Dubrovsky, V. G.; Topovsky, A. V.; Basalaev, M. Yu.
2010-09-15
The classes of exactly solvable multiline soliton potentials and corresponding wave functions of two-dimensional stationary Schroedinger equation via {partial_derivative}-dressing method are constructed and their physical interpretation is discussed.
Scattering waves using exact controllability methods
NASA Astrophysics Data System (ADS)
Bristeau, M. O.; Glowinski, R.; Periaux, J.
1993-01-01
The main goal of this paper is to introduce a novel method for solving the Helmholtz equations from acoustics and two-dimensional electromagnetics. The key idea of the method is to go back to the original wave equation and look for time periodic solutions. In order to find these solutions, we essentially use a least squares/shooting method which is closely related to exact controllability and to the Hilbert uniqueness method of Lions (1988). From this formulation and by analogy with other controllability problems, we derive a conjugate gradient algorithm (in an appropriate Hilbert space) which has quite good convergence properties. Numerical experiments concerning the scattering of planar waves by convex or nonconvex obstacles show the efficiency of the new algorithm, particularly for air intakelike reflectors and two-dimensional aircraft related bodies.
Exact Steady Azimuthal Internal Waves in the f-Plane
NASA Astrophysics Data System (ADS)
Hsu, Hung-Chu
2017-03-01
We present an explicit exact solution of the nonlinear governing equations with Coriolis and centripetal terms in the f-plane approximation for internal geophysical trapped waves with a uniform current near the equator. This solution describes in the Lagrangian framework azimuthal equatorial internal waves propagating westward in a stratified rotational fluid.
Exact Nonlinear Internal Equatorial Waves in the f-plane
NASA Astrophysics Data System (ADS)
Hsu, Hung-Chu
2016-07-01
We present an explicit exact solution of the nonlinear governing equations for internal geophysical water waves propagating westward above the thermocline in the f-plane approximation near the equator. Moreover, the mass transport velocity induced by this internal equatorial wave is eastward and a westward current occurs in the transition zone between the great depth where the water is still and the thermocline.
Pseudopotential Method for Higher Partial Wave Scattering
Idziaszek, Zbigniew; Calarco, Tommaso
2006-01-13
We present a zero-range pseudopotential applicable for all partial wave interactions between neutral atoms. For p and d waves, we derive effective pseudopotentials, which are useful for problems involving anisotropic external potentials. Finally, we consider two nontrivial applications of the p-wave pseudopotential: we solve analytically the problem of two interacting spin-polarized fermions confined in a harmonic trap, and we analyze the scattering of p-wave interacting particles in a quasi-two-dimensional system.
AdS waves as exact solutions to quadratic gravity
Guellue, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram; Guerses, Metin
2011-04-15
We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior.
Exact Steady Azimuthal Edge Waves in Rotating Fluids
NASA Astrophysics Data System (ADS)
Ionescu-Kruse, Delia
2016-09-01
The full problem of water waves travelling along a constant sloping beach with the shoreline parallel to the Equator, written in a moving frame with the origin at a point on the rotating Earth is introduced. An exact steady solution of this problem moving only in the azimuthal direction, with no variations in this direction, is obtained. The solution is discussed in turn in spherical coordinates, in cylindrical coordinates and in the tangent-plan approximations.
S-Wave Dispersion Relations: Exact Left Hand E-Plane Discontinuity from the Born Series
NASA Technical Reports Server (NTRS)
Bessis, D.; Temkin, A.
1999-01-01
We show, for a superposition of Yukawa potentials, that the left hand cut discontinuity in the complex E plane of the (S-wave) scattering amplitude is given exactly, in an interval depending on n, by the discontinuity of the Born series stopped at order n. This also establishes an inverse and unexpected correspondence of the Born series at positive high energies and negative low energies. We can thus construct a viable dispersion relation (DR) for the partial (S-) wave amplitude. The high numerical precision achievable by the DR is demonstrated for the exponential potential at zero scattering energy. We also briefly discuss the extension of our results to Field Theory.
Exact matter-wave vortices in a driven optical lattice
NASA Astrophysics Data System (ADS)
Deng, Yan; Hai, Wenhua; Zhou, Zheng
2013-07-01
We investigate vortex dynamics of a periodically driven Bose-Einstein condensate confined in a spatially two-dimensional optical lattice. An exact Floquet solution of the Gross-Pitaevskii equation is obtained for a certain parameter region which can be divided into the phase-jumping and phase-continuing regions. In the former region, the exact solution can describe spatiotemporal evolution of multiple vortices. For a small ratio of driving strength to optical lattice depth the vortices keep nearly unmoved. With the increase of the ratio, the vortices undergo an effective interaction and periodically evolve along some fixed circular orbits that leads the vortex dipoles and quadrupoles to produce and break alternatively. There is a critical ratio in the phase-jumping region beyond which the vortices generate and melt periodically. In the phase-continuing region, the condensate in the exact Floquet state evolves periodically without zero-density nodes. It is numerically demonstrated that the exact solution is stable under an initial perturbation for both parameter regions, except for a subregion of the phase-jumping region in which stability of the condensate is lost. However, the solution is structurally stable under a small parameter perturbation only for the phase-continuing region, while for the whole phase-jumping region the structural stability is destroyed. The results suggest a scheme for creating and controlling matter-wave vortices.
Study of coupled nonlinear partial differential equations for finding exact analytical solutions.
Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H
2015-07-01
Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.
Study of coupled nonlinear partial differential equations for finding exact analytical solutions
Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.
2015-01-01
Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256
Exact traveling wave solutions for system of nonlinear evolution equations.
Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H
2016-01-01
In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.
Stokes waves revisited: Exact solutions in the asymptotic limit
NASA Astrophysics Data System (ADS)
Davies, Megan; Chattopadhyay, Amit K.
2016-03-01
The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic "secular variation" in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n -ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.
NASA Astrophysics Data System (ADS)
Sahadevan, R.; Prakash, P.
2017-01-01
We show how invariant subspace method can be extended to time fractional coupled nonlinear partial differential equations and construct their exact solutions. Effectiveness of the method has been illustrated through time fractional Hunter-Saxton equation, time fractional coupled nonlinear diffusion system, time fractional coupled Boussinesq equation and time fractional Whitman-Broer-Kaup system. Also we explain how maximal dimension of the time fractional coupled nonlinear partial differential equations can be estimated.
Exact diffusion constant for the one-dimensional partially asymmetric exclusion model
NASA Astrophysics Data System (ADS)
Derrida, B.; Mallick, K.
1997-02-01
We calculate exactly the diffusion constant associated with the fluctuations of the current for the partial asymmetric exclusion model on a ring with an arbitrary number of particles and holes. We also give the diffusion constant of a tagged particle on that ring. Our approach extends, using the deformed harmonic oscillator algebra, a result already known for the fully asymmetric case. In the limit of weak asymmetry, we extract from our exact expression the crossover between the Edwards - Wilkinson and the Kardar - Parisi - Zhang equations in (1 + 1) dimensions.
Localized light waves: Paraxial and exact solutions of the wave equation (a review)
NASA Astrophysics Data System (ADS)
Kiselev, A. P.
2007-04-01
Simple explicit localized solutions are systematized over the whole space of a linear wave equation, which models the propagation of optical radiation in a linear approximation. Much attention has been paid to exact solutions (which date back to the Bateman findings) that describe wave beams (including Bessel-Gauss beams) and wave packets with a Gaussian localization with respect to the spatial variables and time. Their asymptotics with respect to free parameters and at large distances are presented. A similarity between these exact solutions and harmonic in time fields obtained in the paraxial approximation based on the Leontovich-Fock parabolic equation has been studied. Higher-order modes are considered systematically using the separation of variables method. The application of the Bateman solutions of the wave equation to the construction of solutions to equations with dispersion and nonlinearity and their use in wavelet analysis, as well as the summation of Gaussian beams, are discussed. In addition, solutions localized at infinity known as the Moses-Prosser “acoustic bullets”, as well as their harmonic in time counterparts, “ X waves”, waves from complex sources, etc., have been considered. Everywhere possible, the most elementary mathematical formalism is used.
Superconformal partial waves in Grassmannian field theories
NASA Astrophysics Data System (ADS)
Doobary, Reza; Heslop, Paul
2015-12-01
We derive superconformal partial waves for all scalar four-point functions on a super Grassmannian space Gr( m| n, 2 m|2 n) for all m, n. This family of four-point functions includes those of all (arbitrary weight) half BPS operators in both N=4 SYM ( m = n = 2) and in N = 2 superconformal field theories in four dimensions ( m = 2 , n = 1) on analytic superspace. It also includes four-point functions of all (arbitrary dimension) scalar fields in non-supersymmetric conformal field theories ( m = 2 , n = 0) on Minkowski space, as well as those of a certain class of representations of the compact SU(2 n) coset spaces. As an application we then specialise to N=4 SYM and use these results to perform a detailed superconformal partial wave analysis of the four-point functions of arbitrary weight half BPS operators. We discuss the non-trivial separation of protected and unprotected sectors for the <2222>, <2233> and <3333> cases in an SU( N) gauge theory at finite N. The <2233> correlator predicts a non-trivial protected twist four sector for <3333> which we can completely determine using the knowledge that there is precisely one such protected twist four operator for each spin.
Generalized and exact solutions for oblique shock waves of real gases with application to real air
NASA Astrophysics Data System (ADS)
Kouremenos, D. A.; Antonopoulos, K. A.
1989-12-01
The present work presents a generalized method for calculating oblique shock waves of real gases, based on the Redlich-Kwong (1949) equation of state. Also described is an exact method applicable when the exact equation of state and enthalpy function of a real gas are available. Application of the generalized and the exact methods in the case of real air showed that the former is very accurate and at least twenty times faster than the latter. An additional contribution of the study is the derivation of real gas oblique shock wave equations, which are of the same algebraic form as the well known ideal gas normal shock wave relations.
Gershgorin, B.; Majda, A.J.
2011-02-20
A statistically exactly solvable model for passive tracers is introduced as a test model for the authors' Nonlinear Extended Kalman Filter (NEKF) as well as other filtering algorithms. The model involves a Gaussian velocity field and a passive tracer governed by the advection-diffusion equation with an imposed mean gradient. The model has direct relevance to engineering problems such as the spread of pollutants in the air or contaminants in the water as well as climate change problems concerning the transport of greenhouse gases such as carbon dioxide with strongly intermittent probability distributions consistent with the actual observations of the atmosphere. One of the attractive properties of the model is the existence of the exact statistical solution. In particular, this unique feature of the model provides an opportunity to design and test fast and efficient algorithms for real-time data assimilation based on rigorous mathematical theory for a turbulence model problem with many active spatiotemporal scales. Here, we extensively study the performance of the NEKF which uses the exact first and second order nonlinear statistics without any approximations due to linearization. The role of partial and sparse observations, the frequency of observations and the observation noise strength in recovering the true signal, its spectrum, and fat tail probability distribution are the central issues discussed here. The results of our study provide useful guidelines for filtering realistic turbulent systems with passive tracers through partial observations.
On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.
Yang, Xiao-Jun; Tenreiro Machado, J A; Baleanu, Dumitru; Cattani, Carlo
2016-08-01
This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.
Exact finite difference schemes for the non-linear unidirectional wave equation
NASA Technical Reports Server (NTRS)
Mickens, R. E.
1985-01-01
Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.
Dynamical behaviours and exact travelling wave solutions of modified generalized Vakhnenko equation
NASA Astrophysics Data System (ADS)
Xiao, Junjun; Feng, Dahe; Meng, Xia; Cheng, Yuanquan
2017-01-01
By using the bifurcation theory of planar dynamical systems and the qualitative theory of differential equations, we studied the dynamical behaviours and exact travelling wave solutions of the modified generalized Vakhnenko equation (mGVE). As a result, we obtained all possible bifurcation parametric sets and many explicit formulas of smooth and non-smooth travelling waves such as cusped solitons, loop solitons, periodic cusp waves, pseudopeakon solitons, smooth periodic waves and smooth solitons. Moreover, we provided some numerical simulations of these solutions.
Partial Wave Analysis of Coupled Photonic Structures
NASA Technical Reports Server (NTRS)
Fuller, Kirk A.; Smith, David D.; Curreri, Peter A. (Technical Monitor)
2002-01-01
The very high quality factors sustained by microcavity optical resonators are relevant to applications in wavelength filtering, routing, switching, modulation, and multiplexing/demultiplexing. Increases in the density of photonic elements require that attention be paid to how electromagnetic (EM) coupling modifies their optical properties. This is especially true when cavity resonances are involved, in which case, their characteristics may be fundamentally altered. Understanding the optical properties of microcavities that are near or in contact with photonic elements---such as other microcavities, nanostructures, couplers, and substrates---can be expected to advance our understanding of the roles that these structures may play in VLSI photonics, biosensors and similar device technologies. Wc present results from recent theoretical studies of the effects of inter- and intracavity coupling on optical resonances in compound spherical particles. Concentrically stratified spheres and bispheres constituted from homogeneous and stratified spheres are subjects of this investigation. A new formulation is introduced for the absorption of light in an arbitrary layer of a multilayered sphere, which is based on multiple reflections of the spherical partial waves of the Lorenz-Mie solution for scattering by a sphere. Absorption efficiencies, which can be used to profile cavity resonances and to infer fluorescence yields or the onset of nonlinear optical processes in the microcavities, are presented. Splitting of resonances in these multisphere systems is paid particular attention, and consequences for photonic device development and possible performance enhancements through carefully designed architectures that exploit EM coupling are considered.
An Exact Solution for Geophysical Edge Waves in the {β}-Plane Approximation
NASA Astrophysics Data System (ADS)
Ionescu-Kruse, Delia
2015-12-01
By taking into account the {β}-plane effects, we provide an exact nonlinear solution to the geophysical edge-wave problem within the Lagrangian framework. This solution describes trapped waves propagating eastward or westward along a sloping beach with the shoreline parallel to the Equator.
An Exactly Solvable Travelling Wave Equation in the Fisher-KPP Class
NASA Astrophysics Data System (ADS)
Brunet, Éric; Derrida, Bernard
2015-11-01
For a simple one dimensional lattice version of a travelling wave equation, we obtain an exact relation between the initial condition and the position of the front at any later time. This exact relation takes the form of an inverse problem: given the times t_n at which the travelling wave reaches the positions n, one can deduce the initial profile. We show, by means of complex analysis, that a number of known properties of travelling wave equations in the Fisher-KPP class can be recovered, in particular Bramson's shifts of the positions. We also recover and generalize Ebert-van Saarloos' corrections depending on the initial condition.
Exact Travelling Wave Solutions of the Nonlinear Evolution Equations by Auxiliary Equation Method
NASA Astrophysics Data System (ADS)
Kaplan, Melike; Akbulut, Arzu; Bekir, Ahmet
2015-10-01
The auxiliary equation method presents wide applicability to handling nonlinear wave equations. In this article, we establish new exact travelling wave solutions of the nonlinear Zoomeron equation, coupled Higgs equation, and equal width wave equation. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions, and rational functions. It is shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering. Throughout the article, all calculations are made with the aid of the Maple packet program.
Exact numerical solutions for dark waves on the discrete nonlinear Schrödinger equation.
Sánchez-Rey, Bernardo; Johansson, Magnus
2005-03-01
In this paper we study numerically existence and stability of exact dark waves on the (nonintegrable) discrete nonlinear Schrödinger equation for a finite one-dimensional lattice. These are solutions that bifurcate from stationary dark modes with constant background intensity and zero intensity at a site, and whose initial state translates exactly one site each period of the internal oscillations. We show that exact dark waves are characterized by an oscillatory background whose wavelength is closely related with the velocity. Faster dark waves require smaller wavelengths. For slow enough velocity dark waves are linearly stable, but when trying to continue numerically a solution towards higher velocities bifurcations appear, due to rearrangements in the oscillatory tail in order to make possible a decreasing of the wavelength. However, in principle, one might control the stability of an exact dark wave adjusting a phase factor which plays the role of a discreteness parameter. In addition, we also study the regimes of existence and stability for stationary discrete gray modes, which are exact solutions with phase-twisted constant-amplitude background and nonzero minimum intensity. Also such solutions develop envelope oscillations on top of the homogeneous background when continued into moving phase-twisted solutions.
Exact traveling wave solutions of the van der Waals normal form for fluidized granular matter
NASA Astrophysics Data System (ADS)
Abourabia, A. M.; Morad, A. M.
2015-11-01
Analytical solutions of the van der Waals normal form for fluidized granular media have been done to study the phase separation phenomenon by using two different exact methods. The Painlevé analysis is discussed to illustrate the integrability of the model equation. An auto-Bäcklund transformation is presented via the truncated expansion and symbolic computation. The results show that the exact solutions of the model introduce solitary waves of different types. The solutions of the hydrodynamic model and the van der Waals equation exhibit a behavior similar to the one observed in molecular dynamic simulations such that two pairs of shock and rarefaction waves appear and move away, giving rise to the bubbles. The dispersion properties and the relation between group and phase velocities of the model equation are studied using the plane wave assumption. The diagrams are drawn to illustrate the physical properties of the exact solutions, and indicate their stability and bifurcation.
Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents
Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan
2014-01-01
Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves. PMID:24711719
Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents.
Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan
2014-04-08
Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.
NASA Technical Reports Server (NTRS)
Barnes, A.
1983-01-01
An exact nonlinear solution is found to the relativistic kinetic and electrodynamic equations (in their hydromagnetic limit) that describes the large-amplitude fast-mode magnetoacoustic wave propagating normal to the magnetic field in a collisionless, previously uniform plasma. It is pointed out that a wave of this kind will be generated by transverse compression of any collisionless plasma. The solution is in essence independent of the detailed form of the particle momentum distribution functions. The solution is obtained, in part, through the method of characteristics; the wave exhibits the familiar properties of steepening and shock formation. A detailed analysis is given of the ultrarelativistic limit of this wave.
Exact Analysis of Lamb Waves in Piezoelectric Membranes with Distinct Electrode Arrangements
NASA Astrophysics Data System (ADS)
Chen, Yung-Yu
2009-07-01
Lamb wave devices have been widely used in electro-acoustic and microfluidic devices. In order to improve their performances, the phase velocity dispersion and electromechanical coupling coefficient (ECC) of the Lamb wave should be calculated exactly during designing. Accordingly, this paper aims at analyzing exactly Lamb waves in a single piezoelectric membrane with distinct electrode arrangements. First, the transfer matrix method was employed to calculate the phase velocity dispersion. The ECCs under distinct electrical boundary conditions were calculated by the Green's function method. Finally, the calculated ECCs were compared with that by using the acoustic velocity difference method. Results show that the differences exist especially in the case of metalized surface, and the coupling coefficients deeply depend on the electrode arrangements. It is concluded that the S0 mode for the metalized surface case is a better choice for a Lamb wave device due to less dispersion, higher velocity, and larger coupling coefficient.
Amplification of sound waves in an imploding plasma shell: Exact results
Han, S.J.
1988-01-01
In an extended model, a rigorous proof is given for sound-wave amplifications in an imploding plasma shell. It is shown that, in the absence of a massless free surface, the boundary conditions give the exact eigenvalues which determine the asymptotic solution to the problem.
ALFVEN WAVES IN A PARTIALLY IONIZED TWO-FLUID PLASMA
Soler, R.; Ballester, J. L.; Terradas, J.; Carbonell, M. E-mail: joseluis.ballester@uib.es E-mail: marc.carbonell@uib.es
2013-04-20
Alfven waves are a particular class of magnetohydrodynamic waves relevant in many astrophysical and laboratory plasmas. In partially ionized plasmas the dynamics of Alfven waves is affected by the interaction between ionized and neutral species. Here we study Alfven waves in a partially ionized plasma from the theoretical point of view using the two-fluid description. We consider that the plasma is composed of an ion-electron fluid and a neutral fluid, which interact by means of particle collisions. To keep our investigation as general as possible, we take the neutral-ion collision frequency and the ionization degree as free parameters. First, we perform a normal mode analysis. We find the modification due to neutral-ion collisions of the wave frequencies and study the temporal and spatial attenuation of the waves. In addition, we discuss the presence of cutoff values of the wavelength that constrain the existence of oscillatory standing waves in weakly ionized plasmas. Later, we go beyond the normal mode approach and solve the initial-value problem in order to study the time-dependent evolution of the wave perturbations in the two fluids. An application to Alfven waves in the low solar atmospheric plasma is performed and the implication of partial ionization for the energy flux is discussed.
Partial Wave Dispersion Relations: Application to Electron-Atom Scattering
NASA Technical Reports Server (NTRS)
Temkin, A.; Drachman, Richard J.
1999-01-01
In this Letter we propose the use of partial wave dispersion relations (DR's) as the way of solving the long-standing problem of correctly incorporating exchange in a valid DR for electron-atom scattering. In particular a method is given for effectively calculating the contribution of the discontinuity and/or poles of the partial wave amplitude which occur in the negative E plane. The method is successfully tested in three cases: (i) the analytically solvable exponential potential, (ii) the Hartree potential, and (iii) the S-wave exchange approximation for electron-hydrogen scattering.
Condensates of p-Wave Pairs Are Exact Solutions for Rotating Two-Component Bose Gases
Papenbrock, T; Kavoulakis, G. M.
2012-01-01
We derive exact analytical results for the wave functions and energies of harmonically trapped two-component Bose-Einstein condensates with weakly repulsive interactions under rotation. The isospin symmetric wave functions are universal and do not depend on the matrix elements of the two-body interaction. The comparison with the results from numerical diagonalization shows that the ground state and low-lying excitations consist of condensates of p-wave pairs for repulsive contact interactions, Coulomb interactions, and the repulsive interactions between aligned dipoles.
Condensates of p-wave pairs are exact solutions for rotating two-component Bose gases.
Papenbrock, T; Reimann, S M; Kavoulakis, G M
2012-02-17
We derive exact analytical results for the wave functions and energies of harmonically trapped two-component Bose-Einstein condensates with weakly repulsive interactions under rotation. The isospin symmetric wave functions are universal and do not depend on the matrix elements of the two-body interaction. The comparison with the results from numerical diagonalization shows that the ground state and low-lying excitations consist of condensates of p-wave pairs for repulsive contact interactions, Coulomb interactions, and the repulsive interactions between aligned dipoles.
Exact soliton solution of spin chain with an external magnetic field in linear wave background
NASA Astrophysics Data System (ADS)
Li, Qiu-Yan; Xie, Zheng-Wei; Li, Lu; Li, Zai-Dong; Liang, Jiu-Qing
2004-07-01
Employing a simple, straightforward Darboux transformation we construct exact N-soliton solution for anisotropic spin chain driven by an external magnetic field in linear wave background. As a special case the explicit one- and two-soliton solution dressed by the linear wave corresponding to magnon in quantum theory is obtained analytically and its property is discussed in detail. The dispersion law, effective soliton mass, and the energy of each soliton are investigated as well. Our result show that the stability criterion of soliton is related with anisotropic parameter and the amplitude of the linear wave.
Lerma H, S.
2010-07-15
The structure of the exact wave function of the isovectorial pairing Hamiltonian with nondegenerate single-particle levels is discussed. The way that the single-particle splittings break the quartet condensate solution found for N=Z nuclei in a single degenerate level is established. After a brief review of the exact solution, the structure of the wave function is analyzed and some particular cases are considered where a clear interpretation of the wave function emerges. An expression for the exact wave function in terms of the isospin triplet of pair creators is given. The ground-state wave function is analyzed as a function of pairing strength, for a system of four protons and four neutrons. For small and large values of the pairing strength a dominance of two-pair (quartets) scalar couplings is found, whereas for intermediate values enhancements of the nonscalar couplings are obtained. A correlation of these enhancements with the creation of Cooper-like pairs is observed.
MAGNETOACOUSTIC WAVES IN A PARTIALLY IONIZED TWO-FLUID PLASMA
Soler, Roberto; Ballester, Jose Luis; Carbonell, Marc E-mail: joseluis.ballester@uib.es
2013-11-01
Compressible disturbances propagate in a plasma in the form of magnetoacoustic waves driven by both gas pressure and magnetic forces. In partially ionized plasmas the dynamics of ionized and neutral species are coupled due to ion-neutral collisions. As a consequence, magnetoacoustic waves propagating through a partially ionized medium are affected by ion-neutral coupling. The degree to which the behavior of the classic waves is modified depends on the physical properties of the various species and on the relative value of the wave frequency compared to the ion-neutral collision frequency. Here, we perform a comprehensive theoretical investigation of magnetoacoustic wave propagation in a partially ionized plasma using the two-fluid formalism. We consider an extensive range of values for the collision frequency, ionization ratio, and plasma β, so that the results are applicable to a wide variety of astrophysical plasmas. We determine the modification of the wave frequencies and study the frictional damping due to ion-neutral collisions. Approximate analytic expressions for the frequencies are given in the limit case of strongly coupled ions and neutrals, while numerically obtained dispersion diagrams are provided for arbitrary collision frequencies. In addition, we discuss the presence of cutoffs in the dispersion diagrams that constrain wave propagation for certain combinations of parameters. A specific application to propagation of compressible waves in the solar chromosphere is given.
Santos-Sacchi, Joseph
2004-07-01
Measures of membrane capacitance offer insight into a variety of cellular processes. Unfortunately, popular methodologies rely on model simplifications that sensitize them to interference from inevitable changes in resistive components of the traditional cell-clamp model. Here I report on a novel method to measure membrane capacitance that disposes of the usual simplifications and assumptions, yet is immune to such interference and works on the millisecond timescale. It is based on the exact empirical determination of the elusive partial derivative, partial differential Y/partial differential C(m), which heretofore had been approximated. Furthermore, I illustrate how this method extends to the vesicle fusion problem by permitting the determination of partial differential Y(v)/partial differential C(v), thereby providing estimates of fusion pore conductance and vesicle capacitance. Finally, I provide simulation examples and physiological examples of how the method can be used to study processes that are routinely interrogated by measures of membrane capacitance.
An exact solution for effects of topography on free Rayleigh waves
Savage, W.Z.
2004-01-01
An exact solution for the effects of topography on Rayleigh wave amplification is presented. The solution is obtained by incorporating conformal mapping into complex-variable stress functions developed for free Rayleigh wave propagation in an elastic half-space with a flat upper surface. Results are presented for free Rayleigh wave propagation across isolated symmetric ridges and valleys. It is found for wavelengths that are comparable to ridge widths that horizontal Rayleigh wave amplitudes are amplified at ridge crests and that vertical amplitudes are strongly reduced near ridge crests relative to horizontal and vertical amplitudes of free Rayleigh waves in the flat case. Horizontal amplitudes are strongly deamplified at valley bottoms relative to those for the flat case for Rayleigh wavelengths comparable to valley widths. Wave amplitudes in the symmetric ridges and valleys asymptotically approach those for the flat case with increased wavelengths, increased ridge and valley widths, and with horizontal distance from and depth below the isolated ridges and valleys. Also, prograde particle motion is predicted near crests of narrow ridges and near the bottoms of narrow valleys. Finally, application of the theory at two sites known for topographic wave amplification gives a predicted surface wave amplification ratio of 3.80 at the ridge center for a frequency of 1.0 Hz at Robinwood Ridge in northern California and a predicted surface wave amplification ratio of 1.67 at the ridge center for the same frequency at the Cedar Hill Nursery site at Tarzana in southern California.
Correlations of πN partial waves for multireaction analyses
Doring, M.; Revier, J.; Ronchen, D.; ...
2016-06-15
In the search for missing baryonic resonances, many analyses include data from a variety of pion- and photon-induced reactions. For elastic πN scattering, however, usually the partial waves of the SAID (Scattering Analysis Interactive Database) or other groups are fitted, instead of data. We provide the partial-wave covariance matrices needed to perform correlated χ2 fits, in which the obtained χ2 equals the actual χ2 up to nonlinear and normalization corrections. For any analysis relying on partial waves extracted from elastic pion scattering, this is a prerequisite to assess the significance of resonance signals and to assign any uncertainty on results.more » Lastly, the influence of systematic errors is also considered.« less
Exact relativistic expressions for wave refraction in a generally moving fluid.
Cavalleri, G; Tonni, E; Barbero, F
2013-04-01
The law for the refraction of a wave when the two fluids and the interface are moving with relativistic velocities is given in an exact form, at the same time correcting a first order error in a previous paper [Cavalleri and Tonni, Phys. Rev. E 57, 3478 (1998)]. The treatment is then extended to a generally moving fluid with variable refractive index, ready to be applied to the refraction of acoustic, electromagnetic, or magnetohydrodynamic waves in the atmosphere of rapidly rotating stars. In the particular case of a gas cloud receding because of the universe expansion, our result can be applied to predict observable micro- and mesolensings. The first order approximation of our exact result for the deviation due to refraction of the light coming from a further quasar has a relativistic dependence equal to the one obtained by Einsteins' linearized theory of gravitation.
Some Exact Results for the Schroedinger Wave Equation with a Time Dependent Potential
NASA Technical Reports Server (NTRS)
Campbell, Joel
2009-01-01
The time dependent Schroedinger equation with a time dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wave function at the origin, one may derive the wave function everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the p otential lead to conservation of the normalization of the probability density.
Matter-Wave Fields for Double-Slit Atom Interferometry: Variational Versus Exact Solitons
NASA Astrophysics Data System (ADS)
Ndifon Ngek, Isaiah; Moïse Dikandé, Alain; Moubissi, Alain Brice
2016-12-01
A major challenge in the theoretical modeling of double-slit interferometry involving matter-wave fields is the appropriate waveform to be assigned to this field. While all the studies carried out to date on this issue deal with variational fields, experiments suggest that the optical field is generated by splitting a single-hump Bose-Einstein condensate into two spatially and temporally entangled pulses indicating the possibility of fully controlling the subsequent motion of the two output pulses. To probe the consistency of variational and exact soliton solutions to the field equation, we solve the Gross-Pitaevskii equation with an optical potential barrier assumed to act as a beam splitter, while including gravity. The exact solution is compared with the two most common variational wavefunctions, namely, the Hermite-Gaussian and super-sech modes. From numerical simulations, evidence is given of the exact solution as being the most appropriate matter-wave structure that provides a coherent description of the generation and spatio-temporal evolution of matter-wave optical fields in a hypothetical implementation of double-slit atom interferometry.
Bohmian mechanics in the exact factorization of electron-nuclear wave functions
NASA Astrophysics Data System (ADS)
Suzuki, Yasumitsu; Watanabe, Kazuyuki
2016-09-01
The exact factorization of an electron-nuclear wave function [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010), 10.1103/PhysRevLett.105.123002] allows us to define the rigorous nuclear time-dependent Schrödinger equation (TDSE) with a time-dependent potential-energy surface (TDPES) that fully accounts for the coupling to the electronic motion and drives the nuclear wave-packet dynamics. Here, we study whether the propagation of multiple classical trajectories can reproduce the quantum nuclear motion in strong-field processes when their motions are governed by the quantum Hamilton-Jacobi equation derived by applying Bohmian mechanics to this exact nuclear TDSE. We demonstrate that multiple classical trajectories propagated by the force from the gradient of the exact TDPES plus the Bohmian quantum potential can reproduce the strong-field dissociation dynamics of a one-dimensional model of the H2 + molecule. Our results show that the force from the Bohmian quantum potential plays a non-negligible role in yielding quantum nuclear dynamics in the strong-field process studied here, where ionization and/or splitting of nuclear probability density occurs.
Es'kin, V A; Kudrin, A V; Petrov, E Yu
2011-06-01
The behavior of electromagnetic fields in nonlinear media has been a topical problem since the discovery of materials with a nonlinearity of electromagnetic properties. The problem of finding exact solutions for the source-excited nonlinear waves in curvilinear coordinates has been regarded as unsolvable for a long time. In this work, we present the first solution of this type for a cylindrically symmetric field excited by a pulsed current filament in a nondispersive medium that is simultaneously inhomogeneous and nonlinear. Assuming that the medium has a power-law permittivity profile in the linear regime and lacks a center of inversion, we derive an exact solution for the electromagnetic field excited by a current filament in such a medium and discuss the properties of this solution.
Wave optics simulation approach for partial spatially coherent beams.
Xiao, Xifeng; Voelz, David
2006-08-07
A numerical wave optics approach for simulating a partial spatially coherent beam is presented. The approach involves the application of a sequence of random phase screens to an initial beam field and the summation of the intensity results after propagation. The relationship between the screen parameters and the spatial coherence function for the beam is developed and the approach is verified by comparing results with analytic formulations for a Gaussian Schell-model beam. The approach can be used for modeling applications such as free space optical laser links that utilize partially coherent beams.
Impact of Plunging Breaking Wave on a Partially Submerged Cube
NASA Astrophysics Data System (ADS)
Wang, A.; Ikeda, C. M.; Duncan, J. H.
2012-11-01
The impact of a plunging breaking wave on a partially submerged rigid cube (L = 30 . 5 cm) is studied experimentally in a wave tank that is 14.8 m long, 1.15 m wide and 2.2 m high with a water depth of 0.91 m. A single repeatable plunging breaker is generated from a dispersively focused wave packet (average frequency of 1.14 Hz) that is created with a programmable wave maker. The water surface profiles at the vertical center plane of the cube are measured with a cinematic LIF technique. The cube is centered in the width of the tank and mounted from above with the front face oriented with its normal in the vertical long center plane of the tank and tilted at angles of 0 and 20 degrees downward relative to horizontal. For the range of horizontal cube positions used here, during the wave impact, the water free surface forms a circular arc between the water contact point on the front face of the cube and the wave crest. As the wave impact continues, this arc converges to a point and a fast-moving vertical jet is formed. The effect of the submergence and tilt angle of the cube on the jet formation are explored. This work is supported by the Office of Naval Research.
Chakrabarti, Nikhil; Maity, Chandan; Schamel, Hans
2011-04-08
Compressional waves in a magnetized plasma of arbitrary resistivity are treated with the lagrangian fluid approach. An exact nonlinear solution with a nontrivial space and time dependence is obtained with boundary conditions as in Harris' current sheet. The solution shows competition among hydrodynamic convection, magnetic field diffusion, and dispersion. This results in a collapse of density and the magnetic field in the absence of dispersion. The dispersion effects arrest the collapse of density but not of the magnetic field. A possible application is in the early stage of magnetic star formation.
Exact Quantization of Einstein-Rosen Waves Coupled to Massless Scalar Matter
NASA Astrophysics Data System (ADS)
Barbero G., J. Fernando; Garay, Iñaki; Villaseñor, Eduardo J.
2005-07-01
We show in this Letter that gravity coupled to a massless scalar field with full cylindrical symmetry can be exactly quantized by an extension of the techniques used in the quantization of Einstein-Rosen waves. This system provides a useful test bed to discuss a number of issues in quantum general relativity, such as the emergence of the classical metric, microcausality, and large quantum gravity effects. It may also provide an appropriate framework to study gravitational critical phenomena from a quantum point of view, issues related to black hole evaporation, and the consistent definition of test fields and particles in quantum gravity.
Properties of Baryons from Bonn-Gatchina Partial Wave Analysis
NASA Astrophysics Data System (ADS)
Sarantsev, Andrey
The recent results from the Bonn-Gatchinal partial wave analysis are reported. The analysis includes a large number of new pseudoscalar meson photoproduction data taken with polarized beam and target. The analysis also includes the information about photoproduction of vector mesons, which reveals resonant signals at masses above 2 GeV. The impact of the new data on spectrum of baryons and their properties is discussed.
Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations.
Islam, S M Rayhanul; Khan, Kamruzzaman; Akbar, M Ali
2015-01-01
In this paper, we implement the exp(-Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations play significant role in nonlinear sciences. We obtained four types of explicit function solutions, namely hyperbolic, trigonometric, exponential and rational function solutions of the variables in the considered equations. It has shown that the applied method is quite efficient and is practically well suited for the aforementioned problems and so for the other NLEEs those arise in mathematical physics and engineering fields. PACS numbers: 02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fq.
Impact of plunging breaking waves on a partially submerged cube
NASA Astrophysics Data System (ADS)
Wang, A.; Ikeda, C.; Duncan, J. H.
2013-11-01
The impact of a deep-water plunging breaking wave on a partially submerged cube is studied experimentally in a tank that is 14.8 m long and 1.2 m wide with a water depth of 0.91 m. The breakers are created from dispersively focused wave packets generated by a programmable wave maker. The water surface profile in the vertical center plane of the cube is measured using a cinematic laser-induced fluorescence technique with movie frame rates ranging from 300 to 4,500 Hz. The pressure distribution on the front face of the cube is measured with 24 fast-response sensors simultaneously with the wave profile measurements. The cube is positioned vertically at three heights relative to the mean water level and horizontally at a distance from the wave maker where a strong vertical water jet is formed. The portion of the water surface between the contact point on the front face of the cube and the wave crest is fitted with a circular arc and the radius and vertical position of the fitted circle is tracked during the impact. The vertical acceleration of the contact point reaches more than 50 times the acceleration of gravity and the pressure distribution just below the free surface shows a localized high-pressure region with a very high vertical pressure gradient. This work is supported by the Office of Naval Research under grant N000141110095.
MAGNETOHYDRODYNAMIC WAVES IN A PARTIALLY IONIZED FILAMENT THREAD
Soler, R.; Oliver, R.; Ballester, J. L. E-mail: ramon.oliver@uib.es
2009-07-10
Oscillations and propagating waves are commonly seen in high-resolution observations of filament threads, i.e., the fine-structures of solar filaments/prominences. Since the temperature of prominences is typically of the order of 10{sup 4} K, the prominence plasma is only partially ionized. In this paper, we study the effect of neutrals on the wave propagation in a filament thread modeled as a partially ionized homogeneous magnetic flux tube embedded in an homogeneous and fully ionized coronal plasma. Ohmic and ambipolar magnetic diffusion are considered in the basic resistive magnetohydrodynamic (MHD) equations. We numerically compute the eigenfrequencies of kink, slow, and Alfven linear MHD modes and obtain analytical approximations in some cases. We find that the existence of propagating modes is constrained by the presence of critical values of the longitudinal wavenumber. In particular, the lower and upper frequency cutoffs of kink and Alfven waves owe their existence to magnetic diffusion parallel and perpendicular to magnetic field lines, respectively. The slow mode only has a lower frequency cutoff, which is caused by perpendicular magnetic diffusion and is significantly affected by the ionization degree. In addition, ion-neutral collision is the most efficient damping mechanism for short wavelengths, while ohmic diffusion dominates in the long-wavelength regime.
Shear Wave Generation by Decoupled and Partially Coupled Explosions
NASA Astrophysics Data System (ADS)
Baker, G. E.; Xu, H.; Stevens, J. L.
2008-12-01
Decoupling is a means of evading detection by detonation of an explosion within a large cavity, which reduces the amplitude of the seismic waves. Such explosions are however still detectable with the current global seismic network, so their discrimination is important. A fully decoupled explosion detonated in the center of a spherical cavity will be a purely compressional seismic source, and so its discrimination should be straightforward. In practice however, decoupled explosions generate S waves, often identical to and sometimes even larger (relative to P) than S waves from comparable tamped explosions. If the source were purely compressional, the S waves must be the result of conversion from P and/or Rg. Asymmetries however, such as asphericity of the cavity or offset or asymmetry of the explosion, can lead to the direct generation of S waves even from a fully decoupled explosion. Fracturing or asymmetry of the nonlinear region about the cavity of a partially decoupled explosion could also result in direct generation of S waves. Most historical decoupling data have been studied extensively, but usually with the goal of quantifying P-wave decoupling. We identify S waves in the historical records, identify observations that can be used to distinguish their genesis, and model the observations to test the proposed mechanisms. Travel times and a bubble pulse peak in the P but not S spectra of water-filled cavity explosions in salt at the Soviet Azgir test site indicate that the S is generated at the source. The observed nearfield S radiation pattern of the US decoupled explosion Sterling is matched by source modeling that includes the flat floor (due to melted and recrystallized salt) of the cavity. The similarity of the Sterling coda waveforms with distance indicates their source is at or very near the cavity. Calculations of the extent and orientation of fracturing by both the Azgir and Sterling explosions predict minimal effects on the resulting waveforms. Both
Direct Calculation of the Scattering Amplitude Without Partial Wave Analysis
NASA Technical Reports Server (NTRS)
Shertzer, J.; Temkin, A.; Fisher, Richard R. (Technical Monitor)
2001-01-01
Two new developments in scattering theory are reported. We show, in a practical way, how one can calculate the full scattering amplitude without invoking a partial wave expansion. First, the integral expression for the scattering amplitude f(theta) is simplified by an analytic integration over the azimuthal angle. Second, the full scattering wavefunction which appears in the integral expression for f(theta) is obtained by solving the Schrodinger equation with the finite element method (FEM). As an example, we calculate electron scattering from the Hartree potential. With minimal computational effort, we obtain accurate and stable results for the scattering amplitude.
Laboratory monitoring of P-waves in partially saturated sand
NASA Astrophysics Data System (ADS)
Barrière, J.; Bordes, C.; Brito, D.; Sénéchal, P.; Perroud, H.
2011-12-01
Seismic data depends on a variety of hydrogeological properties of the prospected porous media such as porosity, permeability and fluid saturation. We have performed a laboratory experiment in the kiloHertz range in order to analyze the role of partial saturation on direct propagating P-waves phase velocity and attenuation. The experiment consists of a sand-filled tank 107 cm x 34 cm x 35cm equipped with accelerometers and water capacitance probes. The P-waves seismic propagation is generated by hitting a steel ball on a granite plate on the one lateral side of the container. Several imbibition/drainage cycles are performed between the water residual saturation and the gas residual saturation. The laboratory seismic data are processed by two Continuous Wavelet Transforms using one real mother wavelet (Mexican hat) and one complex (Morlet) to recover velocity and attenuation as a function of frequency. Phase velocity of direct P-wave decreases with an increase of water content and is quite consistent with the low frequency limit of the Biot's theory both for imbibition and drainage. The interpretation of the P-waves attenuation needs to go beyond the macroscopic fluid flow of Biot's theory and to introduce a viscoelastic contribution linked to the grain to grain overall losses which are described by a constant Q-model. A strong hysteresis between imbibition and drainage is observed and explained by introducing an effective permeability depending on water and gas relative permeabilities (Van Genuchten model).
Exact analytical representations for broadband transmission properties of quarter-wave multilayers.
Grigoriev, Victor; Biancalana, Fabio
2011-10-01
The formalism of the scattering matrix is applied to describe the transmission properties of multilayered structures with deep variations of the refractive index and arbitrary arrangements of the layers. We show that there is an exact analytical formula for the transmission spectrum, which is valid for the full spectral range and which contains only a limited number of parameters for structures satisfying the quarter-wave condition. These parameters are related to the poles of the scattering matrix, and we present an efficient algorithm to find them, which is based on considering the ray propagation inside the structure and subsequent application of the harmonic inversion technique. These results are significant for analyzing the reshaping of ultrashort pulses in multilayered structures.
NASA Astrophysics Data System (ADS)
Li, Jibin
In this paper, we consider the exact explicit solutions for the famous generalized Hénon-Heiles (H-H) system. Corresponding to the three integrable cases, on the basis of the investigation of the dynamical behavior and level curves of the planar dynamical systems, we find all possible explicit exact parametric representations of solutions in the invariant manifolds of equilibrium points in the four-dimensional phase space. These solutions contain quasi-periodic solutions, homoclinic solutions, periodic solutions as well as blow-up solutions. Therefore, we answer the question: what are the flows in the center manifolds and homoclinic manifolds of the generalized Hénon-Heiles (H-H) system. As an application of the above results, we consider the traveling wave solutions for the coupled (n + 1)-dimensional Klein-Gordon-Schrödinger Equations with quadratic power nonlinearity.
Some new traveling wave exact solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli equations.
Qi, Jian-ming; Zhang, Fu; Yuan, Wen-jun; Huang, Zi-feng
2014-01-01
We employ the complex method to obtain all meromorphic exact solutions of complex (2+1)-dimensional Boiti-Leon-Pempinelli equations (BLP system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic traveling wave exact solutions of the equations (BLP) are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions ur,2 (z) and simply periodic solutions us,2-6(z) which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. For these new traveling wave solutions, we give some computer simulations to illustrate our main results.
NASA Astrophysics Data System (ADS)
Miroshnikov, Victor
2015-11-01
The Navier-Stokes system of PDEs is reduced to a system of the vorticity, continuity, Helmholtz, and Lamb-Helmholtz PDEs. The periodic Dirichlet problems are formulated for conservative internal waves vanishing at infinity in upper and lower domains. Stationary kinematic Fourier (SKF) structures, stationary kinematic Euler-Fourier (SKEF) structures, stationary dynamic Euler-Fourier (SDEF) structures, and SKEF-SDEF structures of three spatial variables and time are constructed to consider kinematic and dynamic problems of the three-dimensional theory of the Newtonian flows with harmonic velocity. Exact solutions for propagation and interaction of N internal waves in the upper and lower domains are developed by the method of decomposition in invariant structures and implemented through experimental and theoretical programming in Maple. Main results are summarized in a global existence theorem for the strong solutions. The SKEF, SDEF, and SKEF-SDEF structures of the cumulative flows are visualized by two-parametric surface plots for six fluid-dynamic variables.
Exact density functional and wave function embedding schemes based on orbital localization
NASA Astrophysics Data System (ADS)
Hégely, Bence; Nagy, Péter R.; Ferenczy, György G.; Kállay, Mihály
2016-08-01
Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.
The Thomas and Effimov Effects for General Partial Waves
NASA Astrophysics Data System (ADS)
Sternberg, James; Macek, Joseph
2006-05-01
Description of the two-body interactions between particles is a fundamental step in modeling many-body systems. Because s-wave scattering dominates at ultra-cold temperatures, zero-range potentials (ZRPs) have been a popular way to describe the two-body interactions. Recent experiments enhance higher partial waves and this has led to interest in extending the zero-range model beyond l=0Stock:2005. In this work we use a ZRP model to examine three body systems. Of particular importance in these systems is the Thomas effect, which is the divergence of the wave function when all three particles are close together. The Thomas effect is known for spin zero particles when l=0. In addition there is the Effimov effect, in which there are an infinite number of three body bound states if the zero-range potential boundary conditions separate in hyperspherical coordinates as the scattering length al->∞. We show that the Effimov effect occurs for not only the well-known l=0 case, but for spin 1/2 fermions via the l=1 pseudopotential of ref. [1] This research is supported by Department of Energy Grant DE-FG02-02ER15283 [1] Ren'e Stock, Andrew Silberfarb, Eric. L. Bolda, and Ivan H. Deutsch, Phys Rev. Lett. 94 023202 (2005)
NASA Technical Reports Server (NTRS)
Shebalin, John V.
1988-01-01
An exact analytic solution is found for a basic electromagnetic wave-charged particle interaction by solving the nonlinear equations of motion. The particle position, velocity, and corresponding time are found to be explicit functions of the total phase of the wave. Particle position and velocity are thus implicit functions of time. Applications include describing the motion of a free electron driven by an intense laser beam..
Treatment of Ion-Atom Collisions Using a Partial-Wave Expansion of the Projectile Wavefunction
ERIC Educational Resources Information Center
Wong, T. G.; Foster, M.; Colgan, J.; Madison, D. H.
2009-01-01
We present calculations of ion-atom collisions using a partial-wave expansion of the projectile wavefunction. Most calculations of ion-atom collisions have typically used classical or plane-wave approximations for the projectile wavefunction, since partial-wave expansions are expected to require prohibitively large numbers of terms to converge…
Baryon Spectroscopy Through Partial-Wave Analysis and Meson Photoproduction
Manley, D. Mark
2016-09-08
The principal goal of this project is the experimental and phenomenological study of baryon spectroscopy. The PI's group consists of himself and three graduate students. This final report summarizes research activities by the PI's group during the period 03/01/2015 to 08/14/2016. During this period, the PI co-authored 11 published journal papers and one proceedings article and presented three invited talks. The PI's general interest is the investigation of the baryon resonance spectrum up to masses of ~ 2 GeV. More detail is given on two research projects: Neutral Kaon Photoproduction and Partial-Wave Analyses of γp → η p, γn → η n, and γp → K⁺ Λ.
Search for Higher Flavor Multiplets in Partial Wave Analyses
Yakov Azimov; Richard Arndt; I.I. Strakovsky; Ron Workman; K. Goeke
2005-04-01
The possible existence of higher multi-quark flavor multiplets of baryons is investigated. We argue that the S-matrix should have poles with any quantum numbers, including those which are exotic. This argument provides a novel justification for the existence of hadrons with arbitrary exotic structure. Though it does not constitute a proof, there are still no theoretical arguments against exotics. We then consider KN and piN scattering. Conventional and modified partial-wave analyses provide several sets of candidates for correlated pairs (Theta1, Delta), each of which could label a related 27-plet. Properties of the pairs (masses, mass orderings, spin-parity quantum numbers) do not quite correspond to the current theoretical expectations. Decay widths of the candidates are either wider or narrower than expected. Possible reasons for such disagreements are briefly discussed.
Exact periodic and solitary waves and their interactions for the (2+1)-dimensional KdV equation
NASA Astrophysics Data System (ADS)
Peng, Yan-Ze
2006-02-01
A general solution involving three arbitrary functions is first obtained for a (2+1)-dimensional KdV equation by means of WTC truncation method. Then exact periodic wave solutions are expressed in terms of rational functions of the Jacobi elliptic functions. Limit cases are studied and some interesting, new solitary structures are revealed. The interaction properties between Jacobi elliptic waves (various limit cases) are investigated numerically. The fusion and fission of y-periodic solitary waves is for the first time reported.
Song, Jong-Won; Giorgi, Giacomo; Yamashita, Koichi; Hirao, Kimihiko
2013-06-28
Integrable singularity in the exact exchange calculations in hybrid functionals is an old and well-known problem in plane-wave basis. Recently, we developed a hybrid functional named Gaussian-attenuating Perdew-Burke-Ernzerhof (Gau-PBE), which uses a Gaussian function as a modified Coulomb potential for the exact exchange. We found that the modified Coulomb potential of Gaussian function enables the exact exchange calculation in plane-wave basis to be singularity-free and, as a result, the Gau-PBE functional shows faster energy convergence on k and q grids for the exact exchange calculations. Also, a tight comparison (same k and q meshes) between Gau-PBE and two other hybrid functionals, i.e., PBE0 and HSE06, indicates Gau-PBE functional as the least computational time consuming. The Gau-PBE functional employed in conjunction with a plane wave basis provides bandgaps with higher accuracy than the PBE0 and HSE06 in agreement with bandgaps previously calculated using Gaussian-type-orbitals.
