results. For simulation data corresponding to a 3D model with a TTI anticlinal structure, a standard vertical transverse isotropic inversion is not able to image a resistor, while for a 3D model with a TTI synclinal structure the inversion produces a false resistive anomaly. If inversion uses the proposed forward solver that can handle TTI anisotropy, it produces resistivity images consistent with the true models.

Co-rotational thermo-mechanically coupled multi-field framework and finite element for the large displacement analysis of multi-layered shape memory alloy beam-like structures

NASA Astrophysics Data System (ADS)

Solomou, Alexandros G.; Machairas, Theodoros T.; Karakalas, Anargyros A.; Saravanos, Dimitris A.

2017-06-01

A thermo-mechanically coupled finite element (FE) for the simulation of multi-layered shape memory alloy (SMA) beams admitting large displacements and rotations (LDRs) is developed to capture the geometrically nonlinear effects which are present in many SMA applications. A generalized multi-field beam theory implementing a SMA constitutive model based on small strain theory, thermo-mechanically coupled governing equations and multi-field kinematic hypotheses combining first order shear deformation assumptions with a sixth order polynomial temperature field through the thickness of the beam section are extended to admit LDRs. The co-rotational formulation is adopted, where the motion of the beam is decomposed to rigid body motion and relative small deformation in the local frame. A new generalized multi-layered SMA FE is formulated. The nonlinear transient spatial discretized equations of motion of the SMA structure are synthesized and solved using the Newton-Raphson method combined with an implicit time integration scheme. Correlations of models incorporating the present beam FE with respective results of models incorporating plane stress SMA FEs, demonstrate excellent agreement of the predicted LDRs response, temperature and phase transformation fields, as well as, significant gains in computational time.

The frequency-difference and frequency-sum acoustic-field autoproducts.

PubMed

Worthmann, Brian M; Dowling, David R

2017-06-01

The frequency-difference and frequency-sum autoproducts are quadratic products of solutions of the Helmholtz equation at two different frequencies (ω + and ω - ), and may be constructed from the Fourier transform of any time-domain acoustic field. Interestingly, the autoproducts may carry wave-field information at the difference (ω + - ω - ) and sum (ω + + ω - ) frequencies even though these frequencies may not be present in the original acoustic field. This paper provides analytical and simulation results that justify and illustrate this possibility, and indicate its limitations. The analysis is based on the inhomogeneous Helmholtz equation and its solutions while the simulations are for a point source in a homogeneous half-space bounded by a perfectly reflecting surface. The analysis suggests that the autoproducts have a spatial phase structure similar to that of a true acoustic field at the difference and sum frequencies if the in-band acoustic field is a plane or spherical wave. For multi-ray-path environments, this phase structure similarity persists in portions of the autoproduct fields that are not suppressed by bandwidth averaging. Discrepancies between the bandwidth-averaged autoproducts and true out-of-band acoustic fields (with potentially modified boundary conditions) scale inversely with the product of the bandwidth and ray-path arrival time differences.

Saturation spectroscopy of an optically opaque argon plasma

NASA Astrophysics Data System (ADS)

Eshel, Ben; Rice, Christopher A.; Perram, Glen P.

2018-02-01

A pure argon (Ar) plasma formed by a capacitively coupled radio-frequency discharge was analyzed using Doppler-free saturation spectroscopy. The expected line shape was a characteristic of sub-Doppler spectra in the presence of velocity-changing collisions, a narrow Lorentzian centered on a Doppler pedestal, but the observed line shapes contain a multi-peak structure, attributed to opacity of the medium. Laser absorption and inter-modulated fluorescence spectroscopy measurements were made to validate opacity as a driving factor of the observed line shapes. Spectral line shapes are further complicated by the spatial dependence of the pump laser, probe laser and of the absorbing medium, as well as the large absorbance of the transition under investigation. A numerical line shape was derived by accounting for the spatial variation of the pump and probe with a saturated line shape obtained from the rate equations for an equivalent two-level system. This simulated line shape shows good qualitative agreement with the trends observed in the data.

Hamiltonian structure of the Lotka-Volterra equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1990-03-01

The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.

Aero-servo-viscoelasticity theory: Lifting surfaces, plates, velocity transients, flutter, and instability

NASA Astrophysics Data System (ADS)

Merrett, Craig G.

