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.
Exact Solitary Water Waves with Vorticity
NASA Astrophysics Data System (ADS)
Hur, Vera Mikyoung
2008-05-01
The solitary water wave problem is to find steady free surface waves which approach a constant level of depth in the far field. The main result is the existence of a family of exact solitary waves of small amplitude for an arbitrary vorticity. Each solution has a supercritical parameter value and decays exponentially at infinity. The proof is based on a generalized implicit function theorem of the Nash-Moser type. The first approximation to the surface profile is given by the “KdV” equation. With a supercritical value of the surface tension coefficient, a family of small amplitude solitary waves of depression with subcritical parameter values is constructed for an arbitrary vorticity.
Are Electron Partial Waves Real
NASA Astrophysics Data System (ADS)
Yenen, O.; McLaughlin, K. W.
2005-05-01
Experiments determining the partial wave content of electrons are uncommon. The standard approach to partial wave expansion of the wavefunction of electrons often ignores their spin. In this non-relativistic approximation the partial waves are labeled by their orbital angular momentum quantum number, e.g. d-waves. As our previous work has shown, this non-relativistic approximation usually fails for photoelectrons. Partial waves should be further specified by their total angular momentum. With d-waves for example, one would need to distinguish between d3/2 and d5/2 partial waves. Although energetically degenerate, fully relativistic d3/2 and d5/2 partial waves of photoelectrons have fundamentally different angular distributions. Using experimental and theoretical methods we have developed, we obtain partial wave probabilities of photoelectrons from polarization measurements of ionic fluorescence. We found that for selected states of the residual ion, there are energy regions where the photoelectron is in a single partial wave with predictable angular distributions.
Symmetrized quartic polynomial oscillators and their partial exact solvability
NASA Astrophysics Data System (ADS)
Znojil, Miloslav
2016-04-01
Sextic polynomial oscillator is probably the best known quantum system which is partially exactly alias quasi-exactly solvable (QES), i.e., which possesses closed-form, elementary-function bound states ψ (x) at certain couplings and energies. In contrast, the apparently simpler and phenomenologically more important quartic polynomial oscillator is not QES. A resolution of the paradox is proposed: The one-dimensional Schrödinger equation is shown QES after the analyticity-violating symmetrization V (x) = A | x | + Bx2 + C | x|3 +x4 of the quartic polynomial potential.
Exact Faraday rotation in the cylindrical Einstein-Maxwell waves
Arafah, M.R.; Fakioglu, S.; Halilsoy, M. )
1990-07-15
We obtain the exact behavior of the cross-polarized cylindrical Einstein-Maxwell waves that generalizes the well-known Einstein-Rosen waves. In the presence of the second mode of polarization the outgoing waves interact with the incoming ones to exhibit an analogous effect of the Faraday rotation.
Exact and Explicit Internal Equatorial Water Waves with Underlying Currents
NASA Astrophysics Data System (ADS)
Kluczek, Mateusz
2016-07-01
In this paper we present an exact and explicit solution to the geophysical governing equations in the Equatorial region, which represents internal oceanic waves in the presence of a constant underlying current.
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.
Exact and explicit solitary wave solutions to some nonlinear equations
Jiefang Zhang
1996-08-01
Exact and explicit solitary wave solutions are obtained for some physically interesting nonlinear evolutions and wave equations in physics and other fields by using a special transformation. These equations include the KdV-Burgers equation, the MKdV-Burgers equation, the combined KdV-MKdV equation, the Newell-Whitehead equation, the dissipative {Phi}{sup 4}-model equation, the generalized Fisher equation, and the elastic-medium wave equation.
Nonlinear progressive acoustic-gravity waves: Exact solutions
NASA Astrophysics Data System (ADS)
Godin, Oleg
2013-04-01
We consider finite-amplitude mechanical waves in an inhomogeneous, compressible fluid in a uniform gravity field. The fluid is assumed to be inviscid, and wave motion is considered as an adiabatic thermodynamic process. The fluid either occupies an unbounded domain or has free and/or rigid boundaries. Wave motion is described by the momentum, continuity, and state equations in Lagrangian coordinates. We consider generic inhomogeneous fluids; no specific assumptions are made regarding the equation of state or spatial variations of the mass density or the sound speed in the absence of waves. The density and the sound speed are piece-wise continuous functions of position. The discontinuities represent fluid-fluid interfaces, such as the air-sea interface. Following a recent work on linear acoustic-gravity waves [O. A. Godin, Incompressible wave motion of compressible fluids, Phys. Rev. Lett., 108, 194501 (2012)], here we investigate a particular class of non-linear wave motions in fluids, in which pressure remains constant in each moving fluid parcel. Exact, analytic solutions of the non-linear hydrodynamics equations are obtained for two distinct scenarios. In the first scenario, the fluid is either unbounded or has a free surface. In the latter case, the exact analytic solution can be interpreted as a progressive surface wave. In the second scenario, the fluid has a free surface and a sloping, plane rigid boundary. Then the exact analytic solution represents an edge wave propagating horizontally along the rigid boundary. In both scenarios, the flow field associated with the finite-amplitude waves is rotational. When the sound speed tends to infinity, our results reduce to well-known finite-amplitude waves in incompressible fluids. In another limit, when the wave amplitude tends to zero, the exact solutions reduce to known results for linear waves in compressible fluids. The possibility of extending the theory to rotating fluids and fluids with a shearing background
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.