A family of exact travelling wave solutions of (2+1)-dimensional KdV4 equation
NASA Astrophysics Data System (ADS)
Ayhan, Burcu; Bekir, Ahmet; Ozer, M. Naci
2017-01-01
Nonlinear evolution equations have a wide range of applications in science and engineering. In recent years many power-ful methods to construct exact solutions of nonlinear evolution equations. In this paper we present (1/G' ) expansion method, extended simplest equation method (SEM) and the modification of the truncated expansion (MTEM) method for (2 + 1) dimensional KdV4 equation to establish new exact solutions. So periodic and hyperbolic function solutions are obtained for this equation. The effi-ciency of the these methods for finding travelling wave solutions of the high order nonlinear evolution equations is demonstrated.
Brunet, Eric; Derrida, Bernard
2004-01-01
We calculate exactly the velocity and diffusion constant of a microscopic stochastic model of N evolving particles which can be described by a noisy traveling-wave equation with a noise of order N(-1/2). Our model can be viewed as the infinite range limit of a directed polymer in random medium with N sites in the transverse direction. Despite some peculiarities of the traveling-wave equations in the absence of noise, our exact solution allows us to test the validity of a simple cutoff approximation and to show that, in the weak noise limit, the position of the front can be completely described by the effect of the noise on the first particle.
Overlap of exact and Gross-Pitaevskii wave functions in Bose-Einstein condensates of dilute gases
NASA Astrophysics Data System (ADS)
Klaiman, Shachar; Cederbaum, Lorenz S.
2016-12-01
It has been proven theoretically for bosons with two-body repulsive interaction potentials in the dilute limit that the Gross-Pitaevskii equation provides the exact energy and density per particle as does the basic many-particle Schrödinger equation [E. H. Lieb and R. Seiringer, Phys. Rev. Lett. 88, 170409 (2002), 10.1103/PhysRevLett.88.170409]. Here, we investigate the overlap of the Gross-Pitaevskii and exact ground-state wave functions. It is found that this overlap is always smaller than unity and may even vanish despite the fact that both wave functions provide the same energy and density per particle. Consequences are discussed.
NASA Astrophysics Data System (ADS)
Brunet, Éric; Derrida, Bernard
2004-07-01
We calculate exactly the velocity and diffusion constant of a microscopic stochastic model of N evolving particles which can be described by a noisy traveling-wave equation with a noise of order N-1/2 . Our model can be viewed as the infinite range limit of a directed polymer in random medium with N sites in the transverse direction. Despite some peculiarities of the traveling-wave equations in the absence of noise, our exact solution allows us to test the validity of a simple cutoff approximation and to show that, in the weak noise limit, the position of the front can be completely described by the effect of the noise on the first particle.
H-He elastic scattering at low energies: Contribution of nonzero partial waves
Sinha, Prabal K.; Ghosh, A.S.
2005-01-01
The present study reports the nonzero partial wave elastic cross sections together with s-wave results for the scattering of an antihydrogen atom off a gaseous helium target at thermal energies (up to 10{sup -2} a.u.). We have used a nonadiabatic atomic orbital method having different basis sets to investigate the system. The consideration of all the significant partial waves (up to J=24) reduces the oscillatory nature present in the individual partial wave cross section. The added elastic cross section is almost constant up to 10{sup -7} a.u. and then decreases steadily and very slowly with increasing energy.
Kurokawa, Yusaku I; Nakashima, Hiroyuki; Nakatsuji, Hiroshi
2014-06-07
We derived the necessary conditions that must be satisfied by the non-relativistic time-independent exact wave functions for many-particle systems at a two-particle coalescence (or cusp) point. Some simple conditions are known to be Kato's cusp condition (CC) and Rassolov and Chipman's CC. In a previous study, we derived an infinite number of necessary conditions that two-particle wave functions must satisfy at a coalescence point. In the present study, we extend these conditions to many-particle systems. They are called general coalescence conditions (GCCs), and Kato's CC and Rassolov and Chipman's CC are included as special conditions. GCCs can be applied not only to Coulombic systems but also to any system in which the interaction between two particles is represented in a power series of inter-particle distances. We confirmed the correctness of our derivation of the GCCs by applying the exact wave function of a harmonium in electron-electron and electron-nucleus coalescence situations. In addition, we applied the free complement (FC) wave functions of a helium atom to the GCCs to examine the accuracy of the FC wave function in the context of a coalescence situation.
Erokhin, N. S. Zakharov, V. E.; Zol’nikova, N. N.; Mikhailovskaya, L. A.
2015-02-15
Different variants of resonance tunneling of a transverse electromagnetic wave through a plasma layer containing short-scale (subwavelength) inhomogeneities, including evanescence regions to which approximate methods are inapplicable, are analyzed in the framework of an exactly solvable one-dimensional model. Complex plasma density profiles described by a number of free parameters determining the permittivity modulation depth, the characteristic scale lengths of plasma structures, their number, and the thickness of the inhomogeneous plasma layer are considered. It is demonstrated that reflection-free propagation of the wave incident on the layer from vacuum (the effect of wave-barrier transillumination) can be achieved for various sets of such structures, including plasma density profiles containing a stochastic component. Taking into account cubic nonlinearity, it is also possible to obtain an exact solution to the one-dimensional problem on the nonlinear transillumination of nonuniform plasma. In this case, the thicknesses of the evanescence regions decrease appreciably. The problem of resonance tunneling of electromagnetic waves through such barriers is of interest for a number of practical applications.
Wave Directional Characteristics on a Partially Sheltered Coast.
1982-01-01
California Sea Grant Program, IMR Ref. 78-102. Pawka, S. S., V. Hsiao, 0. H. Shemdin , and D. L. Inman, 1978, "Comparison of wave directional spectra...Pawka, S. S., S. V. Hsiao, 0. H. Shemdin , and D. L. Inman, 1980, "Com- parisons between wave directional spectra from SAR and pressure sensor arrays...effects of wave induced airflow, are under 77 active investigation (Evans and Shemdin ,1980). Previous ground truth experiments, reported in Mcleish et al
Analytical expressions for partial wave two-body Coulomb transition matrices at ground-state energy
NASA Astrophysics Data System (ADS)
Kharchenko, V. F.
2016-11-01
Leaning upon the Fock method of the stereographic projection of the three-dimensional momentum space onto the four-dimensional unit sphere the possibility of the analytical solving of the Lippmann-Schwinger integral equation for the partial wave two-body Coulomb transition matrix at the ground bound state energy has been studied. In this case new expressions for the partial p-, d- and f-wave two-body Coulomb transition matrices have been obtained in the simple analytical form. The developed approach can also be extended to determine analytically the partial wave Coulomb transition matrices at the energies of excited bound states.
NASA Astrophysics Data System (ADS)
Vitanov, Nikolay K.
2011-03-01
We discuss the class of equations ∑i,j=0mAij(u){∂iu}/{∂ti}∂+∑k,l=0nBkl(u){∂ku}/{∂xk}∂=C(u) where Aij( u), Bkl( u) and C( u) are functions of u( x, t) as follows: (i) Aij, Bkl and C are polynomials of u; or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.
NASA Astrophysics Data System (ADS)
Liu, Yin-Ping; Li, Zhi-Bin
2003-03-01
Based on a type of elliptic equation, a new algebraic method to construct a series of exact solutions for nonlinear evolution equations is proposed, meanwhile, its complete implementation TRWS in Maple is presented. The TRWS can output a series of travelling wave solutions entirely automatically, which include polynomial solutions, exponential function solutions, triangular function solutions, hyperbolic function solutions, rational function solutions, Jacobi elliptic function solutions, and Weierstrass elliptic function solutions. The effectiveness of the package is illustrated by applying it to a variety of equations. Not only are previously known solutions recovered but also new solutions and more general form of solutions are obtained.
Complex space source theory of partially coherent light wave.
Seshadri, S R
2010-07-01
The complex space source theory is used to derive a general integral expression for the vector potential that generates the extended full Gaussian wave in terms of the input value of the vector potential of the corresponding paraxial beam. The vector potential and the fields are assumed to fluctuate on a time scale that is large compared to the wave period. The Poynting vector in the propagation direction averaged over a wave period is expressed in terms of the cross-spectral density of the fluctuating vector potential across the input plane. The Schell model is assumed for the cross-spectral density. The radiation intensity distribution and the power radiated are determined. The effect of spatial coherence on the radiation intensity distribution and the radiated power are investigated for different values of the physical parameters. Illustrative numerical results are provided to bring out the effect of spatial coherence on the propagation characteristics of the fluctuating light wave.
Workman, R. L.; Tiator, L.; Wunderlich, Y.; ...
2017-01-19
Here, we compare the methods of amplitude reconstruction, for a complete experiment and a truncated partial-wave analysis, applied to the photoproduction of pseudoscalar mesons. The approach is pedagogical, showing in detail how the amplitude reconstruction (observables measured at a single energy and angle) is related to a truncated partial-wave analysis (observables measured at a single energy and a number of angles).
Partial reflections of radio waves from the lower ionosphere
NASA Technical Reports Server (NTRS)
Connolly, D. J.; Tanenbaum, S. B.
1972-01-01
The addition of phase difference measurements to partial reflection experiments is discussed, and some advantages of measuring electron density this way are pointed out. The additional information obtained reduces the requirement for an accurate predetermination of collision frequency. Calculations are also made to estimate the errors expected in partial-reflection experiments due to the assumption of Fresnel reflection and to the neglect of coupling between modes. In both cases, the errors are found to be of the same order as known errors in the measurements due to current instrumental limitations.
Extracting scattering phase shifts in higher partial waves from lattice QCD calculations
Luu, Thomas; Savage, Martin J.
2011-06-01
Lüscher’s method is routinely used to determine meson-meson, meson-baryon, and baryon-baryon s-wave scattering amplitudes below inelastic thresholds from lattice QCD calculations—presently at unphysical light-quark masses. In this work we review the formalism and develop the requisite expressions to extract phase shifts describing meson-meson scattering in partial waves with angular momentum l≤6 and l=9. The implications of the underlying cubic symmetry, and strategies for extracting the phase shifts from lattice QCD calculations, are presented, along with a discussion of the signal-to-noise problem that afflicts the higher partial waves.
Treatment of ion-atom collisions using a partial-wave expansion of the projectile wavefunction
Foster, M; Colgan, J; Wong, T G; Madison, D H
2008-01-01
We present calculations of ion-atom collisions using a partial-wave expansion of the projectile wavefunction. Most calculations of ion-atom collisions have typically used classical or plane-wave approximations for the projectile wavefunction, since partial-wave expansions are expected to require prohibitively large numbers of terms to converge scattering quantities. Here we show that such calculations are possible using modern high-performance computing. We demonstrate the utility of our method by examining elastic scattering of protons by hydrogen and helium atoms, problems familiar to undergraduate students of atomic scattering. Application to ionization of helium using partial-wave expansions of the projectile wavefunction, which has long been desirable in heavy-ion collision physics, is thus quite feasible.
Shock-wave structure in a partially ionized gas
NASA Technical Reports Server (NTRS)
Lu, C. S.; Huang, A. B.
1974-01-01
The structure of a steady plane shock in a partially ionized gas has been investigated using the Boltzmann equation with a kinetic model as the governing equation and the discrete ordinate method as a tool. The effects of the electric field induced by the charge separation on the shock structure have also been studied. Although the three species of an ionized gas travel with approximately the same macroscopic velocity, the individual distribution functions are found to be very different. In a strong shock the atom distribution function may have double peaks, while the ion distribution function has only one peak. Electrons are heated up much earlier than ions and atoms in a partially ionized gas. Because the interactions of electrons with atoms and with ions are different, the ion temperature can be different from the atom temperature.
Matter-wave exact periodic solutions in optical lattices with periodic potential
NASA Astrophysics Data System (ADS)
Liu, Changfu; Zhu, Aijun
2013-10-01
Some special matter-wave periodic solutions for the Gross-Pitaevskii equation with periodic potential in the multidimensional optical lattices, are obtained through restricting parameters and some balance conditions between the optical potentials and interaction energies. The results show that the same type of periodic solutions in the same dimension possesses the same norm but different phases and they are all bounded. Especially, the numerics shows that two class (2+1)-dimensional periodic solutions are stable.
Evaluation of partial widths and branching ratios from resonance wave functions
Goldzak, Tamar; Gilary, Ido; Moiseyev, Nimrod
2010-11-15
A quantum system in a given resonance state has different open channels for decay. Partial widths are the decay rates of the resonance (metastable) state into the different open channels. Here we present a rigorous derivation of the partial widths from the solution of a time-dependent Schroedinger equation with outgoing boundary conditions. We show that the sum of the partial widths obtained from the resonance wave function is equal to the total width. The difference with respect to previous studies on partial widths and branching ratios is discussed.
Analysis of non linear partially standing waves from 3D velocity measurements
NASA Astrophysics Data System (ADS)
Drevard, D.; Rey, V.; Svendsen, Ib; Fraunie, P.
2003-04-01
Surface gravity waves in the ocean exhibit an energy spectrum distributed in both frequency and direction of propagation. Wave data collection is of great importance in coastal zones for engineering and scientific studies. In particular, partially standing waves measurements near coastal structures and steep or barred beaches may be a requirement, for instance for morphodynamic studies. The aim of the present study is the analysis of partially standing surface waves icluding non-linear effects. According to 1st order Stokes theory, synchronous measurements of horizontal and vertical velocity components allow calculation of rate of standing waves (Drevard et al, 2003). In the present study, it is demonstrated that for deep water conditions, partially standing 2nd order Stokes waves induced velocity field is still represented by the 1st order solution for the velocity potential contrary to the surface elevation which exhibits harmonic components. For intermediate water depth, harmonic components appear not only in the surface elevation but also in the velocity fields, but their weight remains much smaller, because of the vertical decreasing wave induced motion. For irregular waves, the influence of the spectrum width on the non-linear effects in the analysis is discussed. Keywords: Wave measurements ; reflection ; non-linear effects Acknowledgements: This work was initiated during the stay of Prof. Ib Svendsen, as invited Professor, at LSEET in autumn 2002. This study is carried out in the framework of the Scientific French National Programmes PNEC ART7 and PATOM. Their financial supports are acknowledged References: Drevard, D., Meuret, A., Rey, V. Piazzola, J. And Dolle, A.. (2002). "Partially reflected waves measurements using Acoustic Doppler Velocimeter (ADV)", Submitted to ISOPE 03, Honolulu, Hawaii, May 2003.
March, N H; Nagy, A
2008-11-21
Following some studies of integral(n)(r)inverted DeltaV(r)dr by earlier workers for the density functional theory (DFT) one-body potential V(r) generating the exact ground-state density, we consider here the special case of spherical atoms. The starting point is the differential virial theorem, which is used, as well as the Hiller-Sucher-Feinberg [Phys. Rev. A 18, 2399 (1978)] identity to show that the scalar quantity paralleling the above vector integral, namely, integral(n)(r) partial differential(V)(r)/partial differential(r)dr, is determined solely by the electron density n(0) at the nucleus for the s-like atoms He and Be. The force - partial differential(V)/ partial differential(r) is then related to the derivative of the exchange-correlation potential V(xc)(r) by terms involving only the external potential in addition to n(r). The resulting integral constraint should allow some test of the quality of currently used forms of V(xc)(r). The article concludes with results from the differential virial theorem and the Hiller-Sucher-Feinberg identity for the exact many-electron theory of spherical atoms, as well as for the DFT for atoms such as Ne with a closed p shell.
NASA Technical Reports Server (NTRS)
Shertzer, Janine; Temkin, Aaron
2007-01-01
In the first two papers in this series, we developed a method for studying electron-hydrogen scattering that does not use partial wave analysis. We constructed an ansatz for the wave function in both the static and static exchange approximations and calculated the full scattering amplitude. Here we go beyond the static exchange approximation, and include correlation in the wave function via a modified polarized orbital. This correlation function provides a significant improvement over the static exchange approximation: the resultant elastic scattering amplitudes are in very good agreement with fully converged partial wave calculations for electron-hydrogen scattering. A fully variational modification of this approach is discussed in the conclusion of the article Popular summary of Direct calculation of the scattering amplitude without partial wave expansion. III ....." by J. Shertzer and A. Temkin. In this paper we continue the development of In this paper we continue the development of a new approach to the way in which researchers have traditionally used to calculate the scattering cross section of (low-energy) electrons from atoms. The basic mathematical problem is to solve the Schroedinger Equation (SE) corresponding the above physical process. Traditionally it was always the case that the SE was reduced to a sequence of one-dimensional (ordinary) differential equations - called partial waves which were solved and from the solutions "phase shifts" were extracted, from which the scattering cross section was calculated.
Exact soliton-on-plane-wave solutions for two-component Bose-Einstein condensates.
Li, Lu; Malomed, Boris A; Mihalache, Dumitru; Liu, W M
2006-06-01
By means of the Darboux transformation, we obtain analytical solutions for a soliton set on top of a plane-wave background in coupled Gross-Pitaevskii equations describing a binary Bose-Einstein condensate. We consider basic properties of the solutions with and without the cross interaction [cross phase modulation (XPM)] between the two components of the background. In the absence of the XPM, this solutions maintain properties of one-component condensates, such as the modulation instability (MI); in the presence of the cross interaction, the solutions exhibit different properties, such as restriction of the MI and soliton splitting.
Exact soliton-on-plane-wave solutions for two-component Bose-Einstein condensates
Li Lu; Malomed, Boris A.; Mihalache, Dumitru; Liu, W. M.
2006-06-15
By means of the Darboux transformation, we obtain analytical solutions for a soliton set on top of a plane-wave background in coupled Gross-Pitaevskii equations describing a binary Bose-Einstein condensate. We consider basic properties of the solutions with and without the cross interaction [cross phase modulation (XPM)] between the two components of the background. In the absence of the XPM, this solutions maintain properties of one-component condensates, such as the modulation instability (MI); in the presence of the cross interaction, the solutions exhibit different properties, such as restriction of the MI and soliton splitting.
NASA Astrophysics Data System (ADS)
Li, Zhi-Bin; Liu, Yin-Ping
2004-11-01
In Maple 8, by taking advantage of the package RIF contained in DEtools, we developed a package RAEEM which is a comprehensive and complete implementation of such methods as the tanh-method, the extended tanh-method, the Jacobi elliptic function method and the elliptic equation method. RAEEM can entirely automatically output a series of exact traveling wave solutions, including those of polynomial, exponential, triangular, hyperbolic, rational, Jacobi elliptic, Weierstrass elliptic type. The effectiveness of the package is illustrated by applying it to a large variety of equations. In addition to recovering previously known solutions, we also obtain more general forms of some solutions and new solutions. Program summaryTitle of program: RAEEM Catalogue identifier: ADUP Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUP Program obtained from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers: PC Pentium IV Installations: Copy Operating systems: Windows 98/2000/XP Program language used: Maple 8 Memory required to execute with typical data: depends on the problem, minimum about 8M words No. of bits in a word: 8 No. of lines in distributed program, including test data, etc.: 3163 No. of bytes in distributed program, including the test data, etc.: 26 720 Distribution format: tar.gz Nature of physical problem: Our program provides exact traveling wave solutions, which describe various phenomena in nature, and thus can give more insight into the physical aspects of problems. These solutions may be easily used in further applications. Restriction on the complexity of the problem: The program can handle system of nonlinear evolution equations with any number of independent and dependent variables, in which each equation is a polynomial (or can be converted to a polynomial) in the dependent variables and their derivatives. Typical running time: It depends on the input equations as well as the degrees of the desired polynomial solutions. For
New results on the Roper resonance and the P11 partial wave
NASA Astrophysics Data System (ADS)
Sarantsev, A. V.; Fuchs, M.; Kotulla, M.; Thoma, U.; Ahrens, J.; Annand, J. R. M.; Anisovich, A. V.; Anton, G.; Bantes, R.; Bartholomy, O.; Beck, R.; Beloglazov, Yu.; Castelijns, R.; Crede, V.; Ehmanns, A.; Ernst, J.; Fabry, I.; Flemming, H.; Fösel, A.; Funke, Chr.; Gothe, R.; Gridnev, A.; Gutz, E.; Höffgen, St.; Horn, I.; Hößl, J.; Hornidge, D.; Janssen, S.; Junkersfeld, J.; Kalinowsky, H.; Klein, F.; Klempt, E.; Koch, H.; Konrad, M.; Kopf, B.; Krusche, B.; Langheinrich, J.; Löhner, H.; Lopatin, I.; Lotz, J.; McGeorge, J. C.; MacGregor, I. J. D.; Matthäy, H.; Menze, D.; Messchendorp, J. G.; Metag, V.; Nikonov, V. A.; Novinski, D.; Novotny, R.; Ostrick, M.; van Pee, H.; Pfeiffer, M.; Radkov, A.; Rosner, G.; Rost, M.; Schmidt, C.; Schoch, B.; Suft, G.; Sumachev, V.; Szczepanek, T.; Walther, D.; Watts, D. P.; Weinheimer, Chr.; CB-ELSA; A2-TAPS Collaborations
2008-01-01
Properties of the Roper resonance, the first scalar excitation of the nucleon, are determined. Pole positions and residues of the P11 partial wave are studied in a combined analysis of pion- and photo-induced reactions. We find the Roper pole at { (1371 ± 7) - i (92 ± 10) } MeV and an elasticity of 0.61 ± 0.03. The largest decay coupling is found for the Nσ (σ = (ππ)-S-wave). The analysis is based on new data on γp → pπ0π0 for photons in the energy range from the two-pion threshold to 820 MeV from TAPS at Mainz and from 0.4 to 1.3 GeV from Crystal Barrel at Bonn and includes further data from other experiments. The partial wave analysis excludes the possibility that the Roper resonance is split into two states with different partial decay widths.
New results on the Roper resonance and the P partial wave
NASA Astrophysics Data System (ADS)
Cb-Elsa; A2-Taps Collaborations; Sarantsev, A. V.; Fuchs, M.; Kotulla, M.; Thoma, U.; Ahrens, J.; Annand, J. R. M.; Anisovich, A. V.; Anton, G.; Bantes, R.; Bartholomy, O.; Beck, R.; Beloglazov, Yu.; Castelijns, R.; Crede, V.; Ehmanns, A.; Ernst, J.; Fabry, I.; Flemming, H.; Fösel, A.; Funke, Chr.; Gothe, R.; Gridnev, A.; Gutz, E.; Höffgen, St.; Horn, I.; Hößl, J.; Hornidge, D.; Janssen, S.; Junkersfeld, J.; Kalinowsky, H.; Klein, F.; Klempt, E.; Koch, H.; Konrad, M.; Kopf, B.; Krusche, B.; Langheinrich, J.; Löhner, H.; Lopatin, I.; Lotz, J.; McGeorge, J. C.; MacGregor, I. J. D.; Matthäy, H.; Menze, D.; Messchendorp, J. G.; Metag, V.; Nikonov, V. A.; Novinski, D.; Novotny, R.; Ostrick, M.; van Pee, H.; Pfeiffer, M.; Radkov, A.; Rosner, G.; Rost, M.; Schmidt, C.; Schoch, B.; Suft, G.; Sumachev, V.; Szczepanek, T.; Walther, D.; Watts, D. P.; Weinheimer, Chr.
2008-01-01
Properties of the Roper resonance, the first scalar excitation of the nucleon, are determined. Pole positions and residues of the P partial wave are studied in a combined analysis of pion- and photo-induced reactions. We find the Roper pole at {(1371±7)-i(92±10)} MeV and an elasticity of 0.61±0.03. The largest decay coupling is found for the Nσ (σ=(ππ)-S-wave). The analysis is based on new data on γp→pππ for photons in the energy range from the two-pion threshold to 820 MeV from TAPS at Mainz and from 0.4 to 1.3 GeV from Crystal Barrel at Bonn and includes further data from other experiments. The partial wave analysis excludes the possibility that the Roper resonance is split into two states with different partial decay widths.
Shape Waves in 2D Josephson Junctions: Exact Solutions and Time Dilation
NASA Astrophysics Data System (ADS)
Gulevich, D. R.; Kusmartsev, F. V.; Savel'Ev, Sergey; Yampol'Skii, V. A.; Nori, Franco
2008-09-01
We predict a new class of excitations propagating along a Josephson vortex in two-dimensional Josephson junctions. These excitations are associated with the distortion of a Josephson vortex line and have an analogy with shear waves in solid mechanics. Their shapes can have an arbitrary profile, which is retained when propagating. We derive a universal analytical expression for the energy of arbitrary shape excitations, investigate their influence on the dynamics of a vortex line, and discuss conditions where such excitations can be created. Finally, we show that such excitations play the role of a clock for a relativistically moving Josephson vortex and suggest an experiment to measure a time dilation effect analogous to that in special relativity.
Shape waves in 2D Josephson junctions: exact solutions and time dilation.
Gulevich, D R; Kusmartsev, F V; Savel'ev, Sergey; Yampol'skii, V A; Nori, Franco
2008-09-19
We predict a new class of excitations propagating along a Josephson vortex in two-dimensional Josephson junctions. These excitations are associated with the distortion of a Josephson vortex line and have an analogy with shear waves in solid mechanics. Their shapes can have an arbitrary profile, which is retained when propagating. We derive a universal analytical expression for the energy of arbitrary shape excitations, investigate their influence on the dynamics of a vortex line, and discuss conditions where such excitations can be created. Finally, we show that such excitations play the role of a clock for a relativistically moving Josephson vortex and suggest an experiment to measure a time dilation effect analogous to that in special relativity.
NASA Technical Reports Server (NTRS)
Shertzer, Janine; Temkin, Aaron
2004-01-01
The development of a practical method of accurately calculating the full scattering amplitude, without making a partial wave decomposition is continued. The method is developed in the context of electron-hydrogen scattering, and here exchange is dealt with by considering e-H scattering in the static exchange approximation. The Schroedinger equation in this approximation can be simplified to a set of coupled integro-differential equations. The equations are solved numerically for the full scattering wave function. The scattering amplitude can most accurately be calculated from an integral expression for the amplitude; that integral can be formally simplified, and then evaluated using the numerically determined wave function. The results are essentially identical to converged partial wave results.
Partial-wave analysis of nucleon-nucleon elastic scattering data
NASA Astrophysics Data System (ADS)
Workman, Ron L.; Briscoe, William J.; Strakovsky, Igor I.
2016-12-01
Energy-dependent and single-energy fits to the existing nucleon-nucleon database have been updated to incorporate recent measurements. The fits cover a region from threshold to 3 GeV, in the laboratory kinetic energy, for proton-proton scattering, with an upper limit of 1.3 GeV for neutron-proton scattering. Experiments carried out at the COSY-WASA and COSY-ANKE facilities have had a significant impact on the partial-wave solutions. Results are discussed in terms of both partial-wave and direct reconstruction amplitudes.
Exact non-Born-Oppenheimer wave functions for three-particle Hookean systems with arbitrary masses
Lopez, Xabier; Ugalde, Jesus M.; Echevarria, Lorenzo; Ludena, Eduardo V.
2006-10-15
A Hookean model of a three-body problem for particles with arbitrary masses and charges where two of them interact with each other through a Coulomb potential and with the third through a harmonic potential is presented. It is shown that a condition relating the masses to the harmonic coupling constants must be satisfied in order to render this problem separable. A general exact analytic solution written in terms of the relative interparticle coordinates is given as well as general expressions for the total and binding energies of this three-body system. We apply these results to examine electronic, muonic, antiprotonic, and pionic families of non-Born-Oppenheimer Hookean systems. The first contains the atoms or atomic ions: Ps{sup -}(e{sup +}e{sup -}e{sup -}), H{sup -}(p{sup +}e{sup -}e{sup -}), D{sup -}(d{sup +}e{sup -}e{sup -}), T{sup -}(p{sup +}e{sup -}e{sup -}), {sup 4}He(he{sup +2}e{sup -}e{sup -}), and the following molecular ions: Ps{sub 2}{sup +}(e{sup -}e{sup +}e{sup +}), H{sub 2}{sup +}(e{sup -}p{sup +}p{sup +}), HD{sup +}(e{sup -}d{sup +}p{sup +}), HT{sup +}(e{sup -}t{sup +}p{sup +}), DT{sup +}(e{sup -}d{sup +}t{sup +}), D{sub 2}{sup +}(e{sup -}d{sup +}d{sup +}), T{sub 2}{sup +}(e{sup -}t{sup +}t{sup +}). The muonic and antiprotonic families are similar to the electronic ones except that the species are formed replacing e{sup -} by {mu}{sup -} or p{sup -}. The pionic family comprises exotic atoms containing at least one pion. We also apply these results to two-electron three-dimensional spherical quantum dots and for these systems we examine the effect of electronic correlation, particularly on the singlet-triplet transitions and on the collective motion of the electrons and center of mass leading to ''floppy''dynamics.
Petrović, Nikola Z; Belić, Milivoj; Zhong, Wei-Ping
2011-02-01
We obtain exact traveling wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with variable coefficients and polynomial Kerr nonlinearity of an arbitrarily high order. Exact solutions, given in terms of Jacobi elliptic functions, are presented for the special cases of cubic-quintic and septic models. We demonstrate that the widely used method for finding exact solutions in terms of Jacobi elliptic functions is not applicable to the nonlinear Schrödinger equation with saturable nonlinearity.
NASA Astrophysics Data System (ADS)
Kupershtokh, A. L.; Karpov, D. I.
2016-10-01
A stochastic model of partial discharges inside gas inclusions in condensed dielectrics was developed. The possibility of a "relay-race" wave propagation mechanism of partial discharges in a linear chain of gas inclusions is shown. The lattice Boltzmann method is successfully implemented for three-dimensional computer simulations of flows of dielectric fluid with bubbles. Growth and elongation of bubbles in a liquid dielectric under the action of a strong electric field are simulated. The physical model of propagation of partial discharges along a chain of gas bubbles in a liquid is formulated.
Attenuation measurements of ultrasonic P-wave and S-wave in partially frozen unconsolidated sands
NASA Astrophysics Data System (ADS)
Matsushima, J.; Suzuki, M.; Kato, Y.; Rokugawa, S.; Kato, A.
2012-12-01
Seismic attenuation which controls both the amplitude decay of seismic waves and the accompanying frequency change is a signature of the wave-rock interaction. Seismic attenuation in rocks is a highly variable parameter, which depends on the confining pressure, porosity, degree of fluid saturation, and fluid type. Although seismic attenuation has been widely used to estimate physical conditions and rock properties in various fields, the loss mechanisms responsible for seismic attenuation often are unclear and controversial. To elucidate a plausible mechanism for seismic attenuation, the joint use of both P- and S-waves will provide more helpful information because these two types of waves respond differently to fluid and solid combinations. We have conducted ultrasonic P- and S-wave transmission measurements to examine the influence of ice-brine coexisting system grown in the pore space of unconsolidated sands on ultrasonic P- and S-waves. We observed the variations of a transmitted wave with a frequency content of 100-1000 kHz , changing its temperature from 20°C to -15°C. We use not only impulse-type signals but also sweep-type signals to prevent from the spectral leakage effect caused by the effect of windowing. We concern with attenuation at ultrasonic frequencies of 500-1000 kHz for P-waves and 100-400 kHz for S-waves. Our observation of the variation of the Poisson's ratio and the ratio of P- to S-wave attenuation with changing temperature indicates the possibilities of the joint use of both P- and S-waves to elucidate a plausible mechanism for seismic attenuation.
Manafian Heris, Jalil; Lakestani, Mehrdad
2014-01-01
We establish exact solutions including periodic wave and solitary wave solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota system. We employ this system by using a generalized (G'/G)-expansion and the generalized tanh-coth methods. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that these methods, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.
Scherrer, Arne; Agostini, Federica; Gross, E. K. U.; Sebastiani, Daniel; Vuilleumier, Rodolphe
2015-08-21
The nuclear velocity perturbation theory (NVPT) for vibrational circular dichroism (VCD) is derived from the exact factorization of the electron-nuclear wave function. This new formalism offers an exact starting point to include correction terms to the Born-Oppenheimer (BO) form of the molecular wave function, similar to the complete-adiabatic approximation. The corrections depend on a small parameter that, in a classical treatment of the nuclei, is identified as the nuclear velocity. Apart from proposing a rigorous basis for the NVPT, we show that the rotational strengths, related to the intensity of the VCD signal, contain a new contribution beyond-BO that can be evaluated with the NVPT and that only arises when the exact factorization approach is employed. Numerical results are presented for chiral and non-chiral systems to test the validity of the approach.
NASA Astrophysics Data System (ADS)
Scherrer, Arne; Agostini, Federica; Sebastiani, Daniel; Gross, E. K. U.; Vuilleumier, Rodolphe
2015-08-01
The nuclear velocity perturbation theory (NVPT) for vibrational circular dichroism (VCD) is derived from the exact factorization of the electron-nuclear wave function. This new formalism offers an exact starting point to include correction terms to the Born-Oppenheimer (BO) form of the molecular wave function, similar to the complete-adiabatic approximation. The corrections depend on a small parameter that, in a classical treatment of the nuclei, is identified as the nuclear velocity. Apart from proposing a rigorous basis for the NVPT, we show that the rotational strengths, related to the intensity of the VCD signal, contain a new contribution beyond-BO that can be evaluated with the NVPT and that only arises when the exact factorization approach is employed. Numerical results are presented for chiral and non-chiral systems to test the validity of the approach.
NASA Technical Reports Server (NTRS)
Weatherford, C. A.; Onda, K.; Temkin, A.
1985-01-01
The noniterative partial-differential-equation (PDE) approach to electron-molecule scattering of Onda and Temkin (1983) is modified to account for the effects of exchange explicitly. The exchange equation is reduced to a set of inhomogeneous equations containing no integral terms and solved noniteratively in a difference form; a method for propagating the solution to large values of r is described; the changes in the polarization potential of the original PDE method required by the inclusion of exact static exchange are indicated; and the results of computations for e-N2 scattering in the fixed-nuclei approximation are presented in tables and graphs and compared with previous calculations and experimental data. Better agreement is obtained using the modified PDE method.
NASA Astrophysics Data System (ADS)
Mori, Koichi
2010-12-01
Exact solutions to special cases of the general Riemann problem, in which two nonuniform and nonstationary flows are initially separated by a discontinuity at the origin, are proposed. By describing the evolution of flows using a family of the group-invariant solutions derived by Ovsiannikov [Dokl. Akad. Nauk S.S.S.R. 111, 439 (1958)] the flows ahead of and behind a shock wave accelerated at a constant rate are formulated analytically. Transition relations across a contact discontinuity and a characteristic wave in a nonuniform and nonstationary flow are formulated as well. The entire flow field is solved by combining these waves.
Alam, Md Nur; Akbar, M Ali
2013-01-01
The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.
Extension of the Temkin-Poet model to L>0 partial waves: The generalized exchange approximation
NASA Astrophysics Data System (ADS)
Temkin, A.; Shertzer, J.; Bhatia, A. K.
1998-02-01
The Temkin-Poet (TP) model of electron-hydrogen scattering is here generalized to L>0 partial waves in such a way as to be a clear generalization of the exchange approximation (EA). This generalized exchange approximation (GEA) leads to a pair of coupled partial differential equations (PDE's). Boundary conditions are formulated, and the PDE's are solved by a finite element method program adapted from a previous partial wave calculation of the full problem [Shertzer and Botero, Phys. Rev. A 49, 3673 (1994)]. Calculations are carried out for 1,3P and 1,3D partial waves in the elastic region. Phase shifts are bounded from below, as is rigorously required, by exchange approximate phase shifts. But the GEA can yield resonances: in the elastic region, in addition to the 1S resonance of the TP model, there is a 3P resonance whose position and width are in close proximity to the lowest 3P resonance of the full theory. The GEA distinguishes between singlet and triplet scattering for all L, and it contains inelastic and ionization channels in the appropriate energy regions. It is expected that the GEA will have its greatest utility in the ionization domain, as a nontrivial test of the many recent methods being developed.
NASA Astrophysics Data System (ADS)
Pradhan, O.; Matsushima, J.; Suzuki, M.
2012-12-01
Methane hydrate bearing sediment possesses unique seismic wave propagation properties. Both high seismic wave velocity and high wave attenuation are observed in methane hydrate bearing sediment. We used brine with salinity 2% in analogous to methane hydrate for conducting laboratory waveform measurement and characterization by using nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) technique. When brine undergoes freezing, only pure water freezes into ice and salt remains in solution with successively increasing salinity and decreasing freezing point of the solution. Unfrozen brine is enclosed inside micro pores in ice, with exhibiting solid-liquid coexisting system. We used conventional pulse transmission technique to measure compressional wave velocity in partially frozen brine when brine is subjected cooling down to -12oC. Waveform measurement shows sudden increase in compressional wave velocity at temperature -3oC. Below -3oC, velocity increases slightly. Largest wave attenuation is observed at around -3oC. We conducted MRI experiment by using instrument Varian Unity Inova 4.7T. T1 weighted and diffusion weighted (DW) MR images were prepared by applying magnetic field gradient of 0.3 gauss/cm. We observe the spatial distribution of pores, microstructures and heterogeneity in partially frozen brine sample slices. Two dimensional apparent diffusion coefficient (ADC) maps are prepared from DW images with b-values 0 and 81 s/mm2 respectively. We estimate porosity quantitatively from each MR slices at temperature -3, -5, -7 and -12oC by using image analysis technique. Gassmann equation is applied to calculate compressional wave velocity from the porosity data and compared with the measured velocity obtained by waveform analysis technique. The NMR results show the existence of high and low mobility unfrozen brine in the pore space. MR imaging shows the heterogeneously distributed porosity values within a single slice with low porosity and high
PARTIAL REFLECTION AND TRAPPING OF A FAST-MODE WAVE IN SOLAR CORONAL ARCADE LOOPS
Kumar, Pankaj; Innes, D. E.
2015-04-20
We report on the first direct observation of a fast-mode wave propagating along and perpendicular to cool (171 Å) arcade loops observed by the Solar Dynamics Observatory/Atmospheric Imaging Assembly (AIA). The wave was associated with an impulsive/compact flare near the edge of a sunspot. The EUV wavefront expanded radially outward from the flare center and decelerated in the corona from 1060 to 760 km s{sup −1} within ∼3–4 minutes. Part of the EUV wave propagated along a large-scale arcade of cool loops and was partially reflected back to the flare site. The phase speed of the wave was about 1450 km s{sup −1}, which is interpreted as a fast-mode wave. A second overlying loop arcade, orientated perpendicular to the cool arcade, is heated and becomes visible in the AIA hot channels. These hot loops sway in time with the EUV wave, as it propagated to and fro along the lower loop arcade. We suggest that an impulsive energy release at one of the footpoints of the arcade loops causes the onset of an EUV shock wave that propagates along and perpendicular to the magnetic field.
Raman rogue waves in a partially mode-locked fiber laser.
Runge, Antoine F J; Aguergaray, Claude; Broderick, Neil G R; Erkintalo, Miro
2014-01-15
We report on an experimental study of spectral fluctuations induced by intracavity Raman conversion in a passively partially mode-locked, all-normal dispersion fiber laser. Specifically, we use dispersive Fourier transformation to measure single-shot spectra of Raman-induced noise-like pulses, demonstrating that for low cavity gain values Raman emission is sporadic and follows rogue-wave-like probability distributions, while a saturated regime with Gaussian statistics is obtained for high pump powers. Our experiments further reveal intracavity rogue waves originating from cascaded Raman dynamics.
1987-08-01
solution of the Korteweg-de Vries equation ( KdV ), working our way up to the derivation of the multi-soliton solution of the sine-Gordon equation (sG...SOLITARY WAVE SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS j DiS~~Uj~l. _’UDistribution/Willy Hereman AvaiiLi -itY Codes Technical Summary Report...Key Words: soliton theory, solitary waves, coupled KdV , evolution equations , direct methods, Harry Dym, sine-Gordon Mathematics Department, University
Zubarev, Nikolay M; Zubareva, Olga V
2010-10-01
Nonlinear waves on sheets of dielectric liquid in the presence of an external tangential electric field are studied theoretically. It is shown that waves of arbitrary shape in three-dimensional geometry can propagate along (or against) the electric field direction without distortion, i.e., the equations of motion admit a wide class of exact traveling wave solutions. This unusual situation occurs for nonconducting ideal liquids with high dielectric constants in the case of a sufficiently strong field strength. Governing equations for evolution of plane symmetric waves on fluid sheets are derived using conformal variables. A dispersion relation for the evolution of small perturbations of the traveling wave solutions is obtained. It follows from this relation that, regardless of the wave shape, the amplitudes of small-scale perturbations do not increase with time and, hence, the traveling waves are stable. We also study the interaction of counterpropagating symmetric waves with small but finite amplitudes. The corresponding solution of the equations of motion describes the nonlinear superposition of the oppositely directed waves. The results obtained are applicable for the description of long waves on fluid sheets in a horizontal magnetic field.
Space-time analogy for partially coherent plane-wave-type pulses.
Lancis, Jesús; Torres-Company, Víctor; Silvestre, Enrique; Andrés, Pedro
2005-11-15
In this Letter we extend the well-known space-time duality to partially coherent wave fields and, as a limit case, to incoherent sources. We show that there is a general analogy between the paraxial diffraction of quasi-monochromatic beams of limited spatial coherence and the temporal distortion of partially coherent plane-wave pulses in parabolic dispersive media. Next, coherence-dependent effects in the propagation of Gaussian Schell-model pulses are retrieved from that of their spatial counterpart, the Gaussian Schell-model beam. Finally, the last result allows us to present a source linewidth analysis in an optical fiber communication system operating around the 1.55 microm wavelength window.
Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II
NASA Technical Reports Server (NTRS)
Shertzer, J.; Temkin, A.
2003-01-01
As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE) can be reduced to a 2d partial differential equation (pde), and was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation. The resultant equation can be reduced to a pair of coupled pde's, to which the finite element method can still be applied. The resultant scattering amplitudes, both singlet and triplet, as a function of angle can be calculated for various energies. The results are in excellent agreement with converged partial wave results.
NASA Technical Reports Server (NTRS)
Shertzer, Janine; Temkin, A.
2003-01-01
As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE), which can be reduced to a 2d partial differential equation (pde), was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation, which is reducible to a pair of coupled pde's. The resultant scattering amplitudes, both singlet and triplet, calculated as a function of energy are in excellent agreement with converged partial wave results.
NASA Technical Reports Server (NTRS)
Hayes, E. F.; Kouri, D. J.
1971-01-01
Coupled integral equations are derived for the full scattering amplitudes for both reactive and nonreactive channels. The equations do not involve any partial wave expansion and are obtained using channel operators for reactive and nonreactive collisions. These coupled integral equations are similar in nature to equations derived for purely nonreactive collisions of structureless particles. Using numerical quadrature techniques, these equations may be reduced to simultaneous algebraic equations which may then be solved.
A Rosetta Stone relating conventions in photo-meson partial wave analyses
NASA Astrophysics Data System (ADS)
Sandorfi, A. M.; Dey, B.; Sarantsev, A.; Tiator, L.; Workman, R.
2012-04-01
A new generation of complete experiments in pseudoscalar meson photo-production is being pursued at several laboratories. While new data are emerging, there is some confusion regarding definitions of asymmetries and the conventions used in partial wave analyses (PWA). We present expressions for constructing asymmetries as coordinate-system independent ratios of cross sections, along with the names used for these ratios by different PWA groups.
A Rosetta Stone Relating Conventions In Photo-Meson Partial Wave Analyses
A.M. Sandorfi, B. Dey, A. Sarantsev, L. Tiator, R. Workman
2012-04-01
A new generation of complete experiments in pseudoscalar meson photo-production is being pursued at several laboratories. While new data are emerging, there is some confusion regarding definitions of asymmetries and the conventions used in partial wave analyses (PWA). We present expressions for constructing asymmetries as coordinate-system independent ratios of cross sections, along with the names used for these ratios by different PWA groups.
NASA Astrophysics Data System (ADS)
Marston, Philip L.; Zhang, Likun
2016-11-01
When evaluating radiation forces on spheres in soundfields (with or without orbital-angular momentum) the interpretation of analytical results is greatly simplified by retaining the use of s-function notation for partial-wave coefficients imported into acoustics from quantum scattering theory in the 1970s. This facilitates easy interpretation of various efficiency factors. For situations in which dissipation is negligible, each partial-wave s-function becomes characterized by a single parameter: a phase shift allowing for all possible situations. These phase shifts are associated with scattering by plane traveling waves and the incident wavefield of interest is separately parameterized. (When considering outcomes, the method of fabricating symmetric objects having a desirable set of phase shifts becomes a separate issue.) The existence of negative radiation force "islands" for beams reported in 2006 by Marston is manifested. This approach and consideration of conservation theorems illustrate the unphysical nature of various claims made by other researchers. This approach is also directly relevant to objects in standing waves. Supported by ONR.
HEATING OF THE PARTIALLY IONIZED SOLAR CHROMOSPHERE BY WAVES IN MAGNETIC STRUCTURES
Shelyag, S.; Przybylski, D.; Khomenko, E.; Vicente, A. de
2016-03-01
In this paper, we show a “proof of concept” of the heating mechanism of the solar chromosphere due to wave dissipation caused by the effects of partial ionization. Numerical modeling of non-linear wave propagation in a magnetic flux tube, embedded in the solar atmosphere, is performed by solving a system of single-fluid quasi-MHD equations, which take into account the ambipolar term from the generalized Ohm’s law. It is shown that perturbations caused by magnetic waves can be effectively dissipated due to ambipolar diffusion. The energy input by this mechanism is continuous and shown to be more efficient than dissipation of static currents, ultimately leading to chromospheric temperature increase in magnetic structures.
Heating of the Partially Ionized Solar Chromosphere by Waves in Magnetic Structures
NASA Astrophysics Data System (ADS)
Shelyag, S.; Khomenko, E.; de Vicente, A.; Przybylski, D.
2016-03-01
In this paper, we show a “proof of concept” of the heating mechanism of the solar chromosphere due to wave dissipation caused by the effects of partial ionization. Numerical modeling of non-linear wave propagation in a magnetic flux tube, embedded in the solar atmosphere, is performed by solving a system of single-fluid quasi-MHD equations, which take into account the ambipolar term from the generalized Ohm’s law. It is shown that perturbations caused by magnetic waves can be effectively dissipated due to ambipolar diffusion. The energy input by this mechanism is continuous and shown to be more efficient than dissipation of static currents, ultimately leading to chromospheric temperature increase in magnetic structures.
Ebrahimi, V.; Esfandyari-Kalejahi, A.
2014-09-15
In this paper, first we represent the differences between spatial and temporal dispersions and their dependence on the measurement techniques for electrostatic waves in unmagnetized collisionless plasma. Then, three different experimental data are compared to the solutions of exact nonextensive dispersion relations for electron-ion and pair plasma. The results confirm the existence of new acoustic plasma waves. Furthermore, these comparisons yield a Maxwellian and a nonextensive plasma with nonextensive parameter q larger than one, and a Maxwellian plasma with some abnormal dispersion properties.
RESONANTLY DAMPED KINK MAGNETOHYDRODYNAMIC WAVES IN A PARTIALLY IONIZED FILAMENT THREAD
Soler, R.; Oliver, R.; Ballester, J. L. E-mail: ramon.oliver@uib.e
2009-12-10
Transverse oscillations of solar filament and prominence threads have been frequently reported. These oscillations have the common features of being of short period (2-10 minutes) and being damped after a few periods. The observations are interpreted as kink magnetohydrodynamic (MHD) wave modes, whereas resonant absorption in the Alfven continuum and ion-neutral collisions are candidates to be the damping mechanisms. Here, we study both analytically and numerically the time damping of kink MHD waves in a cylindrical, partially ionized filament thread embedded in a coronal environment. The thread model is composed of a straight and thin, homogeneous filament plasma, with a transverse inhomogeneous transitional layer where the plasma physical properties vary continuously from filament to coronal conditions. The magnetic field is homogeneous and parallel to the thread axis. We find that the kink mode is efficiently damped by resonant absorption for typical wavelengths of filament oscillations, the damping times being compatible with the observations. Partial ionization does not affect the process of resonant absorption, and the filament plasma ionization degree is only important for the damping for wavelengths much shorter than those observed. To our knowledge, this is the first time that the phenomenon of resonant absorption is studied in a partially ionized plasma.
Investigation of guided wave propagation in pipes fully and partially embedded in concrete.
Leinov, Eli; Lowe, Michael J S; Cawley, Peter
2016-12-01
The application of long-range guided-wave testing to pipes embedded in concrete results in unpredictable test-ranges. The influence of the circumferential extent of the embedding-concrete around a steel pipe on the guided wave propagation is investigated. An analytical model is used to study the axisymmetric fully embedded pipe case, while explicit finite-element and semi-analytical finite-element simulations are utilised to investigate a partially embedded pipe. Model predictions and simulations are compared with full-scale guided-wave tests. The transmission-loss of the T(0,1)-mode in an 8 in. steel pipe fully embedded over an axial length of 0.4 m is found to be in the range of 32-36 dB while it reduces by a factor of 5 when only 50% of the circumference is embedded. The transmission-loss in a fully embedded pipe is mainly due to attenuation in the embedded section while in a partially embedded pipe it depend strongly on the extent of mode-conversion at entry to the embedded-section; low loss modes with energy concentrated in the region of the circumference not-covered with concrete have been identified. The results show that in a fully embedded pipe, inspection beyond a short distance will not be possible, whereas when the concrete is debonded over a fraction of the pipe circumference, inspection of substantially longer lengths may be possible.
Plante, David T.; Goldstein, Michael R.; Cook, Jesse D.; Smith, Richard; Riedner, Brady A.; Rumble, Meredith E.; Jelenchick, Lauren; Roth, Andrea; Tononi, Giulio; Benca, Ruth M.; Peterson, Michael J.