Modern flight vehicles are fabricated from composite materials resulting in flexible structures that behave differently from the more traditional elastic metal structures. Composite materials offer a number of advantages compared to metals, such as improved strength to mass ratio, and intentional material property anisotropy. Flexible aircraft structures date from the Wright brothers' first aircraft with fabric covered wooden frames. The flexibility of the structure was used to warp the lifting surface for flight control, a concept that has reappeared as aircraft morphing. These early structures occasionally exhibited undesirable characteristics during flight such as interactions between the empennage and the aft fuselage, or control problems with the elevators. The research to discover the cause and correction of these undesirable characteristics formed the first foray into the field of aeroelasticity. Aeroelasticity is the intersection and interaction between aerodynamics, elasticity, and inertia or dynamics. Aeroelasticity is well suited for metal aircraft, but requires expansion to improve its applicability to composite vehicles. The first is a change from elasticity to viscoelasticity to more accurately capture the solid mechanics of the composite material. The second change is to include control systems. While the inclusion of control systems in aeroelasticity lead to aero-servo-elasticity, more control possibilities exist for a viscoelastic composite material. As an example, during the lay-up of carbon-epoxy plies, piezoelectric control patches are inserted between different plies to give a variety of control options. The expanded field is called aero-servo-viscoelasticity. The phenomena of interest in aero-servo-viscoelasticity are best classified according to the type of structure considered, either a lifting surface or a panel, and the type of dynamic stability present. For both types of structures, the governing equations are integral-partial differential equations. The spatial component of the governing equations is eliminated using a series expansion of basis functions and by applying Galerkin's method. The number of terms in the series expansion affects the convergence of the spatial component, and convergence is best determined by the von Koch rules that previously appeared for column buckling problems. After elimination of the spatial component, an ordinary integral-differential equation in time remains. The dynamic stability of elastic and viscoelastic problems is assessed using the determinant of the governing system of equations and the time component of the solution in the form exp (lambda t). The determinant is in terms of lambda where the values of lambda are the latent roots of the aero-servo-viscoelastic system. The real component of lambda dictates the stability of the system. If all the real components are negative, the system is stable. If at least one real component is zero and all others are negative, the system is neutrally stable. If one or more real components are positive, the system is unstable. In aero-servo-viscoelasticity, the neutrally stable condition is termed flutter. For an aero-servo-viscoelastic lifting surface, the unstable condition is historically termed torsional divergence. The more general aero-servo-viscoelastic theory has produced a number of important results, enumerated in the following list: 1. Subsonic panel flutter can occur before panel instability. This result overturned a long held assumption in aeroelasticity, and was produced by the novel application of the von Koch rules for convergence. Further, experimental results from the 1950s by the Air Force were retrieved to provide additional proof. 2. An expanded definition for flutter of a lifting surface. The legacy definition is that flutter is the first occurrence of simple harmonic motion of a structure, and the flight velocity at which this motion occurs is taken as the flutter speed. The expanded definition indicates that the flutter condition should be taken when simple harmonic motion occurs and certain additional velocity derivatives are satisfied. 3. The viscoelastic material behavior imposes a flutter time indicating that the presence of flutter should be verified for the entire life time of a flight vehicle. 4. An expanded definition for instability of a lifting surface or panel. Traditionally, instability is treated as a static phenomenon. The static case is only a limiting case of dynamic instability for a viscoelastic structure. Instability occurs when a particular combination of flight velocity and time are reached leading to growing displacements of the structure. 5. The inclusion of flight velocity transients that occur during maneuvers. Two- and three-dimensional unsteady incompressible and compressible aerodynamics were reformulated for a time dependent velocity. The inclusion of flight velocity transients does affect the flutter and instability conditions for a lifting surface and a panel. The applications of aero-servo-viscoelasticity are to aircraft design, wind turbine blades, submarine's stealth coatings and hulls, and land transportation to name a few examples. One caveat regarding this field of research is that general predictions for an application are not always possible as the stability of a structure depends on the phase relations between the various parameters such as mass, stiffness, damping, and the aerodynamic loads. The viscoelastic material parameters in particular alter the system parameters in directions that are difficult to predict. The inclusion of servo controls permits an additional design factor and can improve the performance of a structure beyond the native performance; however over-control is possible so a maximum limit to useful control does exist. Lastly, the number of material and control parameters present in aero-servo-viscoelasticity are amenable to optimization protocols to produce the optimal structure for a given mission.

Generalized continuity equations from two-field Schrödinger Lagrangians

NASA Astrophysics Data System (ADS)

Spourdalakis, A. G. B.; Pappas, G.; Morfonios, C. Â. V.; Kalozoumis, P. A.; Diakonos, F. K.; Schmelcher, P.

2016-11-01

A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and whose global invariance under dilation and phase variations leads to a mixed continuity equation for the two fields. In combination with discrete spatial symmetries of the underlying Hamiltonian, the mixed continuity equation is shown to produce bilocal conservation laws for a single field. This leads to generalized conserved charges for vanishing boundary currents and to divergenceless bilocal currents for stationary states. The formalism reproduces the bilocal continuity equation obtained in the special case of P T -symmetric quantum mechanics and paraxial optics.

Multi criteria evaluation for universal soil loss equation based on geographic information system

NASA Astrophysics Data System (ADS)

Purwaamijaya, I. M.