2015-01-01
Objective Changes in slow waves during non-rapid eye movement (NREM) sleep in response to acute total sleep deprivation are well-established measures of sleep homeostasis. This investigation utilized high-density electroencephalography (hdEEG) to examine topographic changes in slow waves during repeated partial sleep deprivation. Methods Twenty-four participants underwent a 6-day sleep restriction protocol. Spectral and period-amplitude analyses of sleep hdEEG data were used to examine changes in slow wave energy, count, amplitude, and slope relative to baseline. Results Changes in slow wave energy were dependent on the quantity of NREM sleep utilized for analysis, with widespread increases during sleep restriction and recovery when comparing data from the first portion of the sleep period, but restricted to recovery sleep if the entire sleep episode was considered. Period-amplitude analysis was less dependent on the quantity of NREM sleep utilized, and demonstrated topographic changes in the count, amplitude, and distribution of slow waves, with frontal increases in slow wave amplitude, numbers of high-amplitude waves, and amplitude/slopes of low amplitude waves resulting from partial sleep deprivation. Conclusions Topographic changes in slow waves occur across the course of partial sleep restriction and recovery. Significance These results demonstrate a homeostatic response to partial sleep loss in humans. PMID:26596212
Highly directive Fabry-Perot leaky-wave nanoantennas based on optical partially reflective surfaces
Lorente-Crespo, M.; Mateo-Segura, C.
2015-05-04
Nanoantennas enhance the conversion between highly localized electromagnetic fields and far-field radiation. Here, we investigate the response of a nano-patch partially reflective surface backed with a silver mirror to an optical source embedded at the centre of the structure. Using full wave simulations, we demonstrate a two orders of magnitude increased directivity compared to the isotropic radiator, 50% power confinement to a 13.8° width beam and a ±16 nm bandwidth. Our antenna does not rely on plasmonic phenomena thus reducing non-radiative losses and conserving source coherence.
Partial wave analysis of 3 π with pion and photon beams
NASA Astrophysics Data System (ADS)
Jackura, Andrew; Mikhasenko, Mikhail; Szczepaniak, Adam; Ketzer, Bernhard; Joint Physics Analysis Center Collaboration
2016-09-01
We present some results on the analysis of 3 π resonances from peripheral scattering of pions off of nuclear targets. The analysis is motivated by the recent release of the largest data set on diffractively produced three pions by the COMPASS collaboration. The model emphasizes the 3 π production process and their final state interactions which satisfy S-matrix principles. We apply our model to fit partial wave intensities and relative phases from COMPASS in the JPC =2-+ sector and search for resonances. We then discuss the extension of our formalism to photon beams to be used in the GlueX experiment.
Nucleon-nucleon scattering in the 1S0 partial wave in the modified Weinberg approach
NASA Astrophysics Data System (ADS)
Gasparyan, A. M.; Epelbaum, E.; Gegelia, J.; Krebs, H.
2016-03-01
Nucleon-nucleon scattering in the 1S0 partial wave is considered in chiral effective field theory within the recently suggested renormalizable formulation based on the Kadyshevsky equation. Contact interactions are taken into account beyond the leading-order approximation. The subleading contact terms are included non-perturbatively by means of subtractive renormalization. The dependence of the phase shifts on the choice of the renormalization condition is discussed. Perturbative inclusion of the subleading contact interaction is found to be justified only very close to threshold. The low-energy theorems are reproduced significantly better compared with the leading order results.
NASA Astrophysics Data System (ADS)
Akhmediev, Nail; Ankiewicz, Adrian
2011-04-01
We study modulation instability (MI) of the discrete constant-background wave of the Ablowitz-Ladik (A-L) equation. We derive exact solutions of the A-L equation which are nonlinear continuations of MI at longer times. These periodic solutions comprise a family of two-parameter solutions with an arbitrary background field and a frequency of initial perturbation. The solutions are recurrent, since they return the field state to the original constant background solution after the process of nonlinear evolution has passed. These solutions can be considered as a complete resolution of the Fermi-Pasta-Ulam paradox for the A-L system. One remarkable consequence of the recurrent evolution is the nonlinear phase shift gained by the constant background wave after the process. A particular case of this family is the rational solution of the first-order or fundamental rogue wave.
Akhmediev, Nail; Ankiewicz, Adrian
2011-04-01
We study modulation instability (MI) of the discrete constant-background wave of the Ablowitz-Ladik (A-L) equation. We derive exact solutions of the A-L equation which are nonlinear continuations of MI at longer times. These periodic solutions comprise a family of two-parameter solutions with an arbitrary background field and a frequency of initial perturbation. The solutions are recurrent, since they return the field state to the original constant background solution after the process of nonlinear evolution has passed. These solutions can be considered as a complete resolution of the Fermi-Pasta-Ulam paradox for the A-L system. One remarkable consequence of the recurrent evolution is the nonlinear phase shift gained by the constant background wave after the process. A particular case of this family is the rational solution of the first-order or fundamental rogue wave.
NASA Astrophysics Data System (ADS)
Xiao, Xifeng
One of the main drawbacks that prevent the extensive application of free space laser communications is the atmospheric turbulence through which the beam must propagate. For the past four decades, much attention has been devoted to finding different methods to overcome this difficulty. A partially coherent beam (PCB) has been recognized as an effective approach to improve the performance of an atmospheric link. It has been examined carefully with most analyses considering the Gaussian Schell-model (GSM) beam. However, practical PCBs may not follow GSM theory and are better examined through some numerical simulation approach such as a wave optics simulation. Consequently, an approach for modeling the spatially PCB in wave optics simulation is presented here. The approach involves the application of a sequence of random phase screens to an initial beam field and the summation of the intensity results after propagation. The relationship between the screen parameters and the spatial coherence function for the beam is developed and the approach is verified by comparing results with analytic formulations for a Gaussian Schell-model (GSM) beam. A variety of simulation studies were performed for this dissertation. The propagation through turbulence of a coherent beam and a particular version of a PCB, a pseudo-partially coherent beam (PPCB), is analyzed. The beam is created with a sequence of several Gaussian random phase screens for each atmospheric realization. The average intensity profiles, the scintillation index and aperture averaging factor for a horizontal propagation scenario are examined. Comparisons between these results and their corresponding analytic results for the well-known GSM beam are also made. Cumulative probability density functions for the received irradiance are initially investigated. Following the general simulation investigations, a performance metric is proposed as a general measure for optimizing the transverse coherence length of a partial
NASA Astrophysics Data System (ADS)
Santucci, F.; Santini, P. M.
2016-10-01
We study the generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one-dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2 + 1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel inverse scattering transform, and it has been recently shown to be a prototype model equation in the description of the two-dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single-valued discontinuous profiles (shocks). Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if m(n-1)≤slant 2. Lastly, the analytic aspects of such wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a shock. These results, contained in the 2012 master’s thesis of one of the authors (FS) [1], generalize those obtained in [2] for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.
NASA Astrophysics Data System (ADS)
Li, Jia; Wu, Pinghui; Chang, Liping
2016-02-01
Within the first-order Born approximation, the spectrum of light generated by the scattering of a partially coherent wave from a quasi-homogeneous (QH) medium is derived. In particular, the partially coherent incident wave is produced by Young's pinholes. It is shown that the spectrum of the scattered field is identical to the spectrum of incident plane waves if the Fourier transform of the normalized correlation coefficient (NCC) of the scattering potential satisfies a certain scaling law. The scaling law is valid when the medium size is sufficiently small compared with the space between Young' pinholes. Furthermore, comparisons are made between our conditions with the previous results.
SAID Partial Wave Analyses from CNS DAC (Center for Nuclear Studies Data Analysis Center)
George Washington University (GW) has one of the largest university-based nuclear-physics groups in the nation. Many of the current and future projects are geared to Thomas Jefferson National Accelerator Facility (JLab) at Newport News, VA. JLab is the world's premier electron accelerator for nuclear physics, and GW is one of the charter members of the governing body of JLab, the Southeastern Universities Research Association (SURA). The George Washington Data Analysis Center (DAC) was created in 1998 by an agreement among the Department of Energy, Jefferson Lab, and the GW Center for Nuclear Studies.The activities of the DAC fall into four distinct categories: 1) Performing partial-wave analyses of fundamental two- and three-body reactions; 2) Maintenance of databases associated with these reactions; 3) Development of software to disseminate DAC results (as well as the results of competing model-independent analyses and potential approaches); and 4) Phenomenological and theoretical investigations which bridge the gap between theory and experiment; in particular, the extraction of N* and D * hadronic and electromagnetic couplings. Partial Wave Analyses (and the associated databases) available at GW are: Pion-Nucleon, Kaon-Nucleon, Nucleon-Nucleon, Pion Photoproduction, Pion Electroproduction, Kaon Photoproduction, Eta Photoproduction, Eta-Prime Photoproduction, Pion-Deuteron (elastic), and Pion-Deuteron to Proton+Proton. [Taken from http://www.gwu.edu/~ndl/dac.htm">http://www.gwu.edu/~ndl/dac.htm
Two-nucleon higher partial-wave scattering from lattice QCD
NASA Astrophysics Data System (ADS)
Berkowitz, Evan; Kurth, Thorsten; Nicholson, Amy; Joó, Bálint; Rinaldi, Enrico; Strother, Mark; Vranas, Pavlos M.; Walker-Loud, André
2017-02-01
We present a determination of nucleon-nucleon scattering phase shifts for ℓ ≥ 0. The S, P, D and F phase shifts for both the spin-triplet and spin-singlet channels are computed with lattice Quantum ChromoDynamics. For ℓ > 0, this is the first lattice QCD calculation using the Lüscher finite-volume formalism. This required the design and implementation of novel lattice methods involving displaced sources and momentum-space cubic sinks. To demonstrate the utility of our approach, the calculations were performed in the SU (3)-flavor limit where the light quark masses have been tuned to the physical strange quark mass, corresponding to mπ =mK ≈ 800 MeV. In this work, we have assumed that only the lowest partial waves contribute to each channel, ignoring the unphysical partial wave mixing that arises within the finite-volume formalism. This assumption is only valid for sufficiently low energies; we present evidence that it holds for our study using two different channels. Two spatial volumes of V ≈(3.5 fm) 3 and V ≈(4.6 fm) 3 were used. The finite-volume spectrum is extracted from the exponential falloff of the correlation functions. Said spectrum is mapped onto the infinite volume phase shifts using the generalization of the Lüscher formalism for two-nucleon systems.
Liu, Jian-Guo; Du, Jian-Qiang; Zeng, Zhi-Fang; Ai, Guo-Ping
2016-10-01
The Korteweg-de Vries (KdV)-type models have been shown to describe many important physical situations such as fluid flows, plasma physics, and solid state physics. In this paper, a new (2 + 1)-dimensional KdV equation is discussed. Based on the Hirota's bilinear form and a generalized three-wave approach, we obtain new exact solutions for the new (2 + 1)-dimensional KdV equation. With the help of symbolic computation, the properties for some new solutions are presented with some figures.
NASA Astrophysics Data System (ADS)
Liu, Jian-Guo; Du, Jian-Qiang; Zeng, Zhi-Fang; Ai, Guo-Ping
2016-10-01
The Korteweg-de Vries (KdV)-type models have been shown to describe many important physical situations such as fluid flows, plasma physics, and solid state physics. In this paper, a new (2 + 1)-dimensional KdV equation is discussed. Based on the Hirota's bilinear form and a generalized three-wave approach, we obtain new exact solutions for the new (2 + 1)-dimensional KdV equation. With the help of symbolic computation, the properties for some new solutions are presented with some figures.
Two-fluid modeling of magnetosonic wave propagation in the partially ionized solar chromosphere
NASA Astrophysics Data System (ADS)
Maneva, Yana; Alvarez Laguna, Alejandro; Lani, Andrea; Poedts, Stefaan
2016-04-01
We perform 2D two-fluid simulations to study the effects of ion-neutral interactions on the propagation of magnetosonic waves in the partially ionized solar chromosphere, where the number density of neutrals significantly exceeds the number density of protons at low heights. Thus modeling the neutral-ion interactions and studying the effect of neutrals on the ambient plasma properties becomes important for better understanding the observed emission lines and the propagation of disturbances from the photosphere to the transition region and the corona. The role of charged particles (electrons and ions) is combined within resistive MHD approach with Coulomb collisions and anisotropic heat flux determined by Braginskii's transport coefficients. The electromagnetic fields are evolved according to the full Maxwell equations, allowing for propagation of higher frequency waves neglected by the standard MHD approximation. Separate mass, momentum and energy conservation equations are considered for the neutrals and the interaction between the different fluids is determined by the chemical reactions, such as impact ionization, radiative recombination and charge exchange, provided as additional source terms. To initialize the system we consider an ideal gas equation of state with equal initial temperatures for the electrons, ions and the neutrals and different density profiles. The initial temperature and density profiles are height-dependent and follow VAL C atmospheric model for the solar chromosphere. We have searched for a chemical and collisional equilibrium between the ions and the neutrals to minimize any unphysical outflows and artificial heating induced by initial pressure imbalances. Including different magnetic field profiles brings new source of plasma heating through Ohmic dissipation. The excitation and propagation of the magnetosonic waves depends on the type of the external velocity driver. As the waves propagate through the gravitationally stratified media
Bulanov, Sergei V; Esirkepov, Timur Zh; Kando, Masaki; Koga, James K; Bulanov, Stepan S
2011-11-01
When the parameters of electron-extreme power laser interaction enter the regime of dominated radiation reaction, the electron dynamics changes qualitatively. The adequate theoretical description of this regime becomes crucially important with the use of the radiation friction force either in the Lorentz-Abraham-Dirac form, which possesses unphysical runaway solutions, or in the Landau-Lifshitz form, which is a perturbation valid for relatively low electromagnetic wave amplitude. The goal of the present paper is to find the limits of the Landau-Lifshitz radiation force applicability in terms of the electromagnetic wave amplitude and frequency. For this, a class of the exact solutions to the nonlinear problems of charged particle motion in the time-varying electromagnetic field is used.
NASA Astrophysics Data System (ADS)
Bulanov, Sergei V.; Esirkepov, Timur Zh.; Kando, Masaki; Koga, James K.; Bulanov, Stepan S.
2011-11-01
When the parameters of electron-extreme power laser interaction enter the regime of dominated radiation reaction, the electron dynamics changes qualitatively. The adequate theoretical description of this regime becomes crucially important with the use of the radiation friction force either in the Lorentz-Abraham-Dirac form, which possesses unphysical runaway solutions, or in the Landau-Lifshitz form, which is a perturbation valid for relatively low electromagnetic wave amplitude. The goal of the present paper is to find the limits of the Landau-Lifshitz radiation force applicability in terms of the electromagnetic wave amplitude and frequency. For this, a class of the exact solutions to the nonlinear problems of charged particle motion in the time-varying electromagnetic field is used.
Correlations of $\pi N$ partial waves for multireaction analyses
Doring, M.; Revier, J.; Ronchen, D.; Workman, R. L.
2016-06-15
In the search for missing baryonic resonances, many analyses include data from a variety of pion- and photon-induced reactions. For elastic πN scattering, however, usually the partial waves of the SAID (Scattering Analysis Interactive Database) or other groups are fitted, instead of data. We provide the partial-wave covariance matrices needed to perform correlated χ^{2} fits, in which the obtained χ^{2} equals the actual χ^{2} up to nonlinear and normalization corrections. For any analysis relying on partial waves extracted from elastic pion scattering, this is a prerequisite to assess the significance of resonance signals and to assign any uncertainty on results. Lastly, the influence of systematic errors is also considered.
On the partial wave method for self energy calculations for non-hydrogenic electrons
NASA Astrophysics Data System (ADS)
Hagelstein, Peter L.
1994-07-01
A method for computing the self-energy correction for highly-ionized and high-Z many electron atoms is proposed and developed. The method is based on a partical wave analysis, and is immediately applicable to general potentials and many-electron wavefunctions. In this work we discuss the general approach, develop a formalism amenable to practical anal- ysis, provide the angular momentum reduction for arbitrary one-electron orbitals, and describe the computation of the twdimensional integrals and their kernels required for the partial wave analysis. Analytical results allowing for a practical renormalization scheme are discussed. This work is exploratory and developmental, and the present document provides a status report of our eforts. To date we have obtained numerical evidence that the method successfully handles the renormalization, and we report on significant progress in numerical methods for evaluating and approximating the two-dimensional integrals which occur in the method. We believe that this method can ultimately achieve an accuracy which is competitive with that of modern Brown's method calculations. The methods discussed within this work for approximating the two-dimensional radial matrix eIements including the full retarded couIomb interaction can be applied to other relativistic atomic physics calculations as a practical way to obtain improvements over the coulomb and Breit approximations.
A Composite Fermion Hofstadter Problem: Partially Polarized Density Wave States in the FQHE
NASA Astrophysics Data System (ADS)
Murthy, Ganpathy
2000-03-01
It is well known that the 2/5 FQH state can have two translationally invariant ground states, one of which is a singlet and the other fully polarized. A quantum phase transition occurs between these two as a function of the Zeeman field. This can be simply explained in terms of the crossing of Composite Fermion Landau levels. However, recently Kukushkin et al (PRL 82, 3665 (99)) have seen plateaus of half the maximal polarization in the 2/5 fraction at intermediate Zeeman fields. Similar plateaus, which are not allowed for translationally invariant CF states, are seen in other fractions as well. I propose a class of novel partially polarized spin/charge density wave states which display the co-existence of density wave and quantum Hall order (the Hall crystal state). The physical properties of the states, including gaps and collective excitations are computed using the formalism for the FQHE developed recently by Shankar and myself (for details see Murthy and Shankar in "Composite Fermions", Olle Heinonen, Editor).
X-ray standing wave analysis of nanostructures using partially coherent radiation
Tiwari, M. K. Das, Gangadhar; Bedzyk, M. J.
2015-09-07
The effect of longitudinal (or temporal) coherence on total reflection assisted x-ray standing wave (TR-XSW) analysis of nanoscale materials is quantitatively demonstrated by showing how the XSW fringe visibility can be strongly damped by decreasing the spectral resolution of the incident x-ray beam. The correction for nonzero wavelength dispersion (δλ ≠ 0) of the incident x-ray wave field is accounted for in the model computations of TR-XSW assisted angle dependent fluorescence yields of the nanostructure coatings on x-ray mirror surfaces. Given examples include 90 nm diameter Au nanospheres deposited on a Si(100) surface and a 3 nm thick Zn layer trapped on top a 100 nm Langmuir-Blodgett film coating on a Au mirror surface. Present method opens up important applications, such as enabling XSW studies of large dimensioned nanostructures using conventional laboratory based partially coherent x-ray sources.
Fast solution of elliptic partial differential equations using linear combinations of plane waves
NASA Astrophysics Data System (ADS)
Pérez-Jordá, José M.
2016-02-01
Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations A x =b , where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O (N logN ) memory and executing an iteration in O (N log2N ) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.
Fast solution of elliptic partial differential equations using linear combinations of plane waves.
Pérez-Jordá, José M
2016-02-01
Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.
Wen, Xiao-Yong; Yan, Zhenya; Malomed, Boris A
2016-12-01
An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, the perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.
NASA Astrophysics Data System (ADS)
Wen, Xiao-Yong; Yan, Zhenya; Malomed, Boris A.
2016-12-01
An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, the perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.
NASA Astrophysics Data System (ADS)
Klochko, M. S.
2014-06-01
The surface waves and bulk acoustic bands were studied taking into account the interaction between the nearest and next-nearest neighbors in a cubic crystal. Expressions for the dispersion relations, the frequencies at which the surface waves split off the bulk spectrum, and the parameters of the amplitude attenuation have been obtained for the crystalline systems in which the surface waves are single-component and single-partial. The calculations were conducted taking into account the discrete nature of crystal lattice for arbitrary values of the two-dimensional wave vector. The analysis has demonstrated that the results obtained in the long-wavelength limit are in full agreement with those calculated in the framework of linear nonlocal elasticity theory. The influence of an adsorbed surface monolayer on the characteristics of the surface waves was studied.
Hansson, T; Lisak, M; Anderson, D
2012-02-10
It is shown that the evolution equations describing partially coherent wave propagation in noninstantaneous Kerr media are integrable and have an infinite number of invariants. A recursion relation for generating these invariants is presented, and it is demonstrated how to express them in the coherent density, self-consistent multimode, mutual coherence, and Wigner formalisms.
NASA Astrophysics Data System (ADS)
Yenen, Orhan
2003-05-01
Recent trends in AMO physics is to move from being a passive observer to an active controller of the outcome of quantum phenomena. Full controls of quantum processes require complete information about the quantum system; experiments which measure all the information allowed by quantum mechanics are called "Quantum Mechanically Complete Experiments". For example, when an isolated atom is photoionized, conservation laws limit the allowed partial waves of the photoelectron to a maximum of three. A quantum mechanically complete photoionization experiment then will have to determine all three partial wave probabilities and the two independent phases between the partial waves as a function of ionizing photon energy. From these five parameters all the quantities quantum mechanics allows one to measure can be determined for the "Residual Ion + Photoelectron" system. We have developed experimental methods [1, 2] to determine all three partial wave probabilities of photoelectrons when the residual ion is left in an excited state. Experimentally, Ar atoms are photoionized by circularly polarized synchrotron radiation produced by a unique VUV (vacuum ultraviolet) phase retarder we have installed at the Advanced Light Source (ALS) in Berkeley, CA. We measure the linear and circular polarization of the fine-structure-resolved fluorescent photons from the excited residual ions at specific directions. From the measurements one obtains the relativistic partial wave probabilities of the photoelectron. Our measurements highlight the significance of multielectron processes in photoionization dynamics and provide stringent tests of theory. The results indicate significant spin-dependent relativistic interactions during photoionization. [1] O. Yenen et al., Phys. Rev. Lett. 86, 979 (2001). [2] K. W. McLaughlin et al., Phys. Rev. Lett. 88, 123003 (2002).
Spreading speed and travelling wave solutions of a partially sedentary population
NASA Astrophysics Data System (ADS)
Volkov, Darko; Lui, Roger
2007-12-01
In this paper, we extend the population genetics model of Weinberger (1978, Asymptotic behavior of a model in population genetics. Nonlinear Partial Differential Equations and Applications (J. Chadam ed.). Lecture Notes in Mathematics, vol. 648. New York: Springer, pp. 47-98.) to the case where a fraction of the population does not migrate after the selection process. Mathematically, we study the asymptotic behaviour of solutions to the recursion un+1 = Qg[un], where ... In the above definition of Qg, K is a probability density function and f behaves qualitatively like the Beverton-Holt function. Under some appropriate conditions on K and f, we show that for each unit vector{xi} [isin] Rd, there exists a c*g({xi}) which has an explicit formula and is the spreading speed of Qg in the direction{xi} . We also show that for each c [≥] c*g({xi}), there exists a travelling wave solution in the direction{xi} which is continuous if gf '(0) [≤] 1.
Partial wave analyses of J/ψ→γππ and γππ
NASA Astrophysics Data System (ADS)
BES Collaboration; Ablikim, M.; Bai, J. Z.; Ban, Y.; Bian, J. G.; Cai, X.; Chen, H. F.; Chen, H. S.; Chen, H. X.; Chen, J. C.; Chen, Jin; Chen, Y. B.; Chi, S. P.; Chu, Y. P.; Cui, X. Z.; Dai, Y. S.; Diao, L. Y.; Deng, Z. Y.; Dong, Q. F.; Du, S. X.; Fang, J.; Fang, S. S.; Fu, C. D.; Gao, C. S.; Gao, Y. N.; Gu, S. D.; Gu, Y. T.; Guo, Y. N.; Guo, Y. Q.; Guo, Z. J.; Harris, F. A.; He, K. L.; He, M.; Heng, Y. K.; Hu, H. M.; Hu, T.; Huang, G. S.; Huang, X. T.; Ji, X. B.; Jiang, X. S.; Jiang, X. Y.; Jiao, J. B.; Jin, D. P.; Jin, S.; Jin, Yi; Lai, Y. F.; Li, G.; Li, H. B.; Li, H. H.; Li, J.; Li, R. Y.; Li, S. M.; Li, W. D.; Li, W. G.; Li, X. L.; Li, X. N.; Li, X. Q.; Li, Y. L.; Liang, Y. F.; Liao, H. B.; Liu, B. J.; Liu, C. X.; Liu, F.; Liu, Fang; Liu, H. H.; Liu, H. M.; Liu, J.; Liu, J. B.; Liu, J. P.; Liu, Q.; Liu, R. G.; Liu, Z. A.; Lou, Y. C.; Lu, F.; Lu, G. R.; Lu, J. G.; Luo, C. L.; Ma, F. C.; Ma, H. L.; Ma, L. L.; Ma, Q. M.; Ma, X. B.; Mao, Z. P.; Mo, X. H.; Nie, J.; Olsen, S. L.; Peng, H. P.; Ping, R. G.; Qi, N. D.; Qin, H.; Qiu, J. F.; Ren, Z. Y.; Rong, G.; Shan, L. Y.; Shang, L.; Shen, C. P.; Shen, D. L.; Shen, X. Y.; Sheng, H. Y.; Sun, H. S.; Sun, J. F.; Sun, S. S.; Sun, Y. Z.; Sun, Z. J.; Tan, Z. Q.; Tang, X.; Tong, G. L.; Varner, G. S.; Wang, D. Y.; Wang, L.; Wang, L. L.; Wang, L. S.; Wang, M.; Wang, P.; Wang, P. L.; Wang, W. F.; Wang, Y. F.; Wang, Z.; Wang, Z. Y.; Wang, Zhe; Wang, Zheng; Wei, C. L.; Wei, D. H.; Wu, N.; Xia, X. M.; Xie, X. X.; Xu, G. F.; Xu, X. P.; Xu, Y.; Yan, M. L.; Yang, H. X.; Yang, Y. X.; Ye, M. H.; Ye, Y. X.; Yi, Z. Y.; Yu, G. W.; Yuan, C. Z.; Yuan, J. M.; Yuan, Y.; Zang, S. L.; Zeng, Y.; Zeng, Yu; Zhang, B. X.; Zhang, B. Y.; Zhang, C. C.; Zhang, D. H.; Zhang, H. Q.; Zhang, H. Y.; Zhang, J. W.; Zhang, J. Y.; Zhang, S. H.; Zhang, X. M.; Zhang, X. Y.; Zhang, Yiyun; Zhang, Z. P.; Zhao, D. X.; Zhao, J. W.; Zhao, M. G.; Zhao, P. P.; Zhao, W. R.; Zhao, Z. G.; Zheng, H. Q.; Zheng, J. P.; Zheng, Z. P.; Zhou, L.; Zhou, N. F.; Zhu, K. J.; Zhu, Q. M.; Zhu, Y. C.; Zhu, Y. S.; Zhu, Yingchun; Zhu, Z. A.; Zhuang, B. A.; Zhuang, X. A.; Zou, B. S.
2006-11-01
Results are presented on J/ψ radiative decays to ππ and ππ based on a sample of 58M J/ψ events taken with the BES II detector. Partial wave analyses are carried out using the relativistic covariant tensor amplitude method in the 1.0 to 2.3GeV/cππ mass range. There are conspicuous peaks due to the f(1270) and two 0 states in the 1.45 and 1.75 GeV/c mass regions. The first 0 state has a mass of 1466±6±20MeV/c, a width of 108-11+14±25MeV/c, and a branching fraction B(J/ψ→γf(1500)→γππ)=(0.67±0.02±0.30)×10. Spin 0 is strongly preferred over spin 2. The second 0 state peaks at 1765-3+4±13MeV/c with a width of 145±8±69MeV/c. If this 0 is interpreted as coming from f(1710), the ratio of its branching fractions to ππ and KK¯ is 0.41-0.17+0.11.
Calculation of scattering amplitude without partial wave analysis: Inclusion of exchange
NASA Astrophysics Data System (ADS)
Temkin, Aaron; Shertzer, Janine
2002-05-01
In Ref. [1], a method is given for calculating the scattering amplitude f(Ω) directly. The idea is to calculate the complete wave function Ψ_k( r) numerically and use it in an integral expression for f(Ω). The original application was for electron scattering from static hydrogen without exchange. The Schrödinger equation (SE) reduces to a 2D partial differential equation (PDE), which is solved using the finite element method (FEM) [2]. The integral over dφr is done analytically, reducing the integral expression for f(Ω_k) to a 2D integral. Here we extend the method to include the effects of exchange. The SE can be reduced to a pair of 2D coupled PDE's which are again solved by the FEM. The formal expression for f(Ω) consists of two integrals, f^=fd f_e; fd is formally the same integral as the no-exchange f. We have also succeeded in reducing fe to a 2D integral. Results will be presented at the meeting. [1] J. Shertzer and A. Temkin, Phys. Rev. A 63, 062714 (2001). [2] J. Shertzer and J. Botero, Phys. Rev. A 49, 3673 (1994).
NASA Astrophysics Data System (ADS)
Gulevich, D. R.; Kusmartsev, F. V.; Savel'Ev, Sergey; Yampol'Skii, V. A.; Nori, Franco
2009-09-01
We predict a class of excitations propagating along a Josephson vortex in two-dimensional Josephson junctions. These excitations are associated with the distortion of a Josephson vortex line of an arbitrary profile. We derive a universal analytical expression for the energy of arbitrary-shape excitations, investigate their influence on the dynamics of a vortex line, and discuss conditions where such excitations can be created. Finally, we show that such excitations play the role of a clock for a relativistically-moving Josephson vortex and suggest an experiment to measure a time-dilation effect analogous to that in special relativity. The position of the shape excitation on a Josephson vortex acts like a “minute hand” showing the time in the rest frame associated with the vortex. Remarkably, at some conditions, the shape wave can carry negative energy: a vortex with the shape excitation can have less energy than the same vortex without it.
Bello-Rivas, Juan M.; Elber, Ron
2015-03-07
A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied.
Exact solutions for nonlinear foam drainage equation
NASA Astrophysics Data System (ADS)
Zayed, E. M. E.; Al-Nowehy, Abdul-Ghani
2017-02-01
In this paper, the modified simple equation method, the exp-function method, the soliton ansatz method, the Riccati equation expansion method and the ( G^' }/G)-expansion method are used to construct exact solutions with parameters of the nonlinear foam drainage equation. When these parameters are taken to be special values, the solitary wave solutions and the trigonometric function solutions are derived from the exact solutions. The obtained results confirm that the proposed methods are efficient techniques for analytic treatments of a wide variety of nonlinear partial differential equations in mathematical physics. We compare our results together with each other yielding from these integration tools. Also, our results have been compared with the well-known results of others.
Exact solutions for nonlinear foam drainage equation
NASA Astrophysics Data System (ADS)
Zayed, E. M. E.; Al-Nowehy, Abdul-Ghani
2016-09-01
In this paper, the modified simple equation method, the exp-function method, the soliton ansatz method, the Riccati equation expansion method and the ( G^' }/G) -expansion method are used to construct exact solutions with parameters of the nonlinear foam drainage equation. When these parameters are taken to be special values, the solitary wave solutions and the trigonometric function solutions are derived from the exact solutions. The obtained results confirm that the proposed methods are efficient techniques for analytic treatments of a wide variety of nonlinear partial differential equations in mathematical physics. We compare our results together with each other yielding from these integration tools. Also, our results have been compared with the well-known results of others.
Almassalha, Luay M; Bauer, Greta M; Chandler, John E; Gladstein, Scott; Cherkezyan, Lusik; Stypula-Cyrus, Yolanda; Weinberg, Samuel; Zhang, Di; Thusgaard Ruhoff, Peder; Roy, Hemant K; Subramanian, Hariharan; Chandel, Navdeep S; Szleifer, Igal; Backman, Vadim
2016-10-18
The organization of chromatin is a regulator of molecular processes including transcription, replication, and DNA repair. The structures within chromatin that regulate these processes span from the nucleosomal (10-nm) to the chromosomal (>200-nm) levels, with little known about the dynamics of chromatin structure between these scales due to a lack of quantitative imaging technique in live cells. Previous work using partial-wave spectroscopic (PWS) microscopy, a quantitative imaging technique with sensitivity to macromolecular organization between 20 and 200 nm, has shown that transformation of chromatin at these length scales is a fundamental event during carcinogenesis. As the dynamics of chromatin likely play a critical regulatory role in cellular function, it is critical to develop live-cell imaging techniques that can probe the real-time temporal behavior of the chromatin nanoarchitecture. Therefore, we developed a live-cell PWS technique that allows high-throughput, label-free study of the causal relationship between nanoscale organization and molecular function in real time. In this work, we use live-cell PWS to study the change in chromatin structure due to DNA damage and expand on the link between metabolic function and the structure of higher-order chromatin. In particular, we studied the temporal changes to chromatin during UV light exposure, show that live-cell DNA-binding dyes induce damage to chromatin within seconds, and demonstrate a direct link between higher-order chromatin structure and mitochondrial membrane potential. Because biological function is tightly paired with structure, live-cell PWS is a powerful tool to study the nanoscale structure-function relationship in live cells.
NASA Astrophysics Data System (ADS)
Zhang, Di; Graff, Taylor; Crawford, Susan; Subramanian, Hariharan; Thompson, Sebastian; Derbas, Justin R.; Lyengar, Radha; Roy, Hemant K.; Brendler, Charles B.; Backman, Vadim
2016-02-01
Prostate Cancer (PC) is the second leading cause of cancer deaths in American men. While prostate specific antigen (PSA) test has been widely used for screening PC, >60% of the PSA detected cancers are indolent, leading to unnecessary clinical interventions. An alternative approach, active surveillance (AS), also suffer from high expense, discomfort and complications associated with repeat biopsies (every 1-3 years), limiting its acceptance. Hence, a technique that can differentiate indolent from aggressive PC would attenuate the harms from over-treatment. Combining microscopy with spectroscopy, our group has developed partial wave spectroscopic (PWS) microscopy, which can quantify intracellular nanoscale organizations (e.g. chromatin structures) that are not accessible by conventional microscopy. PWS microscopy has previously been shown to predict the risk of cancer in seven different organs (N ~ 800 patients). Herein we use PWS measurement of label-free histologically-normal prostatic epithelium to distinguish indolent from aggressive PC and predict PC risk. Our results from 38 men with low-grade PC indicated that there is a significant increase in progressors compared to non-progressors (p=0.002, effect size=110%, AUC=0.80, sensitivity=88% and specificity=72%), while the baseline clinical characteristics were not significantly different. We further improved the diagnostic power by performing nuclei-specific measurements using an automated system that separates in real-time the cell nuclei from the remaining prostate epithelium. In the long term, we envision that the PWS based prognostication can be coupled with AS without any change to the current procedure to mitigate the harms caused by over-treatment.
Resolving Difficulties of a Single-Channel Partial-Wave Analysis
NASA Astrophysics Data System (ADS)
Hunt, Brian; Manley, D. Mark
2016-03-01
The goal of our research is to determine better the properties of nucleon resonances using techniques of a global multichannel partial-wave analysis. Currently, many predicted resonances have not been found, while the properties of several known resonances are relatively uncertain. To resolve these issues, one must analyze many different reactions in a multichannel fit. Other groups generally approach this problem by generating an energy-dependent fit from the start. This is a fit where all channels are analyzed together. The method is powerful, but due to the complex nature of resonances, certain model-dependent assumptions have to be introduced from the start. The current work tries to resolve these issues by first generating single-energy solutions in which experimental data are analyzed in narrow energy bins. The single-energy solutions can then be used to constrain the energy-dependent solution in a comparatively unbiased manner. Our work focuses on adding three new single-energy solutions into the global fit. These reactions are γp --> ηp , γn --> ηn , and γp -->K+ Λ . During this talk, I will discuss the difficulties of this approach, our methods to overcome these difficulties, and a few preliminary results. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Medium Energy Nuclear Physics, under Award Nos. DE-FG02-01ER41194 and DE-SC0014323 and by the Kent State University Department of Physics.
Almassalha, Luay M.; Bauer, Greta M.; Chandler, John E.; Gladstein, Scott; Cherkezyan, Lusik; Stypula-Cyrus, Yolanda; Weinberg, Samuel; Zhang, Di; Thusgaard Ruhoff, Peder; Roy, Hemant K.; Subramanian, Hariharan; Chandel, Navdeep S.; Szleifer, Igal; Backman, Vadim
2016-01-01
The organization of chromatin is a regulator of molecular processes including transcription, replication, and DNA repair. The structures within chromatin that regulate these processes span from the nucleosomal (10-nm) to the chromosomal (>200-nm) levels, with little known about the dynamics of chromatin structure between these scales due to a lack of quantitative imaging technique in live cells. Previous work using partial-wave spectroscopic (PWS) microscopy, a quantitative imaging technique with sensitivity to macromolecular organization between 20 and 200 nm, has shown that transformation of chromatin at these length scales is a fundamental event during carcinogenesis. As the dynamics of chromatin likely play a critical regulatory role in cellular function, it is critical to develop live-cell imaging techniques that can probe the real-time temporal behavior of the chromatin nanoarchitecture. Therefore, we developed a live-cell PWS technique that allows high-throughput, label-free study of the causal relationship between nanoscale organization and molecular function in real time. In this work, we use live-cell PWS to study the change in chromatin structure due to DNA damage and expand on the link between metabolic function and the structure of higher-order chromatin. In particular, we studied the temporal changes to chromatin during UV light exposure, show that live-cell DNA-binding dyes induce damage to chromatin within seconds, and demonstrate a direct link between higher-order chromatin structure and mitochondrial membrane potential. Because biological function is tightly paired with structure, live-cell PWS is a powerful tool to study the nanoscale structure–function relationship in live cells. PMID:27702891
NASA Astrophysics Data System (ADS)
Li, Jia; Chang, Liping; Chen, Feinan
2016-12-01
Based on the first-order Born approximation, the correlation between intensity fluctuations is derived for a partially coherent, electromagnetic plane wave scattering from a spatially quasi-homogeneous medium. Young's pinholes are utilized to control the degree of coherence of the incident field. For the electromagnetic scattering case, it is shown that the CIF of the scattered field strongly depends on the degree of polarization of the incident wave, Young's pinhole parameter, effective radius and correlation length of the medium. The influences of these parameters on the CIF distributions are revealed by numerical calculations.
Marie, James John
2006-05-01
The JETSET experiment (PS202) conducted at CERN was designed to search for gluonic resonances in the mass range between 2.14 and 2.43 GeV/c^{2} using the channel, p$\\bar{p}$→ΦΦ→4K+/-. This channel is OZI suppressed, thus any observed enhancement of the cross section above a level consistent with the OZI rule could indicate possible resonating gluonic degrees of freedom. In fact, the measured cross section is two orders of magnitude larger than the OZI prediction and shows an enhancement centered near 2.2 GeV/c^{2} of width 50-100 MeV/c^{2}. A partial wave analysis (PWA) has been conducted in order to search for the dominant partial waves. The formalism and methods of this PWA will be fully developed. This analysis has revealed the dominance of J^{pc} = 2^{++} together with a significant J^{pc} = 4^{++} component. Because the Φ resonance is only 4 MeV wide, the PWA is relatively insensitive to the presence of competing channels coupling to the 4K^{±} final state. The partial wave analysis was
NASA Astrophysics Data System (ADS)
Martínez-Gómez, David; Soler, Roberto; Terradas, Jaume
2017-03-01
The presence of neutral species in a plasma has been shown to greatly affect the properties of magnetohydrodynamic waves. For instance, the interaction between ions and neutrals through momentum transfer collisions causes the damping of Alfvén waves and alters their oscillation frequency and phase speed. When the collision frequencies are larger than the frequency of the waves, single-fluid magnetohydrodynamic approximations can accurately describe the effects of partial ionization, since there is a strong coupling between the various species. However, at higher frequencies, the single-fluid models are not applicable and more complex approaches are required. Here, we use a five-fluid model with three ionized and two neutral components, which takes into consideration Hall’s current and Ohm’s diffusion in addition to the friction due to collisions between different species. We apply our model to plasmas composed of hydrogen and helium, and allow the ionization degree to be arbitrary. By analyzing the corresponding dispersion relation and numerical simulations, we study the properties of small-amplitude perturbations. We discuss the effect of momentum transfer collisions on the ion-cyclotron resonances and compare the importance of magnetic resistivity, and ion–neutral and ion–ion collisions on the wave damping at various frequency ranges. Applications to partially ionized plasmas of the solar atmosphere are performed.
NASA Astrophysics Data System (ADS)
Deutscher, R.; Everts, H. U.
1993-03-01
We study the ground state properties of the S=$\\frac{1}{2}$ Heisenberg antiferromagnet (HAF) on the triangular lattice with nearest-neighbour ($J$) and next-nearest neighbour ($\\alpha J$) couplings. Classically, this system is known to be ordered in a $120^\\circ$ N\\'eel type state for values $-\\infty<\\alpha\\le 1/8$ of the ratio $\\alpha$ of these couplings and in a collinear state for $1/8<\\alpha<1$. The order parameter ${\\cal M}$ and the helicity $\\chi$ of the $120^\\circ$ structure are obtained by numerical diagonalisation of finite periodic systems of up to $N=30$ sites and by applying the spin-wave (SW) approximation to the same finite systems. We find a surprisingly good agreement between the exact and the SW results in the entire region $-\\infty<\\alpha< 1/8$. It appears that the SW theory is still valid for the simple triangular HAF ($\\alpha=0$) although the sublattice magnetisation ${\\cal M}$ is substantially reduced from its classical value by quantum fluctuations. Our numerical results for the order parameter ${\\cal N}$ of the collinear order support the previous conjecture of a first order transition between the $120^\\circ$ and the collinear order at $\\alpha \\simeq 1/8$.
Partially coherent fundamental Gaussian wave generated by a fluctuating planar current source.
Seshadri, S R
2010-06-01
The propagation characteristics of a spatially localized electromagnetic wave produced by a planar current source of different states of spatial coherence are analyzed by the use of a Gaussian Schell-model source. A linearly polarized fundamental electromagnetic Gaussian wave with the electric field perpendicular to the direction of propagation is treated. The effects of the degree of coherence of the source distribution on the radiation intensity distribution and the total radiated power are determined.
NASA Astrophysics Data System (ADS)
Altshuler, Gennady; Manor, Ofer
2016-07-01
We use both theory and experiment to study the response of thin and free films of a partially wetting liquid to a MHz vibration, propagating in the solid substrate in the form of a Rayleigh surface acoustic wave (SAW). We generalise the previous theory for the response of a thin fully wetting liquid film to a SAW by including the presence of a small but finite three phase contact angle between the liquid and the solid. The SAW in the solid invokes a convective drift of mass in the liquid and leaks sound waves. The dynamics of a film that is too thin to support the accumulation of the sound wave leakage is governed by a balance between the drift and capillary stress alone. We use theory to demonstrate that a partially wetting liquid film, supporting a weak capillary stress, will spread along the path of the SAW. A partially wetting film, supporting an appreciable capillary stress, will however undergo a concurrent dynamic wetting and dewetting at the front and the rear, respectively, such that the film will displace, rather than spread, along the path of the SAW. The result of the theory for a weak capillary stress is in agreement with the previous experimental and theoretical studies on the response of thin silicon oil films to a propagating SAW. No corresponding previous results exist for the case of an appreciable capillary stress. We thus complement the large capillary limit of our theory by undertaking an experimental procedure where we explore the response of films of water and a surfactant solutions to a MHz SAW, which is found to be in qualitative agreement with the theory at this limit.
Kamelger, Florian Stefan; Jeschke, Johannes; Piza-Katzer, Hildegunde
2014-01-01
Extracorporeal shock wave therapy (ESWT) enhances tissue vascularization and neoangiogenesis. Recent animal studies showed improved soft tissue regeneration using ESWT. In most cases, deep partial-thickness burns require skin grafting; the outcome is often unsatisfactory in function and aesthetic appearance. The aim of this study was to demonstrate the effect of ESWT on skin regeneration after deep partial-thickness burns. Under general anesthesia, two standardized deep partial-thickness burns were induced on the back of 30 male Wistar rats. Immediately after the burn, ESWT was given to rats of group 1 (N = 15), but not to group 2 (N = 15). On days 5, 10, and 15, five rats of each group were analyzed. Reepithelialization rate was defined, perfusion units were measured, and histological analysis was performed. Digital photography was used for visual documentation. A wound score system was used. ESWT enhanced the percentage of wound closure in group 1 as compared to group 2 (P < 0.05). The reepithelialization rate was improved significantly on day 15 (P < 0.05). The wound score showed a significant increase in the ESWT group. ESWT improves skin regeneration of deep partial-thickness burns in rats. It may be a suitable and cost effective treatment alternative in this type of burn wounds in the future. PMID:25431664
Henao-Escobar, W; Domínguez-Renedo, O; Alonso-Lomillo, M A; Arcos-Martínez, M J
2015-10-01
This work presents the simultaneous determination of cadaverine, histamine, putrescine and tyramine by square wave voltammetry using a boron-doped diamond electrode. A multivariate calibration method based on partial least square regressions has allowed the resolution of the very high overlapped voltammetric signals obtained for the analyzed biogenic amines. Prediction errors lower than 9% have been obtained when concentration of quaternary mixtures were calculated. The developed procedure has been applied in the analysis of ham samples, which results are in good agreement with those obtained using the standard HPLC method.
Cut-off wavenumber of Alfvén waves in partially ionized plasmas of the solar atmosphere
NASA Astrophysics Data System (ADS)
Zaqarashvili, T. V.; Carbonell, M.; Ballester, J. L.; Khodachenko, M. L.
2012-08-01
Context. Alfvén wave dynamics in partially ionized plasmas of the solar atmosphere shows that there is indeed a cut-off wavenumber, i.e. the Alfvén waves with wavenumbers higher than the cut-off value are evanescent. The cut-off wavenumber appears in single-fluid magnetohydrodynamic (MHD) approximation but it is absent in a multi-fluid approach. Up to now, an explanation for the existence of the cut-off wavenumber is still missing. Aims: The aim of this paper is to point out the reason for the appearance of a cut-off wavenumber in single-fluid MHD. Methods: Beginning with three-fluid equations (with electrons, protons and neutral hydrogen atoms), we performed consecutive approximations until we obtained the usual single-fluid description. We solved the dispersion relation of linear Alfvén waves at each step and sought the approximation responsible of the cut-off wavenumber appearance. Results: We have found that neglecting inertial terms significantly reduces the real part of the Alfvén frequency although it never becomes zero. Therefore, the cut-off wavenumber does not exist at this stage. However, when the inertial terms together with the Hall term in the induction equation are neglected, the real part of the Alfvén frequency becomes zero. Conclusions: The appearance of a cut-off wavenumber, when Alfvén waves in partially ionized regions of the solar atmosphere are studied, is the result of neglecting inertial and Hall terms, therefore it has no physical origin.
Off-shell Jost solutions for Coulomb and Coulomb-like interactions in all partial waves
Laha, U.; Bhoi, J.
2013-01-15
By exploiting the theory of ordinary differential equations, with judicious use of boundary conditions, interacting Green's functions and their integral transforms together with certain properties of higher transcendental functions, useful analytical expressions for the off-shell Jost solutions for motion in Coulomb and Coulomb-nuclear potentials are derived in maximal reduced form through different approaches to the problem in the representation space. The exact analytical expressions for the off-shell Jost solutions for Coulomb and Coulomb-like potentials are believed to be useful for the description of the charged particle scattering/reaction processes.
NASA Astrophysics Data System (ADS)
Saha Ray, S.; Sahoo, S.
2017-01-01
In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely time fractional modified Kawahara equations by using the ( G^'/G)-expansion method via fractional complex transform. As a result, new types of exact analytical solutions are obtained.
Exactly conservative integrators
Shadwick, B.A.; Bowman, J.C.; Morrison, P.J.
1995-07-19
Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves invariants. We illustrate the general method by applying it to the Three-Wave truncation of the Euler equations, the Volterra-Lotka predator-prey model, and the Kepler problem. We discuss our method in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.
Salgado, Carlos W.; Weygand, Dennis P.
2014-04-01
Meson spectroscopy is going through a revival with the advent of high statistics experiments and new advances in the theoretical predictions. The Constituent Quark Model (CQM) is finally being expanded considering more basic principles of field theory and using discrete calculations of Quantum Chromodynamics (lattice QCD). These new calculations are approaching predictive power for the spectrum of hadronic resonances and decay modes. It will be the task of the new experiments to extract the meson spectrum from the data and compare with those predictions. The goal of this report is to describe one particular technique for extracting resonance information from multiparticle final states. The technique described here, partial wave analysis based on the helicity formalism, has been used at Brookhaven National Laboratory (BNL) using pion beams, and Jefferson Laboratory (Jlab) using photon beams. In particular this report broaden this technique to include production experiments using linearly polarized real photons or quasi-real photons. This article is of a didactical nature. We describe the process of analysis, detailing assumptions and formalisms, and is directed towards people interested in starting partial wave analysis.
Wave simulation in partially frozen porous media with fractal freezing conditions
NASA Astrophysics Data System (ADS)
Carcione, José M.; Santos, Juan E.; Ravazzoli, Claudia L.; Helle, Hans B.
2003-12-01
A recent article [J. M. Carcione and G. Seriani, J. Comput. Phys. 170, 676 (2001)] proposes a modeling algorithm for wave simulation in a three-phase porous medium composed of sand grains, ice, and water. The differential equations hold for uniform water (ice) content. Here, we obtain the variable-porosity differential equations by using the analogy with the two-phase case and the complementary energy theorem. The displacements of the rock and ice frames and the variation of fluid content are the generalized coordinates, and the stress components and fluid pressure are the generalized forces. We simulate wave propagation in a frozen porous medium with fractal variations of porosity and, therefore, realistic freezing conditions.
Analysis of Shear Wave Generation by Decoupled and Partially Coupled Explosions
2009-07-31
solution for the seismic waves generated by an explosion in an arbitrarily prestressed elastic medium. In this paper, we generalize the solution to allow... prestress does not change, but will be non-zero for a tamped explosion with tectonic strain release. The third integral therefore represents the...response of the medium to a change in prestress , the second integral represents the response of the medium to the applied stress from the explosion, and
NASA Astrophysics Data System (ADS)
Farsaei, Amir Ashkan; Mokhtari-Koushyar, Farzad; Javad Seyed-Talebi, Seyed Mohammad; Kavehvash, Zahra; Shabany, Mahdi
2016-03-01
Active millimeter-wave imaging based on synthetic aperture focusing offers certain unique and practical advantages in nondestructive testing applications. Traditionally, the imaging for this purpose is performed through a long procedure of raster scanning with a single antenna across a two-dimensional grid, leading to a slow, bulky, and expensive scanning platform. In this paper, an improved bistatic structure based on radial compressive sensing is proposed, where one fixed transmitter antenna and a linear array of receiving antennas are used. The main contributions of this paper are (a) reducing the scanning time, (b) improving the output quality, and (c) designing an inexpensive setup. These improvements are the result of the underlying proposed simpler scanning structure and faster reconstruction process.
NASA Astrophysics Data System (ADS)
Almqvist, B.; Misra, S.; Biedermann, A. R.; Mainprice, D.
2013-12-01
We studied the magnetic and elastic wave speed anisotropy of a synthetically prepared quartz-mica schist, prior to, during and after experimental melting. The synthetic rock was manufactured from a mixture of powders with equal volumes of quartz and muscovite. The powders were initially compacted with 200 MPa uniaxial stress at room temperature and sealed in a stainless steel canister. Subsequently the sealed canister was isostatically pressed at 180 MPa and 580 °C for 24 hours. This produced a solid medium with ~25 % porosity. Mica developed a preferred grain-shape alignment due to the initial compaction with differential load, where mica flakes tend to orient perpendicular to the applied stress and hence define a synthetic foliation plane. In the last stage we used a Paterson gas-medium apparatus, to pressurize and heat the specimens up to 300 MPa and 750 °C for a six hour duration. This stage initially compacted the rock, followed by generation of melt, and finally crystallization of new minerals from the melt. Elastic wave speed measurements were performed in situ at pressure and temperature, with a transducer assembly mounted next to the sample. Magnetic measurements were performed before and after the partial melt experiments. Anisotropy was measured in low- and high-field, using a susceptibility bridge and torsion magnetometer, respectively. Additionally we performed measurements of hysteresis, isothermal remanent magnetization (IRM) and susceptibility as a function of temperature, to investigate the magnetic properties of the rock. The elastic wave speed, before the melting-stage of the experiment, exhibits a distinct anisotropy with velocities parallel to the foliation being about 15 % higher than normal to the foliation plane. Measurements of the magnetic anisotropy in the bulk sample show that anisotropy is originating from the preferred orientation of muscovite, with a prominent flattening fabric. In contrast, specimens that underwent partial melting
Hyde, Milo W; Basu, Santasri; Spencer, Mark F; Cusumano, Salvatore J; Fiorino, Steven T
2013-03-25
The scattering of a partially-coherent wave from a statistically rough material surface is investigated via derivation of the scattered field cross-spectral density function. Two forms of the cross-spectral density are derived using the physical optics approximation. The first is applicable to smooth-to-moderately rough surfaces and is a complicated expression of source and surface parameters. Physical insight is gleaned from its analytical form and presented in this work. The second form of the cross-spectral density function is applicable to very rough surfaces and is remarkably physical. Its form is discussed at length and closed-form expressions are derived for the angular spectral degree of coherence and spectral density radii. Furthermore, it is found that, under certain circumstances, the cross-spectral density function maintains a Gaussian Schell-model form. This is consistent with published results applicable only in the paraxial regime. Lastly, the closed-form cross-spectral density functions derived here are rigorously validated with scatterometer measurements and full-wave electromagnetic and physical optics simulations. Good agreement is noted between the analytical predictions and the measured and simulated results.
NASA Astrophysics Data System (ADS)
Caldwell, Warren B.; Klemperer, Simon L.; Rai, Shyam S.; Lawrence, Jesse F.
2009-11-01
Seismic shear-wave velocities are sensitive to the partial melts that should be present in the Himalayan orogen if low-viscosity channel flow is active at the present day. We analyzed regional earthquakes in the western Himalaya and Tibet recorded on 16 broadband seismometers deployed across the NW Indian Himalaya, from the Indian platform to the Karakoram Range. We used a multiple filter technique to calculate the group velocity dispersion of fundamental-mode Rayleigh waves, and then inverted the dispersion records to obtain separate one-dimensional shear-wave velocity models for five geologic provinces: the Tibetan plateau, Ladakh arc complex, Indus Tsangpo suture zone, Tethyan Himalaya, and Himalayan thrust belt. Our velocity models show a low-velocity layer (LVL) with 7-17% velocity reduction centered at ~ 30 km depth and apparently continuous from the Tethyan Himalaya to the Tibetan plateau. This LVL shows good spatial correspondence with observations of low resistivity from magnetotelluric studies along the same profile. Of the possible explanations for low velocity and low resistivity in the mid-crust, only the presence of melts or aqueous fluids (or both) satisfactorily explains both sets of observations. Elevated heat flow observed in the NW Himalaya implies that if aqueous fluids are present in the mid-crust, then the mid-crust is well above its solidus. Comparison of our results with laboratory measurements and theoretical models suggests 3-7% melt is present in a channel in the upper-middle crust of the NW Himalaya at the present day, and the physical conditions to enable active channel flow may be present.
Quantization of wave equations and hermitian structures in partial differential varieties.
Paneitz, S M; Segal, I E
1980-12-01
Sufficiently close to 0, the solution variety of a nonlinear relativistic wave equation-e.g., of the form squarevarphi + m(2)varphi + gvarphi(p) = 0-admits a canonical Lorentz-invariant hermitian structure, uniquely determined by the consideration that the action of the differential scattering transformation in each tangent space be unitary. Similar results apply to linear time-dependent equations or to equations in a curved asymptotically flat space-time. A close relation of the Riemannian structure to the determination of vacuum expectation values is developed and illustrated by an explicit determination of a perturbative 2-point function for the case of interaction arising from curvature. The theory underlying these developments is in part a generalization of that of M. G. Krein and collaborators concerning stability of differential equations in Hilbert space and in part a precise relation between the unitarization of given symplectic linear actions and their full probabilistic quantization. The unique causal structure in the infinite symplectic group is instrumental in these developments.
Quantization of wave equations and hermitian structures in partial differential varieties
Paneitz, S. M.; Segal, I. E.
1980-01-01
Sufficiently close to 0, the solution variety of a nonlinear relativistic wave equation—e.g., of the form □ϕ + m2ϕ + gϕp = 0—admits a canonical Lorentz-invariant hermitian structure, uniquely determined by the consideration that the action of the differential scattering transformation in each tangent space be unitary. Similar results apply to linear time-dependent equations or to equations in a curved asymptotically flat space-time. A close relation of the Riemannian structure to the determination of vacuum expectation values is developed and illustrated by an explicit determination of a perturbative 2-point function for the case of interaction arising from curvature. The theory underlying these developments is in part a generalization of that of M. G. Krein and collaborators concerning stability of differential equations in Hilbert space and in part a precise relation between the unitarization of given symplectic linear actions and their full probabilistic quantization. The unique causal structure in the infinite symplectic group is instrumental in these developments. PMID:16592923
NASA Technical Reports Server (NTRS)
Bean, T. A.; Bowhill, S. A.
1973-01-01
Partial-reflection data collected for the eclipse of July 10, 1972 as well as for July 9 and 11, 1972, are analyzed to determine eclipse effects on D-region electron densities. The partial-reflection experiment was set up to collect data using an on-line PDP-15 computer and DECtape storage. The electron-density profiles show good agreement with results from other eclipses. The partial-reflection programs were changed after the eclipse data collection to improve the operation of the partial-reflection system. These changes were mainly due to expanded computer hardware and have simplified the operations of the system considerably.
Das, J.N.; Paul, S.; Chakrabarti, K.
2004-04-01
Here we report a set of converged cross-section results for double photoionization of helium atoms obtained in the hyperspherical partial wave theory for equal energy sharing kinematics at 6 eV energy above threshold. The calculated cross section results are generally in excellent agreement with the absolute measured results of Doerner et al. [Phys. Rev. 57, 1074 (1998)].
NASA Astrophysics Data System (ADS)
Hetmaniuk, Ulrich Ladislas
Fast solvers are often designed for problems posed on simple domains. Unfortunately, engineering applications deal with arbitrary domains. To allow the use of fast solvers, fictitious domain methods have been developed. They usually define an auxiliary problem on a rectangle or a parallelepiped. In aerospace and military applications, many scatterers are composed of one major axisymmetric component and a few features. Therefore, the aim of this thesis is to define, for the scattering of acoustic waves, fictitious domain methods which exploit such local axisymmetry. The original exterior problem is first approximated by introducing an absorbing boundary condition on an artificial boundary. A family of absorbing conditions is reviewed. For some simple scatterers, numerical experiments on the position of the artificial boundary reveal that the error induced by the absorbing condition is bounded, as the wave number increases, when the artificial boundary is fixed. Then, for a class of partially axisymmetric scatterers, the truncated computational domain is embedded into an axisymmetric domain. Helmholtz problems are formulated inside this axisymmetric domain and inside each feature. Lagrange multipliers are introduced at the interfaces between the features and the axisymmetric domain to enforce a set of carefully constructed constraints. This formulation is analyzed at the continuous level and is shown to be equivalent to the original one. For the Helmholtz equation defined over the axisymmetric domain, the solution is approximated by truncated Fourier series and finite elements. Properties of this discretization method for the Helmholtz equation are also analyzed on a two-dimensional model problem. Numerical experiments are performed to illustrate the analytical results. For the auxiliary problem inside each feature, classical finite elements are used to approximate the solution. The constraints are enforced pointwise. The resulting algebraic system is solved either
NASA Astrophysics Data System (ADS)
Tokgöz, Çaǧatay; Dardona, Sameh
2016-09-01
Electrical failures in avionics systems may result from connector faults. If fault precursors are not detected in advance, they may lead to hard failures such as open and short circuits that could ultimately result in fire or loss of flight critical systems. Therefore, It is crucial to detect, locate, and characterize fault precursors for timely preventive maintenance and mitigation before hard failures occur. In this paper, a physics-based connector model consisting of multiple coaxial line sections with different characteristic impedances and lengths is proposed. Method of Moments (MoM) analyses were performed using commercial electromagnetic simulation software, FEKO, for transverse electric and magnetic (TEM) wave propagation through a connector. The physical parameters of the connector were optimized to match the measured S parameters for multiple insertion depths. The proposed models represent the connector for multiple insertion depths by varying only two length parameters at a time while other parameters are fixed. Insertion depth-dependent resonant frequency shifts observed during measurement are also captured by the model over the full range of fully inserted to barely touching contacts. Hence, the models provide accurate representations of the connector and properly detect precursors to partial insertion faults.
NASA Astrophysics Data System (ADS)
Kuruoǧlu, Zeki C.
2016-11-01
Direct numerical solution of the coordinate-space integral-equation version of the two-particle Lippmann-Schwinger (LS) equation is considered without invoking the traditional partial-wave decomposition. The singular kernel of the three-dimensional LS equation in coordinate space is regularized by a subtraction technique. The resulting nonsingular integral equation is then solved via the Nystrom method employing a direct-product quadrature rule for three variables. To reduce the computational burden of discretizing three variables, advantage is taken of the fact that, for central potentials, the azimuthal angle can be integrated out, leaving a two-variable reduced integral equation. A regularization method for the kernel of the two-variable integral equation is derived from the treatment of the singularity in the three-dimensional equation. A quadrature rule constructed as the direct product of single-variable quadrature rules for radial distance and polar angle is used to discretize the two-variable integral equation. These two- and three-variable methods are tested on the Hartree potential. The results show that the Nystrom method for the coordinate-space LS equation compares favorably in terms of its ease of implementation and effectiveness with the Nystrom method for the momentum-space version of the LS equation.
Partial wave analysis of the reaction {gamma}p{yields}p{omega} and the search for nucleon resonances
Williams, M.; Applegate, D.; Bellis, M.; Meyer, C. A.; Dey, B; Dickson, R.; Krahn, Z.; McCracken, M. E.; Moriya, K.; Schumacher, R. A.; Adhikari, K. P.; Careccia, S. L.; Dodge, G. E.; Guler, N.; Klein, A.; Mayer, M.; Nepali, C. S.; Niroula, M. R.; Seraydaryan, H.; Tkachenko, S.
2009-12-15
An event-based partial wave analysis (PWA) of the reaction {gamma}p{yields}p{omega} has been performed on a high-statistics dataset obtained using the CLAS at Jefferson Lab for center-of-mass energies from threshold up to 2.4 GeV. This analysis benefits from access to the world's first high-precision spin-density matrix element measurements, available to the event-based PWA through the decay distribution of {omega}{yields}{pi}{sup +}{pi}{sup -}{pi}{sup 0}. The data confirm the dominance of the t-channel {pi}{sup 0} exchange amplitude in the forward direction. The dominant resonance contributions are consistent with the previously identified states F{sub 15}(1680) and D{sub 13}(1700) near threshold, as well as the G{sub 17}(2190) at higher energies. Suggestive evidence for the presence of a J{sup P}=5/2{sup +} state around 2 GeV, a ''missing'' state, has also been found. Evidence for other states is inconclusive.
Partial wave analysis of the reaction γp→pω and the search for nucleon resonances
Williams, M.; Applegate, D.; Bellis, M.; ...
2009-12-30
We performed an event-based partial wave analysis (PWA) of the reaction γ p -> p ω on a high-statistics dataset obtained using the CLAS at Jefferson Lab for center-of-mass energies from threshold up to 2.4 GeV. This analysis benefits from access to the world's first high precision spin density matrix element measurements, available to the event-based PWA through the decay distribution of omega-> π+ π - π0. The data confirm the dominance of the t-channel π0 exchange amplitude in the forward direction. The dominant resonance contributions are consistent with the previously identified states F[15](1680) and D[13](1700) near threshold, as wellmore » as the G[17](2190) at higher energies. Suggestive evidence for the presence of a J(P)=5/2+ state around 2 GeV, a "missing" state, has also been found. Evidence for other states is inconclusive.« less
Dubrovsky, V. G.; Topovsky, A. V.
2013-03-15
New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.
Foust, F. R.; Bell, T. F.; Spasojevic, M.; Inan, U. S.
2011-06-15
We present results showing the measured Landau damping rate using a high-order discontinuous Galerkin particle-in-cell (DG-PIC) [G. B. Jacobs and J. S. Hesthaven, J. Comput. Phys. 214, 96 (2006)] method. We show that typical damping rates measured in particle-in-cell (PIC) simulations can differ significantly from the linearized Landau damping coefficient and propose a simple numerical method to solve the plasma dispersion function exactly for moderate to high damping rates. Simulation results show a high degree of agreement between the high-order PIC results and this calculated theoretical damping rate.
Menouar, Salah; Maamache, Mustapha; Choi, Jeong Ryeol
2010-08-15
The quantum states of time-dependent coupled oscillator model for charged particles subjected to variable magnetic field are investigated using the invariant operator methods. To do this, we have taken advantage of an alternative method, so-called unitary transformation approach, available in the framework of quantum mechanics, as well as a generalized canonical transformation method in the classical regime. The transformed quantum Hamiltonian is obtained using suitable unitary operators and is represented in terms of two independent harmonic oscillators which have the same frequencies as that of the classically transformed one. Starting from the wave functions in the transformed system, we have derived the full wave functions in the original system with the help of the unitary operators. One can easily take a complete description of how the charged particle behaves under the given Hamiltonian by taking advantage of these analytical wave functions.
Esfandyari-Kalejahi, A.; Ebrahimi, V.
2014-03-15
We have derived generalized dispersion relations for longitudinal waves in collisionless thermal plasma using linear Vlasov-Poisson kinetic model and nonextensive distributions for electrons. The Maxwellian limit of the dispersion relations, where the q-nonextensive parameter tends to one, is calculated. The generalized dispersion relations are reduced to polynomials for some specific values of q. The well-known modes of oscillations such as the Langmuir and electron acoustic waves have been obtained by solving the dispersion relations. Some new modes of oscillation are also found. Finally, the dependence of the oscillation modes and damps on q is discussed.
NASA Astrophysics Data System (ADS)
Bulanov, S. S.; Esirkepov, T. Zh; Kando, M.; Koga, J. K.; Bulanov, S. V.
2013-02-01
When the effects of radiation reaction dominate the interaction of electrons with intense laser pulses, the electron dynamics changes qualitatively. The adequate theoretical description of this regime becomes crucially important with the use of the radiation friction force either in the Lorentz-Abraham-Dirac form, which possess unphysical runaway solutions, or in the Landau-Lifshitz form, which is a perturbation valid for relatively low electromagnetic wave amplitude. The goal of the present paper is to find the limits of the Landau-Lifshitz radiation force applicability in terms of the electromagnetic wave amplitude and frequency.
New Travelling Solitary Wave and Periodic Solutions of the Generalized Kawahara Equation
Chen Huaitang; Yin Huicheng
2007-09-06
A simple elliptic equation method is used for constructing exact trevelling wave solutions of nonlinear partial differential equations(PDEs) in a unified way. With the aid of Maple, more new travelling solitary wave and periodic solutions are obtained for the generalized Kawahara equation.
NASA Astrophysics Data System (ADS)
Laundy, David; Alcock, Simon G.; Alianelli, Lucia; Sutter, John P.; Sawhney, Kawal J. S.; Chubar, Oleg
2014-09-01
A full wave propagation of X-rays from source to sample at a storage ring beamline requires simulation of the electron beam source and optical elements in the beamline. The finite emittance source causes the appearance of partial coherence in the wave field. Consequently, the wavefront cannot be treated exactly with fully coherent wave propagation or fully incoherent ray tracing. We have used the wavefront code Synchrotron Radiation Workshop (SRW) to perform partially coherent wavefront propagation using a parallel computing cluster at the Diamond Light Source. Measured mirror profiles have been used to correct the wavefront for surface errors.
NASA Astrophysics Data System (ADS)
Chrysos, Michael
2016-03-01
Relying on a simple analytic two-atom model in which the anisotropy of the interaction dipole polarizability obeys an inverse power law as a function of separation, we offer mathematical and numerical evidence that, in a monoatomic gas, the free-free Raman spectrum for a collisional pair of two different isotopes, a-a', may vastly differ from that for a-a. This result is obtained even if a and a' are assumed to have the same mass and zero nuclear spin and even if a-a and a-a' are subject to the same interaction polarizability and potential. The mechanism responsible for this effect is inherent in the parity of the partial-wave rotational quantum number J: given that the contribution of each partial wave to the Raman cross section is controlled by a polarizability-transition matrix-element and that each of those matrix-elements has a radial component with a magnitude slightly smaller than that of the preceding partial wave, a deficit which disfavors the odd-numbered waves is accumulated upon summing over J. In the far high-frequency wing, this deficit tends to generate spectral intensities for a-a' about half as great as the a-a ones, a tendency which becomes all the more effective as temperature is decreased. We show for instance that, for the spectral branch ΔJ = 2, the fractional difference between the free-free differential cross sections for a-a and a-a' is /1 2 /( 1 - x2 ) 3 1 + 3 x 4 , with x = √{ E / E ' } (E (E') being the initial (final) state energy of the pair and E' - E = hcν (ν > 0)). Remarkably, this quantity is zero at ν ≈ 0 but goes to /1 2 for ν ≫ 0. For ΔJ = 0, analogous conclusions may be drawn from the expression ( 1 + /ln ( 1+x/1-x ) 2 arctan x ) - 1 .
NASA Astrophysics Data System (ADS)
Yao, Ruo-Xia; Wang, Wei; Chen, Ting-Hua
2014-11-01
Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.
Singleton, Jr., Robert; Israel, Daniel M.; Doebling, Scott William; Woods, Charles Nathan; Kaul, Ann; Walter, Jr., John William; Rogers, Michael Lloyd
2016-05-09
For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.
Lin, D.-H.
2004-05-01
Partial wave theory of a three dimensional scattering problem for an arbitrary short range potential and a nonlocal Aharonov-Bohm magnetic flux is established. The scattering process of a 'hard sphere'-like potential and the magnetic flux is examined. An anomalous total cross section is revealed at the specific quantized magnetic flux at low energy which helps explain the composite fermion and boson model in the fractional quantum Hall effect. Since the nonlocal quantum interference of magnetic flux on the charged particles is universal, the nonlocal effect is expected to appear in a quite general potential system and will be useful in understanding some other phenomena in mesoscopic physics.
Exact solutions and singularities in string theory
Horowitz, G.T. ); Tseytlin, A.A. )
1994-10-15
We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail.
Exact propagators for some degenerate hyperbolic operators
NASA Astrophysics Data System (ADS)
Beals, Richard; Kannai, Yakar
2006-10-01
Exact propagators are obtained for the degenerate second order hyperbolic operators ∂2 t - t 2 l Δ x , l=1,2,..., by analytic continuation from the degenerate elliptic operators ∂2 t + t 2 l Δ x . The partial Fourier transforms are also obtained in closed form, leading to integral transform formulas for certain combinations of Bessel functions and modified Bessel functions.
Nakashima, Hiroyuki; Nakatsuji, Hiroshi
2013-07-28
We propose here fast antisymmetrization procedures for the partially correlated wave functions that appear in the free complement-local Schrödinger equation (FC-LSE) method. Pre-analysis of the correlation diagram, referred to as dot analysis, combined with the determinant update technique based on the Laplace expansion, drastically reduces the orders of the antisymmetrization computations. When the complement functions include only up to single-correlated terms, the order of computations is O(N{sup 3}), which is the same as the non-correlated case. Similar acceleration is obtained for general correlated functions as a result of dot analysis. This algorithm has been successfully used in our laboratory in actual FC-LSE calculations for accurately solving the many-electron Schrödinger equations of atoms and molecules. The proposed method is general and applicable to the sampling-type methodology of other partially correlated wave functions like those in the quantum Monte Carlo and modern Hylleraas-type methods.
Nakashima, Hiroyuki; Nakatsuji, Hiroshi
2013-07-28
We propose here fast antisymmetrization procedures for the partially correlated wave functions that appear in the free complement-local Schrödinger equation (FC-LSE) method. Pre-analysis of the correlation diagram, referred to as dot analysis, combined with the determinant update technique based on the Laplace expansion, drastically reduces the orders of the antisymmetrization computations. When the complement functions include only up to single-correlated terms, the order of computations is O(N(3)), which is the same as the non-correlated case. Similar acceleration is obtained for general correlated functions as a result of dot analysis. This algorithm has been successfully used in our laboratory in actual FC-LSE calculations for accurately solving the many-electron Schrödinger equations of atoms and molecules. The proposed method is general and applicable to the sampling-type methodology of other partially correlated wave functions like those in the quantum Monte Carlo and modern Hylleraas-type methods.
NASA Technical Reports Server (NTRS)
Vranish, John M. (Inventor)
2010-01-01
A partial gear bearing including an upper half, comprising peak partial teeth, and a lower, or bottom, half, comprising valley partial teeth. The upper half also has an integrated roller section between each of the peak partial teeth with a radius equal to the gear pitch radius of the radially outwardly extending peak partial teeth. Conversely, the lower half has an integrated roller section between each of the valley half teeth with a radius also equal to the gear pitch radius of the peak partial teeth. The valley partial teeth extend radially inwardly from its roller section. The peak and valley partial teeth are exactly out of phase with each other, as are the roller sections of the upper and lower halves. Essentially, the end roller bearing of the typical gear bearing has been integrated into the normal gear tooth pattern.
Exact Damping for Relativistic Plasma Waves
NASA Astrophysics Data System (ADS)
Swanson, D. G.
2000-10-01
The damping coefficient for a relativistic plasma may be reduced to a single integral with no approximations through use of the Newberger sum rules when k_z=0. Expanding the integral in a series, the leading term agrees with the leading term of the weak relativistic function F_7/2(z), but the remaining terms are not alike. The single expansion parameter is proportional to λ z, indicating that the result may NOT be accurately expressed as a series involving products of Bessel functions of argument λ times functions F_q(z). Expressions for the imaginary parts of all dielectric tensor elements will be presented. The real parts of the tensor elements are not as simple, but because the elements are analytic, they must likewise be modified.
1985-09-23
6420 5697 26898 0 0 10:18:30 1.06 4420 18019 11092 0 0 10:20:07 1.06 3420 14879 1115 0 0 10:21:4 1.06 2700 5674 0 0 0 10:23:21 1.08 2300 5739 1264 0 0...for Detection and Measurement of Discharge (Corona) Pulses in Evaluation of Insulation Systems," ASTM D1868-73. 5. R. J. Densley, "Partial Discharge...under Direct-Voltage Conditions," Ch. 11 in Engineering Dielectrics, Vol. 1: Corona Measurement and Interpretation, ASTM 669, eds. R. Bartnikas and E. J
On exactly conservative integrators
Bowman, J.C.; Shadwick, B.A.; Morrison, P.J.
1997-06-01
Traditional explicit numerical discretizations of conservative systems generically predict artificial secular drifts of nonlinear invariants. These algorithms are based on polynomial functions of the time step. The authors discuss a general approach for developing explicit algorithms that conserve such invariants exactly. They illustrate the method by applying it to the truncated two-dimensional Euler equations.
Exact integrability in quantum field theory
Thacker, H.B.
1980-08-01
The treatment of exactly integrable systems in various branches of two-dimensional classical and quantum physics has recently been placed in a unified framework by the development of the quantum inverse method. This method consolidates a broad range of developments in classical nonlinear wave (soliton) physics, statistical mechanics, and quantum field theory. The essential technique for analyzing exactly integrable quantum systems was invested by Bethe in 1931. The quantum-mechanical extension of the inverse scattering method and its relationship to the methods associated with Bethe's ansatz are examined here. (RWR)
Bliokh, K Yu; Bliokh, Yu P
2007-06-01
We present a solution to the problem of partial reflection and refraction of a polarized paraxial Gaussian beam at the interface between two transparent media. The Fedorov-Imbert transverse shifts of the centers of gravity of the reflected and refracted beams are calculated. Our results differ in the general case from those derived previously by other authors. In particular, they obey general conservation law for the beams' total angular momentum but do not obey one-particle conservation laws for individual photons, which have been proposed by [Onoda Phys. Rev. Lett. 93, 083901 (2004)]. We ascertain that these circumstances relate to the artificial model accepted in the literature for the polarized beam; this model does not fit to real beams. The present paper resolves the recent controversy and confirms the results of our previous paper [Bliokh Phys. Rev. Lett. 96, 073903 (2006)]. In addition, a diffraction effect of angular transverse shifts of the reflected and refracted beams is described.
NASA Astrophysics Data System (ADS)
Murthy, Ganpathy
2000-01-01
It is well known that the ν = 2/5 state is unpolarized at zero Zeeman energy, while it is fully polarized at large Zeeman energies. A novel state with a charge/spin density wave order for composite fermions is proposed to exist at intermediate values of the Zeeman coupling for ν = 2/5. This state has half the maximum possible polarization, and can be extended to other incompressible fractions. A Hartree-Fock calculation based on the new approach for all fractional quantum Hall states developed by R. Shankar and the author is used to demonstrate the stability of this state to single-particle excitations and to compute gaps. A very recent experiment shows direct evidence for this state.
Murthy
2000-01-10
It is well known that the nu = 2/5 state is unpolarized at zero Zeeman energy, while it is fully polarized at large Zeeman energies. A novel state with a charge/spin density wave order for composite fermions is proposed to exist at intermediate values of the Zeeman coupling for nu = 2/5. This state has half the maximum possible polarization, and can be extended to other incompressible fractions. A Hartree-Fock calculation based on the new approach for all fractional quantum Hall states developed by R. Shankar and the author is used to demonstrate the stability of this state to single-particle excitations and to compute gaps. A very recent experiment shows direct evidence for this state.
Exact Relativistic `Antigravity' Propulsion
NASA Astrophysics Data System (ADS)
Felber, Franklin S.
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Bliokh, K. Yu.; Bliokh, Yu. P.
2007-06-15
We present a solution to the problem of partial reflection and refraction of a polarized paraxial Gaussian beam at the interface between two transparent media. The Fedorov-Imbert transverse shifts of the centers of gravity of the reflected and refracted beams are calculated. Our results differ in the general case from those derived previously by other authors. In particular, they obey general conservation law for the beams' total angular momentum but do not obey one-particle conservation laws for individual photons, which have been proposed by [Onoda et al. Phys. Rev. Lett. 93, 083901 (2004)]. We ascertain that these circumstances relate to the artificial model accepted in the literature for the polarized beam; this model does not fit to real beams. The present paper resolves the recent controversy and confirms the results of our previous paper [Bliokh et al. Phys. Rev. Lett. 96, 073903 (2006)]. In addition, a diffraction effect of angular transverse shifts of the reflected and refracted beams is described.
Linearly exact parallel closures for slab geometry
NASA Astrophysics Data System (ADS)
Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun
2013-08-01
Parallel closures are obtained by solving a linearized kinetic equation with a model collision operator using the Fourier transform method. The closures expressed in wave number space are exact for time-dependent linear problems to within the limits of the model collision operator. In the adiabatic, collisionless limit, an inverse Fourier transform is performed to obtain integral (nonlocal) parallel closures in real space; parallel heat flow and viscosity closures for density, temperature, and flow velocity equations replace Braginskii's parallel closure relations, and parallel flow velocity and heat flow closures for density and temperature equations replace Spitzer's parallel transport relations. It is verified that the closures reproduce the exact linear response function of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for Landau damping given a temperature gradient. In contrast to their approximate closures where the vanishing viscosity coefficient numerically gives an exact response, our closures relate the heat flow and nonvanishing viscosity to temperature and flow velocity (gradients).
Catterall, Simon; Kaplan, David B.; Unsal, Mithat
2009-03-31
We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.
NASA Astrophysics Data System (ADS)
Yasuda, Seiji; Miura, Hitoshi; Nakamoto, Taishi
2009-11-01
We carried out three-dimensional hydrodynamics simulations of the disruption of a partially-molten dust particle exposed to high-speed gas flow to examine the compound chondrule formation due to mutual collisions between the fragments (fragment-collision model; [Miura, H., Yasuda, S., Nakamoto, T., 2008a. Icarus194, 811-821]). In the shock-wave heating model, which is one of the most plausible models for chondrule formation, the gas friction heats and melts the surface of the cm-sized dust particle (parent particle) and then the strong gas ram pressure causes the disruption of the molten surface layer. The hydrodynamics simulation shows details of the disruptive motion of the molten surface, production of many fragments and their trajectories parting from the parent particle, and mutual collisions among them. In our simulation, we identified 32 isolated fragments extracted from the parent particle. The size distribution of the fragments was similar to that obtained from the aerodynamic experiment in which a liquid layer was attached to a solid core and it was exposed to a gas flow. We detected 12 collisions between the fragments, which may result in the compound chondrule formation. We also analyzed the paths of all the fragments in detail and found the importance of the shadow effect in which a fragment extracted later blocks the gas flow toward a fragment extracted earlier. We examined the collision velocity and impact parameter of each collision and found that 11 collisions should result in coalescence. It means that the ratio of coalescent bodies to single bodies formed in this disruption of a parent particle is R=11/(32-11)=0.52. We concluded that compound chondrule formation can occur just after the disruption of a cm-sized molten dust particle in shock-wave heating.
ERIC Educational Resources Information Center
Huang, Yi Ting; Spelke, Elizabeth; Snedeker, Jesse
2013-01-01
Number words are generally used to refer to the exact cardinal value of a set, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics ("two" means exactly two), many linguistic accounts propose that numbers have lower-bounded semantics (at least two), and…
Exact approaches for scaffolding
2015-01-01
This paper presents new structural and algorithmic results around the scaffolding problem, which occurs prominently in next generation sequencing. The problem can be formalized as an optimization problem on a special graph, the "scaffold graph". We prove that the problem is polynomial if this graph is a tree by providing a dynamic programming algorithm for this case. This algorithm serves as a basis to deduce an exact algorithm for general graphs using a tree decomposition of the input. We explore other structural parameters, proving a linear-size problem kernel with respect to the size of a feedback-edge set on a restricted version of Scaffolding. Finally, we examine some parameters of scaffold graphs, which are based on real-world genomes, revealing that the feedback edge set is significantly smaller than the input size. PMID:26451725
Partial wave analysis of the reaction p (3.5 GeV) + p → pK+ Λ to search for the " ppK-" bound state
NASA Astrophysics Data System (ADS)
Agakishiev, G.; Arnold, O.; Belver, D.; Belyaev, A.; Berger-Chen, J. C.; Blanco, A.; Böhmer, M.; Boyard, J. L.; Cabanelas, P.; Chernenko, S.; Dybczak, A.; Epple, E.; Fabbietti, L.; Fateev, O.; Finocchiaro, P.; Fonte, P.; Friese, J.; Fröhlich, I.; Galatyuk, T.; Garzón, J. A.; Gernhäuser, R.; Göbel, K.; Golubeva, M.; González-Díaz, D.; Guber, F.; Gumberidze, M.; Heinz, T.; Hennino, T.; Holzmann, R.; Ierusalimov, A.; Iori, I.; Ivashkin, A.; Jurkovic, M.; Kämpfer, B.; Karavicheva, T.; Koenig, I.; Koenig, W.; Kolb, B. W.; Kornakov, G.; Kotte, R.; Krása, A.; Krizek, F.; Krücken, R.; Kuc, H.; Kühn, W.; Kugler, A.; Kunz, T.; Kurepin, A.; Ladygin, V.; Lalik, R.; Lapidus, K.; Lebedev, A.; Lopes, L.; Lorenz, M.; Maier, L.; Mangiarotti, A.; Markert, J.; Metag, V.; Michel, J.; Müntz, C.; Münzer, R.; Naumann, L.; Pachmayer, Y. C.; Palka, M.; Parpottas, Y.; Pechenov, V.; Pechenova, O.; Pietraszko, J.; Przygoda, W.; Ramstein, B.; Reshetin, A.; Rustamov, A.; Sadovsky, A.; Salabura, P.; Schmah, A.; Schwab, E.; Siebenson, J.; Sobolev, Yu. G.; Spataro, S.; Spruck, B.; Ströbele, H.; Stroth, J.; Sturm, C.; Tarantola, A.; Teilab, K.; Tlusty, P.; Traxler, M.; Tsertos, H.; Vasiliev, T.; Wagner, V.; Weber, M.; Wendisch, C.; Wüstenfeld, J.; Yurevich, S.; Zanevsky, Y.; Sarantsev, A. V.
2015-03-01
Employing the Bonn-Gatchina partial wave analysis framework (PWA), we have analyzed HADES data of the reaction p (3.5 GeV) + p → pK+ Λ. This reaction might contain information about the kaonic cluster " ppK-" (with quantum numbers JP =0- and total isospin I = 1 / 2) via its decay into pΛ. Due to interference effects in our coherent description of the data, a hypothetical K ‾ NN (or, specifically " ppK-") cluster signal need not necessarily show up as a pronounced feature (e.g. a peak) in an invariant mass spectrum like pΛ. Our PWA analysis includes a variety of resonant and non-resonant intermediate states and delivers a good description of our data (various angular distributions and two-hadron invariant mass spectra) without a contribution of a K ‾ NN cluster. At a confidence level of CLs = 95% such a cluster cannot contribute more than 2-12% to the total cross section with a pK+ Λ final state, which translates into a production cross-section between 0.7 μb and 4.2 μb, respectively. The range of the upper limit depends on the assumed cluster mass, width and production process.
Partial wave analysis of the reaction p(3.5 GeV) + p → pK+ Λ to search for the "ppK–" bound state
Agakishiev, G.; Arnold, O.; Belver, D.; ...
2015-01-26
Employing the Bonn–Gatchina partial wave analysis framework (PWA), we have analyzed HADES data of the reaction p(3.5GeV) + p → pK+Λ. This reaction might contain information about the kaonic cluster “ppK-” (with quantum numbers JP=0- and total isospin I =1/2) via its decay into pΛ. Due to interference effects in our coherent description of the data, a hypothetical K ¯NN (or, specifically “ppK-”) cluster signal need not necessarily show up as a pronounced feature (e.g. a peak) in an invariant mass spectrum like pΛ. Our PWA analysis includes a variety of resonant and non-resonant intermediate states and delivers a goodmore » description of our data (various angular distributions and two-hadron invariant mass spectra) without a contribution of a K ¯NN cluster. At a confidence level of CLs=95% such a cluster cannot contribute more than 2–12% to the total cross section with a pK+ Λ final state, which translates into a production cross-section between 0.7 μb and 4.2 μb, respectively. The range of the upper limit depends on the assumed cluster mass, width and production process.« less
Andreev, Pavel A; Iqbal, Z
2016-03-01
We consider the separate spin evolution of electrons and positrons in electron-positron and electron-positron-ion plasmas. We consider the oblique propagating longitudinal waves in these systems. Working in a regime of high-density n(0) ∼ 10(27) cm(-3) and high-magnetic-field B(0)=10(10) G, we report the presence of the spin-electron acoustic waves and their dispersion dependencies. In electron-positron plasmas, similarly to the electron-ion plasmas, we find one spin-electron acoustic wave (SEAW) at the propagation parallel or perpendicular to the external field and two spin-electron acoustic waves at the oblique propagation. At the parallel or perpendicular propagation of the longitudinal waves in electron-positron-ion plasmas, we find four branches: the Langmuir wave, the positron-acoustic wave, and a pair of waves having spin nature, they are the SEAW and the wave discovered in this paper, called the spin-electron-positron acoustic wave (SEPAW). At the oblique propagation we find eight longitudinal waves: the Langmuir wave, the Trivelpiece--Gould wave, a pair of positron-acoustic waves, a pair of SEAWs, and a pair of SEPAWs. Thus, for the first time, we report the existence of the second positron-acoustic wave existing at the oblique propagation and the existence of SEPAWs.
NASA Astrophysics Data System (ADS)
Fuster, Andrea; Pabst, Cornelia
2016-11-01
In this work we present Finsler gravitational waves. These are a Finslerian version of the well-known p p -waves, generalizing the very special relativity line element. Our Finsler p p -waves are an exact solution of Finslerian Einstein's equations in vacuum and describe gravitational waves propagating in an anisotropic background.
An ansatz for solving nonlinear partial differential equations in mathematical physics.
Akbar, M Ali; Ali, Norhashidah Hj Mohd
2016-01-01
In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.
New Exact Solution of Dirac-Coulomb Equation with Exact Boundary Condition
NASA Astrophysics Data System (ADS)
Chen, Ruida
2008-04-01
It usually writes the boundary condition of the wave equation in the Coulomb field as a rough form without considering the size of the atomic nucleus. The rough expression brings on that the solutions of the Klein-Gordon equation and the Dirac equation with the Coulomb potential are divergent at the origin of the coordinates, also the virtual energies, when the nuclear charges number Z>137, meaning the original solutions do not satisfy the conditions for determining solution. Any divergences of the wave functions also imply that the probability density of the meson or the electron would rapidly increase when they are closing to the atomic nucleus. What it predicts is not a truth that the atom in ground state would rapidly collapse to the neutron-like. We consider that the atomic nucleus has definite radius and write the exact boundary condition for the hydrogen and hydrogen-like atom, then newly solve the radial Dirac-Coulomb equation and obtain a new exact solution without any mathematical and physical difficulties. Unexpectedly, the K value constructed by Dirac is naturally written in the barrier width or the equivalent radius of the atomic nucleus in solving the Dirac equation with the exact boundary condition, and it is independent of the quantum energy. Without any divergent wave function and the virtual energies, we obtain a new formula of the energy levels that is different from the Dirac formula of the energy levels in the Coulomb field.
NASA Astrophysics Data System (ADS)
Saha Ray, S.
2016-09-01
In this article, the Jacobi elliptic function method viz. the mixed dn-sn method has been presented for finding the travelling wave solutions of the Davey-Stewartson equations. As a result, some solitary wave solutions and doubly periodic solutions are obtained in terms of Jacobi elliptic functions. Moreover, solitary wave solutions are obtained as simple limits of doubly periodic functions. These solutions can be useful to explain some physical phenomena, viz. evolution of a three-dimensional wave packet on water of finite depth. The proposed Jacobi elliptic function method is efficient, powerful and can be used in order to establish newer exact solutions for other kinds of nonlinear fractional partial differential equations arising in mathematical physics.
Exact solutions for Weyl fermions with gravity
NASA Astrophysics Data System (ADS)
Cianci, Roberto; Fabbri, Luca; Vignolo, Stefano
2015-10-01
We consider the single-handed spinor field in interaction with its own gravitational field described by the set of field equations given by the Weyl field equations written in terms of derivatives that are covariant with respect to the gravitational connection plus Einstein field equations soured with the energy tensor of the spinor: for the Weyl spinor and the ensuing spacetime of Weyl-Lewis-Papapetrou structure, we find all exact solutions. The obtained solution for the metric tensor is that of a PP-wave spacetime, while the spinor field is a flag-dipole.
Supersymmetric Ito equation: Bosonization and exact solutions
Ren Bo; Yu Jun; Lin Ji
2013-04-15
Based on the bosonization approach, the N=1 supersymmetric Ito (sIto) system is changed to a system of coupled bosonic equations. The approach can effectively avoid difficulties caused by intractable fermionic fields which are anticommuting. By solving the coupled bosonic equations, the traveling wave solutions of the sIto system are obtained with the mapping and deformation method. Some novel types of exact solutions for the supersymmetric system are constructed with the solutions and symmetries of the usual Ito equation. In the meanwhile, the similarity reduction solutions of the model are also studied with the Lie point symmetry theory.
NASA Astrophysics Data System (ADS)
Cisterna, Adolfo; Hassaïne, Mokhtar; Oliva, Julio
2015-11-01
This paper is devoted to showing that the bosonic sector of R2 supergravity in four dimensions, constructed with the F term, admits a variety of exact and analytic solutions which include pp and anti-de Sitter (AdS) waves, asymptotically flat and AdS black holes and wormholes, as well as product spacetimes. The existence of static black holes and wormholes implies that a combination involving the Ricci scalar plus the norm of the field strength of the auxiliary two-form Bμ ν must be a constant. We focus on this sector of the theory, which has two subsectors depending on whether such a combination vanishes.
NASA Astrophysics Data System (ADS)
Endom, Joerg
2014-05-01
negligible any more. Locating for example the exact position of joints, rebars on site, getting correct calibration information or overlaying measurements of independent methods requires high accuracy positioning for all data. Different technologies of synchronizing and stabilizing are discussed in this presentation. Furthermore a scale problem for interdisciplinary work between the geotechnical engineer, the civil engineer, the surveyor and the geophysicist is presented. Manufacturers as well as users are addressed to work on a unified methodology that could be implemented in future. This presentation is a contribution to COST Action TU1208.
Huang, Yi Ting; Spelke, Elizabeth; Snedeker, Jesse
2014-01-01
Number words are generally used to refer to the exact cardinal value of a set, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics (two means EXACTLY TWO), many linguistic accounts propose that numbers have lower-bounded semantics (AT LEAST TWO), and that speakers restrict their reference through a pragmatic inference (scalar implicature). We address this debate through studies of children who are in the process of acquiring the meanings of numbers. Adults and 2- and 3-year-olds were tested in a novel paradigm that teases apart semantic and pragmatic aspects of interpretation (the covered box task). Our findings establish that when scalar implicatures are cancelled in the critical trials of this task, both adults and children consistently give exact interpretations for number words. These results, in concert with recent work on real-time processing, provide the first unambiguous evidence that number words have exact semantics. PMID:25285053
Partial differential equation-based localization of a monopole source from a circular array.
Ando, Shigeru; Nara, Takaaki; Levy, Tsukassa
2013-10-01
Wave source localization from a sensor array has long been the most active research topics in both theory and application. In this paper, an explicit and time-domain inversion method for the direction and distance of a monopole source from a circular array is proposed. The approach is based on a mathematical technique, the weighted integral method, for signal/source parameter estimation. It begins with an exact form of the source-constraint partial differential equation that describes the unilateral propagation of wide-band waves from a single source, and leads to exact algebraic equations that include circular Fourier coefficients (phase mode measurements) as their coefficients. From them, nearly closed-form, single-shot and multishot algorithms are obtained that is suitable for use with band-pass/differential filter banks. Numerical evaluation and several experimental results obtained using a 16-element circular microphone array are presented to verify the validity of the proposed method.
Exact Classical and Quantum Dynamics in Background Electromagnetic Fields
NASA Astrophysics Data System (ADS)
Heinzl, Tom; Ilderton, Anton
2017-03-01
Analytic results for (Q)ED processes in external fields are limited to a few special cases, such as plane waves. However, the strong focusing of intense laser fields implies a need to go beyond the plane wave model. By exploiting Poincaré symmetry and superintegrability we show how to construct, and solve without approximation, new models of laser-matter interactions. We illustrate the method with a model of a radially polarized (TM) laser beam, for which we exactly determine the classical orbits and quantum wave functions. Including in this way the effects of transverse field structure should improve predictions and analyses for experiments at intense laser facilities.
Exact Lyapunov dimension of the universal attractor for the complex Ginzburg-Landau equation
Doering, C.R.; Gibbon, J.D.; Holm, D.D.; Nicolaenko, B.
1987-12-28
We present an exact analytic computation of the Lyapunov dimension of the universal attractor of the complex Ginzburg-Landau partial differential equation for a finite range of its parameter values. We obtain upper bounds on the attractor's dimension when the parameters do not permit an exact evaluation by our methods. The exact Lyapunov dimension agrees with an estimate of the number of degrees of freedom based on a simple linear stability analysis and mode-counting argument.
Exact solution for a non-Markovian dissipative quantum dynamics.
Ferialdi, Luca; Bassi, Angelo
2012-04-27
We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.
NASA Astrophysics Data System (ADS)
Askari, E.; Daneshmand, F.; Amabili, M.
2011-10-01
Internal bodies (baffles) are used as damping devices to suppress the fluid sloshing motion in fluid-structure interaction systems. An analytical method is developed in the present article to investigate the effects of a rigid internal body on bulging and sloshing frequencies and modes of a cylindrical container partially filled with a fluid. The internal body is a thin-walled and open-ended cylindrical shell that is coaxially and partially submerged inside the container. The interaction between the fluid and the structure is taken into account to calculate the sloshing and bulging frequencies and modes of the coupled system using the Rayleigh quotient, Ritz expansion and Galerkin method. It is shown that the present formulation is an appropriate and new approach to tackle the problem with good accuracy. The effects of fluid level, number of nodal diameters, internal body radius and submergence ratio on the dynamic characteristics of the coupled system are also investigated.
NASA Astrophysics Data System (ADS)
Rudnick, Roberta L.; Jackson, Ian
1995-06-01
Ultrasonic compressional wave velocities measured at 1.0 GPa and room temperature are compared with calculated velocities (based on single-crystal data and modal mineralogy) for a suite of mafic granulite xenoliths from the Chudleigh volcanic province, north Queensland, Australia. The xenoliths have nearly constant major element compositions but widely variable modal mineralogy, reflecting recrystallization under variable pressure-temperature conditions at depth in the continental crust (20-45 km). They thus provide an excellent opportunity to investigate velocity variation with depth in a mafic lower crust. Measured P wave velocities, corrected for the decompression-induced breakdown of garnet, range from 6.9 to 7.6 km/sec and correlate with derivation depth. These velocities are 5-12% lower than the calculated velocities (7.5-8.0 km/sec), apparently as a result of grain boundary alteration as well as irreversible changes that occurred in the xenoliths during rapid decompression. Calculated P wave velocities are similar to those estimated by Furlong and Fountain (1986) and Sobolev and Babeyko (1989) for mafic granulites formed through basaltic underplating of the continental crust. Depending upon in situ temperature, P wave velocities in the deepest samples may be interpreted as crustal (e.g., 7.3-7.6 km/sec, if heat flow is high) or mantle (7.7-7.8 km/sec, in areas of low heat flow). The range of velocities in the xenolith suite is larger than predicted for a fully equilibrated underplated basaltic layer, highlighting the importance of kinetic effects in determining the ultimate velocity profile of magmatically underplated crust. Comparison of our results with seismic profiles illustrates that the lower crust rarely reaches such high velocities, suggesting quartz-bearing rocks (country rocks?) are present within magmatically underplated layers of the deep crust.
Exact models for isotropic matter
NASA Astrophysics Data System (ADS)
Thirukkanesh, S.; Maharaj, S. D.
2006-04-01
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.
Exact controllability of complex networks
Yuan, Zhengzhong; Zhao, Chen; Di, Zengru; Wang, Wen-Xu; Lai, Ying-Cheng
2013-01-01
Controlling complex networks is of paramount importance in science and engineering. Despite the recent development of structural controllability theory, we continue to lack a framework to control undirected complex networks, especially given link weights. Here we introduce an exact controllability paradigm based on the maximum multiplicity to identify the minimum set of driver nodes required to achieve full control of networks with arbitrary structures and link-weight distributions. The framework reproduces the structural controllability of directed networks characterized by structural matrices. We explore the controllability of a large number of real and model networks, finding that dense networks with identical weights are difficult to be controlled. An efficient and accurate tool is offered to assess the controllability of large sparse and dense networks. The exact controllability framework enables a comprehensive understanding of the impact of network properties on controllability, a fundamental problem towards our ultimate control of complex systems. PMID:24025746
What Exactly is Space Logistics?
2011-01-01
information on the space shuttle in the news and have inferred by now that resupply missions to the International Space Sta- tion, Hubble Space ... Telescope repair missions, and satellite deployment missions are space logistics—and you would be technically correct. The science of logistics as applied...What Exactly is Space Logistics? James C. Breidenbach Report Documentation Page Form ApprovedOMB No. 0704-0188 Public reporting burden for the
An exact solution for the oscillating two-stream instability
NASA Astrophysics Data System (ADS)
Kaup, D. J.
1980-07-01
In the present paper, an exact solution of the oscillating two-stream instability is obtained for the case where the initial pump profile has a constant phase. The solution points to a very rapid partial pump depletion when the scaled pump energy is approximately pi/2, 3pi/2, 5pi/2, etc., to filamentation of a square pump profile undergoing any such partial depletion, and to stability when the scaled pump energy is just above npi and instability when it is just below npi.
Layden, B.; Cairns, Iver H.; Robinson, P. A.; Percival, D. J.
2012-07-15
The quadratic longitudinal response function describes the second-order nonlinear response of a plasma to electrostatic wave fields. An explicit expression for this function in the weak-turbulence regime requires the evaluation of velocity-space integrals involving the velocity distribution function and various resonant denominators. Previous calculations of the quadratic longitudinal response function were performed by approximating the resonant denominators to facilitate the integration. Here, we evaluate these integrals exactly for a non-relativistic collisionless unmagnetized isotropic Maxwellian plasma in terms of generalized plasma dispersion functions, and correct certain aspects of expressions previously derived for these functions. We show that in the appropriate limits the exact expression reduces to the approximate form used for interactions between two fast waves and one slow wave, such as the electrostatic decay of Langmuir waves into Langmuir waves and ion sound waves, and the scattering of Langmuir waves off thermal ions.