2018-05-01

The purpose of this research were to produce(l) a conceptual, functional model designed and implementation for universal soil loss equation (usle), (2) standard operational procedure for multi criteria evaluation of universal soil loss equation (usle) using geographic information system, (3) overlay land cover, slope, soil and rain fall layers to gain universal soil loss equation (usle) using multi criteria evaluation, (4) thematic map of universal soil loss equation (usle) in watershed, (5) attribute table of universal soil loss equation (usle) in watershed. Descriptive and formal correlation methods are used for this research. Cikapundung Watershed, Bandung, West Java, Indonesia was study location. This research was conducted on January 2016 to May 2016. A spatial analysis is used to superimposed land cover, slope, soil and rain layers become universal soil loss equation (usle). Multi criteria evaluation for universal soil loss equation (usle) using geographic information system could be used for conservation program.

Modulation of localized solutions in a system of two coupled nonlinear Schrödinger equations.

PubMed

Cardoso, W B; Avelar, A T; Bazeia, D

2012-08-01

In this work we study localized solutions of a system of two coupled nonlinear Schrödinger equations, with the linear (potential) and nonlinear coefficients engendering spatial and temporal dependencies. Similarity transformations are used to convert the nonautonomous coupled equations into autonomous ones and we use the trial orbit method to help us solving them, presenting solutions in a general way. Numerical experiments are then used to verify the stability of the localized solutions.

Parameter estimation problems for distributed systems using a multigrid method

NASA Technical Reports Server (NTRS)

Ta'asan, Shlomo; Dutt, Pravir

1990-01-01

The problem of estimating spatially varying coefficients of partial differential equations is considered from observation of the solution and of the right hand side of the equation. It is assumed that the observations are distributed in the domain and that enough observations are given. A method of discretization and an efficient multigrid method for solving the resulting discrete systems are described. Numerical results are presented for estimation of coefficients in an elliptic and a parabolic partial differential equation.

Computational Predictions of Rear Surface Velocities for Metal Plates under Ballistic Impact

DTIC Science & Technology

2015-06-01

Appendix A. Comparison between ALEGRA and ALE3D 17 Appendix B. Equations of State 19 Appendix C. Constitutive Model 25 List of Symbols, Abbreviations...to a spatial resolution of 0.2 and 0.058 mm, respec- tively. 2.2 Material Models Each material can be modified via its equation of state or...and the most appropriate model is not always clear. An equation of state (EOS), which relates thermodynamic properties such as tem- perature pressure

Cosmological aspects of the Eisenhart-Duval lift

NASA Astrophysics Data System (ADS)

Cariglia, M.; Galajinsky, A.; Gibbons, G. W.; Horvathy, P. A.

2018-04-01

A cosmological extension of the Eisenhart-Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed by the Ermakov-Milne-Pinney equation. Killing isometries include spatial translations and rotations, Newton-Hooke boosts and translation in the null direction. Geodesic motion in Ermakov-Milne-Pinney cosmoi is analyzed. The derivation of the Ermakov-Lewis invariant, the Friedmann equations and the Dmitriev-Zel'dovich equations within the Eisenhart-Duval framework is presented.

Finite Volume Method for Pricing European Call Option with Regime-switching Volatility

NASA Astrophysics Data System (ADS)

Lista Tauryawati, Mey; Imron, Chairul; Putri, Endah RM

2018-03-01

In this paper, we present a finite volume method for pricing European call option using Black-Scholes equation with regime-switching volatility. In the first step, we formulate the Black-Scholes equations with regime-switching volatility. we use a finite volume method based on fitted finite volume with spatial discretization and an implicit time stepping technique for the case. We show that the regime-switching scheme can revert to the non-switching Black Scholes equation, both in theoretical evidence and numerical simulations.

Solving constant-coefficient differential equations with dielectric metamaterials

NASA Astrophysics Data System (ADS)

Zhang, Weixuan; Qu, Che; Zhang, Xiangdong

2016-07-01

Recently, the concept of metamaterial analog computing has been proposed (Silva et al 2014 Science 343 160-3). Some mathematical operations such as spatial differentiation, integration, and convolution, have been performed by using designed metamaterial blocks. Motivated by this work, we propose a practical approach based on dielectric metamaterial to solve differential equations. The ordinary differential equation can be solved accurately by the correctly designed metamaterial system. The numerical simulations using well-established numerical routines have been performed to successfully verify all theoretical analyses.

Spatial and Temporal Evaluation of Soil Erosion with RUSLE: A Case Study in an Olive Orchard Microcathment in Spain

EPA Science Inventory

Soil loss is commonly estimated using the Revised Universal Soil Loss Equation (RUSLE). Since RUSLE is an empirically based soil loss model derived from surveys on plots, the high spatial and temporal variability of erosion in Mediterranean environments and scale effects provoke...