Pressure induced breather overturning on deep water: Exact solution
NASA Astrophysics Data System (ADS)
Abrashkin, A. A.; Oshmarina, O. E.
2014-08-01
A vortical model of breather overturning on deep water is proposed. The action of wind is simulated by nonuniform pressure on the free surface. The fluid motion is described by an exact solution of 2D hydrodynamic equations for an inviscid fluid in Lagrangian variables. Fluid particles rotate in circles of different radii. Formation of contraflexure points on the breather profile is studied. The mechanism of wave breaking and the role of flow vorticity are discussed.
Exact Solutions of Relativistic Bound State Problem for Spinless Bosons
NASA Astrophysics Data System (ADS)
Aslanzadeh, M.; Rajabi, A. A.
2017-01-01
We investigated in detail the relativistic bound states of spin-zero bosons under the influence of Coulomb-plus-linear potentials with an arbitrary combination of scalar and vector couplings. Through an exact analytical solution of three-dimensional Klein-Gordon equation, closed form expressions were derived for energy eigenvalues and wave functions and some correlations between potential parameters were found. We also presented the relativistic description of bound states and nonrelativistic limit of the problem in some special cases.
Gilbert, Kenneth E; Di, Xiao
2007-05-01
A method for exactly representing a point source starting field in a Fourier parabolic equation calculation is presented. The formulation is based on an exact, analytic expression for the field in vertical wave number space (k space). The field in vertical coordinate space (z space) is obtained via a Fourier transform of the k-space field. Thus, one can directly control the Fourier components of the starting field, so that nonpropagating components are excluded. The relation of the exact starting field to the standard Gaussian starting field is demonstrated analytically. Examples of the numerical implementation of the exact starting field are given.
Akbar, M Ali; Ali, Norhashidah Hj Mohd; Mohyud-Din, Syed Tauseef
2013-01-01
The (G'/G)-expansion method is one of the most direct and effective method for obtaining exact solutions of nonlinear partial differential equations (PDEs). In the present article, we construct the exact traveling wave solutions of nonlinear evolution equations in mathematical physics via the (2 + 1)-dimensional breaking soliton equation by using two methods: namely, a further improved (G'/G)-expansion method, where G(ξ) satisfies the auxiliary ordinary differential equation (ODE) [G'(ξ)](2) = p G (2)(ξ) + q G (4)(ξ) + r G (6)(ξ); p, q and r are constants and the well known extended tanh-function method. We demonstrate, nevertheless some of the exact solutions bring out by these two methods are analogous, but they are not one and the same. It is worth mentioning that the first method has not been exercised anybody previously which gives further exact solutions than the second one. PACS numbers 02.30.Jr, 05.45.Yv, 02.30.Ik.
NASA Astrophysics Data System (ADS)
Park, Yongcheol; Yoo, Hyun Jae; Lee, Won Sang; Lee, Choon-Ki; Lee, Joohan; Park, Hadong; Kim, Jinseok; Kim, Yeadong
2015-12-01
Mt. Melbourne is a late Cenozoic intraplate volcano located ∼30 km northeast of Jang Bogo Station in Antarctica. The volcano is quiescent with fumarolic activity at the summit. To monitor volcanic activity and glacial movements near Jang Bogo Station, a seismic network was installed during the 2010-11 Antarctic summer field season. The network is maintained during the summer field season every year, and the number of stations has been increased. We used continuous seismic data recorded by the network and an Italian seismic station (TNV) at Mario Zucchelli Station to develop a 3-D P-wave velocity model for the Mt. Melbourne area based on the teleseismic P-wave tomographic method. The new 3-D model presented a relative velocity structure for the lower part of the crust and upper mantle between depths of 30 and 160 km and revealed the presence of two low-velocity anomalies beneath Mt. Melbourne and the Priestley Fault. The low-velocity anomaly beneath Mt. Melbourne may be caused by the edge flow of hot mantle material at the lithospheric step between the thick East Antarctic Craton and thin Ross Sea crust. The other low-velocity anomaly along the Priestley Fault may have been beneath Mt. Melbourne and moved to the southern tip of the Deep Freeze Range, where the crustal thickness is relatively thin. The anomaly was trapped on the fault line and laterally flowed along the fault line in the northwest direction.
Exact analytical solutions for ADAFs
NASA Astrophysics Data System (ADS)
Habibi, Asiyeh; Abbassi, Shahram; Shadmehri, Mohsen
2017-02-01
We obtain two-dimensional exact analytic solutions for the structure of the hot accretion flows without wind. We assume that the only non-zero component of the stress tensor is Trϕ. Furthermore, we assume that the value of viscosity coefficient α varies with θ. We find radially self-similar solutions and compare them with the numerical and the analytical solutions already studied in the literature. The no-wind solution obtained in this paper may be applied to the nuclei of some cool-core clusters.
Partially coherent vectorial nonparaxial beams.
Duan, Kailiang; Lü, Baida
2004-10-01
Generalized vectorial Rayleigh-Sommerfeld diffraction integrals are developed for the cross-spectral-density matrices of spatially partially coherent beams. Using the Gaussian Schell-model (GSM) beam as an example, we derive the expressions for the propagation of cross-spectral-density matrices and intensity of partially coherent vectorial nonparaxial beams, and the corresponding far-field asymptotic forms, beyond the paraxial approximation. The propagation of the vectorial nonparaxial GSM beams are evaluated and analyzed. It is shown that a 3 x 3 cross-spectral-density matrix or a vector theory is required for the exact description of nonparaxial GSM beams.
Christodoulides, D N; Joseph, R L
1984-06-01
The propagation of nonlinear optical pulses in fibers is discussed, taking into account physical effects arising from nonlinearity, dispersion, and transverse confinement. The wave equation is solved by treating the radial dependence of the field in an exact way. The conditions supporting bright solitary waves are presented and compared with previous results.
Some exact solutions for debris and avalanche flows
NASA Astrophysics Data System (ADS)
Pudasaini, Shiva P.
2011-04-01
Exact analytical solutions to simplified cases of nonlinear debris avalanche model equations are necessary to calibrate numerical simulations of flow depth and velocity profiles on inclined surfaces. These problem-specific solutions provide important insight into the full behavior of the system. In this paper, we present some new analytical solutions for debris and avalanche flows and then compare these solutions with experimental data to measure their performance and determine their relevance. First, by combining the mass and momentum balance equations with a Bagnold rheology, a new and special kinematic wave equation is constructed in which the flux and the wave celerity are complex nonlinear functions of the pressure gradient and the flow depth itself. The new model can explain the mechanisms of wave advection and distortion, and the quasiasymptotic front bore observed in many natural and laboratory debris and granular flows. Exact time-dependent solutions for debris flow fronts and associated velocity profiles are then constructed. We also present a novel semiexact two-dimensional plane velocity field through the flow depth. Second, starting with the force balance between gravity, the pressure gradient, and Bagnold's grain-inertia or macroviscous forces, we construct a simple and very special nonlinear ordinary differential equation to model the steady state debris front profile. An empirical pressure gradient enhancement factor is introduced to adequately stretch the flow front and properly model nonhydrostatic pressure in granular and debris avalanches. An exact solution in explicit form is constructed, and is expressed in terms of the Lambert-Euler omega function. Third, we consider rapid flows of frictional granular materials down a channel. The steady state mass and the momentum balance equations are combined together with the Coulomb friction law. The Chebyshev radicals are employed and the exact solutions are developed for the velocity profile and the
Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance.
Chen, Shihua; Grelu, Philippe; Soto-Crespo, J M
2014-01-01
Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves.
Exact finite elements for conduction and convection
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507
Exact finite elements for conduction and convection
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An approach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions.
Odd and even partial waves of ηπ- and η‧π- in π- p →η (‧)π- p at 191 GeV / c
NASA Astrophysics Data System (ADS)
Adolph, C.; Akhunzyanov, R.; Alexeev, M. G.; Alexeev, G. D.; Amoroso, A.; Andrieux, V.; Anosov, V.; Austregesilo, A.; Badełek, B.; Balestra, F.; Barth, J.; Baum, G.; Beck, R.; Bedfer, Y.; Berlin, A.; Bernhard, J.; Bicker, K.; Bielert, E. R.; Bieling, J.; Birsa, R.; Bisplinghoff, J.; Bodlak, M.; Boer, M.; Bordalo, P.; Bradamante, F.; Braun, C.; Bressan, A.; Büchele, M.; Burtin, E.; Capozza, L.; Chiosso, M.; Chung, S. U.; Cicuttin, A.; Crespo, M. L.; Curiel, Q.; Dalla Torre, S.; Dasgupta, S. S.; Dasgupta, S.; Denisov, O. Yu.; Donskov, S. V.; Doshita, N.; Duic, V.; Dünnweber, W.; Dziewiecki, M.; Efremov, A.; Elia, C.; Eversheim, P. D.; Eyrich, W.; Faessler, M.; Ferrero, A.; Finger, M.; Finger, M.; Fischer, H.; Franco, C.; du Fresne von Hohenesche, N.; Friedrich, J. M.; Frolov, V.; Gautheron, F.; Gavrichtchouk, O. P.; Gerassimov, S.; Geyer, R.; Gnesi, I.; Gobbo, B.; Goertz, S.; Gorzellik, M.; Grabmüller, S.; Grasso, A.; Grube, B.; Grussenmeyer, T.; Guskov, A.; Haas, F.; von Harrach, D.; Hahne, D.; Hashimoto, R.; Heinsius, F. H.; Herrmann, F.; Hinterberger, F.; Höppner, Ch.; Horikawa, N.; d'Hose, N.; Huber, S.; Ishimoto, S.; Ivanov, A.; Ivanshin, Yu.; Iwata, T.; Jahn, R.; Jary, V.; Jasinski, P.; Jörg, P.; Joosten, R.; Kabuß, E.; Ketzer, B.; Khaustov, G. V.; Khokhlov, Yu. A.; Kisselev, Yu.; Klein, F.; Klimaszewski, K.; Koivuniemi, J. H.; Kolosov, V. N.; Kondo, K.; Königsmann, K.; Konorov, I.; Konstantinov, V. F.; Kotzinian, A. M.; Kouznetsov, O.; Krämer, M.; Kroumchtein, Z. V.; Kuchinski, N.; Kunne, F.; Kurek, K.; Kurjata, R. P.; Lednev, A. A.; Lehmann, A.; Levillain, M.; Levorato, S.; Lichtenstadt, J.; Maggiora, A.; Magnon, A.; Makke, N.; Mallot, G. K.; Marchand, C.; Martin, A.; Marzec, J.; Matousek, J.; Matsuda, H.; Matsuda, T.; Meshcheryakov, G.; Meyer, W.; Michigami, T.; Mikhailov, Yu. V.; Miyachi, Y.; Nagaytsev, A.; Nagel, T.; Nerling, F.; Neubert, S.; Neyret, D.; Novy, J.; Nowak, W.-D.; Nunes, A. S.; Olshevsky, A. G.; Orlov, I.; Ostrick, M.; Panknin, R.; Panzieri, D.; Parsamyan, B.; Paul, S.; Peshekhonov, D. V.; Platchkov, S.; Pochodzalla, J.; Polyakov, V. A.; Pretz, J.; Quaresma, M.; Quintans, C.; Ramos, S.; Regali, C.; Reicherz, G.; Rocco, E.; Rossiyskaya, N. S.; Ryabchikov, D. I.; Rychter, A.; Samoylenko, V. D.; Sandacz, A.; Sarkar, S.; Savin, I. A.; Sbrizzai, G.; Schiavon, P.; Schill, C.; Schlüter, T.; Schmidt, K.; Schmieden, H.; Schönning, K.; Schopferer, S.; Schott, M.; Shevchenko, O. Yu.; Silva, L.; Sinha, L.; Sirtl, S.; Slunecka, M.; Sosio, S.; Sozzi, F.; Srnka, A.; Steiger, L.; Stolarski, M.; Sulc, M.; Sulej, R.; Suzuki, H.; Szabelski, A.; Szameitat, T.; Sznajder, P.; Takekawa, S.; ter Wolbeek, J.; Tessaro, S.; Tessarotto, F.; Thibaud, F.; Uhl, S.; Uman, I.; Virius, M.; Wang, L.; Weisrock, T.; Wilfert, M.; Windmolders, R.; Wollny, H.; Zaremba, K.; Zavertyaev, M.; Zemlyanichkina, E.; Ziembicki, M.; Zink, A.
2015-01-01
Exclusive production of ηπ- and η‧π- has been studied with a 191 GeV / cπ- beam impinging on a hydrogen target at COMPASS (CERN). Partial-wave analyses reveal different odd/even angular momentum (L) characteristics in the inspected invariant mass range up to 3 GeV /c2. A striking similarity between the two systems is observed for the L = 2 , 4 , 6 intensities (scaled by kinematical factors) and the relative phases. The known resonances a2 (1320) and a4 (2040) are in line with this similarity. In contrast, a strong enhancement of η‧π- over ηπ- is found for the L = 1 , 3 , 5 waves, which carry non- q q bar quantum numbers. The L = 1 intensity peaks at 1.7 GeV /c2 in η‧π- and at 1.4 GeV /c2 in ηπ-, the corresponding phase motions with respect to L = 2 are different.
Exact Bremsstrahlung and effective couplings
NASA Astrophysics Data System (ADS)
Mitev, Vladimir; Pomoni, Elli
2016-06-01
We calculate supersymmetric Wilson loops on the ellipsoid for a large class of mathcal{N} = 2 SCFT using the localization formula of Hama and Hosomichi. From them we extract the radiation emitted by an accelerating heavy probe quark as well as the entanglement entropy following the recent works of Lewkowycz-Maldacena and Fiol-Gerchkovitz-Komargodski. Comparing our results with the mathcal{N} = 4 SYM ones, we obtain interpolating functions f ( g 2) such that a given mathcal{N} = 2 SCFT observable is obtained by replacing in the corresponding mathcal{N} = 4 SYM result the coupling constant by f ( g 2). These "exact effective couplings" encode the finite, relative renormalization between the mathcal{N} = 2 and the mathcal{N} = 4 gluon propagator and they interpolate between the weak and the strong coupling. We discuss the range of their applicability.
Exact propagators in harmonic superspace
NASA Astrophysics Data System (ADS)
Kuzenko, Sergei M.
2004-10-01
Within the background field formulation in harmonic superspace for quantum N = 2 super-Yang-Mills theories, the propagators of the matter, gauge and ghost superfields possess a complicated dependence on the SU(2) harmonic variables via the background vector multiplet. This dependence is shown to simplify drastically in the case of an on-shell vector multiplet. For a covariantly constant background vector multiplet, we exactly compute all the propagators. In conjunction with the covariant multi-loop scheme developed in arxiv:hep-th/0302205, these results provide an efficient (manifestly N = 2 supersymmetric) technical setup for computing multi-loop quantum corrections to effective actions in N = 2 supersymmetric gauge theories, including the N = 4 super-Yang-Mills theory.
High Resolution Thermometry for EXACT
NASA Technical Reports Server (NTRS)
Panek, J. S.; Nash, A. E.; Larson, M.; Mulders, N.
2000-01-01
High Resolution Thermometers (HRTs) based on SQUID detection of the magnetization of a paramagnetic salt or a metal alloy has been commonly used for sub-nano Kelvin temperature resolution in low temperature physics experiments. The main applications to date have been for temperature ranges near the lambda point of He-4 (2.177 K). These thermometers made use of materials such as Cu(NH4)2Br4 *2H2O, GdCl3, or PdFe. None of these materials are suitable for EXACT, which will explore the region of the He-3/He-4 tricritical point at 0.87 K. The experiment requirements and properties of several candidate paramagnetic materials will be presented, as well as preliminary test results.
NASA Technical Reports Server (NTRS)
Title, A. M. (Inventor)
1978-01-01
A birefringent filter module comprises, in seriatum. (1) an entrance polarizer, (2) a first birefringent crystal responsive to optical energy exiting the entrance polarizer, (3) a partial polarizer responsive to optical energy exiting the first polarizer, (4) a second birefringent crystal responsive to optical energy exiting the partial polarizer, and (5) an exit polarizer. The first and second birefringent crystals have fast axes disposed + or -45 deg from the high transmitivity direction of the partial polarizer. Preferably, the second crystal has a length 1/2 that of the first crystal and the high transmitivity direction of the partial polarizer is nine times as great as the low transmitivity direction. To provide tuning, the polarizations of the energy entering the first crystal and leaving the second crystal are varied by either rotating the entrance and exit polarizers, or by sandwiching the entrance and exit polarizers between pairs of half wave plates that are rotated relative to the polarizers. A plurality of the filter modules may be cascaded.
NASA Astrophysics Data System (ADS)
Azbel, Mark Ya.
2005-07-01
Exact law of mortality dynamics in changing populations and environment is derived. It includes no explicit characteristics of animal- environment interactions (metabolism etc) which are a must for life; it is universal for all animals, from single cell yeast to humans, with their drastically different biology, evolutionary history, and complexity; it is rapidly (within few percent of life span) reversible. Such law is unique for live systems with their homeostatic self-adjustment to environment (cf. thermodynamics of liquids and glasses). The law which is valid for all live, and only live, systems is their specific natural law. Mortality is an instrument of natural selection and biological diversity. Its law, which is preserved in evolution of all species, is a conservation law of mortality, selection, evolution, biology. The law implies new kind of intrinsic mortality and adaptation which dominate in evolutionary unprecedented protected populations and, in contrast to species specific natural selection, proceed via universal stepwise rungs and reduce to universal cellular mechanism. The law demonstrates that intrinsic mortality and at least certain aspects of aging are disposable evolutionary byproducts, and directed genetic and/or biological changes may yield healthy and vital Methuselah lifespan. This is consistent with experiments. Universality implies that single cell yeast may provide a master key to the cellular mechanism of universal mortality, aging, selection, evolution, and its regulation in all animals. One may look for its manifestations in animal cells also, e.g., in their replicative senescence and cancer. Evolutionary origin and genetic nature of universality are suggested.
Exact dynamics of finite Glauber-Fock photonic lattices
Rodriguez-Lara, B. M.
2011-11-15
The dynamics of Glauber-Fock lattice of size N is given through exact diagonalization of the corresponding Hamiltonian; the spectra {l_brace}{lambda}{sub k}{r_brace} is given as the roots of the Nth Hermite polynomial, H{sub N}({lambda}{sub k}/{radical}(2))=0, and the eigenstates are given in terms of Hermite polynomials evaluated at these roots. The exact dynamics is used to study coherent phenomena in discrete lattices. Due to the symmetry and spacing of the eigenvalues {l_brace}{lambda}{sub k}{r_brace}, oscillatory behavior is predicted with highly localized spectra, that is, near complete revivals of the photon number and partial recovery of the initial state at given waveguides.
A Reduced Basis Method with Exact-Solution Certificates for Steady Symmetric Coercive Equations
2015-01-14
A Reduced Basis Method with Exact -Solution Certificates for Steady Symmetric Coercive Equations Masayuki Yano Department of Mechanical Engineering...bounds of the energy associated with the infinite-dimensional weak solution of parametrized steady symmetric coercive partial differential equations with...identify algebraic conditions for the reduced basis approx- imation of the dual variable that results in an exact satisfaction of the dual feasibility
Exactly solvable Hermite, Laguerre, and Jacobi type quantum parametric oscillators
NASA Astrophysics Data System (ADS)
A. Büyükaşık, Şirin; ćayiç, Zehra
2016-12-01
We introduce exactly solvable quantum parametric oscillators, which are generalizations of the quantum problems related with the classical orthogonal polynomials of Hermite, Laguerre, and Jacobi type, introduced in the work of Büyükaşık et al. [J. Math. Phys. 50, 072102 (2009)]. Quantization of these models with specific damping, frequency, and external forces is obtained using the Wei-Norman Lie algebraic approach. This determines the evolution operator exactly in terms of two linearly independent homogeneous solutions and a particular solution of the corresponding classical equation of motion. Then, time-evolution of wave functions and coherent states are found explicitly. Probability densities, expectation values, and uncertainty relations are evaluated and their properties are investigated under the influence of the external terms.
Observations of running penumbral waves.
NASA Technical Reports Server (NTRS)
Zirin, H.; Stein, A.
1972-01-01
Quiet sunspots with well-developed penumbrae show running intensity waves with period running around 300 sec. The waves appear connected with umbral flashes of exactly half the period. Waves are concentric, regular, with velocity constant around 10 km/sec. They are probably sound waves and show intensity fluctuation in H alpha centerline or wing of 10 to 20%. The energy is tiny compared to the heat deficit of the umbra.
Low-drag exact coherent states in Newtonian channel flow
NASA Astrophysics Data System (ADS)
Park, Jae Sung; Graham, Michael
2013-11-01
Exact coherent states have been known to nicely capture the main features of turbulent flows such as near-wall coherent structures and streak spacing. In this study, we numerically calculate new classes of exact coherent states, specifically nonlinear traveling wave solutions, for Newtonian channel flow, which display low-drag flow features such as weak streamwise vortices and nearly nonexistent streamwise variations like those observed in polymer solutions and in Newtonian hibernating turbulence. Traveling wave solutions with various symmetries are found. While some of the structures clearly display nonlinear critical layer dynamics, in others this connection is not as clear. Dynamical trajectories are computed and some of the solutions are shown to lie on the basin boundary between laminar and turbulent flows and are thus edge-states of the flow. Lastly, the dependence of Reynolds number for the solutions is investigated. We find one intriguing family whose mean velocity profile appears to approach the so-called maximum drag reduction asymptote found in polymer solutions, despite the fact that fluid studied here is Newtonian. Our results suggest that these traveling wave solutions may play a role as promising targets for turbulence control strategies for drag reduction. This work was supported by the Air Force Office of Scientific Research through grant FA9550-11-1-0094 (Flow Interactions and Control Program).
Systems of Nonlinear Hyperbolic Partial Differential Equations
1997-12-01
McKinney) Travelling wave solutions of the modified Korteweg - deVries -Burgers Equation . J. Differential Equations , 116 (1995), 448-467. 4. (with D.G...SUBTITLE Systems of Nonlinear Hyperbolic Partial Differential Equations 6. AUTHOR’S) Michael Shearer PERFORMING ORGANIZATION NAMES(S) AND...DISTRIBUTION CODE 13. ABSTRACT (Maximum 200 words) This project concerns properties of wave propagation in partial differential equations that are nonlinear
NASA Astrophysics Data System (ADS)
Symes, L. M.; Blakie, P. B.
2017-01-01
We develop numerical methods for solving the spin-2 Gross-Pitaevskii equation. The basis of our work is a two-way splitting of this evolution equation that leads to two exactly solvable subsystems. Utilizing second-order and fourth-order composition schemes we realize two fully symplectic integration algorithms, the first such algorithms for evolving spin-2 condensates. We demonstrate the accuracy of these algorithms against other methods on application to an exact continuous wave solution that we derive.
Symes, L M; Blakie, P B
2017-01-01
We develop numerical methods for solving the spin-2 Gross-Pitaevskii equation. The basis of our work is a two-way splitting of this evolution equation that leads to two exactly solvable subsystems. Utilizing second-order and fourth-order composition schemes we realize two fully symplectic integration algorithms, the first such algorithms for evolving spin-2 condensates. We demonstrate the accuracy of these algorithms against other methods on application to an exact continuous wave solution that we derive.
Exact and approximate solutions to the oblique shock equations for real-time applications
NASA Technical Reports Server (NTRS)
Hartley, T. T.; Brandis, R.; Mossayebi, F.
1991-01-01
The derivation of exact solutions for determining the characteristics of an oblique shock wave in a supersonic flow is investigated. Specifically, an explicit expression for the oblique shock angle in terms of the free stream Mach number, the centerbody deflection angle, and the ratio of the specific heats, is derived. A simpler approximate solution is obtained and compared to the exact solution. The primary objectives of obtaining these solutions is to provide a fast algorithm that can run in a real time environment.
NASA Astrophysics Data System (ADS)
Azbel‧, Mark Ya.
2005-08-01
The exact law of mortality dynamics in changing populations and environment is derived. It includes no explicit characteristics of animal-environment interactions (metabolism, etc.) which are a must for life; it is universal for all animals, from single-cell yeast to humans, with their drastically different biology, evolutionary history, and complexity; it is rapidly (within few percent of life span) reversible. Such a law is unique for live systems with their homeostatic self-adjustment to environment (cf. thermodynamics of liquids and glasses). The law which is valid for all live, and only live, systems is their specific natural law. Mortality is an instrument of natural selection and biological diversity. Its law, which is preserved in evolution of all species, is a conservation law of mortality, selection, evolution, biology. The law implies new kinds of intrinsic mortality and adaptation which dominate in evolutionary unprecedented protected populations and, in contrast to species-specific natural selection, proceed via universal stepwise rungs and reduce to universal cellular mechanism. The law demonstrates that intrinsic mortality and at least certain aspects of aging are disposable evolutionary byproducts, and directed genetic and/or biological changes may yield healthy and vital Methuselah lifespan. This is consistent with experiments. Universality implies that single-cell yeast may provide a master key to the cellular mechanism of universal mortality, aging, selection, evolution, and its regulation in all animals. One may look for its manifestations in animal cells also, e.g., in their replicative senescence and cancer. Evolutionary origin and genetic nature of universality are suggested.
Quasi-exactly solvable quasinormal modes
Ho, C.-L.; Cho, H.-T.
2007-11-20
We consider quasinormal modes with complex energies from the point of view of the theory of quasi-exactly solvable (QES) models. We demonstrate that it is possible to find new potentials which admit exactly solvable or QES quasinormal modes by suitable complexification of parameters defining the QES potentials. Particularly, we obtain one QES and four exactly solvable potentials out of the five one-dimensional QES systems based on the sl(2) algebra.
Exact computations for the coherence estimate.
Nadarajah, Saralees; Kotz, Samuel
2007-07-01
The recent paper by Miranda de Sa et al. [10] developed methods for computing the sampling distribution of the coherence estimate between two signals. However, the methods were based on some approximations because it was claimed that exact calculations required extensive computations. In this technical note, we provide analytical expressions and 1-line programs for the exact computation of various measures of the sampling distribution. Besides being exact, our programs have several advantages over the methods suggested in [10].
Exact significance test for Markov order
NASA Astrophysics Data System (ADS)
Pethel, S. D.; Hahs, D. W.
2014-02-01
We describe an exact significance test of the null hypothesis that a Markov chain is nth order. The procedure utilizes surrogate data to yield an exact test statistic distribution valid for any sample size. Surrogate data are generated using a novel algorithm that guarantees, per shot, a uniform sampling from the set of sequences that exactly match the nth order properties of the observed data. Using the test, the Markov order of Tel Aviv rainfall data is examined.
Wave propagation in laminated orthotropic circular cylindrical shells
NASA Technical Reports Server (NTRS)
Srinivas, S.
1976-01-01
An exact three-dimensional analysis of wave propagation in laminated orthotropic circular cylindrical-shells is developed. Numerical results are presented for three-ply shells, and for various axial wave lengths, circumferential wave numbers, and thicknesses. Results from a thin shell theory and a refined approximate theory are compared with the exact results.
The exact fundamental solution for the Benes tracking problem
NASA Astrophysics Data System (ADS)
Balaji, Bhashyam
2009-05-01
The universal continuous-discrete tracking problem requires the solution of a Fokker-Planck-Kolmogorov forward equation (FPKfe) for an arbitrary initial condition. Using results from quantum mechanics, the exact fundamental solution for the FPKfe is derived for the state model of arbitrary dimension with Benes drift that requires only the computation of elementary transcendental functions and standard linear algebra techniques- no ordinary or partial differential equations need to be solved. The measurement process may be an arbitrary, discrete-time nonlinear stochastic process, and the time step size can be arbitrary. Numerical examples are included, demonstrating its utility in practical implementation.
Spin-wave modes of ferromagnetic films
NASA Astrophysics Data System (ADS)
Arias, R. E.
2016-10-01
The spin-wave modes of ferromagnetic films have been studied for a long time experimentally as well as theoretically, either in the magnetostatic approximation or also considering the exchange interaction. A theoretical method is presented that allows one to determine with ease the exact frequency dispersion relations of dipole-exchange modes under general conditions: an obliquely applied magnetic field, and surface boundary conditions that allow for partial pinning, which may be of different origins. The method is a generalization of Green's theorem to the problem of solving the linear dynamics of ferromagnetic spin-wave modes. Convolution integral equations for the magnetization and the magnetostatic potential of the modes are derived on the surfaces of the film. For the translation-invariant film these become simple local algebraic equations at each in-plane wave vector. Eigenfrequencies result from imposing a 6 ×6 determinant to be null, and spin-wave modes follow everywhere through solving linear 6 ×6 inhomogeneous systems. An interpretation of the results is that the Green's functions represent six independent plane-wave solutions to the equations of motion, with six associated complex perpendicular wave vectors: volume modes correspond to the cases in which two of these are purely real at a given frequency. Furthermore, the convolution extinction equations enforce the boundary conditions: this is possible at specific eigenfrequencies for a given in-plane wave vector. Magnetostatic modes may also be obtained in detail. At low frequencies and for some obliquely applied magnetic fields, magnetostatic and dipole-exchange volume modes may have forward or backward character depending on the frequency range.
Partial wave analysis of the reaction $\gamma p\to p\omega $ and the search for nucleon resonances
Williams, M.; Applegate, D.; Bellis, M.; Meyer, C. A.; Adhikari, K. P.; Anghinolfi, M.; Baghdasaryan, H.; Ball, J.; Battaglieri, M.; Bedlinskiy, I.; Berman, B. L.; Biselli, A. S.; Briscoe, W. J.; Brooks, W. K.; Burkert, V. D.; Careccia, S. L.; Carman, D. S.; Cole, P. L.; Collins, P.; Crede, V.; D’Angelo, A.; Daniel, A.; De Vita, R.; De Sanctis, E.; Deur, A.; Dey, B.; Dhamija, S.; Dickson, R.; Djalali, C.; Dodge, G. E.; Doughty, D.; Dugger, M.; Dupre, R.; Alaoui, A. El; Elouadrhiri, L.; Eugenio, P.; Fedotov, G.; Fegan, S.; Fradi, A.; Gabrielyan, M. Y.; Garçon, M.; Gilfoyle, G. P.; Giovanetti, K. L.; Girod, F. X.; Gohn, W.; Golovatch, E.; Gothe, R. W.; Griffioen, K. A.; Guidal, M.; Guler, N.; Guo, L.; Hafidi, K.; Hakobyan, H.; Hanretty, C.; Hassall, N.; Hicks, K.; Holtrop, M.; Ilieva, Y.; Ireland, D. G.; Ishkhanov, B. S.; Isupov, E. L.; Jawalkar, S. S.; Jo, H. S.; Johnstone, J. R.; Joo, K.; Keller, D.; Khandaker, M.; Khetarpal, P.; Kim, W.; Klein, A.; Klein, F. J.; Krahn, Z.; Kubarovsky, V.; Kuleshov, S. V.; Kuznetsov, V.; Livingston, K.; Lu, H. Y.; Mayer, M.; McAndrew, J.; McCracken, M. E.; McKinnon, B.; Mirazita, M.; Mokeev, V.; Moreno, B.; Moriya, K.; Morrison, B.; Munevar, E.; Nadel-Turonski, P.; Nepali, C. S.; Niccolai, S.; Niculescu, G.; Niculescu, I.; Niroula, M. R.; Niyazov, R. A.; Osipenko, M.; Ostrovidov, A. I.; Paris, M.; Park, K.; Park, S.; Pasyuk, E.; Pereira, S. Anefalos; Perrin, Y.; Pisano, S.; Pogorelko, O.; Pozdniakov, S.; Price, J. W.; Procureur, S.; Protopopescu, D.; Ricco, G.; Ripani, M.; Ritchie, B. G.; Rosner, G.; Rossi, P.; Sabatié, F.; Saini, M. S.; Salamanca, J.; Salgado, C.; Schott, D.; Schumacher, R. A.; Seraydaryan, H.; Sharabian, Y. G.; Smith, E. S.; Sober, D. I.; Sokhan, D.; Stepanyan, S. S.; Stoler, P.; Strakovsky, I. I.; Strauch, S.; Taiuti, M.; Tedeschi, D. J.; Tkachenko, S.; Ungaro, M.; Vineyard, M. F.; Voutier, E.; Watts, D. P.; Weygand, D. P.; Wood, M. H.; Zhang, J.; Zhao, B.
2009-12-30
We performed an event-based partial wave analysis (PWA) of the reaction γ p -> p ω on a high-statistics dataset obtained using the CLAS at Jefferson Lab for center-of-mass energies from threshold up to 2.4 GeV. This analysis benefits from access to the world's first high precision spin density matrix element measurements, available to the event-based PWA through the decay distribution of omega-> π^{+} π^{ -} π^{0}. The data confirm the dominance of the t-channel π^{0} exchange amplitude in the forward direction. The dominant resonance contributions are consistent with the previously identified states F[15](1680) and D[13](1700) near threshold, as well as the G[17](2190) at higher energies. Suggestive evidence for the presence of a J(P)=5/2^{+} state around 2 GeV, a "missing" state, has also been found. Evidence for other states is inconclusive.
Agakishiev, G.; Arnold, O.; Belver, D.; Belyaev, A.; Berger-Chen, J. C.; Blanco, A.; Böhmer, M.; Boyard, J. L.; Cabanelas, P.; Chernenko, S.; Dybczak, A.; Epple, E.; Fabbietti, L.; Fateev, O.; Finocchiaro, P.; Fonte, P.; Friese, J.; Fröhlich, I.; Galatyuk, T.; Garzón, J. A.; Gernhäuser, R.; Göbel, K.; Golubeva, M.; González-Díaz, D.; Guber, F.; Gumberidze, M.; Heinz, T.; Hennino, T.; Holzmann, R.; Ierusalimov, A.; Iori, I.; Ivashkin, A.; Jurkovic, M.; Kämpfer, B.; Karavicheva, T.; Koenig, I.; Koenig, W.; Kolb, B. W.; Kornakov, G.; Kotte, R.; Krása, A.; Krizek, F.; Krücken, R.; Kuc, H.; Kühn, W.; Kugler, A.; Kunz, T.; Kurepin, A.; Ladygin, V.; Lalik, R.; Lapidus, K.; Lebedev, A.; Lopes, L.; Lorenz, M.; Maier, L.; Mangiarotti, A.; Markert, J.; Metag, V.; Michel, J.; Müntz, C.; Münzer, R.; Naumann, L.; Pachmayer, Y. C.; Palka, M.; Parpottas, Y.; Pechenov, V.; Pechenova, O.; Pietraszko, J.; Przygoda, W.; Ramstein, B.; Reshetin, A.; Rustamov, A.; Sadovsky, A.; Salabura, P.; Schmah, A.; Schwab, E.; Siebenson, J.; Sobolev, Yu. G.; Spataro, S.; Spruck, B.; Ströbele, H.; Stroth, J.; Sturm, C.; Tarantola, A.; Teilab, K.; Tlusty, P.; Traxler, M.; Tsertos, H.; Vasiliev, T.; Wagner, V.; Weber, M.; Wendisch, C.; Wüstenfeld, J.; Yurevich, S.; Zanevsky, Y.; Sarantsev, A. V.
2015-01-26
Employing the Bonn–Gatchina partial wave analysis framework (PWA), we have analyzed HADES data of the reaction p(3.5GeV) + p → pK^{+}Λ. This reaction might contain information about the kaonic cluster “ppK^{-}” (with quantum numbers J^{P}=0^{-} and total isospin I =1/2) via its decay into pΛ. Due to interference effects in our coherent description of the data, a hypothetical K ¯NN (or, specifically “ppK^{-}”) cluster signal need not necessarily show up as a pronounced feature (e.g. a peak) in an invariant mass spectrum like pΛ. Our PWA analysis includes a variety of resonant and non-resonant intermediate states and delivers a good description of our data (various angular distributions and two-hadron invariant mass spectra) without a contribution of a K ¯NN cluster. At a confidence level of CL_{s}=95% such a cluster cannot contribute more than 2–12% to the total cross section with a pK^{+} Λ final state, which translates into a production cross-section between 0.7 μb and 4.2 μb, respectively. The range of the upper limit depends on the assumed cluster mass, width and production process.
A class of exact classical solutions to string theory.
Coley, A A
2002-12-31
We show that the recently obtained class of spacetimes for which all of the scalar curvature invariants vanish (which can be regarded as generalizations of pp-wave spacetimes) are exact solutions in string theory to all perturbative orders in the string tension scale. As a result the spectrum of the theory can be explicitly obtained, and these spacetimes are expected to provide some hints for the study of superstrings on more general backgrounds. Since these Lorentzian spacetimes suffer no quantum corrections to all loop orders they may also offer insights into quantum gravity.
Lin, Cheng-Horng
2016-01-01
There are more than 7 million people living near the Tatun volcano group in northern Taiwan. For the safety of the Taipei metropolis, in particular, it has been debated for decades whether or not these volcanoes are active. Here I show evidence of a deep magma reservoir beneath the Taipei metropolis from both S-wave shadows and P-wave delays. The reservoir is probably composed of either a thin magma layer overlay or many molten sills within thick partially molten rocks. Assuming that 40% of the reservoir is partially molten, its total volume could be approximately 350 km3. The exact location and geometry of the magma reservoir will be obtained after dense seismic arrays are deployed in 2017–2020. PMID:28008931
Lin, Cheng-Horng
2016-12-23
There are more than 7 million people living near the Tatun volcano group in northern Taiwan. For the safety of the Taipei metropolis, in particular, it has been debated for decades whether or not these volcanoes are active. Here I show evidence of a deep magma reservoir beneath the Taipei metropolis from both S-wave shadows and P-wave delays. The reservoir is probably composed of either a thin magma layer overlay or many molten sills within thick partially molten rocks. Assuming that 40% of the reservoir is partially molten, its total volume could be approximately 350 km(3). The exact location and geometry of the magma reservoir will be obtained after dense seismic arrays are deployed in 2017-2020.
NASA Astrophysics Data System (ADS)
Lin, Cheng-Horng
2016-12-01
There are more than 7 million people living near the Tatun volcano group in northern Taiwan. For the safety of the Taipei metropolis, in particular, it has been debated for decades whether or not these volcanoes are active. Here I show evidence of a deep magma reservoir beneath the Taipei metropolis from both S-wave shadows and P-wave delays. The reservoir is probably composed of either a thin magma layer overlay or many molten sills within thick partially molten rocks. Assuming that 40% of the reservoir is partially molten, its total volume could be approximately 350 km3. The exact location and geometry of the magma reservoir will be obtained after dense seismic arrays are deployed in 2017–2020.
Exact treatment of the Jaynes-Cummings model under the action of an external classical field
Abdalla, M. Sebawe; Khalil, E.M.; Obada, A.S.-F.
2011-09-15
We consider the usual Jaynes-Cummings model (JCM), in the presence of an external classical field. Under a certain canonical transformation for the Pauli operators, the system is transformed into the usual JCM. Using the equations of motion in the Heisenberg picture, exact solutions for the time-dependent dynamical operators are obtained. In order to calculate the expectation values of these operators, the wave function has been constructed. It has been shown that the classical field augments the atomic frequency {omega}{sub 0} and mixes the original atomic states. Changes of squeezing from one quadrature to another is also observed for a strong value of the coupling parameter of the classical field. Furthermore, the system in this case displays partial entanglement and the state of the field losses its purity. - Highlights: > The time-dependent JCM, in the presence of the classical field, is still one of the essential problems in the quantum optics. > A new approach is applied through a certain canonical transformation. > The classical field augments the atomic frequency {omega}{sub 0} and mixes the original atomic states.
Exact adler function in supersymmetric QCD.
Shifman, M; Stepanyantz, K
2015-02-06
The Adler function D is found exactly in supersymmetric QCD. Our exact formula relates D(Q(2)) to the anomalous dimension of the matter superfields γ(α(s)(Q(2))). En route we prove another theorem: the absence of the so-called singlet contribution to D. While such singlet contributions are present in individual supergraphs, they cancel in the sum.
Exact Analytical Solutions for Elastodynamic Impact
2015-11-30
ARL-RP-0559 ● NOV 2015 US Army Research Laboratory Exact Analytical Solutions for Elastodynamic Impact by George A Gazonas...ARL-RP-0559 ● NOV 2015 US Army Research Laboratory Exact Analytical Solutions for Elastodynamic Impact by George A Gazonas...
NASA Astrophysics Data System (ADS)
Kim, E.-H.; Boardsen, S. A.; Johnson, J. R.; Slavin, J. A.
2016-02-01
This chapter provides a brief overview of the observed characteristics of ultra-low-frequency (ULF) waves at Mercury. It shows how field-aligned propagating ULF waves at Mercury can be generated by externally driven fast compressional waves (FWs) via mode conversion at the ion-ion hybrid resonance. Then, the chapter reviews the interpretation that the strong magnetic compressional waves near and its harmonics observed with 20 of Mercury's magnetic equator could be the ion Bernstein wave (IBW) mode. A recent statistical study of ULF waves at Mercury based on MESSENGER data reported the occurrence and polarization of the detected waves. The chapter further introduces the field line resonance and the electromagnetic ion Bernstein waves to explain such waves, and shows that both theories can partially explain the observations.
Effect of fracture compliance on wave propagation within a fluid-filled fracture.
Nakagawa, Seiji; Korneev, Valeri A
2014-06-01
Open and partially closed fractures can trap seismic waves. Waves propagating primarily within fluid in a fracture are sometimes called Krauklis waves, which are strongly dispersive at low frequencies. The behavior of Krauklis waves has previously been examined for an open, fluid-filled channel (fracture), but the impact of finite fracture compliance resulting from contacting asperities and porous fillings in the fracture (e.g., debris, proppants) has not been fully investigated. In this paper, a dispersion equation is derived for Krauklis wave propagation in a fracture with finite fracture compliance, using a modified linear-slip-interface model (seismic displacement-discontinuity model). The resulting equation is formally identical to the dispersion equation for the symmetric fracture interface wave, another type of guided wave along a fracture. The low-frequency solutions of the newly derived dispersion equations are in good agreement with the exact solutions available for an open fracture. The primary effect of finite fracture compliance on Krauklis wave propagation is to increase wave velocity and attenuation at low frequencies. These effects can be used to monitor changes in the mechanical properties of a fracture.
Exact Solutions and Conservation Laws for a New Integrable Equation
Gandarias, M. L.; Bruzon, M. S.
2010-09-30
In this work we study a generalization of an integrable equation proposed by Qiao and Liu from the point of view of the theory of symmetry reductions in partial differential equations. Among the solutions we obtain a travelling wave with decaying velocity and a smooth soliton solution. We determine the subclass of these equations which are quasi-self-adjoint and we get a nontrivial conservation law.
A procedure to construct exact solutions of nonlinear fractional differential equations.
Güner, Özkan; Cevikel, Adem C
2014-01-01
We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.
A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations
Güner, Özkan; Cevikel, Adem C.
2014-01-01
We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. PMID:24737972
NASA Astrophysics Data System (ADS)
Zhang, Jinliang; Hu, Wuqiang; Ma, Yu
2016-12-01
In this paper, the famous Klein-Gordon-Zakharov equations are firstly generalized, the new special types of Klein-Gordon-Zakharov equations with the positive fractional power terms (gKGZE) are presented. In order to derive the exact solutions of new special gKGZE, the subsidiary higher order ordinary differential equations (sub-ODEs) with the positive fractional power terms are introduced, and with the aids of the Sub-ODE, the exact solutions of three special types of the gKGZE are derived, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of gKGZE satisfy certain constraint conditions.
A Formulation of Asymptotic and Exact Boundary Conditions Using Local Operators
NASA Technical Reports Server (NTRS)
Hagstrom, T.; Hariharan, S. I.
1998-01-01
In this paper we describe a systematic approach for constructing asymptotic boundary conditions for isotropic wave-like equations using local operators. The conditions take a recursive form with increasing order of accuracy. In three dimensions the recursion terminates and the resulting conditions are exact for solutions which are described by finite combinations of angular spherical harmonics. First, we develop the expansion for the two-dimensional wave equation and construct a sequence of easily implementable boundary conditions. We show that in three dimensions and analogous conditions are again easily implementable in addition to being exact. Also, we provide extensions of these ideas to hyperbolic systems. Namely, Maxwell's equations for TM waves are used to demonstrate the construction. Finally, we provide numerical examples to demonstrate the effectiveness of these conditions for a model problem governed by the wave equation.
Exact coherent structures: from fluid turbulence to cardiac arrhythmias
NASA Astrophysics Data System (ADS)
Grigoriev, Roman; Marcotte, Christopher; Byrne, Gregory
2014-03-01
Ventricular fibrillation, a life threatening cardiac arrhythmia, is an example of spatiotemporally chaotic state dominated by multiple interacting spiral waves. Recent studies of weak fluid turbulence suggest that spatiotemporal chaos in general can be understood as a walk among exact unstable regular solutions (exact coherent states, ECS) of nonlinear evolution equations. Several classes of ECS are believed to play a dominant role; most typically these are equilibria and periodic orbits or relative equilibria and relative periodic orbits for systems with global continuous symmetries. Numerical methods originally developed in the context of fluid turbulence can also be applied to models of cardiac dynamics which possess translational and rotational symmetries and, indeed, allowed us to identify relative equilibria and periodic orbits describing isolated spirals with, respectively, fixed and drifting cores. In order to find regular solutions featuring multiple interacting spirals a new approach is required that takes into consideration the dynamics of slowly drifting cores associated with local, rather than global, symmetries. We describe how local symmetries can be reduced and more general types of ECS computed that dominate spiral wave chaos in models of cardiac tissue.
Exact simulation of polarized light reflectance by particle deposits
NASA Astrophysics Data System (ADS)
Ramezan Pour, B.; Mackowski, D. W.
2015-12-01
The use of polarimetric light reflection measurements as a means of identifying the physical and chemical characteristics of particulate materials obviously relies on an accurate model of predicting the effects of particle size, shape, concentration, and refractive index on polarized reflection. The research examines two methods for prediction of reflection from plane parallel layers of wavelength—sized particles. The first method is based on an exact superposition solution to Maxwell's time harmonic wave equations for a deposit of spherical particles that are exposed to a plane incident wave. We use a FORTRAN-90 implementation of this solution (the Multiple Sphere T Matrix (MSTM) code), coupled with parallel computational platforms, to directly simulate the reflection from particle layers. The second method examined is based upon the vector radiative transport equation (RTE). Mie theory is used in our RTE model to predict the extinction coefficient, albedo, and scattering phase function of the particles, and the solution of the RTE is obtained from adding—doubling method applied to a plane—parallel configuration. Our results show that the MSTM and RTE predictions of the Mueller matrix elements converge when particle volume fraction in the particle layer decreases below around five percent. At higher volume fractions the RTE can yield results that, depending on the particle size and refractive index, significantly depart from the exact predictions. The particle regimes which lead to dependent scattering effects, and the application of methods to correct the vector RTE for particle interaction, will be discussed.
Noncommutativity from exact renormalization group dualities
NASA Astrophysics Data System (ADS)
Gangopadhyay, Sunandan; Scholtz, Frederik G.
2014-08-01
Here we demonstrate, first, the construction of dualities using the exact renormalization group approach and, second, that spatial noncommutativity can emerge as such a duality. This is done in a simple quantum mechanical setting that establishes an exact duality between the commutative and noncommutative quantum Hall systems with harmonic interactions. It is also demonstrated that this link can be understood as a blocking (coarse graining) transformation in time that relates commutative and noncommutative degrees of freedom.
The fractional coupled KdV equations: Exact solutions and white noise functional approach
NASA Astrophysics Data System (ADS)
Hossam, A. Ghany; S. Okb El Bab, A.; M. Zabel, A.; Abd-Allah, Hyder
2013-08-01
Variable coefficients and Wick-type stochastic fractional coupled KdV equations are investigated. By using the modified fractional sub-equation method, Hermite transform, and white noise theory the exact travelling wave solutions and white noise functional solutions are obtained, including the generalized exponential, hyperbolic, and trigonometric types.
Exact solutions of Wick-type stochastic equations with variable coefficients
NASA Astrophysics Data System (ADS)
Kim, Hyunsoo; Sakthivel, Rathinasamy
In this paper, we consider the Wick-type stochastic generalized Boussinesq equation and Wick-type stochastic Kadomtsev-Petviashvili equation with variable coefficients. By employing the (GG)-expansion method with the aid of symbolic computation and Hermite transformation, we derive new exact travelling wave solutions, which mclude hyperbolic and trigonometric solutions for the considered equations.
Exact solution of a quantum forced time-dependent harmonic oscillator
NASA Technical Reports Server (NTRS)
Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN
1992-01-01
The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.
Exact solutions of optical pulse propagation in nonlinear meta-materials
NASA Astrophysics Data System (ADS)
Nanda, Lipsa
2017-01-01
An analytical and simulation based method has been used to exactly solve the nonlinear wave propagation in bulk media exhibiting frequency dependent dielectric susceptibility and magnetic permeability. The method has been further extended to investigate the intensity distribution in a nonlinear meta-material with negative refractive index where both ɛ and μ are dispersive and negative in nature.
Wave climate assessment by satellite remote sensing
Barstow, S.F.; Krogstad, H.E.
1995-12-31
Satellite remote sensing is quickly becoming a major information source for wave climate assessments. The present paper surveys various measurement principles and illustrates applications of satellite altimeter wave data from both the GEOSAT, Topex/Poseidon and ERS-1 Exact Repeat missions. The paper also discusses use of Wave Mode and Image Mode SAR data obtained by ERS-1.
The exact forces on classical nuclei in non-adiabatic charge transfer
Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu; Min, Seung Kyu; Gross, E. K. U.; Maitra, Neepa T.
2015-02-28
The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect.
Exact Potential Driving the Electron Dynamics in Enhanced Ionization of H(2)(+).
Khosravi, Elham; Abedi, Ali; Maitra, Neepa T
2015-12-31
It was recently shown that the exact factorization of the electron-nuclear wave function allows the construction of a Schrödinger equation for the electronic system, in which the potential contains exactly the effect of coupling to the nuclear degrees of freedom and any external fields. Here we study the exact potential acting on the electron in charge-resonance enhanced ionization in a model one-dimensional H(2)(+) molecule. We show there can be significant differences between the exact potential and that used in the traditional quasistatic analyses, arising from nonadiabatic coupling to the nuclear system, and that these are crucial to include for accurate simulations of time-resolved ionization dynamics and predictions of the ionization yield.
Critical behavior for scalar nonlinear waves
NASA Astrophysics Data System (ADS)
Masoero, Davide; Raimondo, Andrea; Antunes, Pedro R. S.
2015-02-01
In the long wave regime, nonlinear waves may undergo a phase transition from a smooth behavior to a fast oscillatory behavior. In this study, we consider this phenomenon, which is commonly known as dispersive shock, in the light of Dubrovin's universality conjecture (Dubrovin, 2006; Dubrovin and Elaeva, 2012) and we argue that the transition can be described by a special solution of a model universal partial differential equation. This universal solution is constructed using the string equation. We provide a classification of universality classes and an explicit description of the transition with special functions, thereby extending Dubrovin's universality conjecture to a wider class of equations. In particular, we show that the Benjamin-Ono equation belongs to a novel universality class with respect to those known previously, and we compute its string equation exactly. We describe our results using the language of statistical mechanics, where we show that dispersive shocks share many of the features of the tricritical point in statistical systems, and we also build a dictionary of the relations between nonlinear waves and statistical mechanics.
Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar
2014-01-01
In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.
NASA Astrophysics Data System (ADS)
Cooper, Fred; Khare, Avinash; Comech, Andrew; Mihaila, Bogdan; Dawson, John F.; Saxena, Avadh
2017-01-01
We discuss the stability properties of the solutions of the general nonlinear Schrödinger equation (NLSE) in 1+1 dimensions in an external potential derivable from a parity-time ({ P }{ T }) symmetric superpotential W(x) that we considered earlier, Kevrekidis et al (2015 Phys. Rev. E 92 042901). In particular we consider the nonlinear partial differential equation \\{{{i}} {\\partial }t+{\\partial }x2-{V}-(x)+| \\psi (x,t){| }2κ \\} \\psi (x,t)=0, for arbitrary nonlinearity parameter κ. We study the bound state solutions when {V}-(x) =(1/4-{b}2){\\text{sech}}2(x), which can be derived from two different superpotentials W(x), one of which is complex and { P }{ T } symmetric. Using Derrick's theorem, as well as a time dependent variational approximation, we derive exact analytic results for the domain of stability of the trapped solution as a function of the depth b 2 of the external potential. We compare the regime of stability found from these analytic approaches with a numerical linear stability analysis using a variant of the Vakhitov-Kolokolov (V-K) stability criterion. The numerical results of applying the V-K condition give the same answer for the domain of stability as the analytic result obtained from applying Derrick's theorem. Our main result is that for κ \\gt 2 a new regime of stability for the exact solutions appears as long as b\\gt {b}{{crit}}, where {b}{{crit}} is a function of the nonlinearity parameter κ. In the absence of the potential the related solitary wave solutions of the NLSE are unstable for κ \\gt 2.
Connecting exact coherent states to turbulent dynamics in channel flow
NASA Astrophysics Data System (ADS)
Park, Jae Sung; Graham, Michael D.
2015-11-01
The discovery of nonlinear traveling wave solutions to the Navier-Stokes equations or exact coherent states has greatly advanced the understanding of the nature of turbulent shear flows. These solutions are unstable saddle points in state space, while the time evolution of a turbulent flow is a dynamical trajectory wandering around them. In this regard, it is of interest to investigate how closely the turbulent trajectories approach these invariant states. Here, we present connections between turbulent trajectories and one intriguing solution family in channel flow. A state space visualization of turbulent trajectories is presented in a three-dimensional space. The lifetime of the trajectories is well represented by closeness to two distinct solutions resembling in many ways the active and hibernating phases of minimal channel turbulence (Xi & Graham PRL 2010). The connections are then examined by comparing mean profiles and flow structures. More importantly, the connections are confirmed by calculating the L2 distance between the trajectories and the traveling waves. Lastly, paths of an intermittent bursting phenomenon are identified in state space and the relationship between bursting paths and the traveling waves or hibernating turbulence is further discussed. This work was supported by the Air Force Office of Scientific Research through grant FA9550-15-1-0062 (Flow Interactions and Control Program).
Exact axisymmetric solutions of the Maxwell equations in a nonlinear nondispersive medium.
Petrov, E Yu; Kudrin, A V
2010-05-14
The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of special importance and, at the same time, is an extremely complicated problem. It seems almost impossible to find a rigorous solution to such a problem even for any model of nonlinearity. We obtain the first exact solution of this type. We present a new method for deriving exact solutions of the Maxwell equations in a nonlinear medium without dispersion and give examples of the obtained solutions that describe propagation of cylindrical electromagnetic waves in a nonlinear nondispersive medium and free electromagnetic oscillations in a cylindrical cavity resonator filled with such a medium.
NASA Astrophysics Data System (ADS)
Liu, Ping; Wang, Ya-Xiong; Ren, Bo; Li, Jin-Hua
2016-12-01
Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. Supported by the National Natural Science Foundation of China under Grant Nos. 11305031 and 11305106, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205
Classes of exact Einstein Maxwell solutions
NASA Astrophysics Data System (ADS)
Komathiraj, K.; Maharaj, S. D.
2007-12-01
We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.
Exactly solvable chaos in an electromechanical oscillator
NASA Astrophysics Data System (ADS)
Owens, Benjamin A. M.; Stahl, Mark T.; Corron, Ned J.; Blakely, Jonathan N.; Illing, Lucas
2013-09-01
A novel electromechanical chaotic oscillator is described that admits an exact analytic solution. The oscillator is a hybrid dynamical system with governing equations that include a linear second order ordinary differential equation with negative damping and a discrete switching condition that controls the oscillatory fixed point. The system produces provably chaotic oscillations with a topological structure similar to either the Lorenz butterfly or Rössler's folded-band oscillator depending on the configuration. Exact solutions are written as a linear convolution of a fixed basis pulse and a sequence of discrete symbols. We find close agreement between the exact analytical solutions and the physical oscillations. Waveform return maps for both configurations show equivalence to either a shift map or tent map, proving the chaotic nature of the oscillations.
Exact coherent structures for the turbulent cascade
NASA Astrophysics Data System (ADS)
Eckhardt, Bruno; Zammert, Stefan
2016-11-01
The exact coherent structures that are connected with the transition to turbulence in interior flows usually extend across the full height of the domain. Using exact coherent states that are localized in the shear direction together with scaling ideas for the Navier-Stokes equation that combine length and Reynolds number, we show how such large scale structures can be morphed into smaller scale coherent structures. As the Reynolds number increases, more of these states with ever smaller scales appear, all the way down to the Kolmogorov scale. We present the structure and dynamical properties of several families of exact coherent solution in plane Couette flow, with different degrees of spatial localization: Some of them remain localized in the center and help to built the turbulence cascade, others are localized near the walls and contribute to shaping the boundary layer profile.
Coriolis-coupled wave packet dynamics of H + HLi reaction.
Padmanaban, R; Mahapatra, S
2006-05-11
We investigated the effect of Coriolis coupling (CC) on the initial state-selected dynamics of H+HLi reaction by a time-dependent wave packet (WP) approach. Exact quantum scattering calculations were obtained by a WP propagation method based on the Chebyshev polynomial scheme and ab initio potential energy surface of the reacting system. Partial wave contributions up to the total angular momentum J=30 were found to be necessary for the scattering of HLi in its vibrational and rotational ground state up to a collision energy approximately 0.75 eV. For each J value, the projection quantum number K was varied from 0 to min (J, K(max)), with K(max)=8 until J=20 and K(max)=4 for further higher J values. This is because further higher values of K do not have much effect on the dynamics and also because one wishes to maintain the large computational overhead for each calculation within the affordable limit. The initial state-selected integral reaction cross sections and thermal rate constants were calculated by summing up the contributions from all partial waves. These were compared with our previous results on the title system, obtained within the centrifugal sudden and J-shifting approximations, to demonstrate the impact of CC on the dynamics of this system.
DFT calculations with the exact functional
NASA Astrophysics Data System (ADS)
Burke, Kieron
2014-03-01
I will discuss several works in which we calculate the exact exchange-correlation functional of density functional theory, mostly using the density-matrix renormalization group method invented by Steve White, our collaborator. We demonstrate that a Mott-Hubard insulator is a band metal. We also perform Kohn-Sham DFT calculations with the exact functional and prove that a simple algoritm always converges. But we find convergence becomes harder as correlations get stronger. An example from transport through molecular wires may also be discussed. Work supported by DOE grant DE-SC008696.
Exactly solvable birth and death processes
Sasaki, Ryu
2009-10-15
Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable 'matrix' quantum mechanics, which is recently proposed by Odake and the author [S. Odake and R. Sasaki, J. Math. Phys. 49, 053503 (2008)]. The (q-) Askey scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of q{sup x} (with x being the population) corresponding to the q-Racah polynomial.
Exact solution of the robust knapsack problem☆
Monaci, Michele; Pferschy, Ulrich; Serafini, Paolo
2013-01-01
We consider an uncertain variant of the knapsack problem in which the weight of the items is not exactly known in advance, but belongs to a given interval, and an upper bound is imposed on the number of items whose weight differs from the expected one. For this problem, we provide a dynamic programming algorithm and present techniques aimed at reducing its space and time complexities. Finally, we computationally compare the performances of the proposed algorithm with those of different exact algorithms presented so far in the literature for robust optimization problems. PMID:24187428
Finding exact spatial soliton profiles in nematic liquid crystals.
Beeckman, J; Neyts, K; Vanbrabant, P J M; James, R; Fernandez, F A
2010-02-15
Finding exact analytical soliton profile solutions is only possible for certain types of non-linear media. In most cases one must resort to numerical techniques to find the soliton profile. In this work we present numerical calculations of spatial soliton profiles in nematic liquid crystals. The nonlinearity is governed by the optical-field-induced liquid crystal director reorientation, which is described by a system of coupled nonlinear partial differential equations. The soliton profile is found using an iterative scheme whereby the induced waveguide and mode profiles are calculated alternatively until convergence is achieved. In this way it is also possible to find higher order solitons. The results in this work can be used to accurately design all-optical interconnections with soliton beams.
Exact solutions for laminated composite cylindrical shells in cylindrical bending
NASA Technical Reports Server (NTRS)
Yuan, F. G.
1992-01-01
Analytic elasticity solutions for laminated composite cylindrical shells under cylindrical bending are presented. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity, coupled governing partial differential equations are developed. The general expressions for the stresses and displacements in the laminated composite cylinders are discussed. The closed form solutions based on Classical Shell Theory (CST) and Donnell's (1933) theory are also derived for comparison purposes. Three examples illustrate the effect of radius-to-thickness ratio, coupling and stacking sequence. The results show that, in general, CST yields poor stress and displacement distributions for thick-section composite shells, but converges to the exact elasticity solution as the radius-to-thickness ratio increases. It is also shown that Donnell's theory significantly underestimates the stress and displacement response.
NASA Astrophysics Data System (ADS)
Chang, Kao-Hao; Tsaur, Deng-How; Wang, Jeen-Hwa
2014-12-01
A simplified mathematical model, composed of a semi-circular valley partially filled with an inclined alluvial layer under plane SH-wave incidence, is presented. To evaluate the site response theoretically, a rigorous series solution is derived via the region-matching technique. For angular wavefunctions constrained by an inclined free surface, the original form of Graf's addition formula is recast to arbitrarily shift the local coordinate system. The valley geometry, filling material, angle of incidence, and wave frequency are taken as significant parameters in exploring the site effect on ground motions. Also included are the frequency- and time-domain computations. Two canonical cases, the semi-circular vacant canyon and the fully filled semi-circular alluvial valley, with exact analytical solutions, and the partly horizontally filled case previously studied, are taken to be particular cases of the proposed general model. Steady-state results show that the peak amplitudes of motion may increase at low frequencies when the filling layer inclines to the illuminated region. At low-grazing incidence, the phenomenon of wave focusing becomes evident on the shadow side of the filling layer. Transient-state simulations elucidate how a sequence of surface waves travel on the topmost alluvium along opposite directions and interfere with multiple reflected waves within the filling layer.
Exact Relaxation in a Class of Nonequilibrium Quantum Lattice Systems
Cramer, M.; Eisert, J.; Dawson, C. M.; Osborne, T. J.
2008-01-25
A reasonable physical intuition in the study of interacting quantum systems says that, independent of the initial state, the system will tend to equilibrate. In this work we introduce an experimentally accessible setting where relaxation to a steady state is exact, namely, for the Bose-Hubbard model quenched from a Mott quantum phase to the free strong superfluid regime. We rigorously prove that the evolving state locally relaxes to a steady state with maximum entropy constrained by second moments--thus maximizing the entanglement. Remarkably, for this to be true, no time average is necessary. Our argument includes a central limit theorem and exploits the finite speed of information transfer. We also show that for all periodic initial configurations (charge density waves) the system relaxes locally, and identify experimentally accessible signatures in optical lattices as well as implications for the foundations of statistical mechanics.
An exactly solvable three-dimensional nonlinear quantum oscillator
Schulze-Halberg, A.; Morris, J. R.
2013-11-15
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states.
Propagation of microwaves in gradient transmission lines: exactly solvable model
NASA Astrophysics Data System (ADS)
Shvartsburg, A. B.; Silin, N. V.
2015-08-01
Propagation of microwaves along the transmission line with smoothly continuously distributed capacitance and inductance (gradient transmission line) is considered in the framework of an exactly solvable model. The appearance of strong heterogeneity-induced plasma-like dispersion in gradient transmission line determined by the sizes and shapes of these distributions, is visualized by means of this model. Owing to this dispersion the energy transport in the line discussed can be ensured by both travelling and evanescent microwave modes, characterized by the real and imaginary wave numbers, respectively. The reflectance spectra for microwaves, incident on this heterogeneous transition section located between two homogeneous sections of transmission line are presented, the antireflection properties of this section are demonstrated. The interference of evanescent and anti-evanescent microwave modes is shown to provide the effective weakly attenuated energy transfer in the tunneling regime. The analogy between this microwave system and gradient nano-optical photonic barrier in revealed.
Well-posedness and exact controllability of the mass balance equations for an extrusion process
NASA Astrophysics Data System (ADS)
Diagne, Mamadou; Shang, Peipei; Wang, Zhiqiang
2016-07-01
In this paper, we study the well-posedness and exact controllability of a physical model for a food extrusion process in the isothermal case. The model expresses the mass balance in the extruder chamber and consists of a hyperbolic Partial Differential Equation (PDE) and a nonlinear Ordinary Differential Equation (ODE) whose dynamics describes the evolution of a moving interface. By suitable change of coordinates and fixed point arguments, we prove the existence, uniqueness and regularity of the solution, and finally the exact controllability of the coupled system.
Exact Solutions to Time-dependent Mdps
NASA Technical Reports Server (NTRS)
Boyan, Justin A.; Littman, Michael L.
2000-01-01
We describe an extension of the Markov decision process model in which a continuous time dimension is included in the state space. This allows for the representation and exact solution of a wide range of problems in which transitions or rewards vary over time. We examine problems based on route planning with public transportation and telescope observation scheduling.
Verbal Interference Suppresses Exact Numerical Representation
ERIC Educational Resources Information Center
Frank, Michael C.; Fedorenko, Evelina; Lai, Peter; Saxe, Rebecca; Gibson, Edward
2012-01-01
Language for number is an important case study of the relationship between language and cognition because the mechanisms of non-verbal numerical cognition are well-understood. When the Piraha (an Amazonian hunter-gatherer tribe who have no exact number words) are tested in non-verbal numerical tasks, they are able to perform one-to-one matching…
Exact Vlasov Solutions of Kinetic Flux Ropes
NASA Astrophysics Data System (ADS)
Ng, C. S.
2014-12-01
Small-scale magnetic flux ropes have been observed to form within the diffusion region in three-dimensional (3D) kinetic simulations of magnetic reconnection. Such 3D structures and the 2D version of them (plasmoids, secondary islands) could have important dynamical effects on the reconnection physics itself. Small-scale flux ropes have also been observed within the interplanetary space. We have found exact time-steady solutions of kinetic flux ropes by generalizing exact solutions of 2D Bernstein-Greene-Kruskal (BGK) modes in a magnetized plasma with finite magnetic field strength [Ng, Bhattacharjee, and Skiff, Phys. Plasmas 13, 055903 (2006)] to cases with azimuthal magnetic fields so that these structures carry electric current as well as steady electric and magnetic fields. Such fully nonlinear solutions now satisfy exactly the Vlasov-Poisson-Ampere system of equations. Solutions like these could describe small-scale flux ropes observed in reconnection diffusion regions or in the interplanetary space. They are also exact nonlinear solutions that can be used to validate numerical schemes for kinetic simulations. This work is supported by a National Science Foundation grant PHY-1004357.
Th Matching Paradigm: An Exact Test Procedure.
ERIC Educational Resources Information Center
Gillett, Raphael
1985-01-01
Provides a framework based on rook methodology for constructing exact unweighted tests in the matching paradigm. This paradigm tests whether a one-to-one pairing configuration between objects in two arrays contains more pairings of a particular kind than expected under the null hypothesis. The procedure is particularly useful for small samples.…
An Exact Formulation of Bradford's Law.
ERIC Educational Resources Information Center
Leimkuhler, Ferdinand F.
1980-01-01
Demonstrates, with an example, a relatively simple method for fitting Bradford's law to empirical data to estimate the number of journals and articles in a subject collection. An exact discrete formulation illustrates Bradford's law as a special case of the Zipf-Mandlebrot "rank frequency" law. (Author/RAA)
A Series of Exact Solutions of (2+1)-Dimensional CDGKS Equation
NASA Astrophysics Data System (ADS)
Yang, Zong-Hang
2006-11-01
An algebraic method with symbolic computation is devised to uniformly construct a series of exact solutions of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawda equation. The solutions obtained in this paper include solitary wave solutions, rational solutions, triangular periodic solutions, Jacobi and Weierstrass doubly periodic solutions. Among them, the Jacobi periodic solutions exactly degenerate to the solutions at a certain limit condition. Compared with most existing tanh method, the method used here can give new and more general solutions. More importantly, this method provides a guideline to classify the various types of the solution according to some parameters.
Conformal invariance and new exact solutions of the elastostatics equations
NASA Astrophysics Data System (ADS)
Chirkunov, Yu. A.
2017-03-01
We fulfilled a group foliation of the system of n-dimensional (n ≥ 2) Lame equations of the classical static theory of elasticity with respect to the infinite subgroup contained in normal subgroup of main group of this system. It permitted us to move from the Lame equations to the equivalent unification of two first-order systems: automorphic and resolving. We obtained a general solution of the automorphic system. This solution is an n-dimensional analogue of the Kolosov-Muskhelishvili formula. We found the main Lie group of transformations of the resolving system of this group foliation. It turned out that in the two-dimensional and three-dimensional cases, which have a physical meaning, this system is conformally invariant, while the Lame equations admit only a group of similarities of the Euclidean space. This is a big success, since in the method of group foliation, resolving equations usually inherit Lie symmetries subgroup of the full symmetry group that was not used for the foliation. In the three-dimensional case for the solutions of the resolving system, we found the general form of the transformations similar to the Kelvin transformation. These transformations are the consequence of the conformal invariance of the resolving system. In the three-dimensional case with a help of the complex dependent and independent variables, the resolving system is written as a simple complex system. This allowed us to find non-trivial exact solutions of the Lame equations, which direct for the Lame equations practically impossible to obtain. For this complex system, all the essentially distinct invariant solutions of the maximal rank we have found in explicit form, or we reduced the finding of those solutions to the solving of the classical one-dimensional equations of the mathematical physics: the heat equation, the telegraph equation, the Tricomi equation, the generalized Darboux equation, and other equations. For the resolving system, we obtained double wave of a
Mitri, F. G.
2015-09-15
The standard Resonance Scattering Theory (RST) of plane waves is extended for the case of any two-dimensional (2D) arbitrarily-shaped monochromatic beam incident upon an elastic cylinder with arbitrary location using an exact methodology based on Graf’s translational addition theorem for the cylindrical wave functions. The analysis is exact as it does not require numerical integration procedures. The formulation is valid for any cylinder of finite size and material that is immersed in a nonviscous fluid. Partial-wave series expansions (PWSEs) for the incident, internal and scattered linear pressure fields are derived, and the analysis is further extended to obtain generalized expressions for the on-axis and off-axis acoustic radiation force components. The wave-fields are expressed using generalized PWSEs involving the beam-shape coefficients (BSCs) and the scattering coefficients of the cylinder. The off-axial BSCs are expressed analytically in terms of an infinite PWSE with emphasis on the translational offset distance d. Numerical computations are considered for a zeroth-order quasi-Gaussian beam chosen as an example to illustrate the analysis. Acoustic resonance scattering directivity diagrams are calculated by subtracting an appropriate background from the expression of the scattered pressure field. In addition, computations for the radiation force exerted on an elastic cylinder centered on the axis of wave propagation of the beam, and shifted off-axially are analyzed and discussed.
An exact solution for the Hawking effect in a dispersive fluid
NASA Astrophysics Data System (ADS)
Philbin, T. G.
2016-09-01
We consider the wave equation for sound in a moving fluid with a fourth-order anomalous dispersion relation. The velocity of the fluid is a linear function of position, giving two points in the flow where the fluid velocity matches the group velocity of low-frequency waves. We find the exact solution for wave propagation in the flow. The scattering shows amplification of classical waves, leading to spontaneous emission when the waves are quantized. In the dispersionless limit the system corresponds to a 1 +1 -dimensional black-hole or white-hole binary and there is a thermal spectrum of Hawking radiation from each horizon. Dispersion changes the scattering coefficients so that the quantum emission is no longer thermal. The scattering coefficients were previously obtained by Busch and Parentani in a study of dispersive fields in de Sitter space [Phys. Rev. D 86, 104033 (2012)]. Our results give further details of the wave propagation in this exactly solvable case, where our focus is on laboratory systems.
Tree reconstruction from partial orders
Kannan, S.K. ); Warnow, T.J. )
1993-01-01
The problem of constructing trees given a matrix of interleaf distances is motivated by applications in computational evolutionary biology and linguistics. The general problem is to find an edge-weighted tree which most closely approximates the distance matrix. Although the construction problem is easy when the tree exactly fits the distance matrix, optimization problems under all popular criteria are either known or conjectured to be NP-complete. In this paper we consider the related problem where we are given a partial order on the pairwise distances, and wish to construct (if possible) an edge-weighted tree realizing the partial order. In particular we are interested in partial orders which arise from experiments on triples of species, which determine either a linear ordering of the three pairwise distances (called Total Order Model or TOM experiments) or only the pair(s) of minimum distance apart (called Partial Order Model or POM experiments). The POM and TOM experimental model is inspired by the model proposed by Kannan, Lawler, and Warnow for constructing trees from experiments which determine the rooted topology for any triple of species. We examine issues of construction of trees and consistency of TOM and POM experiments, where the trees may either be weighted or unweighted. Using these experiments to construct unweighted trees without nodes of degree two is motivated by a similar problem studied by Winkler, called the Discrete Metric Realization problem, which he showed to be strongly NP-hard. We have the following results: Determining consistency of a set of TOM or POM experiments is NP-Complete whether the tree is weighted or constrained to be unweighted and without degree two nodes. We can construct unweighted trees without degree two nodes from TOM experiments in optimal O(n[sup 3]) time and from POM experiments in O(n[sup 4]) time.
Tree reconstruction from partial orders
Kannan, S.K.; Warnow, T.J.
1993-03-01
The problem of constructing trees given a matrix of interleaf distances is motivated by applications in computational evolutionary biology and linguistics. The general problem is to find an edge-weighted tree which most closely approximates the distance matrix. Although the construction problem is easy when the tree exactly fits the distance matrix, optimization problems under all popular criteria are either known or conjectured to be NP-complete. In this paper we consider the related problem where we are given a partial order on the pairwise distances, and wish to construct (if possible) an edge-weighted tree realizing the partial order. In particular we are interested in partial orders which arise from experiments on triples of species, which determine either a linear ordering of the three pairwise distances (called Total Order Model or TOM experiments) or only the pair(s) of minimum distance apart (called Partial Order Model or POM experiments). The POM and TOM experimental model is inspired by the model proposed by Kannan, Lawler, and Warnow for constructing trees from experiments which determine the rooted topology for any triple of species. We examine issues of construction of trees and consistency of TOM and POM experiments, where the trees may either be weighted or unweighted. Using these experiments to construct unweighted trees without nodes of degree two is motivated by a similar problem studied by Winkler, called the Discrete Metric Realization problem, which he showed to be strongly NP-hard. We have the following results: Determining consistency of a set of TOM or POM experiments is NP-Complete whether the tree is weighted or constrained to be unweighted and without degree two nodes. We can construct unweighted trees without degree two nodes from TOM experiments in optimal O(n{sup 3}) time and from POM experiments in O(n{sup 4}) time.
Liu, Jia; Han, Qiang; Shao, L B; Wang, Z D
2011-07-08
A type of electron pairing model with spin-orbit interactions or Zeeman coupling is solved exactly in the framework of the Richardson ansatz. Based on the exact solutions for the case with spin-orbit interactions, it is shown rigorously that the pairing symmetry is of the p + ip wave and the ground state possesses time-reversal symmetry, regardless of the strength of the pairing interaction. Intriguingly, how Majorana fermions can emerge in the system is also elaborated. Exact results are illustrated for two systems, respectively, with spin-orbit interactions and Zeeman coupling.
Partial polarization by quantum distinguishability
NASA Astrophysics Data System (ADS)
Lahiri, Mayukh; Hochrainer, Armin; Lapkiewicz, Radek; Lemos, Gabriela Barreto; Zeilinger, Anton
2017-03-01
We establish that a connection exists between wave-particle duality of photons and partial polarization of a light beam. We perform a two-path lowest-order (single photon) interference experiment and demonstrate both theoretically and experimentally that the degree of polarization of the light beam emerging from an output of the interferometer depends on path distinguishability. In our experiment, we are able to change the quantum state of the emerging photon from a pure state to a fully mixed state without any direct interaction with the photon. Although most lowest-order interference experiments can be explained by classical theory, our experiment has no genuine classical analog. Our results show that a case exists where the cause of partial polarization is beyond the scope of classical theory.
Rogue waves in Lugiato-Lefever equation with variable coefficients
NASA Astrophysics Data System (ADS)
Kol, Guy; Kingni, Sifeu; Woafo, Paul
2014-11-01
In this paper, we theoretically investigate the generation of optical rogue waves from a Lugiato-Lefever equation with variable coefficients by using the nonlinear Schrödinger equation-based constructive method. Exact explicit rogue-wave solutions of the Lugiato-Lefever equation with constant dispersion, detuning and dissipation are derived and presented. The bright rogue wave, intermediate rogue wave and the dark rogue wave are obtained by changing the value of one parameter in the exact explicit solutions corresponding to the external pump power of a continuous-wave laser.
Hidden algebra method (quasi-exact-solvability in quantum mechanics)
Turbiner, Alexander
1996-02-20
A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland N-body problems ass ociated with an existence of the hidden algebra slN is discussed extensively.
Exact nonlinear excitations in double-degenerate plasmas
Akbari-Moghanjoughi, M.
2012-06-15
In this work, we use the conventional hydrodynamics formalism and incorporate the Chew-Goldberger-Low double-adiabatic theory to evaluate the nonlinear electrostatic ion excitations in double-degenerate (electron spin-orbit degenerate) magnetized quantum plasmas. Based on the Sagdeev pseudopotential method, an exact general pseudopotential is calculated which leads to the allowed Mach-number range criteria for such localized density structures in an anisotropic magnetized plasma. We employ the criteria on the Mach-number range for diverse magnetized quantum plasma with different equations of state. It is remarked that various plasma fractional parameters such as the system dimensionality, ion-temperature, relativistic-degeneracy, Zeeman-energy, and plasma composition are involved in the stability of an obliquely propagating nonlinear ion-acoustic wave in a double-degenerate quantum plasma. Current study is most appropriate for nonlinear wave analysis in dense astrophysical magnetized plasma environments such as white-dwarfs and neutron-star crusts where the strong magnetic fields can be present.
Exact folded-band chaotic oscillator.
Corron, Ned J; Blakely, Jonathan N
2012-06-01
An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.
Exact cumulant Kramers-Moyal-like expansion
NASA Astrophysics Data System (ADS)
Morgado, W. A. M.
2015-11-01
We derive an exact equation, a Cumulant Kramers-Moyal Equation (CKME), quite similar to the Kramers-Moyal Equation (KME), for the probability distribution of a Markovian dynamical system. It can be applied to any well behaved (converging cumulants) continuous time systems, such as Langevin equations or other models. An interesting but significant difference with respect to the KME is that their jump-moments are proportional to cumulants of the dynamical variables, but not proportional to central moments, as is the case for the KME. In fact, they still obey a weaker version of Pawula's theorem, namely Marcinkiewicz's theorem. We compare the results derived from the equations herein with the ones obtained by computing via Gaussian and biased, and unbiased, Poisson Langevin dynamics and a Poisson non-Langevin model. We obtain the exact CKME time-evolution equation for the systems, and in several cases, those are distinct from the Fokker-Planck equation or the KME.
Exact axisymmetric Taylor states for shaped plasmas
Cerfon, Antoine J. O'Neil, Michael
2014-06-15
We present a general construction for exact analytic Taylor states in axisymmetric toroidal geometries. In this construction, the Taylor equilibria are fully determined by specifying the aspect ratio, elongation, and triangularity of the desired plasma geometry. For equilibria with a magnetic X-point, the location of the X-point must also be specified. The flexibility and simplicity of these solutions make them useful for verifying the accuracy of numerical solvers and for theoretical studies of Taylor states in laboratory experiments.
Exact quantization conditions for cluster integrable systems
NASA Astrophysics Data System (ADS)
Franco, Sebastián; Hatsuda, Yasuyuki; Mariño, Marcos
2016-06-01
We propose exact quantization conditions for the quantum integrable systems of Goncharov and Kenyon, based on the enumerative geometry of the corresponding toric Calabi-Yau manifolds. Our conjecture builds upon recent results on the quantization of mirror curves, and generalizes a previous proposal for the quantization of the relativistic Toda lattice. We present explicit tests of our conjecture for the integrable systems associated to the resolved {{{C}}3}/{{{Z}}5} and {{{C}}3}/{{{Z}}6} orbifolds.
Bueyuekasik, Sirin A.; Pashaev, Oktay K.
2010-12-15
We construct a Madelung fluid model with time variable parameters as a dissipative quantum fluid and linearize it in terms of Schroedinger equation with time-dependent parameters. It allows us to find exact solutions of the nonlinear Madelung system in terms of solutions of the Schroedinger equation and the corresponding classical linear ordinary differential equation with variable frequency and damping. For the complex velocity field, the Madelung system takes the form of a nonlinear complex Schroedinger-Burgers equation, for which we obtain exact solutions using complex Cole-Hopf transformation. In particular, we give exact results for nonlinear Madelung systems related with Caldirola-Kanai-type dissipative harmonic oscillator. Collapse of the wave function in dissipative models and possible implications for the quantum cosmology are discussed.
Exact image method for Gaussian beam problems involving a planar interface
NASA Technical Reports Server (NTRS)
Lindell, I. V.
1987-01-01
Exact image method, recently introduced for the solution of electromagnetic field problems involving sources above a planar interface or two homogeneous media, is shown to be valid also for sources located in complex space, which makes its application possible for Gaussian beam analysis. It is demonstrated that the Goos-Hanchen shift and the angular shift of a TE polarized beam are correctly given as asymptotic results by the exact reflection image theory. Also, the apparent image location giving the correct Gaussian beam transmitted through the interface is obtained as another asymptotic check. The present theory makes it possible to calculate the exact coupling from the Gaussian beam to the reflected and refracted beams, as well as to the surface wave.
Freestyle Vs. Boolean: A Comparison of Partial and Exact Match Retrieval Systems.
ERIC Educational Resources Information Center
Paris, Lee Anne H.; Tibbo, Helen R.
1998-01-01
Compares results of traditional Boolean searching with those of Freestyle, LEXIS/NEXIS's natural language application. Study found that though the Boolean searches had better results more often, neither method demonstrated superior performance for every query, suggesting that different queries demand different techniques. Concludes that further…
Exact and Approximate Sizes of Convex Datacubes
NASA Astrophysics Data System (ADS)
Nedjar, Sébastien
In various approaches, data cubes are pre-computed in order to efficiently answer Olap queries. The notion of data cube has been explored in various ways: iceberg cubes, range cubes, differential cubes or emerging cubes. Previously, we have introduced the concept of convex cube which generalizes all the quoted variants of cubes. More precisely, the convex cube captures all the tuples satisfying a monotone and/or antimonotone constraint combination. This paper is dedicated to a study of the convex cube size. Actually, knowing the size of such a cube even before computing it has various advantages. First of all, free space can be saved for its storage and the data warehouse administration can be improved. However the main interest of this size knowledge is to choose at best the constraints to apply in order to get a workable result. For an aided calibrating of constraints, we propose a sound characterization, based on inclusion-exclusion principle, of the exact size of convex cube as long as an upper bound which can be very quickly yielded. Moreover we adapt the nearly optimal algorithm HyperLogLog in order to provide a very good approximation of the exact size of convex cubes. Our analytical results are confirmed by experiments: the approximated size of convex cubes is really close to their exact size and can be computed quasi immediately.
Exact tests for Hardy-Weinberg proportions.
Engels, William R
2009-12-01
Exact conditional tests are often required to evaluate statistically whether a sample of diploids comes from a population with Hardy-Weinberg proportions or to confirm the accuracy of genotype assignments. This requirement is especially common when the sample includes multiple alleles and sparse data, thus rendering asymptotic methods, such as the common chi(2)-test, unreliable. Such an exact test can be performed using the likelihood ratio as its test statistic rather than the more commonly used probability test. Conceptual advantages in using the likelihood ratio are discussed. A substantially improved algorithm is described to permit the performance of a full-enumeration exact test on sample sizes that are too large for previous methods. An improved Monte Carlo algorithm is also proposed for samples that preclude full enumeration. These algorithms are about two orders of magnitude faster than those currently in use. Finally, methods are derived to compute the number of possible samples with a given set of allele counts, a useful quantity for evaluating the feasibility of the full enumeration procedure. Software implementing these methods, ExactoHW, is provided.
A hierarchical exact accelerated stochastic simulation algorithm
NASA Astrophysics Data System (ADS)
Orendorff, David; Mjolsness, Eric
2012-12-01
A new algorithm, "HiER-leap" (hierarchical exact reaction-leaping), is derived which improves on the computational properties of the ER-leap algorithm for exact accelerated simulation of stochastic chemical kinetics. Unlike ER-leap, HiER-leap utilizes a hierarchical or divide-and-conquer organization of reaction channels into tightly coupled "blocks" and is thereby able to speed up systems with many reaction channels. Like ER-leap, HiER-leap is based on the use of upper and lower bounds on the reaction propensities to define a rejection sampling algorithm with inexpensive early rejection and acceptance steps. But in HiER-leap, large portions of intra-block sampling may be done in parallel. An accept/reject step is used to synchronize across blocks. This method scales well when many reaction channels are present and has desirable asymptotic properties. The algorithm is exact, parallelizable and achieves a significant speedup over the stochastic simulation algorithm and ER-leap on certain problems. This algorithm offers a potentially important step towards efficient in silico modeling of entire organisms.
An Exact Procedure for the Evaluation of Reference-Scaled Average Bioequivalence.
Tothfalusi, Laszlo; Endrenyi, Laszlo
2016-03-01
Reference-scaled average bioequivalence (RSABE) has been recommended by Food and Drug Administration (FDA), and in its closely related form by European Medicines Agency (EMA), for the determination of bioequivalence (BE) of highly variable (HV) and narrow therapeutic index (NTI) drug products. FDA suggested that RSABE be evaluated by an approximating procedure. Development of an alternative, numerically exact approach was sought. A new algorithm, called Exact, was derived for the assessment of RSABE. It is based upon the observation that the statistical model of RSABE follows a noncentral t distribution. The parameters of the distribution were derived for crossover and parallel-group study designs. Simulated BE studies of HV and NTI drugs compared the power and consumer risk of the proposed Exact method with those recommended by FDA and EMA. The Exact method had generally slightly higher power than the FDA approach. The consumer risks of the Exact and FDA procedures were generally below the nominal error risk with both methods except for the partial replicate design under certain heteroscedastic conditions. The estimator of RSABE was biased; simulations demonstrated the appropriateness of Hedges' correction. The FDA approach had another, small but meaningful bias. The confidence intervals of RSABE, based on the derived exact, analytical formulas, are uniformly most powerful. Their computation requires in standard cases only a single-line program script. The algorithm assumes that the estimates of the within-subject variances of both formulations are available. With each algorithm, the consumer risk is higher than 5% when the partial replicate design is applied.
Planetary waves in rotating ionosphere
Khantadze, A. G.; Jandieri, V. G.; Jandieri, G. V.
2008-06-15
The problem of propagation of ultralong planetary waves in the Earth's upper atmosphere is considered. A new exact solution to the MHD equations for the ionosphere is obtained in spherical coordinates with allowance for the geomagnetic field and Earth's rotation. A general dispersion relation is derived for planetary waves in the ionospheric E and F regions, and the characteristic features of their propagation in a weakly ionized ionospheric plasma are discussed.
... Jacksonian seizure; Seizure - partial (focal); Temporal lobe seizure; Epilepsy - partial seizures ... Abou-Khalil BW, Gallagher MJ, Macdonald RL. Epilepsies. In: Daroff ... Practice . 7th ed. Philadelphia, PA: Elsevier; 2016:chap 101. ...
NASA Technical Reports Server (NTRS)
Boersma, J.; Rahmat-Samii, Y.
1980-01-01
The diffraction of an arbitrary cylindrical wave by a half-plane has been treated by Rahmat-Samii and Mittra who used a spectral domain approach. In this paper, their exact solution for the total field is expressed in terms of a new integral representation. For large wave number k, two rigorous procedures are described for the exact uniform asymptotic expansion of the total field solution. The uniform expansions obtained are valid in the entire space, including transition regions around the shadow boundaries. The final results are compared with the formulations of two leading uniform theories of edge diffraction, namely, the uniform asymptotic theory and the uniform theory of diffraction. Some unique observations and conclusions are made in relating the two theories.
Spectral theory of a surface-corrugated electron waveguide: The exact scattering-operator approach
NASA Astrophysics Data System (ADS)
Makarov, N. M.; Moroz, A. V.
1999-07-01
We apply the exact surface scattering operator to solve the problem of scalar (electron or sound) wave propagation through a strip with absolutely soft randomly rough boundaries. This approach is nonperturbative in either roughness heights or slopes. We analyzed the roughness-induced dephasing and attenuation of waves both asymptotically and numerically. The analysis proves that the signal is always scattered most effectively into the ``resonant'' waveguide modes, whose transverse wavelength is comparable to the rms roughness height ζ and whose total number is proportional to ζ-1. According to this integral resonance rule, the dephasing dominates over the attenuation and shows a nonanalytic (square-root) dependence on the dispersion ζ2 when (kζ)2<<1 (k is the wave number). In the case (kζ)2>>1, the dephasing and attenuation may well compete. We predict another two surprising effects: reentrant transparency and increase of the phase velocity of the wave.
Partial dynamical symmetry at critical points of quantum phase transitions.
Leviatan, A
2007-06-15
We show that partial dynamical symmetries can occur at critical points of quantum phase transitions, in which case underlying competing symmetries are conserved exactly by a subset of states, and mix strongly in other states. Several types of partial dynamical symmetries are demonstrated with the example of critical-point Hamiltonians for first- and second-order transitions in the framework of the interacting boson model, whose dynamical symmetries correspond to different shape phases in nuclei.
Exact solutions of the derivative nonlinear Schrödinger equation for a nonlinear transmission line.
Kengne, E; Liu, W M
2006-02-01
We consider the derivative nonlinear Schrödinger equation with constant potential as a model for wave propagation on a discrete nonlinear transmission line. This equation can be derived in the small amplitude and long wavelength limit using the standard reductive perturbation method and complex expansion. We construct some exact soliton and elliptic solutions of the mentioned equation by perturbation of its Stokes wave solutions. We find that for some values of the coefficients of the equation and for some parameters of solutions, the graphical representations show some kinds of symmetries such as mirror symmetry and rotational symmetry.
ALmost EXact boundary conditions for transient Schrödinger–Poisson system
Bian, Lei; Pang, Gang; Tang, Shaoqiang; Arnold, Anton
2016-05-15
For the Schrödinger–Poisson system, we propose an ALmost EXact (ALEX) boundary condition to treat accurately the numerical boundaries. Being local in both space and time, the ALEX boundary conditions are demonstrated to be effective in suppressing spurious numerical reflections. Together with the Crank–Nicolson scheme, we simulate a resonant tunneling diode. The algorithm produces numerical results in excellent agreement with those in Mennemann et al. [1], yet at a much reduced complexity. Primary peaks in wave function profile appear as a consequence of quantum resonance, and should be considered in selecting the cut-off wave number for numerical simulations.
Exact solution to the Schrödinger’s equation with pseudo-Gaussian potential
Iacob, Felix; Lute, Marina
2015-12-15
We consider the radial Schrödinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of energy levels for the bound states are calculated along with their corresponding normalized wave-functions. The case of positive energy levels, known as meta-stable states, is also discussed and the magnitude of transmission coefficient through the potential barrier is evaluated.
Interference effects in phased beam tracing using exact half-space solutions.
Boucher, Matthew A; Pluymers, Bert; Desmet, Wim
2016-12-01
Geometrical acoustics provides a correct solution to the wave equation for rectangular rooms with rigid boundaries and is an accurate approximation at high frequencies with nearly hard walls. When interference effects are important, phased geometrical acoustics is employed in order to account for phase shifts due to propagation and reflection. Error increases, however, with more absorption, complex impedance values, grazing incidence, smaller volumes and lower frequencies. Replacing the plane wave reflection coefficient with a spherical one reduces the error but results in slower convergence. Frequency-dependent stopping criteria are then applied to avoid calculating higher order reflections for frequencies that have already converged. Exact half-space solutions are used to derive two additional spherical wave reflection coefficients: (i) the Sommerfeld integral, consisting of a plane wave decomposition of a point source and (ii) a line of image sources located at complex coordinates. Phased beam tracing using exact half-space solutions agrees well with the finite element method for rectangular rooms with absorbing boundaries, at low frequencies and for rooms with different aspect ratios. Results are accurate even for long source-to-receiver distances. Finally, the crossover frequency between the plane and spherical wave reflection coefficients is discussed.
Instability of some equatorially trapped waves
Constantin, Adrian; Germain, Pierre
2013-01-01
[1] A high-frequency asymptotics approach within the Lagrangian framework shows that some exact equatorially trapped three-dimensional waves are linearly unstable when their steepness exceeds a specific threshold. Citation: Constantin, A., and P. Germain (2013), Instability of some equatorially trapped waves, J. Geophys. Res. Oceans, 118, 2802–2810, doi:10.1002/jgrc.20219. PMID:26213669
Nonlinear Evolution of Alfvenic Wave Packets
NASA Technical Reports Server (NTRS)
Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.
1998-01-01
Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
Initial value problem solution of nonlinear shallow water-wave equations.
Kânoğlu, Utku; Synolakis, Costas
2006-10-06
The initial value problem solution of the nonlinear shallow water-wave equations is developed under initial waveforms with and without velocity. We present a solution method based on a hodograph-type transformation to reduce the nonlinear shallow water-wave equations into a second-order linear partial differential equation and we solve its initial value problem. The proposed solution method overcomes earlier limitation of small waveheights when the initial velocity is nonzero, and the definition of the initial conditions in the physical and transform spaces is consistent. Our solution not only allows for evaluation of differences in predictions when specifying an exact initial velocity based on nonlinear theory and its linear approximation, which has been controversial in geophysical practice, but also helps clarify the differences in runup observed during the 2004 and 2005 Sumatran tsunamigenic earthquakes.
NASA Astrophysics Data System (ADS)
Brodin, G.; Stenflo, L.
2017-03-01
Considering a class of solutions where the density perturbations are functions of time, but not of space, we derive a new exact large amplitude wave solution for a cold uniform electron plasma. This result illustrates that most simple analytical solutions can appear even if the density perturbations are large.
Exact, zero-energy, square-integrable solutions of a model related to the Maxwell's fish-eye problem
Makowski, Adam J.
2009-12-15
A model, which admits normalizable wave functions of the Schroedinger equation at the energy of E = 0, is exactly solved and the solutions are compared to the corresponding classical trajectories. The wave functions are proved to be square-integrable for discrete (quantized) values of the coupling constant of the used potential. We also show that our model is a specific version of the well-known Maxwell's fish-eye. This is performed with the help of a suitably chosen conformal mapping.
Exact Pressure Evolution Equation for Incompressible Fluids
NASA Astrophysics Data System (ADS)
Tessarotto, M.; Ellero, M.; Aslan, N.; Mond, M.; Nicolini, P.
2008-12-01
An important aspect of computational fluid dynamics is related to the determination of the fluid pressure in isothermal incompressible fluids. In particular this concerns the construction of an exact evolution equation for the fluid pressure which replaces the Poisson equation and yields an algorithm which is a Poisson solver, i.e., it permits to time-advance exactly the same fluid pressure without solving the Poisson equation. In fact, the incompressible Navier-Stokes equations represent a mixture of hyperbolic and elliptic pde's, which are extremely hard to study both analytically and numerically. This amounts to transform an elliptic type fluid equation into a suitable hyperbolic equation, a result which usually is reached only by means of an asymptotic formulation. Besides being a still unsolved mathematical problem, the issue is relevant for at least two reasons: a) the proliferation of numerical algorithms in computational fluid dynamics which reproduce the behavior of incompressible fluids only in an asymptotic sense (see below); b) the possible verification of conjectures involving the validity of appropriate equations of state for the fluid pressure. Another possible motivation is, of course, the ongoing quest for efficient numerical solution methods to be applied for the construction of the fluid fields {ρ,V,p}, solutions of the initial and boundary-value problem associated to the incompressible N-S equations (INSE). In this paper we intend to show that an exact solution to this problem can be achieved adopting the approach based on inverse kinetic theory (IKT) recently developed for incompressible fluids by Tessarotto et al. [7, 6, 7, 8, 9]. In particular we intend to prove that the evolution of the fluid fields can be achieved by means of a suitable dynamical system, to be identified with the so-called Navier-Stokes (N-S) dynamical system. As a consequence it is found that the fluid pressure obeys a well-defined evolution equation. The result appears
Exact two-component Hamiltonians revisited.
Liu, Wenjian; Peng, Daoling
2009-07-21
Two routes for deriving the exact two-component Hamiltonians are compared. In the first case, as already known, we start directly from the matrix representation of the Dirac operator in a restricted kinetically balanced basis and make a single block diagonalization. In the second case, not considered before, we start instead from the Foldy-Wouthuysen operator and make proper use of resolutions of the identity. The expressions are surprisingly different. It turns out that a mistake was made in the former formulation when going from the Dirac to the Schrodinger picture. The two formulations become equivalent after the mistake is corrected.
Exact two-component Hamiltonians revisited
Liu Wenjian; Peng Daoling
2009-07-21
Two routes for deriving the exact two-component Hamiltonians are compared. In the first case, as already known, we start directly from the matrix representation of the Dirac operator in a restricted kinetically balanced basis and make a single block diagonalization. In the second case, not considered before, we start instead from the Foldy-Wouthuysen operator and make proper use of resolutions of the identity. The expressions are surprisingly different. It turns out that a mistake was made in the former formulation when going from the Dirac to the Schroedinger picture. The two formulations become equivalent after the mistake is corrected.
An exact accelerated stochastic simulation algorithm.
Mjolsness, Eric; Orendorff, David; Chatelain, Philippe; Koumoutsakos, Petros
2009-04-14
An exact method for stochastic simulation of chemical reaction networks, which accelerates the stochastic simulation algorithm (SSA), is proposed. The present "ER-leap" algorithm is derived from analytic upper and lower bounds on the multireaction probabilities sampled by SSA, together with rejection sampling and an adaptive multiplicity for reactions. The algorithm is tested on a number of well-quantified reaction networks and is found experimentally to be very accurate on test problems including a chaotic reaction network. At the same time ER-leap offers a substantial speedup over SSA with a simulation time proportional to the 23 power of the number of reaction events in a Galton-Watson process.
Exact solutions for network rewiring models
NASA Astrophysics Data System (ADS)
Evans, T. S.
2007-03-01
Evolving networks with a constant number of edges may be modelled using a rewiring process. These models are used to describe many real-world processes including the evolution of cultural artifacts such as family names, the evolution of gene variations, and the popularity of strategies in simple econophysics models such as the minority game. The model is closely related to Urn models used for glasses, quantum gravity and wealth distributions. The full mean field equation for the degree distribution is found and its exact solution and generating solution are given.
Exact probability distribution functions for Parrondo's games
NASA Astrophysics Data System (ADS)
Zadourian, Rubina; Saakian, David B.; Klümper, Andreas
2016-12-01
We study the discrete time dynamics of Brownian ratchet models and Parrondo's games. Using the Fourier transform, we calculate the exact probability distribution functions for both the capital dependent and history dependent Parrondo's games. In certain cases we find strong oscillations near the maximum of the probability distribution with two limiting distributions for odd and even number of rounds of the game. Indications of such oscillations first appeared in the analysis of real financial data, but now we have found this phenomenon in model systems and a theoretical understanding of the phenomenon. The method of our work can be applied to Brownian ratchets, molecular motors, and portfolio optimization.
Exactly soluble quantum wormhole in two dimensions
Kim, Won Tae; Son, Edwin J.; Yoon, Myung Seok
2004-11-15
We are presenting a quantum traversable wormhole in an exactly soluble two-dimensional model. This is different from previous works since the exotic negative energy that supports the wormhole is generated from the quantization of classical energy-momentum tensors. This explicit illustration shows the quantum-mechanical energy can be used as a candidate for the exotic source. As for the traversability, after a particle travels through the wormhole, the static initial wormhole geometry gets a back reaction which spoils the wormhole structure. However, it may still maintain the initial structure along with the appropriate boundary condition.
Model for microemulsions: An exactly solvable case
Renlie, L. ); Hoye, J.S. ); Skaf, M.S. ); Stell, G. )
1991-10-01
The microscopic model for microemulsions, introduced earlier by Ciach, Hoye, and Stell (J. Chem. Phys. {bold 90}, 1214 (1989)) is here specialized to a one-dimensional lattice and solved exactly by the transfer matrix method. The microemulsion phase is identified by the formation of thermally distributed surfactant-bounded domains of oil. For this phase we find scattering functions and characteristic lengths that have some of the same features found in experimental data for microemulsions. Mean-field interactions beyond nearest-neighbor sites are introduced in order to study the phase diagram for the nonperiodic phases we encounter.
Shock wave structure in a lattice gas
NASA Astrophysics Data System (ADS)
Broadwell, James E.; Han, Donghee
2007-05-01
The motion and structure of shock and expansion waves in a simple particle system, a lattice gas and cellular automaton, are determined in an exact computation. Shock wave solutions, also exact, of a continuum description, a model Boltzmann equation, are compared with the lattice results. The comparison demonstrates that, as proved by Caprino et al. ["A derivation of the Broadwell equation," Commun. Math. Phys. 135, 443 (1991)] only when the lattice processes are stochastic is the model Boltzmann description accurate. In the strongest shock wave, the velocity distribution function is the bimodal function proposed by Mott-Smith.
Resonant Alfven Wave Excitation
NASA Astrophysics Data System (ADS)
Hameiri, Eliezer
1999-11-01
Much of the theory of the Alfven wave resonance phenomenon was developed for a tokamak configuration where the magnetic field winds around the torus without entering the boundary. Thus, boundary conditions did not have to be considered.( J. Tataronis and W. Grossmann, Z. Phys. 261), 203 (1973). In most space plasma situations such as the magnetosphere or the Sun, as well as in the scrape-off layer of a divertor tokamak, this is not the case. When boundary conditions are considered, it is generally assumed for simplicity that the boundary is perfectly conducting, which implies that the Alfven wave bounce frequencies are real and the resonance phenomenon can be detected by some singularity in the equations. The nature of the singularity is usually described in terms of a Frobenius series.( A.N. Wright and M.J. Thompson, Phys. Plamsas 1), 691 (1994). In this work we consider resistive boundaries, which imply that the fast wave eigenfrequency is real, but the Alfven frequency is not. Thus, there is no exact resonance and no singularity in the equations. The solution of the problem is carried out asymptotically by finding an exact Laplace integral representation for the solution and then matching various regions. The energy transferred to the Alfven wave appears to be rather small.
Inflationary potentials from the exact renormalisation group
NASA Astrophysics Data System (ADS)
Grozdanov, Sašo; Kraljić, David; Svanes, Eirik Eik
2016-08-01
We show that an inflationary slow-roll potential can be derived as an IR limit of the non-perturbative exact renormalisation group equation for a scalar field within the mean-field approximation. The result follows without having to specify a Lagrangian in the UV, which we take to be somewhere below the Planck scale to avoid discussing quantum gravity effects. We assume that the theory contains a scalar mode with suppressed coupling to other fields, and that higher derivative couplings are suppressed. In this framework the exact RG equation becomes a one-dimensional Schrödinger equation, which we solve. The effective IR potential is then dominated by the eigen-states of the RG Hamiltonian with the highest eigenvalues. We find that these potentials can generically give rise to slow-roll inflation, which is fully consistent with recent observations. As an example of how the proposed renormalisation group procedure works, we perform an explicit calculation in the ϕ4 theory in an appendix.
Exact simulation of max-stable processes.
Dombry, Clément; Engelke, Sebastian; Oesting, Marco
2016-06-01
Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes their simulation difficult. Algorithms based on finite approximations are often inexact and computationally inefficient. We present a new algorithm for exact simulation of a max-stable process at a finite number of locations. It relies on the idea of simulating only the extremal functions, that is, those functions in the construction of a max-stable process that effectively contribute to the pointwise maximum. We further generalize the algorithm by Dieker & Mikosch (2015) for Brown-Resnick processes and use it for exact simulation via the spectral measure. We study the complexity of both algorithms, prove that our new approach via extremal functions is always more efficient, and provide closed-form expressions for their implementation that cover most popular models for max-stable processes and multivariate extreme value distributions. For simulation on dense grids, an adaptive design of the extremal function algorithm is proposed.
An exactly solvable model for quantum communications.
Smith, Graeme; Smolin, John A
2013-12-12
Information theory establishes the ultimate limits on performance for noisy communication systems. Accurate models of physical communication devices must include quantum effects, but these typically make the theory intractable. As a result, communication capacities--the maximum possible rates of data transmission--are not known, even for transmission between two users connected by an electromagnetic waveguide with Gaussian noise. Here we present an exactly solvable model of communication with a fully quantum electromagnetic field. This gives explicit expressions for all point-to-point capacities of noisy quantum channels, with implications for quantum key distribution and fibre-optic communications. We also develop a theory of quantum communication networks by solving some rudimentary models including broadcast and multiple-access channels. We compare the predictions of our model with the orthodox Gaussian model and in all cases find agreement to within a few bits. At high signal-to-noise ratios, our simple model captures the relevant physics while remaining amenable to exact solution.
Firpo, M.-C.; Leyvraz, F.; Attuel, G.
2006-12-15
Under the conditions of weak Langmuir turbulence, a self-consistent wave-particle Hamiltonian models the effective nonlinear interaction of a spectrum of M waves with N resonant out-of-equilibrium tail electrons. In order to address its intrinsically nonlinear time-asymptotic behavior, a Monte Carlo code was built to estimate its equilibrium statistical mechanics in both the canonical and microcanonical ensembles. First, the single wave model is considered in the cold beam-plasma instability and in the O'Neil setting for nonlinear Landau damping. O'Neil's threshold, which separates nonzero time-asymptotic wave amplitude states from zero ones, is associated with a second-order phase transition. These two studies provide both a testbed for the Monte Carlo canonical and microcanonical codes, with the comparison with exact canonical results, and an opportunity to propose quantitative results to longstanding issues in basic nonlinear plasma physics. Then, the properly speaking weak turbulence framework is considered through the case of a large spectrum of waves. Focusing on the small coupling limit as a benchmark for the statistical mechanics of weak Langmuir turbulence, it is shown that Monte Carlo microcanonical results fully agree with an exact microcanonical derivation. The wave spectrum is predicted to collapse towards small wavelengths together with the escape of initially resonant particles towards low bulk plasma thermal speeds. This study reveals the fundamental discrepancy between the long-time dynamics of single waves, which can support finite amplitude steady states, and of wave spectra, which cannot.
Teaching Modeling with Partial Differential Equations: Several Successful Approaches
ERIC Educational Resources Information Center
Myers, Joseph; Trubatch, David; Winkel, Brian
2008-01-01
We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…
NASA Technical Reports Server (NTRS)
Wilson, J. W.
1972-01-01
The exact nucleon-deuteron elastic single scattering integral was calculated numerically in order to evaluate errors in sticking factor approximations. A similar analysis made by using S wave separable potentials concluded that errors for these approximations were negligible except near backward angles where they were found to be about 10 percent.
NASA Astrophysics Data System (ADS)
Xu, Si-Liu; Liang, Jian-Chu; Yi, Lin
2010-01-01
The (1+1)-dimensional F-expansion technique and the homogeneous nonlinear balance principle have been generalized and applied for solving exact solutions to a general (3+1)-dimensional nonlinear Schrödinger equation (NLSE) with varying coefficients and a harmonica potential. We found that there exist two kinds of soliton solutions. The evolution features of exact solutions have been numerically studied. The (3+1)D soliton solutions may help us to understand the nonlinear wave propagation in the nonlinear media such as classical optical waves and the matter waves of the Bose-Einstein condensates.
NASA Astrophysics Data System (ADS)
Sabry, R.; Zahran, M. A.; Fan, Engui
2004-05-01
A generalized expansion method is proposed to uniformly construct a series of exact solutions for general variable coefficients non-linear evolution equations. The new approach admits the following types of solutions (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic and solitary wave solutions and (f) Jacobi and Weierstrass doubly periodic wave solutions. The efficiency of the method has been demonstrated by applying it to a generalized variable coefficients KdV equation. Then, new and rich variety of exact explicit solutions have been found.
An exact accelerated stochastic simulation algorithm
NASA Astrophysics Data System (ADS)
Mjolsness, Eric; Orendorff, David; Chatelain, Philippe; Koumoutsakos, Petros
2009-04-01
An exact method for stochastic simulation of chemical reaction networks, which accelerates the stochastic simulation algorithm (SSA), is proposed. The present "ER-leap" algorithm is derived from analytic upper and lower bounds on the multireaction probabilities sampled by SSA, together with rejection sampling and an adaptive multiplicity for reactions. The algorithm is tested on a number of well-quantified reaction networks and is found experimentally to be very accurate on test problems including a chaotic reaction network. At the same time ER-leap offers a substantial speedup over SSA with a simulation time proportional to the 2/3 power of the number of reaction events in a Galton-Watson process.
An exact accelerated stochastic simulation algorithm
Mjolsness, Eric; Orendorff, David; Chatelain, Philippe; Koumoutsakos, Petros
2009-01-01
An exact method for stochastic simulation of chemical reaction networks, which accelerates the stochastic simulation algorithm (SSA), is proposed. The present “ER-leap” algorithm is derived from analytic upper and lower bounds on the multireaction probabilities sampled by SSA, together with rejection sampling and an adaptive multiplicity for reactions. The algorithm is tested on a number of well-quantified reaction networks and is found experimentally to be very accurate on test problems including a chaotic reaction network. At the same time ER-leap offers a substantial speedup over SSA with a simulation time proportional to the 2∕3 power of the number of reaction events in a Galton–Watson process. PMID:19368432
Exactly soluble model of boundary degeneracy
NASA Astrophysics Data System (ADS)
Ganeshan, Sriram; Gorshkov, Alexey V.; Gurarie, Victor; Galitski, Victor M.
2017-01-01
We investigate the topological degeneracy that can be realized in Abelian fractional quantum spin Hall states with multiply connected gapped boundaries. Such a topological degeneracy (also dubbed as "boundary degeneracy") does not require superconducting proximity effect and can be created by simply applying a depletion gate to the quantum spin Hall material and using a generic spin-mixing term (e.g., due to backscattering) to gap out the edge modes. We construct an exactly soluble microscopic model manifesting this topological degeneracy and solve it using the recently developed technique [S. Ganeshan and M. Levin, Phys. Rev. B 93, 075118 (2016), 10.1103/PhysRevB.93.075118]. The corresponding string operators spanning this degeneracy are explicitly calculated. It is argued that the proposed scheme is experimentally reasonable.
Exact order reduction in mode conversion
NASA Astrophysics Data System (ADS)
Swanson, D. G.
1997-11-01
The Exact Order Reduction method(S. Johnston, D. G. Swanson, Bull. Am. Phys. Soc. 41), 1425., which solves the mode conversion equations obtained from the Vlasov equations with high accuracy is shown to work over a broad range of parameters. The results for the scattering parameters are close to the corresponding results from the dispersion relation method, typically within a few percent. The technique is both faster and more robust (converging over a broader range of parameters), as well as solving the most highly accurate set of mode conversion equations. Results both with k_y=3D0 (incidence in midplane) and k_yne0 (oblique incidence) will be presented. abstract.
Exact methods for self interacting neutrinos
Pehlivan, Y.; Balantekin, A. B.; Kajino, Toshitaka
2014-06-24
The effective many-body Hamiltonian which describes vacuum oscillations and self interactions of neutrinos in a two flavor mixing scheme under the single angle approximation has the same dynamical symmetries as the well known BCS pairing Hamiltonian. These dynamical symmetries manifest themselves in terms of a set of constants of motion and can be useful in formulating the collective oscillation modes in an intuitive way. In particular, we show that a neutrino spectral split can be simply viewed as an avoided level crossing between the eigenstates of a mean field Hamiltonian which includes a Lagrange multiplier in order to fix the value of an exact many-body constant of motion. We show that the same dynamical symmetries also exist in the three neutrino mixing scheme by explicitly writing down the corresponding constants of motion.
Exactly isochoric deformations of soft solids
NASA Astrophysics Data System (ADS)
Biggins, John S.; Wei, Z.; Mahadevan, L.
2014-12-01
Many materials of contemporary interest, such as gels, biological tissues and elastomers, are easily deformed but essentially incompressible. Traditional linear theory of elasticity implements incompressibility only to first order and thus permits some volume changes, which become problematically large even at very small strains. Using a mixed coordinate transformation originally due to Gauss, we enforce the constraint of isochoric deformations exactly to develop a linear theory with perfect volume conservation that remains valid until strains become geometrically large. We demonstrate the utility of this approach by calculating the response of an infinite soft isochoric solid to a point force that leads to a nonlinear generalization of the Kelvin solution. Our approach naturally generalizes to a range of problems involving deformations of soft solids and interfaces in two-dimensional and axisymmetric geometries, which we exemplify by determining the solution to a distributed load that mimics muscular contraction within the bulk of a soft solid.
NASA Astrophysics Data System (ADS)
Sarwar, S.; Rashidi, M. M.
2016-07-01
This paper deals with the investigation of the analytical approximate solutions for two-term fractional-order diffusion, wave-diffusion, and telegraph equations. The fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], (1,2), and [1,2], respectively. In this paper, we extended optimal homotopy asymptotic method (OHAM) for two-term fractional-order wave-diffusion equations. Highly approximate solution is obtained in series form using this extended method. Approximate solution obtained by OHAM is compared with the exact solution. It is observed that OHAM is a prevailing and convergent method for the solutions of nonlinear-fractional-order time-dependent partial differential problems. The numerical results rendering that the applied method is explicit, effective, and easy to use, for handling more general fractional-order wave diffusion, diffusion, and telegraph problems.
Bulut, Niyazi; Kłos, Jacek; Alexander, Millard H
2012-03-14
We present converged exact quantum wave packet calculations of reaction probabilities, integral cross sections, and thermal rate coefficients for the title reaction. Calculations have been carried out on the ground 1(2)A' global adiabatic potential energy surface of Deskevich et al. [J. Chem. Phys. 124, 224303 (2006)]. Converged wave packet reaction probabilities at selected values of the total angular momentum up to a partial wave of J = 140 with the HCl reagent initially selected in the v = 0, j = 0-16 rovibrational states have been obtained for the collision energy range from threshold up to 0.8 eV. The present calculations confirm an important enhancement of reactivity with rotational excitation of the HCl molecule. First, accurate integral cross sections and rate constants have been calculated and compared with the available experimental data.
An exact formulation of hyperdynamics simulations.
Chen, L Y; Horing, N J M
2007-06-14
We introduce a new formula for the acceleration weight factor in the hyperdynamics simulation method, the use of which correctly provides an exact simulation of the true dynamics of a system. This new form of hyperdynamics is valid and applicable where the transition state theory (TST) is applicable and also where the TST is not applicable. To illustrate this new formulation, we perform hyperdynamics simulations for four systems ranging from one degree of freedom to 591 degrees of freedom: (1) We first analyze free diffusion having one degree of freedom. This system does not have a transition state. The TST and the original form of hyperdynamics are not applicable. Using the new form of hyperdynamics, we compute mean square displacement for a range of time. The results obtained agree perfectly with the analytical formula. (2) Then we examine the classical Kramers escape rate problem. The rate computed is in perfect agreement with the Kramers formula over a broad range of temperature. (3) We also study another classical problem: Computing the rate of effusion out of a cubic box through a tiny hole. This problem does not involve an energy barrier. Thus, the original form of hyperdynamics excludes the possibility of using a nonzero bias and is inappropriate. However, with the new weight factor formula, our new form of hyperdynamics can be easily implemented and it produces the exact results. (4) To illustrate applicability to systems of many degrees of freedom, we analyze diffusion of an atom adsorbed on the (001) surface of an fcc crystal. The system is modeled by an atom on top of a slab of six atomic layers. Each layer has 49 atoms. With the bottom two layers of atoms fixed, this system has 591 degrees of freedom. With very modest computing effort, we are able to characterize its diffusion pathways in the exchange-with-the-substrate and hop-over-the-bridge mechanisms.
An exact formulation of hyperdynamics simulations
NASA Astrophysics Data System (ADS)
Chen, L. Y.; Horing, N. J. M.
2007-06-01
We introduce a new formula for the acceleration weight factor in the hyperdynamics simulation method, the use of which correctly provides an exact simulation of the true dynamics of a system. This new form of hyperdynamics is valid and applicable where the transition state theory (TST) is applicable and also where the TST is not applicable. To illustrate this new formulation, we perform hyperdynamics simulations for four systems ranging from one degree of freedom to 591 degrees of freedom: (1) We first analyze free diffusion having one degree of freedom. This system does not have a transition state. The TST and the original form of hyperdynamics are not applicable. Using the new form of hyperdynamics, we compute mean square displacement for a range of time. The results obtained agree perfectly with the analytical formula. (2) Then we examine the classical Kramers escape rate problem. The rate computed is in perfect agreement with the Kramers formula over a broad range of temperature. (3) We also study another classical problem: Computing the rate of effusion out of a cubic box through a tiny hole. This problem does not involve an energy barrier. Thus, the original form of hyperdynamics excludes the possibility of using a nonzero bias and is inappropriate. However, with the new weight factor formula, our new form of hyperdynamics can be easily implemented and it produces the exact results. (4) To illustrate applicability to systems of many degrees of freedom, we analyze diffusion of an atom adsorbed on the (001) surface of an fcc crystal. The system is modeled by an atom on top of a slab of six atomic layers. Each layer has 49 atoms. With the bottom two layers of atoms fixed, this system has 591 degrees of freedom. With very modest computing effort, we are able to characterize its diffusion pathways in the exchange-with-the-substrate and hop-over-the-bridge mechanisms.
Critical exact solutions for self-gravitating Dirac fields
NASA Astrophysics Data System (ADS)
Cianci, Roberto; Fabbri, Luca; Vignolo, Stefano
2016-11-01
We consider the Einstein-Dirac field equations describing a self-gravitating massive neutrino, looking for axially symmetric exact solutions; in the search of general solutions, we find some that are specific and which have critical features, such as the fact that the space-time curvature turns out to be flat and the spinor field gives rise to a vanishing bi-linear scalar overline{ψ }ψ =0 with non-vanishing bi-linear pseudo-scalar ioverline{ψ }γ ^5ψ not =0: because in quantum-field theory general computational methods are built on plane-wave solutions, for which the bi-linear pseudo-scalar vanishes while the bi-linear scalar does not vanish, then the solutions we found cannot be treated with the usual machinery of quantum-field theory. This means that for the Einstein-Dirac system there exist admissible solutions which nevertheless cannot be quantized with the common prescriptions; we regard this situation as yet another issue of tension between Einstein gravity and quantum principles. Possible ways to quench this tension can be seen either in enlarging the validity of quantum-field theory or by restricting the space of the solutions of the Einstein-Dirac system of field equations.
NASA Astrophysics Data System (ADS)
Zayed, Elsayed M. E.; Abdelaziz, Mahmoud A. M.
2010-09-01
In this article, the generalized G'/G-expansion method using a generalized wave transformation is applied to find exact traveling wave solutions of the generalized Zakharov-Kuznetsov equation with variable coefficients. As a result, hyperbolic, trigonometric and rational function solutions with parameters are obtained. When these parameters are taken special values, the solitary wave solutions are derived from the hyperbolic function solution. It is shown that the proposed method is direct, effective and can be applied to many other nonlinear evolution equations in mathematical physics.
Effect of selection on ancestry: an exactly soluble case and its phenomenological generalization.
Brunet, E; Derrida, B; Mueller, A H; Munier, S
2007-10-01
We consider a family of models describing the evolution under selection of a population whose dynamics can be related to the propagation of noisy traveling waves. For one particular model that we shall call the exponential model, the properties of the traveling wave front can be calculated exactly, as well as the statistics of the genealogy of the population. One striking result is that, for this particular model, the genealogical trees have the same statistics as the trees of replicas in the Parisi mean-field theory of spin glasses. We also find that in the exponential model, the coalescence times along these trees grow like the logarithm of the population size. A phenomenological picture of the propagation of wave fronts that we introduced in a previous work, as well as our numerical data, suggest that these statistics remain valid for a larger class of models, while the coalescence times grow like the cube of the logarithm of the population size.
Effect of selection on ancestry: An exactly soluble case and its phenomenological generalization
NASA Astrophysics Data System (ADS)
Brunet, É.; Derrida, B.; Mueller, A. H.; Munier, S.
2007-10-01
We consider a family of models describing the evolution under selection of a population whose dynamics can be related to the propagation of noisy traveling waves. For one particular model that we shall call the exponential model, the properties of the traveling wave front can be calculated exactly, as well as the statistics of the genealogy of the population. One striking result is that, for this particular model, the genealogical trees have the same statistics as the trees of replicas in the Parisi mean-field theory of spin glasses. We also find that in the exponential model, the coalescence times along these trees grow like the logarithm of the population size. A phenomenological picture of the propagation of wave fronts that we introduced in a previous work, as well as our numerical data, suggest that these statistics remain valid for a larger class of models, while the coalescence times grow like the cube of the logarithm of the population size.
From Bessel beam to complex-source-point cylindrical wave-function
Mitri, F.G.
2015-04-15
This investigation shows that a scalar Bessel beam can be transformed into the non-paraxial complex-source-point cylindrical wave (CSPCW). High-order CSPCW solutions, termed here high-order quasi-Gaussian cylindrical beams, which exactly satisfy the Helmholtz equation, are derived analytically. Moreover, partial-derivatives of the high-order CSPCW solutions satisfy the Helmholtz equation. In addition, the CSPCW solutions satisfy the nonrelativistic Schrödinger equation within standard quantum mechanics, thus, the results can be used in the description of elementary particle/matter motion and related applications in quantum scattering theory. Furthermore, the analysis is extended to the case of vector beams in which the components of the electromagnetic (EM) field are obtained based on different polarizations of the magnetic and electric vector potentials, which exactly satisfy Maxwell’s vectorial equations and Lorenz’ gauge condition. An attractive feature of the high-order solutions is the rigorous description of strongly focused (or strongly divergent) cylindrical wave-fields without any approximations, nor the need for numerical methods. Possible applications are in beam-forming design using high-aperture or collimated cylindrical laser/electron quasi-Gaussian beams in imaging microscopy, particle manipulation, optical tweezers, and the study of the scattering, and radiation forces on objects. - Highlights: • Bessel beam is transformed into the non-paraxial cylindrical complex-source-point. • Exact high-order tightly focused solutions are derived without any approximations. • The exact solutions also satisfy the nonrelativistic Schrödinger equation. • Electromagnetic beams are obtained as solutions of Maxwell’s vectorial equations. • Applications are in laser/electron beam imaging, tweezers, and radiation force.
Large amplitude relativistic plasma waves
Coffey, Timothy
2010-05-15
Relativistic, longitudinal plasma oscillations are studied for the case of a simple water bag distribution of electrons having cylindrical symmetry in momentum space with the axis of the cylinder parallel to the velocity of wave propagation. The plasma is required to obey the relativistic Vlasov-Poisson equations, and solutions are sought in the wave frame. An exact solution for the plasma density as a function of the electrostatic field is derived. The maximum electric field is presented in terms of an integral over the known density. It is shown that when the perpendicular momentum is neglected, the maximum electric field approaches infinity as the wave phase velocity approaches the speed of light. It is also shown that for any nonzero perpendicular momentum, the maximum electric field will remain finite as the wave phase velocity approaches the speed of light. The relationship to previously published solutions is discussed as is some recent controversy regarding the proper modeling of large amplitude relativistic plasma waves.
The Lockheed alternate partial polarizer universal filter
NASA Technical Reports Server (NTRS)
Title, A. M.
1976-01-01
A tunable birefringent filter using an alternate partial polarizer design has been built. The filter has a transmission of 38% in polarized light. Its full width at half maximum is .09A at 5500A. It is tunable from 4500 to 8500A by means of stepping motor actuated rotating half wave plates and polarizers. Wave length commands and thermal compensation commands are generated by a PPD 11/10 minicomputer. The alternate partial polarizer universal filter is compared with the universal birefringent filter and the design techniques, construction methods, and filter performance are discussed in some detail. Based on the experience of this filter some conclusions regarding the future of birefringent filters are elaborated.
Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms
NASA Astrophysics Data System (ADS)
Chirkunov, Yu. A.; Dobrokhotov, S. Yu.; Medvedev, S. B.; Minenkov, D. S.
2014-03-01
We establish an equivalence of two systems of equations of one-dimensional shallow water models describing the propagation of surface waves over even and sloping bottoms. For each of these systems, we obtain formulas for the general form of their nondegenerate solutions, which are expressible in terms of solutions of the Darboux equation. The invariant solutions of the Darboux equation that we find are simplest representatives of its essentially different exact solutions (those not related by invertible point transformations). They depend on 21 arbitrary real constants; after "proliferation" formulas derived by methods of group theory analysis are applied, they generate a 27-parameter family of essentially different exact solutions. Subsequently using the derived infinitesimal "proliferation" formulas for the solutions in this family generates a denumerable set of exact solutions, whose linear span constitutes an infinite-dimensional vector space of solutions of the Darboux equation. This vector space of solutions of the Darboux equation and the general formulas for nondegenerate solutions of systems of shallow water equations with even and sloping bottoms give an infinite set of their solutions. The "proliferation" formulas for these systems determine their additional nondegenerate solutions. We also find all degenerate solutions of these systems and thus construct a database of an infinite set of exact solutions of systems of equations of the one-dimensional nonlinear shallow water model with even and sloping bottoms.
NASA Astrophysics Data System (ADS)
Olmedo, Oscar; Zhang, J.
2010-05-01
Flux ropes are now generally accepted to be the magnetic configuration of Coronal Mass Ejections (CMEs), which may be formed prior or during solar eruptions. In this study, we model the flux rope as a current-carrying partial torus loop with its two footpoints anchored in the photosphere, and investigate its instability in the context of the torus instability (TI). Previous studies on TI have focused on the configuration of a circular torus and revealed the existence of a critical decay index. Our study reveals that the critical index is a function of the fractional number of the partial torus, defined by the ratio between the arc length of the partial torus above the photosphere and the circumference of a circular torus of equal radius. We refer to this finding the partial torus instability (PTI). It is found that a partial torus with a smaller fractional number has a smaller critical index, thus requiring a more gradually decreasing magnetic field to stabilize the flux rope. On the other hand, the partial torus with a larger fractional number has a larger critical index. In the limit of a circular torus when the fractional number approaches one, the critical index goes to a maximum value that depends on the distribution of the external magnetic field. We demonstrate that the partial torus instability helps us to understand the confinement, growth, and eventual eruption of a flux rope CME.
NASA Astrophysics Data System (ADS)
Zhang, Yu; Xu, Yixian; Xia, Jianghai
2012-12-01
A better understanding of the influences of different surface fluid drainage conditions on the propagation and attenuation of surface waves as the stipulated frequency is varied is a key issue to apply surface wave method to detect subsurface hydrological properties. Our study develops three-dimensional dynamical Green's functions in poroelastic media for Rayleigh waves of possible free surface conditions: permeable - "open pore," impermeable - "closed pore," and partially permeable boundaries. The full transient response of wave fields and spectra due to a stress impulse wavelet on the surface are investigated in the exploration seismic frequency band for typical surface drainage conditions, viscous coupling-damping, solid frame properties and porous fluid flowing configuration. Our numerical results show that, due to the slow dilatational wave - P2 wave, two types of Rayleigh waves, designated as R1 and R2 waves, exist along the surface. R1 wave possesses high energy as classic Rayleigh waves in pure elastic media for each porous materials. A surface fluid drainage condition is a significant factor to influence dispersion and attenuation, especially attenuation of R1 waves. R2 wave for closed pore and partially permeable surfaces is only observed for a low coupling-damping coefficient. The non-physical wave for partially surface conditions causes the R1 wave radiates into the R2 wave in the negative attenuation frequency range. It makes weaker R1 wave and stronger R2 wave to closed pore surface. Moreover, it is observed that wave fields and spectra of R1 wave are sensitive to frame elastic moduli change for an open pore surface, and to pore fluid flow condition change for closed pore and partially permeable surface.
Exact general relativistic disks with magnetic fields
NASA Astrophysics Data System (ADS)
Letelier, Patricio S.
1999-11-01
The well-known ``displace, cut, and reflect'' method used to generate cold disks from given solutions of Einstein equations is extended to solutions of Einstein-Maxwell equations. Four exact solutions of the these last equations are used to construct models of hot disks with surface density, azimuthal pressure, and azimuthal current. The solutions are closely related to Kerr, Taub-NUT, Lynden-Bell-Pinault, and to a one-soliton solution. We find that the presence of the magnetic field can change in a nontrivial way the different properties of the disks. In particular, the pure general relativistic instability studied by Bic̆ák, Lynden-Bell, and Katz [Phys. Rev. D 47, 4334 (1993)] can be enhanced or cured by different distributions of currents inside the disk. These currents, outside the disk, generate a variety of axial symmetric magnetic fields. As far as we know these are the first models of hot disks studied in the context of general relativity.
Exact solutions for extreme black hole magnetospheres
NASA Astrophysics Data System (ADS)
Lupsasca, Alexandru; Rodriguez, Maria J.
2015-07-01
We present new exact solutions of Force-Free Electrodynamics (FFE) in the Near-Horizon region of an Extremal Kerr black hole (NHEK) and offer a complete classifica-tion of the subset that form highest-weight representations of the spacetime's SL(2, ℝ)×U(1) isometry group. For a natural choice of spacetime embedding of this isometry group, the SL(2, ℝ) highest-weight conditions lead to stationary solutions with non-trivial angular de-pendence, as well as axisymmetry when the U(1)-charge vanishes. In addition, we unveil a hidden SL(2, ℂ) symmetry of the equations of FFE that stems from the action of a complex automorphism group, and enables us to generate an SL(2, ℂ) family of (generically time-dependent) solutions. We then obtain still more general solutions with less symmetry by appealing to a principle of linear superposition that holds for solutions with collinear cur-rents. This allows us to resum the highest-weight primaries and their SL(2, ℝ)-descendants.
Exact solutions to magnetized plasma flow
Wang, Zhehui; Barnes, Cris W.
2001-03-01
Exact analytic solutions for steady-state magnetized plasma flow (MPF) using ideal magnetohydrodynamics formalism are presented. Several cases are considered. When plasma flow is included, a finite plasma pressure gradient {nabla}p can be maintained in a force-free state JxB=0 by the velocity gradient. Both incompressible and compressible MPF examples are discussed for a Taylor-state spheromak B field. A new magnetized nozzle solution is given for compressible plasma when U{parallel}B. Transition from a magnetized nozzle to a magnetic nozzle is possible when the B field is strong enough. No physical nozzle would be needed in the magnetic nozzle case. Diverging-, drum- and nozzle-shaped MPF solutions when U{perpendicular}B are also given. The electric field is needed to balance the UxB term in Ohm's law. The electric field can be generated in the laboratory with the proposed conducting electrodes. If such electric fields also exist in stars and galaxies, such as through a dynamo process, then these solutions can be candidates to explain single and double jets.
NASA Technical Reports Server (NTRS)
Busemann, A.; Vinh, N. X.; Culp, R. D.
1976-01-01
The problem of determining the trajectories, partially or wholly contained in the atmosphere of a spherical, nonrotating planet, is considered. The exact equations of motion for three-dimensional, aerodynamically affected flight are derived. Modified Chapman variables are introduced and the equations are transformed into a set suitable for analytic integration using asymptotic expansions. The trajectory is solved in two regions: the outer region, where the force may be considered a gravitational field with aerodynamic perturbations, and the inner region, where the force is predominantly aerodynamic, with gravity as a perturbation. The two solutions are matched directly. A composite solution, valid everywhere, is constructed by additive composition. This approach of directly matched asymptotic expansions applied to the exact equations of motion couched in terms of modified Chapman variables yields an analytical solution which should prove to be a powerful tool for aerodynamic orbit calculations.
Dual solution of Casson fluid over a porous medium: Exact solutions with extra boundary condition
NASA Astrophysics Data System (ADS)
Khan, Najeeb Alam; Khan, Sidra
2016-12-01
In this article we calculate the exact solution of the steady flow of non-Newtonian Casson fluid, over a stretching/shrinking sheet. The governing partial differential equations (PDEs) are transformed into ordinary differential equation (ODE) by using similarity transformation and then solved analytically by utilizing the exact solution. The closed form unique solution is obtained in the case of stretching sheet whereas for shrinking sheet unique and dual solutions are obtained. Influences of Casson fluid and suction/injection parameter on dimensionless velocity function are discussed and plotted graphically; also the effects of skin friction coefficient are presented in graphical form. Comparisons of current solutions with previous study are also made for the verification of the present study.
GENERAL: Exact Solutions to a Combined sinh-cosh-Gordon Equation
NASA Astrophysics Data System (ADS)
Wei, Long
2010-10-01
Based on a transformed Painlevé property and the variable separated ODE method, a function transformation method is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painlevé property and reduce the given PDEs to a variable-coefficient ordinary differential equations, then we seek for solutions to the resulting equations by some methods. As an application, exact solutions for the combined sinh-cosh-Gordon equation are formally derived.
Exact Renormalization Group Analysis of Turbulent Transport by the Shear Flow
NASA Astrophysics Data System (ADS)
E, Weinan; Shen, Hao
2013-11-01
The exact renormalization group (RG) method initiated by Wilson and further developed by Polchinski is used to study the shear flow model proposed by Avellaneda and Majda as a simplified model for the diffusive transport of a passive scalar by a turbulent velocity field. It is shown that this exact RG method is capable of recovering all the scaling regimes as the spectral parameters of velocity statistics vary, found by Avellaneda and Majda in their rigorous study of this model. This gives further confidence that the RG method, if implemented in the right way instead of using drastic truncations as in the Yakhot-Orszag’s approximate RG scheme, does give the correct prediction for the large scale behaviors of solutions of stochastic partial differential equations (PDE). We also derive the analog of the “large eddy simulation” models when a finite amount of small scales are eliminated from the problem.
Spectral Deferred Corrections for Parabolic Partial Differential Equations
2015-06-08
linear differential equation ϕ′(t) = λϕ(t), t ≥ 0 ϕ(0) = 1, (3.31) where λ ∈ C, has exact solution ϕ(t) = eλt. (3.32) Traditionally, for a fixed time step...the second-order differentiation matrix with 16 subintervals and 16 points per subinterval. From Figure 5.2, this matrix approximates the exact ...We describe a new class of algorithms for the solution of parabolic partial differential equa- tions (PDEs). This class of schemes is based on three
Conversion of borehole Stoneley waves to channel waves in coal
Johnson, P.A.; Albright, J.N.
1987-01-01
Evidence for the mode conversion of borehole Stoneley waves to stratigraphically guided channel waves was discovered in data from a crosswell acoustic experiment conducted between wells penetrating thin coal strata located near Rifle, Colorado. Traveltime moveout observations show that borehole Stoneley waves, excited by a transmitter positioned at substantial distances in one well above and below a coal stratum at 2025 m depth, underwent partial conversion to a channel wave propagating away from the well through the coal. In an adjacent well the channel wave was detected at receiver locations within the coal, and borehole Stoneley waves, arising from a second partial conversion of channel waves, were detected at locations above and below the coal. The observed channel wave is inferred to be the third-higher Rayleigh mode based on comparison of the measured group velocity with theoretically derived dispersion curves. The identification of the mode conversion between borehole and stratigraphically guided waves is significant because coal penetrated by multiple wells may be detected without placing an acoustic transmitter or receiver within the waveguide. 13 refs., 6 figs., 1 tab.
Phase Waves in Oscillatory Chemical Reactions.
number of waves emitted from a center of heterogeneous catalysis , the rate of wave emission. the lifetime of each wave, the asymptotic wave pattern, the...A theory is presented for the effect of heterogeneity on an oscillatory chemically reactive system in a stable limit cycle such as in heterogeneous ... catalysis . A perturbation technique is developed free of secular behavior for the solution of the non-linear partial differential equations. The
Quantum scattering theory in light of an exactly solvable model with rearrangement collisions
Varma, S.; Sudarshan, E.C.
1996-04-01
We present an exactly solvable quantum field theory which allows rearrangement collisions. We solve the model in the relevant sectors and demonstrate the orthonormality and completeness of the solutions, and construct the {ital S}-matrix. In light of the exact solutions constructed, we discuss various issues and assumptions in quantum scattering theory, including the isometry of the M{umlt o}ller wave matrix, the normalization and completeness of asymptotic states, and the nonorthogonality of basis states. We show that these common assertions are not obtained in this model. We suggest a general formalism for scattering theory which overcomes these and other shortcomings and limitations of the existing formalisms in the literature. {copyright} {ital 1996 American Institute of Physics.}
Lie symmetry analysis and exact solutions of the quasigeostrophic two-layer problem
NASA Astrophysics Data System (ADS)
Bihlo, Alexander; Popovych, Roman O.
2011-03-01
The quasigeostrophic two-layer model is of superior interest in dynamic meteorology since it is one of the easiest ways to study baroclinic processes in geophysical fluid dynamics. The complete set of point symmetries of the two-layer equations is determined. An optimal set of one- and two-dimensional inequivalent subalgebras of the maximal Lie invariance algebra is constructed. On the basis of these subalgebras, we exhaustively carry out group-invariant reduction and compute various classes of exact solutions. Wherever possible, reference to the physical meaning of the exact solutions is given. In particular, the well-known baroclinic Rossby wave solutions in the two-layer model are rediscovered.
Localized Majorana-Like Modes in a Number-Conserving Setting: An Exactly Solvable Model.
Iemini, Fernando; Mazza, Leonardo; Rossini, Davide; Fazio, Rosario; Diehl, Sebastian
2015-10-09
In this Letter we present, in a number conserving framework, a model of interacting fermions in a two-wire geometry supporting nonlocal zero-energy Majorana-like edge excitations. The model has an exactly solvable line, on varying the density of fermions, described by a topologically nontrivial ground state wave function. Away from the exactly solvable line we study the system by means of the numerical density matrix renormalization group. We characterize its topological properties through the explicit calculation of a degenerate entanglement spectrum and of the braiding operators which are exponentially localized at the edges. Furthermore, we establish the presence of a gap in its single particle spectrum while the Hamiltonian is gapless, and compute the correlations between the edge modes as well as the superfluid correlations. The topological phase covers a sizable portion of the phase diagram, the solvable line being one of its boundaries.
Solitary Waves of the MRLW Equation by Variational Iteration Method
Hassan, Saleh M.; Alamery, D. G.
2009-09-09
In a recent publication, Soliman solved numerically the modified regularized long wave (MRLW) equation by using the variational iteration method (VIM). In this paper, corrected numerical results have been computed, plotted, tabulated, and compared with not only the exact analytical solutions but also the Adomian decomposition method results. Solitary wave solutions of the MRLW equation are exactly obtained as a convergent series with easily computable components. Propagation of single solitary wave, interaction of two and three waves, and also birth of solitons have been discussed. Three invariants of motion have been evaluated to determine the conservation properties of the problem.
Partial knee replacement - slideshow
... page: //medlineplus.gov/ency/presentations/100225.htm Partial knee replacement - series—Normal anatomy To use the sharing ... A.M. Editorial team. Related MedlinePlus Health Topics Knee Replacement A.D.A.M., Inc. is accredited ...
Twisted partially pure spinors
NASA Astrophysics Data System (ADS)
Herrera, Rafael; Tellez, Ivan
2016-08-01
Motivated by the relationship between orthogonal complex structures and pure spinors, we define twisted partially pure spinors in order to characterize spinorially subspaces of Euclidean space endowed with a complex structure.
NASA Astrophysics Data System (ADS)
Kravtsov, V. E.; Yudson, V. I.
2010-11-01
An exact solution is found for the problem of the center-of-band (E=0) anomaly in the one-dimensional Anderson model of localization. By deriving and solving an equation for the generating function Φ(u,ϕ) we obtained an exact expression in quadratures for statistical moments Iq=⟨|ψE(r)|2q⟩ of normalized wave functions ψE(r) which show violation of one-parameter scaling and emergence of an additional length scale at E≈0 .
NASA Astrophysics Data System (ADS)
Pantellini, Filippo; Griton, Léa
2016-10-01
The spatial structure of a steady state plasma flow is shaped by the standing modes with local phase velocity exactly opposite to the flow velocity. The general procedure of finding the wave vectors of all possible standing MHD modes in any given point of a stationary flow requires numerically solving an algebraic equation. We present the graphical procedure (already mentioned by some authors in the 1960's) along with the exact solution for the Alfvén mode and approximate analytic solutions for both fast and slow modes. The technique can be used to identify MHD modes in space and laboratory plasmas as well as in numerical simulations.
Partially coherent nonparaxial beams.
Duan, Kailiang; Lü, Baida
2004-04-15
The concept of a partially coherent nonparaxial beam is proposed. A closed-form expression for the propagation of nonparaxial Gaussian Schell model (GSM) beams in free space is derived and applied to study the propagation properties of nonparaxial GSM beams. It is shown that for partially coherent nonparaxial beams a new parameter f(sigma) has to be introduced, which together with the parameter f, determines the beam nonparaxiality.
Gravity Forcing Of Surface Waves
NASA Astrophysics Data System (ADS)
Kenyon, K. E.
2005-12-01
Surface waves in deep water are forced entirely by gravity at the air-sea interface when no other forces act tangent to the surface. Then according to Newton's second law, the fluid acceleration parallel to the surface must equal the component of gravity parallel to the surface. Between crest and trough the fluid accelerates; between trough and crest the fluid decelerates. By replacing Bernoulli's law, gravity forcing becomes the dynamic boundary condition needed to solve the mathematical problem of these waves. Irrotational waves with a sinusoidal profile satisfy the gravity forcing condition, with the usual dispersion relation, provided the slope is small compared to one, as is true also of the Stokes development. However, the exact wave shape can be calculated using the gravity forcing method in a way that is less complex and less time consuming than that of the Stokes perturbation expansion. To the second order the surface elevation is the same as the Stokes result; the third order calculation has not been made yet. Extensions of the gravity forcing method can easily be carried out for multiple wave trains, solitary waves and bores, waves in finite constant mean depths, and internal waves in a two-layer system. For shoaling surface waves gravity forcing provides a physical understanding of the progressive steepening often observed near shore.
NASA Astrophysics Data System (ADS)
Saïdou, Abdoulkary; Alidou, Mohamadou; Ousmanou, Dafounansou; Serge Yamigno, Doka
2014-12-01
We investigated exact traveling soliton solutions for the nonlinear electrical transmission line. By applying a concise and straightforward method, the variable-coefficient discrete (G'/G)-expansion method, we solve the nonlinear differential—difference equations associated with the network. We obtain some exact traveling wave solutions which include hyperbolic function solution, trigonometric function solution, rational solutions with arbitrary function, bright as well as dark solutions.
Olmedo, Oscar; Zhang Jie
2010-07-20
Flux ropes are now generally accepted to be the magnetic configuration of coronal mass ejections (CMEs), which may be formed prior to or during solar eruptions. In this study, we model the flux rope as a current-carrying partial torus loop with its two footpoints anchored in the photosphere, and investigate its stability in the context of the torus instability (TI). Previous studies on TI have focused on the configuration of a circular torus and revealed the existence of a critical decay index of the overlying constraining magnetic field. Our study reveals that the critical index is a function of the fractional number of the partial torus, defined by the ratio between the arc length of the partial torus above the photosphere and the circumference of a circular torus of equal radius. We refer to this finding as the partial torus instability (PTI). It is found that a partial torus with a smaller fractional number has a smaller critical index, thus requiring a more gradually decreasing magnetic field to stabilize the flux rope. On the other hand, a partial torus with a larger fractional number has a larger critical index. In the limit of a circular torus when the fractional number approaches 1, the critical index goes to a maximum value. We demonstrate that the PTI helps us to understand the confinement, growth, and eventual eruption of a flux-rope CME.
NASA Astrophysics Data System (ADS)
Olmedo, Oscar; Zhang, Jie
2010-07-01
Flux ropes are now generally accepted to be the magnetic configuration of coronal mass ejections (CMEs), which may be formed prior to or during solar eruptions. In this study, we model the flux rope as a current-carrying partial torus loop with its two footpoints anchored in the photosphere, and investigate its stability in the context of the torus instability (TI). Previous studies on TI have focused on the configuration of a circular torus and revealed the existence of a critical decay index of the overlying constraining magnetic field. Our study reveals that the critical index is a function of the fractional number of the partial torus, defined by the ratio between the arc length of the partial torus above the photosphere and the circumference of a circular torus of equal radius. We refer to this finding as the partial torus instability (PTI). It is found that a partial torus with a smaller fractional number has a smaller critical index, thus requiring a more gradually decreasing magnetic field to stabilize the flux rope. On the other hand, a partial torus with a larger fractional number has a larger critical index. In the limit of a circular torus when the fractional number approaches 1, the critical index goes to a maximum value. We demonstrate that the PTI helps us to understand the confinement, growth, and eventual eruption of a flux-rope CME.
Application of monochromatic ocean wave forecasts to prediction of wave-induced currents
NASA Technical Reports Server (NTRS)
Poole, L. R.
1975-01-01
The use of monochromatic wind-wave forecasts in prediction of wind-wave-induced currents was assessed. Currents were computed for selected combinations of wind conditions by using a spectrum approach which was developed by using the Bretschneider wave spectrum for partially developed wind seas. These currents were compared with currents computed by using the significant and average monochromatic wave parameters related to the Bretschneider spectrum. Results indicate that forecasts of significant wave parameters can be used to predict surface wind-wave-induced currents. Conversion of these parameters to average wave parameters can furnish reasonable estimates of subsurface current values.
Stability of traveling waves of a diffusive susceptible-infective-removed (SIR) epidemic model
NASA Astrophysics Data System (ADS)
Li, Yan; Li, Wan-Tong; Yang, Yun-Rui
2016-04-01
This paper is concerned with the stability and uniqueness of traveling waves of a delayed diffusive susceptible-infective-removed (SIR) epidemic model. We first prove the exponential stability of traveling waves by using the weighted energy method, where the traveling waves are allowed to be non-monotone. Then we establish the exact asymptotic behavior of traveling waves at -∞ by using Ikehara's theorem. Finally, the uniqueness of traveling waves is proved by the stability result of traveling waves.
Introduction to Wave Turbulence Formalisms for Incoherent Optical Waves
NASA Astrophysics Data System (ADS)
Picozzi, Antonio; Garnier, Josselin; Xu, Gang; Rica, Sergio
We provide an introduction to different wave turbulence formalisms describing the propagation of partially incoherent optical waves in nonlinear media. We consider the nonlinear Schrödinger equation as a representative model accounting for a nonlocal or a noninstantaneous nonlinearity, as well as higher-order dispersion effects. We discuss the wave turbulence kinetic equation describing, e.g., wave condensation or wave thermalization through supercontinuum generation; the Vlasov formalism describing incoherent modulational instabilities and the formation of large scale incoherent localized structures in analogy with long-range gravitational systems; and the weak Langmuir turbulence formalism describing spectral incoherent solitons, as well as spectral shock or collapse singularities. Finally, recent developments and some open questions are discussed, in particular in relation with a wave turbulence formulation of laser systems and different mechanisms of breakdown of thermalization.
Exact time-dependent solutions for a self-regulating gene.
Ramos, A F; Innocentini, G C P; Hornos, J E M
2011-06-01
The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and the analytical solutions are the celebrated confluent Heun functions. Self-regulation plays a major role in the control of gene expression, and it is remarkable that such a microscopic model is completely integrable in terms of well-known complex functions.
Resonance Van Hove singularities in wave kinetics
NASA Astrophysics Data System (ADS)
Shi, Yi-Kang; Eyink, Gregory L.
2016-10-01
Wave kinetic theory has been developed to describe the statistical dynamics of weakly nonlinear, dispersive waves. However, we show that systems which are generally dispersive can have resonant sets of wave modes with identical group velocities, leading to a local breakdown of dispersivity. This shows up as a geometric singularity of the resonant manifold and possibly as an infinite phase measure in the collision integral. Such singularities occur widely for classical wave systems, including acoustical waves, Rossby waves, helical waves in rotating fluids, light waves in nonlinear optics and also in quantum transport, e.g. kinetics of electron-hole excitations (matter waves) in graphene. These singularities are the exact analogue of the critical points found by Van Hove in 1953 for phonon dispersion relations in crystals. The importance of these singularities in wave kinetics depends on the dimension of phase space D =(N - 2) d (d physical space dimension, N the number of waves in resonance) and the degree of degeneracy δ of the critical points. Following Van Hove, we show that non-degenerate singularities lead to finite phase measures for D > 2 but produce divergences when D ≤ 2 and possible breakdown of wave kinetics if the collision integral itself becomes too large (or even infinite). Similar divergences and possible breakdown can occur for degenerate singularities, when D - δ ≤ 2, as we find for several physical examples, including electron-hole kinetics in graphene. When the standard kinetic equation breaks down, then one must develop a new singular wave kinetics. We discuss approaches from pioneering 1971 work of Newell & Aucoin on multi-scale perturbation theory for acoustic waves and field-theoretic methods based on exact Schwinger-Dyson integral equations for the wave dynamics.
Exact special twist method for quantum Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Dagrada, Mario; Karakuzu, Seher; Vildosola, Verónica Laura; Casula, Michele; Sorella, Sandro
2016-12-01
We present a systematic investigation of the special twist method introduced by Rajagopal et al. [Phys. Rev. B 51, 10591 (1995), 10.1103/PhysRevB.51.10591] for reducing finite-size effects in correlated calculations of periodic extended systems with Coulomb interactions and Fermi statistics. We propose a procedure for finding special twist values which, at variance with previous applications of this method, reproduce the energy of the mean-field infinite-size limit solution within an adjustable (arbitrarily small) numerical error. This choice of the special twist is shown to be the most accurate single-twist solution for curing one-body finite-size effects in correlated calculations. For these reasons we dubbed our procedure "exact special twist" (EST). EST only needs a fully converged independent-particles or mean-field calculation within the primitive cell and a simple fit to find the special twist along a specific direction in the Brillouin zone. We first assess the performances of EST in a simple correlated model such as the three-dimensional electron gas. Afterwards, we test its efficiency within ab initio quantum Monte Carlo simulations of metallic elements of increasing complexity. We show that EST displays an overall good performance in reducing finite-size errors comparable to the widely used twist average technique but at a much lower computational cost since it involves the evaluation of just one wave function. We also demonstrate that the EST method shows similar performances in the calculation of correlation functions, such as the ionic forces for structural relaxation and the pair radial distribution function in liquid hydrogen. Our conclusions point to the usefulness of EST for correlated supercell calculations; our method will be particularly relevant when the physical problem under consideration requires large periodic cells.
Focusing of long waves with finite crest over sloping beach
NASA Astrophysics Data System (ADS)
Kanoglu, Utku; Koroglu, Bulent; Aydin, Baran
2014-05-01
Analytical solutions of nonlinear and linear shallow water-wave equations are important in several counts. These solutions not only provide insight to establish relationship among the parameters of the problem, but also could provide benchmark results for numerical studies. Here, first, we introduce a new analytical solution to study three-dimensional evolution and runup of long waves over linearly sloping beach. Then, we extend our solution to study the canonical problem, i.e. long wave propagation over a sloping beach connected with a constant-depth region. Koshimura et al. (1999, Coastal Eng Japan, v. 41(2), pp. 151-164) solved this problem in the presence of a vertical wall at the shoreline. The same form of solution has also appeared in the propagation of edge waves, as presented by Fujima et al. (2000, Coastal Eng Japan, v. 42(2), pp. 211-236) and recently by Geist (2013, Pure Appl Geophys, doi: 10.1007/s00024-012-0491-7). On the other hand, Carrier (1995, in: Tsunami: Progress in Prediction, Disaster Prevention and Warning, Tsuchiya and Shuto (eds.), pp. 1-20) started with the nonlinear shallow-water-wave equations, reduced the problem into the linear one and solved as an initial-value problem. In the present study, we differ from the existing analytical studies providing initial conditions as recently described by Kanoglu et al. (2013, Proc R Soc A, v. 469, 20130015, doi: 10.1098/rspa.2013.0015). They introduced a new exact analytical solution to study the propagation of a finite strip source over constant-depth using the linear shallow-water wave theory showing the existence of focusing points for realistic N-wave-type initial displacements (Tadepalli and Synolakis, 1994, Proc R Soc Lond A, v. 445, pp. 99-112, doi: 10.1098/rspa.1994.0050). Here, we discuss the existence of focusing point -a point where unexpectedly large wave heights may be observed due to the configuration of the initial waveform- for the canonical problem, a phenomenon already shown for
Pan Xiaoyin; Slamet, Marlina; Sahni, Viraht
2010-04-15
We extend our prior work on the construction of variational wave functions {psi} that are functionals of functions {chi}:{psi}={psi}[{chi}] rather than simply being functions. In this manner, the space of variations is expanded over those of traditional variational wave functions. In this article we perform the constrained search over the functions {chi} chosen such that the functional {psi}[{chi}] satisfies simultaneously the constraints of normalization and the exact expectation value of an arbitrary single- or two-particle Hermitian operator, while also leading to a rigorous upper bound to the energy. As such the wave function functional is accurate not only in the region of space in which the principal contributions to the energy arise but also in the other region of the space represented by the Hermitian operator. To demonstrate the efficacy of these ideas, we apply such a constrained search to the ground state of the negative ion of atomic hydrogen H{sup -}, the helium atom He, and its positive ions Li{sup +} and Be{sup 2+}. The operators W whose expectations are obtained exactly are the sum of the single-particle operators W={Sigma}{sub i}r{sub i}{sup n},n=-2,-1,1,2, W={Sigma}{sub i{delta}}(r{sub i}), W=-(1/2){Sigma}{sub i{nabla}i}{sup 2}, and the two-particle operators W={Sigma}{sub n}u{sup n},n=-2,-1,1,2, where u=|r{sub i}-r{sub j}|. Comparisons with the method of Lagrangian multipliers and of other constructions of wave-function functionals are made. Finally, we present further insights into the construction of wave-function functionals by studying a previously proposed construction of functionals {psi}[{chi}] that lead to the exact expectation of arbitrary Hermitian operators. We discover that analogous to the solutions of the Schroedinger equation, there exist {psi}[{chi}] that are unphysical in that they lead to singular values for the expectations. We also explain the origin of the singularity.
Exact Order Reduction Method for Mode Conversion for Harmonics or Two-Ion Hybrid Resonances
NASA Astrophysics Data System (ADS)
Johnston, S.; Swanson, D. G.
1996-11-01
The Exact Order Reduction method(D.G. Swanson, et al., AIP Conference Proceedings 159, 342(1987).) solves the full fourth-order system of equations by taking the numerical solutions of a pair of second-order equations for the fast wave and slow wave, respectively, which are easily obtained, and then uses an associated integral equation to obtain the coupling between the fast and slow waves. In the original method, the integral equations had singularities near the axis which compromised the accuracy and convergence, but by altering the integration path, the numerical problems are resolved. This allows accurate estimates for mode conversion efficiencies in realistic geometries as the integral equation is solved only in a narrow region near resonance, taking the global fast wave solution of the reduced second order equation over the cross section for two of the four basis functions, and the slow wave solutions over the strip for the other basis functions. The method makes virtually no approximations except that it is first order in Larmor radius.
From Bessel beam to complex-source-point cylindrical wave-function
NASA Astrophysics Data System (ADS)
Mitri, F. G.
2015-04-01
This investigation shows that a scalar Bessel beam can be transformed into the non-paraxial complex-source-point cylindrical wave (CSPCW). High-order CSPCW solutions, termed here high-order quasi-Gaussian cylindrical beams, which exactly satisfy the Helmholtz equation, are derived analytically. Moreover, partial-derivatives of the high-order CSPCW solutions satisfy the Helmholtz equation. In addition, the CSPCW solutions satisfy the nonrelativistic Schrödinger equation within standard quantum mechanics, thus, the results can be used in the description of elementary particle/matter motion and related applications in quantum scattering theory. Furthermore, the analysis is extended to the case of vector beams in which the components of the electromagnetic (EM) field are obtained based on different polarizations of the magnetic and electric vector potentials, which exactly satisfy Maxwell's vectorial equations and Lorenz' gauge condition. An attractive feature of the high-order solutions is the rigorous description of strongly focused (or strongly divergent) cylindrical wave-fields without any approximations, nor the need for numerical methods. Possible applications are in beam-forming design using high-aperture or collimated cylindrical laser/electron quasi-Gaussian beams in imaging microscopy, particle manipulation, optical tweezers, and the study of the scattering, and radiation forces on objects.
Lemeshko, Mikhail; Mustafa, Mustafa; Kais, Sabre; Friedrich, Bretislav
2011-04-15
By invoking supersymmetry, we found a condition under which the Stark-effect problem for a polar and polarizable molecule subject to nonresonant electric fields becomes exactly solvable for the |J-tilde=m,m> family of stretched states. The analytic expressions for the wave function and eigenenergy and other expectation values allow one to readily reverse-engineer the problem of finding the values of the interaction parameters required for creating quantum states with preordained characteristics. The method also allows the construction of families of isospectral potentials, realizable with combined fields.
Metric measures of interparticle interaction in an exactly solvable two-electron model atom
Nagy, I.; Aldazabal, I.
2011-09-15
The exact ground-state solutions for the model of two particles in a confining harmonic oscillator potential interacting through a repulsive harmonic oscillator force are used from the standpoint of geometric distances [Phys. Rev. Lett. 106, 050401 (2011).] between wave functions and densities. The distances from the noninteracting reference state are calculated at a specified confinement by increasing the coupling of the interparticle interaction. Based on the analytic expressions for coupling-dependent geometric measures, a discussion of the Hohenberg-Kohn mapping is given.
Coherent Backscattering by Polydisperse Discrete Random Media: Exact T-Matrix Results
NASA Technical Reports Server (NTRS)
Mishchenko, Michael I.; Dlugach, Janna M.; Mackowski, Daniel W.
2011-01-01
The numerically exact superposition T-matrix method is used to compute, for the first time to our knowledge, electromagnetic scattering by finite spherical volumes composed of polydisperse mixtures of spherical particles with different size parameters or different refractive indices. The backscattering patterns calculated in the far-field zone of the polydisperse multiparticle volumes reveal unequivocally the classical manifestations of the effect of weak localization of electromagnetic waves in discrete random media, thereby corroborating the universal interference nature of coherent backscattering. The polarization opposition effect is shown to be the least robust manifestation of weak localization fading away with increasing particle size parameter.
Inverse scattering transform analysis of rogue waves using local periodization procedure
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
Inverse scattering transform analysis of rogue waves using local periodization procedure.
Randoux, Stéphane; Suret, Pierre; El, Gennady
2016-07-07
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.
Single-shot observation of optical rogue waves in integrable turbulence using time microscopy
Suret, Pierre; Koussaifi, Rebecca El; Tikan, Alexey; Evain, Clément; Randoux, Stéphane; Szwaj, Christophe; Bielawski, Serge
2016-01-01
Optical fibres are favourable tabletop laboratories to investigate both coherent and incoherent nonlinear waves. In particular, exact solutions of the one-dimensional nonlinear Schrödinger equation such as fundamental solitons or solitons on finite background can be generated by launching periodic, specifically designed coherent waves in optical fibres. It is an open fundamental question to know whether these coherent structures can emerge from the nonlinear propagation of random waves. However the typical sub-picosecond timescale prevented—up to now—time-resolved observations of the awaited dynamics. Here, we report temporal ‘snapshots' of random light using a specially designed ‘time-microscope'. Ultrafast structures having peak powers much larger than the average optical power are generated from the propagation of partially coherent waves in optical fibre and are recorded with 250 femtoseconds resolution. Our experiment demonstrates the central role played by ‘breather-like' structures such as the Peregrine soliton in the emergence of heavy-tailed statistics in integrable turbulence. PMID:27713416
Single-shot observation of optical rogue waves in integrable turbulence using time microscopy
NASA Astrophysics Data System (ADS)
Suret, Pierre; Koussaifi, Rebecca El; Tikan, Alexey; Evain, Clément; Randoux, Stéphane; Szwaj, Christophe; Bielawski, Serge
2016-10-01
Optical fibres are favourable tabletop laboratories to investigate both coherent and incoherent nonlinear waves. In particular, exact solutions of the one-dimensional nonlinear Schrödinger equation such as fundamental solitons or solitons on finite background can be generated by launching periodic, specifically designed coherent waves in optical fibres. It is an open fundamental question to know whether these coherent structures can emerge from the nonlinear propagation of random waves. However the typical sub-picosecond timescale prevented--up to now--time-resolved observations of the awaited dynamics. Here, we report temporal `snapshots' of random light using a specially designed `time-microscope'. Ultrafast structures having peak powers much larger than the average optical power are generated from the propagation of partially coherent waves in optical fibre and are recorded with 250 femtoseconds resolution. Our experiment demonstrates the central role played by `breather-like' structures such as the Peregrine soliton in the emergence of heavy-tailed statistics in integrable turbulence.
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.
Extraordinary momentum and spin in evanescent waves.
Bliokh, Konstantin Y; Bekshaev, Aleksandr Y; Nori, Franco
2014-03-06
Momentum and spin represent fundamental dynamic properties of quantum particles and fields. In particular, propagating optical waves (photons) carry momentum and longitudinal spin determined by the wave vector and circular polarization, respectively. Here we show that exactly the opposite can be the case for evanescent optical waves. A single evanescent wave possesses a spin component, which is independent of the polarization and is orthogonal to the wave vector. Furthermore, such a wave carries a momentum component, which is determined by the circular polarization and is also orthogonal to the wave vector. We show that these extraordinary properties reveal a fundamental Belinfante's spin momentum, known in field theory and unobservable in propagating fields. We demonstrate that the transverse momentum and spin push and twist a probe Mie particle in an evanescent field. This allows the observation of 'impossible' properties of light and of a fundamental field-theory quantity, which was previously considered as 'virtual'.
Nonautonomous matter waves in a waveguide
Yan Zhenya; Zhang Xiaofei; Liu, W. M.
2011-08-15
We present a physical model that describes the transport of Bose-Einstein-condensed atoms from a reservoir to a waveguide. By using the similarity and Moebius transformations, we study nonautonomous matter waves in Bose-Einstein condensates in the presence of an inhomogeneous source. Then, we find its various types of exact nonautonomous matter-wave solutions, including the W-shaped bright solitary waves, W-shaped and U-shaped dark solitary waves, periodic wave solutions, and rational solitary waves. The results show that these different types of matter-wave structures can be generated and effectively controlled by modulating the amplitude of the source. Our results may raise the possibility of some experiments and potential applications related to Bose-Einstein condensates in the presence of an inhomogeneous source.
Layden, B.; Cairns, Iver H.; Robinson, P. A.
2013-08-15
Electrostatic decay of Langmuir waves into Langmuir and ion sound waves (L→L′+S) and scattering of Langmuir waves off thermal ions (L+i→L′+i′, also called “nonlinear Landau damping”) are important nonlinear weak-turbulence processes. The rates for these processes depend on the quadratic longitudinal response function α{sup (2)} (or, equivalently, the quadratic longitudinal susceptibility χ{sup (2)}), which describes the second-order response of a plasma to electrostatic wave fields. Previous calculations of these rates for an unmagnetized Maxwellian plasma have relied upon an approximate form for α{sup (2)} that is valid where two of the wave fields are fast (i.e., v{sub φ}=ω/k≫V{sub e} where ω is the angular frequency, k is the wavenumber, and V{sub e} is the electron thermal speed) and one is slow (v{sub φ}≪V{sub e}). Recently, an exact expression was derived for α{sup (2)} that is valid for any phase speeds of the three waves in an unmagnetized Maxwellian plasma. Here, this exact α{sup (2)} is applied to the calculation of the three-dimensional rates for electrostatic decay and scattering off thermal ions, and the resulting exact rates are compared with the approximate rates. The calculations are performed using previously derived three-dimensional rates for electrostatic decay given in terms of a general α{sup (2)}, and newly derived three-dimensional rates for scattering off thermal ions; the scattering rate is derived assuming a Maxwellian ion distribution, and both rates are derived assuming arc distributions for the wave spectra. For most space plasma conditions, the approximate rate is found to be accurate to better than 20%; however, for sufficiently low Langmuir phase speeds (v{sub φ}/V{sub e}≈3) appropriate to some spatial domains of the foreshock regions of planetary bow shocks and type II solar radio bursts, the use of the exact rate may be necessary for accurate calculations. The relative rates of electrostatic decay
Oxygen partial pressure sensor
Dees, D.W.
1994-09-06
A method for detecting oxygen partial pressure and an oxygen partial pressure sensor are provided. The method for measuring oxygen partial pressure includes contacting oxygen to a solid oxide electrolyte and measuring the subsequent change in electrical conductivity of the solid oxide electrolyte. A solid oxide electrolyte is utilized that contacts both a porous electrode and a nonporous electrode. The electrical conductivity of the solid oxide electrolyte is affected when oxygen from an exhaust stream permeates through the porous electrode to establish an equilibrium of oxygen anions in the electrolyte, thereby displacing electrons throughout the electrolyte to form an electron gradient. By adapting the two electrodes to sense a voltage potential between them, the change in electrolyte conductivity due to oxygen presence can be measured. 1 fig.
Oxygen partial pressure sensor
Dees, Dennis W.
1994-01-01
A method for detecting oxygen partial pressure and an oxygen partial pressure sensor are provided. The method for measuring oxygen partial pressure includes contacting oxygen to a solid oxide electrolyte and measuring the subsequent change in electrical conductivity of the solid oxide electrolyte. A solid oxide electrolyte is utilized that contacts both a porous electrode and a nonporous electrode. The electrical conductivity of the solid oxide electrolyte is affected when oxygen from an exhaust stream permeates through the porous electrode to establish an equilibrium of oxygen anions in the electrolyte, thereby displacing electrons throughout the electrolyte to form an electron gradient. By adapting the two electrodes to sense a voltage potential between them, the change in electrolyte conductivity due to oxygen presence can be measured.
Methanol partial oxidation reformer
Ahmed, Shabbir; Kumar, Romesh; Krumpelt, Michael
1999-01-01
A partial oxidation reformer comprising a longitudinally extending chamber having a methanol, water and an air inlet and an outlet. An igniter mechanism is near the inlets for igniting a mixture of methanol and air, while a partial oxidation catalyst in the chamber is spaced from the inlets and converts methanol and oxygen to carbon dioxide and hydrogen. Controlling the oxygen to methanol mole ratio provides continuous slightly exothermic partial oxidation reactions of methanol and air producing hydrogen gas. The liquid is preferably injected in droplets having diameters less than 100 micrometers. The reformer is useful in a propulsion system for a vehicle which supplies a hydrogen-containing gas to the negative electrode of a fuel cell.
Methanol partial oxidation reformer
Ahmed, S.; Kumar, R.; Krumpelt, M.
1999-08-17
A partial oxidation reformer is described comprising a longitudinally extending chamber having a methanol, water and an air inlet and an outlet. An igniter mechanism is near the inlets for igniting a mixture of methanol and air, while a partial oxidation catalyst in the chamber is spaced from the inlets and converts methanol and oxygen to carbon dioxide and hydrogen. Controlling the oxygen to methanol mole ratio provides continuous slightly exothermic partial oxidation reactions of methanol and air producing hydrogen gas. The liquid is preferably injected in droplets having diameters less than 100 micrometers. The reformer is useful in a propulsion system for a vehicle which supplies a hydrogen-containing gas to the negative electrode of a fuel cell. 7 figs.
Methanol partial oxidation reformer
Ahmed, S.; Kumar, R.; Krumpelt, M.
1999-08-24
A partial oxidation reformer is described comprising a longitudinally extending chamber having a methanol, water and an air inlet and an outlet. An igniter mechanism is near the inlets for igniting a mixture of methanol and air, while a partial oxidation catalyst in the chamber is spaced from the inlets and converts methanol and oxygen to carbon dioxide and hydrogen. Controlling the oxygen to methanol mole ratio provides continuous slightly exothermic partial oxidation reactions of methanol and air producing hydrogen gas. The liquid is preferably injected in droplets having diameters less than 100 micrometers. The reformer is useful in a propulsion system for a vehicle which supplies a hydrogen-containing gas to the negative electrode of a fuel cell. 7 figs.
Methanol partial oxidation reformer
Ahmed, Shabbir; Kumar, Romesh; Krumpelt, Michael
2001-01-01
A partial oxidation reformer comprising a longitudinally extending chamber having a methanol, water and an air inlet and an outlet. An igniter mechanism is near the inlets for igniting a mixture of methanol and air, while a partial oxidation catalyst in the chamber is spaced from the inlets and converts methanol and oxygen to carbon dioxide and hydrogen. Controlling the oxygen to methanol mole ratio provides continuous slightly exothermic partial oxidation reactions of methanol and air producing hydrogen gas. The liquid is preferably injected in droplets having diameters less than 100 micrometers. The reformer is useful in a propulsion system for a vehicle which supplies a hydrogen-containing gas to the negative electrode of a fuel cell.
Geometric scaling as traveling waves.
Munier, S; Peschanski, R
2003-12-05
We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-Piscounov (KPP) equation to the problem of high energy evolution of the QCD amplitudes. We explain how the traveling wave solutions of this equation are related to geometric scaling, a phenomenon observed in deep-inelastic scattering experiments. Geometric scaling is for the first time shown to result from an exact solution of nonlinear QCD evolution equations. Using general results on the KPP equation, we compute the velocity of the wave front, which gives the full high energy dependence of the saturation scale.
Some general properties of the exact acoustic fields in horns and baffles
NASA Astrophysics Data System (ADS)
Campos, L. M. B. C.
1984-07-01
The propagation of the fundamental, longitudinal acoustic mode in a duct of variable cross-section is considered, and the "Webster" wave equations for the sound pressure and velocity are used to establish some general properties of the exact acoustic fields. The equipartition of kinetic and compression energies is shown (section 2.1) to hold at all stations only for (i) a duct of constant cross-section and (ii) an exponential horn; these are the two cases for which the wave equations for the acoustic velocity and pressure coincide. It is proved (section 2.3) that there are only five duct shapes, forming two dual families, which have constant cut-off frequency(ies): namely, (I) the exponential duct, which is self-dual, and is the only shape with constant (and coincident) cut-offs both for the velocity and pressure; (II) the catenoidal horns, of cross-section S˜cosh 2, sinh 2, which, with their duals (III) the inverse catenoidal ducts S˜sech 2, csch 2, have one constant cut-off frequency, respectively, for the acoustic pressure and velocity. The existence of at least one constant cut-off frequency implies that the corresponding wave equation can be transformed into one with constant coefficients, and thus the acoustic fields calculated exactly in terms of elementary (exponential, circular and hyperbolic) functions; this property also applies to the imaginary transformations of the above shapes, viz., the sinusoidal S˜sin 2 and inverse sinusoidal S˜csc 2 ducts, that have no cut-off frequency, i.e., are acoustically "transparent". It is shown that elementary exact solutions of the Webster equation exist only (section 3.1) for these seven shapes: namely, the exponential, catenoidal, sinusoidal and inverse ducts; it is implied that for all other duct shapes the exact acoustic fields involve special functions, in infinite or finite terms, e.g., Bessel and Hermite functions respectively for power-law and Gaussian horns. Examples of the method of analysis are given by
Exact null controllability of degenerate evolution equations with scalar control
Fedorov, Vladimir E; Shklyar, Benzion
2012-12-31
Necessary and sufficient conditions for the exact null controllability of a degenerate linear evolution equation with scalar control are obtained. These general results are used to examine the exact null controllability of the Dzektser equation in the theory of seepage. Bibliography: 13 titles.
Rogue Waves and Modulational Instability
NASA Astrophysics Data System (ADS)
Zakharov, V. E.; Dyachenko, A.
2015-12-01
The most plausible cause of rogue wave formation in a deep ocean is development of modulational instability of quasimonochromatic wave trains. An adequate model for study of this phenomenon is the Euler equation for potential flow of incompressible fluid with free surface in 2-D geometry. Numerical integration of these equations confirms completely the conjecture of rogue wave formation from modulational instability but the procedure is time consuming for determination of rogue wave appearance probability for a given shape of wave energy spectrum. This program can be realized in framework of simpler model using replacement of the exact interaction Hamiltonian by more compact Hamiltonian. There is a family of such models. The popular one is the Nonlinear Schrodinger equation (NLSE). This model is completely integrable and suitable for numerical simulation but we consider that it is oversimplified. It misses such important phenomenon as wave breaking. Recently, we elaborated much more reliable model that describes wave breaking but is as suitable as NLSE from the point of numerical modeling. This model allows to perform massive numerical experiments and study statistics of rogue wave formation in details.
NASA Astrophysics Data System (ADS)
Hayek, Mohamed
2016-04-01
This work develops a simple exact and explicit solution of the one-dimensional transient and nonlinear Richards' equation for soils in a special case of exponential water retention curve and power law hydraulic conductivity. The exact solution is obtained as traveling wave based on the approach proposed by Philip (1957, 1967) and adopted by Zlotnik et al. (2007). The obtained solution is novel, and it expresses explicitly the water content as function of the depth and time. It can be useful to model infiltration into semi-infinite soils with time-dependent boundary conditions and infiltration with constant boundary condition but space-dependent initial condition. A complete analytical inverse procedure based on the proposed analytical solution is presented which allows the estimation of hydraulic parameters. The proposed exact solution is also important for the verification of numerical schemes as well as for checking the implementation of time-dependent boundary conditions.
Lematre, M; Domenjoud, M; Tran-Huu-Hue, L P
2011-12-01
In this study we develop the exact second order formalism of piezoelectric structures under an external mechanical stress. Indeed, previous models are approximated since they consist in deriving all the equations in the natural coordinate system (corresponding to the pre-stress free case). Hence, our exact formalism proposes to obtain the whole of equations in the current coordinate system (which is the coordinate system after the pre-deformation). Then, this exact formalism is used to derive the modified Christoffel equations and the modified KLM model. Finally, we quantify the correction with the approximate formalism on several transfer functions and electro-mechanical parameters for a non hysteretic material (lithium niobate). In conclusion, we show that for this material, significant corrections are obtained when studying the plane wave velocities and the electrical input impedance (about 4%), whereas other parameters such as coupling coefficient and impulse response are less influenced by the choice of coordinate systems (corrections less than 0.5%).
Partially strong WW scattering
Cheung Kingman; Chiang Chengwei; Yuan Tzuchiang
2008-09-01
What if only a light Higgs boson is discovered at the CERN LHC? Conventional wisdom tells us that the scattering of longitudinal weak gauge bosons would not grow strong at high energies. However, this is generally not true. In some composite models or general two-Higgs-doublet models, the presence of a light Higgs boson does not guarantee complete unitarization of the WW scattering. After partial unitarization by the light Higgs boson, the WW scattering becomes strongly interacting until it hits one or more heavier Higgs bosons or other strong dynamics. We analyze how LHC experiments can reveal this interesting possibility of partially strong WW scattering.
2007-01-01
example, in the Bahia Blanca Estuary (Argentina), the sand wave field terminated when the surficial sand sheet became too thin (Aliotta and Perillo... Rosa Island partially breached near the present-day location of the inlet mouth, but soon closed. It was reopened in March 1929 when the local...and Perillo, 1987) Bahia Blanca Estuary mean 11˚ max 30˚ mean 4˚ (Anthony and Leth, 2002) North Sea 2-4˚ 66 Figure 24. Sand wave
NASA Astrophysics Data System (ADS)
Nazarenko, Sergey
2015-07-01
Wave turbulence is the statistical mechanics of random waves with a broadband spectrum interacting via non-linearity. To understand its difference from non-random well-tuned coherent waves, one could compare the sound of thunder to a piece of classical music. Wave turbulence is surprisingly common and important in a great variety of physical settings, starting with the most familiar ocean waves to waves at quantum scales or to much longer waves in astrophysics. We will provide a basic overview of the wave turbulence ideas, approaches and main results emphasising the physics of the phenomena and using qualitative descriptions avoiding, whenever possible, involved mathematical derivations. In particular, dimensional analysis will be used for obtaining the key scaling solutions in wave turbulence - Kolmogorov-Zakharov (KZ) spectra.
Millimeter Wave Radar for detecting the speech signal applications
NASA Astrophysics Data System (ADS)
Li, Zong-Wen
1996-12-01
MilliMeter Wave (MMW) Doppler Radar with grating structures for the applications of detecting speech signals has been discovered in our laboratory. The operating principle of detection the acoustic wave signals based on the Wave Propagation Theory and Wave Equations of The ElectroMagnetic Wave (EMW) and Acoustic Wave (AW) propagating, scattering, reflecting and interacting has been investigated. The experimental and observation results have been provided to verify that MMW CW 40GHz dielectric integrated radar can detect and identify out exactly the existential speech signals in free space from a person speaking. The received sound signal have been reproduced by the DSP and the reproducer.
Mechanisms of wave transformation in finite-depth water
NASA Technical Reports Server (NTRS)
Shemdin, O. H.; Hsiao, S. V.; Carlson, H. E.; Hasselmann, K.; Schulze, K.
1980-01-01
Mechanisms of wave transformation in finite-depth water are investigated. The linear mechanisms examined are percolation, bottom motion, shoaling, and refraction. The nonlinear mechanisms examined are wave-wave interaction and bottom friction. New exact computations of the nonlinear transfer for finite-depth waves are presented for some directional wave spectra. These mechanisms are found to explain satisfactorily wave decay observations obtained at several sites with different bottom sediment properties. The decay rates at these sites are found to be dominated by different mechanisms which are determined by the bottom conditions. As an example, detailed calculations are presented for data obtained at the Jonswap site.
Three-body scattering theory without knowledge of exact asymptotic boundary conditions
Shakeshaft, Robin
2009-07-15
We formulate the theory of three-body scattering without explicit reference to exact asymptotic boundary conditions on the wave function. The transition rate and amplitude are expressed as volume integrals of the resolvent, which are insensitive to the region of asymptotically large distances. The physical branch of the resolvent is selected through the arrow of time, which is required to point forward in each subchannel. This is accomplished by first expressing the resolvent as an integral over time and then making a conformal transformation of each half of the time plane onto a unit disk. The physical branch corresponds to a path of integration in the upper half of the disk. We have tested the method, using a real discrete basis, by calculating the total cross section for singlet S-wave electron impact ionization of atomic hydrogen; our results are in reasonable agreement overall with the landmark results of Bartlet and Stelbovics [Phys. Rev. Lett. 93, 233201 (2004)].
Three-body scattering theory without knowledge of exact asymptotic boundary conditions
NASA Astrophysics Data System (ADS)
Shakeshaft, Robin
2009-07-01
We formulate the theory of three-body scattering without explicit reference to exact asymptotic boundary conditions on the wave function. The transition rate and amplitude are expressed as volume integrals of the resolvent, which are insensitive to the region of asymptotically large distances. The physical branch of the resolvent is selected through the arrow of time, which is required to point forward in each subchannel. This is accomplished by first expressing the resolvent as an integral over time and then making a conformal transformation of each half of the time plane onto a unit disk. The physical branch corresponds to a path of integration in the upper half of the disk. We have tested the method, using a real discrete basis, by calculating the total cross section for singlet S -wave electron impact ionization of atomic hydrogen; our results are in reasonable agreement overall with the landmark results of Bartlet and Stelbovics [Phys. Rev. Lett. 93, 233201 (2004)].
Symmetries, Integrability and Exact Solutions to the (2+1)-Dimensional Benney Types of Equations
NASA Astrophysics Data System (ADS)
Liu, Han-Ze; Xin, Xiang-Peng
2016-08-01
This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the (2+1)-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method. Supported by the National Natural Science Foundation of China under Grant Nos. 11171041 and 11505090, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009, and the doctorial foundation of Liaocheng University under Grant No. 31805
Exact parent Hamiltonian for the quantum Hall states in a lattice.
Kapit, Eliot; Mueller, Erich
2010-11-19
We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wave function is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next-nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.
The implementation of holography in the plane wave matrix model
NASA Astrophysics Data System (ADS)
Mints, Aleksey Leonidovich
It is expected that at the core of nonperturbative theories of quantum gravity, such as M-theory, lies the realization of the holographic principle, in the sense that a holographic theory should contain one binary degree of freedom per Planck area. Present understanding of such theories requires the holographic encoding of bulk data in large matrices. Currently this mapping is poorly understood. The plane wave matrix model provides a laboratory for isolating aspects of this problem in a controlled setting. At large boosts, configurations of concentric membranes become superselection sectors, whose exact spectra are known. From the bulk point of view one expects product states of individual membranes to be contained within the full spectrum. However, for non-BPS states this inclusion relation is obscured by Gauss law constraints. Its validity rests on nontrivial relations in representation theory, which we identify and verify by explicit computation. Beyond the decoding and partial identification of selected states in large matrices, one would like to get a better understanding of the holographic state counting of these degrees of freedom, i.e., entropy. Contrary to the naive expectation of holography realized in terms of the covariant entropy bound, we present evidence that it is the Bekenstein entropy bound, which is related to area differences, that is manifest in the plane wave matrix model. If holography is implemented in this way, we predict crossover behavior at strong coupling when the energy exceeds N2 in units of the mass scale.
Exp-function method for solving fractional partial differential equations.
Zheng, Bin
2013-01-01
We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.
Tapping of Love waves in an isotropic surface waveguide by surface-to-bulk wave transduction.
NASA Technical Reports Server (NTRS)
Tuan, H.-S.; Chang, C.-P.
1972-01-01
A theoretical study of tapping a Love wave in an isotropic microacoustic surface waveguide is given. The surface Love wave is tapped by partial transduction into a bulk wave at a discontinuity. It is shown that, by careful design of the discontinuity, the converted bulk wave power and the radiation pattern may be controlled. General formulas are derived for the calculation of these important characteristics from a relatively general surface contour deformation.
Acute renal injury after partial hepatectomy
Peres, Luis Alberto Batista; Bredt, Luis Cesar; Cipriani, Raphael Flavio Fachini
2016-01-01
Currently, partial hepatectomy is the treatment of choice for a wide variety of liver and biliary conditions. Among the possible complications of partial hepatectomy, acute kidney injury (AKI) should be considered as an important cause of increased morbidity and postoperative mortality. Difficulties in the data analysis related to postoperative AKI after liver resections are mainly due to the multiplicity of factors to be considered in the surgical patients, moreover, there is no consensus of the exact definition of AKI after liver resection in the literature, which hampers comparison and analysis of the scarce data published on the subject. Despite this multiplicity of risk factors for postoperative AKI after partial hepatectomy, there are main factors that clearly contribute to its occurrence. First factor relates to large blood losses with renal hypoperfusion during the operation, second factor relates to the occurrence of post-hepatectomy liver failure with consequent distributive circulatory changes and hepatorenal syndrome. Eventually, patients can have more than one factor contributing to post-operative AKI, and frequently these combinations of acute insults can be aggravated by sepsis or exposure to nephrotoxic drugs. PMID:27478539
Comparison of exact solution with Eikonal approximation for elastic heavy ion scattering
NASA Technical Reports Server (NTRS)
Dubey, Rajendra R.; Khandelwal, Govind S.; Cucinotta, Francis A.; Maung, Khin Maung
1995-01-01
A first-order optical potential is used to calculate the total and absorption cross sections for nucleus-nucleus scattering. The differential cross section is calculated by using a partial-wave expansion of the Lippmann-Schwinger equation in momentum space. The results are compared with solutions in the Eikonal approximation for the equivalent potential and with experimental data in the energy range from 25A to 1000A MeV.
Dilemmas of partial cooperation.
Stark, Hans-Ulrich
2010-08-01
Related to the often applied cooperation models of social dilemmas, we deal with scenarios in which defection dominates cooperation, but an intermediate fraction of cooperators, that is, "partial cooperation," would maximize the overall performance of a group of individuals. Of course, such a solution comes at the expense of cooperators that do not profit from the overall maximum. However, because there are mechanisms accounting for mutual benefits after repeated interactions or through evolutionary mechanisms, such situations can constitute "dilemmas" of partial cooperation. Among the 12 ordinally distinct, symmetrical 2 x 2 games, three (barely considered) variants are correspondents of such dilemmas. Whereas some previous studies investigated particular instances of such games, we here provide the unifying framework and concisely relate it to the broad literature on cooperation in social dilemmas. Complementing our argumentation, we study the evolution of partial cooperation by deriving the respective conditions under which coexistence of cooperators and defectors, that is, partial cooperation, can be a stable outcome of evolutionary dynamics in these scenarios. Finally, we discuss the relevance of such models for research on the large biodiversity and variation in cooperative efforts both in biological and social systems.
Full and Partial Cloaking in Electromagnetic Scattering
NASA Astrophysics Data System (ADS)
Deng, Youjun; Liu, Hongyu; Uhlmann, Gunther
2017-01-01
In this paper, we consider two regularized transformation-optics cloaking schemes for electromagnetic (EM) waves. Both schemes are based on the blowup construction with the generating sets being, respectively, a generic curve and a planar subset. We derive sharp asymptotic estimates in assessing the cloaking performances of the two constructions in terms of the regularization parameters and the geometries of the cloaking devices. The first construction yields an approximate full-cloak, whereas the second construction yields an approximate partial-cloak. Moreover, by incorporating properly chosen conducting layers, both cloaking constructions are capable of nearly cloaking arbitrary EM contents. This work complements the existing results in Ammari et al. (SIAM J Appl Math 73:2055-2076, 2013), Bao and Liu (SIAM J Appl Math 74:724-742, 2014), Bao et al. (J Math Pure Appl (9) 101:716-733, 2014) on approximate EM cloaks with the generating set being a singular point, and it also extends Deng et al. (On regularized full- and partial-cloaks in acoustic scat- tering. Preprint, arXiv:1502.01174, 2015), Li et al. (Commun Math Phys, 335:671-712, 2015) on regularized full and partial cloaks for acoustic waves governed by the Helmholtz system to the more challenging EM case governed by the full Maxwell system.
A conditionally exactly solvable generalization of the inverse square root potential
NASA Astrophysics Data System (ADS)
Ishkhanyan, A. M.
2016-11-01
We present a conditionally exactly solvable singular potential for the one-dimensional Schrödinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general solution of the problem is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. Discussing the bound-state wave functions vanishing both at infinity and in the origin, we derive the exact equation for the energy spectrum which is written using two Hermite functions of non-integer order. In specific auxiliary variables this equation becomes a mathematical equation that does not refer to a specific physical context discussed. In the two-dimensional space of these auxiliary variables the roots of this equation draw a countable infinite set of open curves with hyperbolic asymptotes. We present an analytic description of these curves by a transcendental algebraic equation for the involved variables. The intersections of the curves thus constructed with a certain cubic curve provide a highly accurate description of the energy spectrum.
Exact-exchange time-dependent density-functional theory for static and dynamic polarizabilities
Hirata, So; Ivanov, Stanislav; Bartlett, Rodney J.; Grabowski, Ireneusz
2005-03-01
Time-dependent density-functional theory (TDDFT) employing the exact-exchange functional has been formulated on the basis of the optimized-effective-potential (OEP) method of Talman and Shadwick for second-order molecular properties and implemented into a Gaussian-basis-set, trial-vector algorithm. The only approximation involved, apart from the lack of correlation effects and the use of Gaussian-type basis functions, was the consistent use of the adiabatic approximation in the exchange kernel and in the linear response function. The static and dynamic polarizabilities and their anisotropy predicted by the TDDFT with exact exchange (TDOEP) agree accurately with the corresponding values from time-dependent Hartree-Fock theory, the exact-exchange counterpart in the wave function theory. The TDOEP is free from the nonphysical asymptotic decay of the exchange potential of most conventional density functionals or from any other manifestations of the incomplete cancellation of the self-interaction energy. The systematic overestimation of the absolute values and dispersion of polarizabilities that plagues most conventional TDDFT cannot be seen in the TDOEP.
NASA Astrophysics Data System (ADS)
Craik, A. D. D.
1989-01-01
An account is given of those flows influenced by body forces that admit exact solutions similar to those identified by Craik and Criminale (1986) when body forces are absent. Bayly's (1986) inviscid Floquet stability analysis of elliptical flows is extended to incorporate a Coriolis force. With the exception of a narrow band of rotation speeds, it is found that elliptical-vortex flows are inviscidly unstable to three-dimensional plane-wave disturbances.
Dissociation between exact and approximate addition in developmental dyslexia.
Yang, Xiujie; Meng, Xiangzhi
2016-09-01
Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact.
Izard, Véronique; Streri, Arlette; Spelke, Elizabeth S
2014-07-01
Exact integer concepts are fundamental to a wide array of human activities, but their origins are obscure. Some have proposed that children are endowed with a system of natural number concepts, whereas others have argued that children construct these concepts by mastering verbal counting or other numeric symbols. This debate remains unresolved, because it is difficult to test children's mastery of the logic of integer concepts without using symbols to enumerate large sets, and the symbols themselves could be a source of difficulty for children. Here, we introduce a new method, focusing on large quantities and avoiding the use of words or other symbols for numbers, to study children's understanding of an essential property underlying integer concepts: the relation of exact numerical equality. Children aged 32-36 months, who possessed no symbols for exact numbers beyond 4, were given one-to-one correspondence cues to help them track a set of puppets, and their enumeration of the set was assessed by a non-verbal manual search task. Children used one-to-one correspondence relations to reconstruct exact quantities in sets of 5 or 6 objects, as long as the elements forming the sets remained the same individuals. In contrast, they failed to track exact quantities when one element was added, removed, or substituted for another. These results suggest an alternative to both nativist and symbol-based constructivist theories of the development of natural number concepts: Before learning symbols for exact numbers, children have a partial understanding of the properties of exact numbers.
Qiang-Dong proper quantization rule and its applications to exactly solvable quantum systems
NASA Astrophysics Data System (ADS)
Serrano, F. A.; Gu, Xiao-Yan; Dong, Shi-Hai
2010-08-01
We propose proper quantization rule, ∫x_Ax_B k(x)dx-∫x0Ax0Bk0(x)dx=nπ, where k(x )=√2M[E -V(x)] /ℏ. The xA and xB are two turning points determined by E =V(x), and n is the number of the nodes of wave function ψ(x ). We carry out the exact solutions of solvable quantum systems by this rule and find that the energy spectra of solvable systems can be determined only from its ground state energy. The previous complicated and tedious integral calculations involved in exact quantization rule are greatly simplified. The beauty and simplicity of the rule come from its meaning—whenever the number of the nodes of ϕ(x ) or the number of the nodes of the wave function ψ(x ) increases by 1, the momentum integral ∫xAxBk(x )dx will increase by π. We apply this proper quantization rule to carry out solvable quantum systems such as the one-dimensional harmonic oscillator, the Morse potential and its generalization, the Hulthén potential, the Scarf II potential, the asymmetric trigonometric Rosen-Morse potential, the Pöschl-Teller type potentials, the Rosen-Morse potential, the Eckart potential, the harmonic oscillator in three dimensions, the hydrogen atom, and the Manning-Rosen potential in D dimensions.
Peaked Periodic Wave Solutions to the Broer–Kaup Equation
NASA Astrophysics Data System (ADS)
Jiang, Bo; Bi, Qin-Sheng
2017-01-01
By qualitative analysis method, a sufficient condition for the existence of peaked periodic wave solutions to the Broer–Kaup equation is given. Some exact explicit expressions of peaked periodic wave solutions are also presented. Supported by National Nature Science Foundation of China under Grant No. 11102076 and Natural Science Fund for Colleges and Universities in Jiangsu Province under Grant No. 15KJB110005
Atmospheric Science Data Center
2013-04-19
article title: Gravity Waves Ripple over Marine Stratocumulus Clouds ... Imaging SpectroRadiometer (MISR), a fingerprint-like gravity wave feature occurs over a deck of marine stratocumulus clouds. Similar ... that occur when a pebble is thrown into a still pond, such "gravity waves" sometimes appear when the relatively stable and stratified air ...
NASA Astrophysics Data System (ADS)
Stepanov, Nikolay S.; Zelekson, Lev A.
2017-03-01
The exact stationary solution of one-dimensional non-relativistic Vlasov equation is obtained in the article. It is shown that in the energy exchange with the self-consistent longitudinal electric field, both wave trapped charged particles and the passing ones take part. It is proved that the trapped electron distribution is fundamentally different from distribution functions described by other authors, which used the Bernstein, Greene, and Kruskal method. So, the correct distribution function is characterized by its sudden change at the equality of wave and electrons' velocity but not on the edges of the potential well. This jump occurs for any arbitrary small value of wave potential. It was also found that the energy density of fast electrons trapped by the wave is less than the energy density of slow trapped electrons. This leads to the fact that the energy of the self-consistent electric field may both increase and decrease due to the nonlinear Landau damping. The conditions under which a similar effect can be observed are defined. Also for the first time, it is shown that the self-generated strong electric field always produces antitropic electron beams.
Circular polarization of obliquely propagating whistler wave magnetic field
Bellan, P. M.
2013-08-15
The circular polarization of the magnetic field of obliquely propagating whistler waves is derived using a basis set associated with the wave partial differential equation. The wave energy is mainly magnetic and the wave propagation consists of this magnetic energy sloshing back and forth between two orthogonal components of magnetic field in quadrature. The wave electric field energy is small compared to the magnetic field energy.
NASA Astrophysics Data System (ADS)
Ellahi, R.; Hussain, F.
2015-11-01
The purpose of this paper is to study the closed-form solutions of peristaltic flow of Jeffery fluid under the simultaneous effects of magnetohydrodynamics (MHD) and partial slip conditions in a rectangular duct. The influence of wave train propagation is also taken into account. The analysis of mathematical model consists of continuity and the momentum equations are carried out under long wavelength (0 < < → ∞) and low Reynolds number (Re → 0) assumptions. The governing equations are first reduced to the dimensionless system of partial differential equation using the appropriate variables and afterwards exact solutions are obtained by applying the method of separation of variables. The role of pertinent parameters such as Hartmann number M, slip parameter β1, volumetric flow rate Q, Jeffery parameter λ1 and the aspect ratio β against the velocity profile, pressure gradient and pressure rise is illustrated graphically. The streamlines have also been presented to discuss the trapping bolus discipline. Comparison with the existing studies is made as a limiting case of the considered problem.at the end.
NASA Astrophysics Data System (ADS)
Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun
In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.
NASA Astrophysics Data System (ADS)
Schatz, George C.; Amaee, B.; Connor, J. N. L.
1987-10-01
We describe a method for calculating cross sections for atom plus diatom reactive collisions based on the centrifugal sudden distorted wave (CSDW) approximation. This method is nearly exact at low energies where reactive cross sections are small. Representative CPU times are given for applications of the CSDW method to the Cl + HCl → ClH + Cl reaction using CDC 7600, Cyber 176, Cyber 205, Cray X-MP and Cray-2 computers. We also present differential cross sections for the Cl + HCl reaction and apply a simple semiclassical model which relates these cross sections to the partial wave reaction probabilities, and to the energy dependence of the reaction probabilities for zero total angular momentum. This model explains why the differential cross sections are backward peaked, and why the oscillatory cross sections seen in earlier, more approximate infinite order sudden calculations are not found in the present results at low energy.
Partially coherent ultrafast spectrography
Bourassin-Bouchet, C.; Couprie, M.-E.
2015-01-01
Modern ultrafast metrology relies on the postulate that the pulse to be measured is fully coherent, that is, that it can be completely described by its spectrum and spectral phase. However, synthesizing fully coherent pulses is not always possible in practice, especially in the domain of emerging ultrashort X-ray sources where temporal metrology is strongly needed. Here we demonstrate how frequency-resolved optical gating (FROG), the first and one of the most widespread techniques for pulse characterization, can be adapted to measure partially coherent pulses even down to the attosecond timescale. No modification of experimental apparatuses is required; only the processing of the measurement changes. To do so, we take our inspiration from other branches of physics where partial coherence is routinely dealt with, such as quantum optics and coherent diffractive imaging. This will have important and immediate applications, such as enabling the measurement of X-ray free-electron laser pulses despite timing jitter. PMID:25744080
Laparoscopic partial splenic resection.
Uranüs, S; Pfeifer, J; Schauer, C; Kronberger, L; Rabl, H; Ranftl, G; Hauser, H; Bahadori, K
1995-04-01
Twenty domestic pigs with an average weight of 30 kg were subjected to laparoscopic partial splenic resection with the aim of determining the feasibility, reliability, and safety of this procedure. Unlike the human spleen, the pig spleen is perpendicular to the body's long axis, and it is long and slender. The parenchyma was severed through the middle third, where the organ is thickest. An 18-mm trocar with a 60-mm Endopath linear cutter was used for the resection. The tissue was removed with a 33-mm trocar. The operation was successfully concluded in all animals. No capsule tears occurred as a result of applying the stapler. Optimal hemostasis was achieved on the resected edges in all animals. Although these findings cannot be extended to human surgery without reservations, we suggest that diagnostic partial resection and minor cyst resections are ideal initial indications for this minimally invasive approach.
Hierarchical partial order ranking.
Carlsen, Lars
2008-09-01
Assessing the potential impact on environmental and human health from the production and use of chemicals or from polluted sites involves a multi-criteria evaluation scheme. A priori several parameters are to address, e.g., production tonnage, specific release scenarios, geographical and site-specific factors in addition to various substance dependent parameters. Further socio-economic factors may be taken into consideration. The number of parameters to be included may well appear to be prohibitive for developing a sensible model. The study introduces hierarchical partial order ranking (HPOR) that remedies this problem. By HPOR the original parameters are initially grouped based on their mutual connection and a set of meta-descriptors is derived representing the ranking corresponding to the single groups of descriptors, respectively. A second partial order ranking is carried out based on the meta-descriptors, the final ranking being disclosed though average ranks. An illustrative example on the prioritization of polluted sites is given.
Partially coherent ultrafast spectrography
NASA Astrophysics Data System (ADS)
Bourassin-Bouchet, C.; Couprie, M.-E.
2015-03-01
Modern ultrafast metrology relies on the postulate that the pulse to be measured is fully coherent, that is, that it can be completely described by its spectrum and spectral phase. However, synthesizing fully coherent pulses is not always possible in practice, especially in the domain of emerging ultrashort X-ray sources where temporal metrology is strongly needed. Here we demonstrate how frequency-resolved optical gating (FROG), the first and one of the most widespread techniques for pulse characterization, can be adapted to measure partially coherent pulses even down to the attosecond timescale. No modification of experimental apparatuses is required; only the processing of the measurement changes. To do so, we take our inspiration from other branches of physics where partial coherence is routinely dealt with, such as quantum optics and coherent diffractive imaging. This will have important and immediate applications, such as enabling the measurement of X-ray free-electron laser pulses despite timing jitter.
Partially integrated exhaust manifold
Hayman, Alan W; Baker, Rodney E
2015-01-20
A partially integrated manifold assembly is disclosed which improves performance, reduces cost and provides efficient packaging of engine components. The partially integrated manifold assembly includes a first leg extending from a first port and terminating at a mounting flange for an exhaust gas control valve. Multiple additional legs (depending on the total number of cylinders) are integrally formed with the cylinder head assembly and extend from the ports of the associated cylinder and terminate at an exit port flange. These additional legs are longer than the first leg such that the exit port flange is spaced apart from the mounting flange. This configuration provides increased packaging space adjacent the first leg for any valving that may be required to control the direction and destination of exhaust flow in recirculation to an EGR valve or downstream to a catalytic converter.
Activated partial thromboplastin time.
Ignjatovic, Vera
2013-01-01
Activated partial thromboplastin time (APTT) is a commonly used coagulation assay that is easy to perform, is affordable, and is therefore performed in most coagulation laboratories, both clinical and research, worldwide. The APTT is based on the principle that in citrated plasma, the addition of a platelet substitute, factor XII activator, and CaCl2 allows for formation of a stable clot. The time required for the formation of a stable clot is recorded in seconds and represents the actual APTT result.
The Third Wave: A Position Paper.
ERIC Educational Resources Information Center
Dyrud, Marilyn A.
2000-01-01
Describes the Third Wave as an "information bomb... exploding in our midst, showering us with a shrapnel of images and drastically changing the way each of us perceives and acts upon our private world." Begins with a description of A. Toffler's Third Wave as an attempt to partially explain what is happening in higher education,…