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
Waves on a vortex filament: exact solutions of dynamical equations
NASA Astrophysics Data System (ADS)
Brugarino, Tommaso; Mongiovi, Maria Stella; Sciacca, Michele
2015-06-01
In this paper, we take into account the dynamical equations of a vortex filament in superfluid helium at finite temperature (1 K < T < 2.17 K) and at very low temperature, which is called Biot-Savart law. The last equation is also valid for a vortex tube in a frictionless, unbounded, and incompressible fluid. Both the equations are approximated by the Local Induction Approximation (LIA) and Fukumoto's approximation. The obtained equations are then considered in the extrinsic frame of reference, where exact solutions (Kelvin waves) are shown. These waves are then compared one to each other in terms of their dispersion relations in the frictionless case. The same equations are then investigated for a quantized vortex line in superfluid helium at higher temperature, where friction terms are needed for a full description of the motion.
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. PMID:27347461
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.
Partial wave analysis using graphics processing units
NASA Astrophysics Data System (ADS)
Berger, Niklaus; Beijiang, Liu; Jike, Wang
2010-04-01
Partial wave analysis is an important tool for determining resonance properties in hadron spectroscopy. For large data samples however, the un-binned likelihood fits employed are computationally very expensive. At the Beijing Spectrometer (BES) III experiment, an increase in statistics compared to earlier experiments of up to two orders of magnitude is expected. In order to allow for a timely analysis of these datasets, additional computing power with short turnover times has to be made available. It turns out that graphics processing units (GPUs) originally developed for 3D computer games have an architecture of massively parallel single instruction multiple data floating point units that is almost ideally suited for the algorithms employed in partial wave analysis. We have implemented a framework for tensor manipulation and partial wave fits called GPUPWA. The user writes a program in pure C++ whilst the GPUPWA classes handle computations on the GPU, memory transfers, caching and other technical details. In conjunction with a recent graphics processor, the framework provides a speed-up of the partial wave fit by more than two orders of magnitude compared to legacy FORTRAN code.
NASA Astrophysics Data System (ADS)
Yang, Xiao-Feng; Deng, Zi-Chen; Li, Qing-Jun; Wei, Yi
2016-07-01
The homogeneous balance of undetermined coefficients method (HBUCM) is firstly proposed to construct not only the exact traveling wave solutions, three-wave solutions, homoclinic solutions, N-soliton solutions, but also multi-symplectic structures of some nonlinear partial differential equations (NLPDEs). By applying the proposed method to the variant Boussinesq equations (VBEs), the exact combined traveling wave solutions and a multi-symplectic structure of the VBEs are obtained directly. Then, the definition and a multi-symplectic structure of the variant Boussinesq-Whitham-Broer-Kaup type equations (VBWBKTEs) which can degenerate to the VBEs, the Whitham-Broer-Kaup equations (WBKEs) and the Broer-Kaup equations (BKEs) are given in the multi-symplectic sense. The HBUCM is also a standard and computable method, which can be generalized to obtain the exact solutions and multi-symplectic structures for some types of NLPDEs.
NASA Astrophysics Data System (ADS)
Ali Akbar, M.; Norhashidah, Hj. Mohd. Ali; E. M. E., Zayed
2012-02-01
In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G'/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves.
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.
NASA Astrophysics Data System (ADS)
Wang, Ying; Guo, Yunxi
2016-07-01
In this paper, we developed, for the first time, the exact expressions of several periodic travelling wave solutions and a solitary wave solution for a shallow water wave model of moderate amplitude. Then, we present the existence theorem of the global weak solutions. Finally, we prove the stability of solution in L1(R) space for the Cauchy problem of the equation.
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.
On exact traveling-wave solutions for local fractional Korteweg-de Vries equation
NASA Astrophysics Data System (ADS)
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.
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. PMID:27586629
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.
A Note on Exact Travelling Wave Solutions for the Klein-Gordon- Zakharov Equations
NASA Astrophysics Data System (ADS)
Zhang, Zai-Yun; Zhang, Ying-Hui; Gan, Xiang-Yang; Yu, De-Ming
2012-04-01
In this paper, we investigate the travelling wave solutions for the Klein-Gordon-Zakharov equations by using the modified trigonometric function series method benefited to the ideas of Z. Y. Zhang, Y. X. Li, Z. H. Liu, and X. J. Miao, Commun. Nonlin. Sci. Numer. Simul. , 3097 (2011). Exact travelling wave solutions are obtained
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.
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 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
The Exact Distributions of FIS under Partial Asexuality in Small Finite Populations with Mutation
Stoeckel, Solenn; Masson, Jean-Pierre
2014-01-01
Reproductive systems like partial asexuality participate to shape the evolution of genetic diversity within populations, which is often quantified by the inbreeding coefficient FIS. Understanding how those mating systems impact the possible distributions of FIS values in theoretical populations helps to unravel forces shaping the evolution of real populations. We proposed a population genetics model based on genotypic states in a finite population with mutation. For populations with less than 400 individuals, we assessed the impact of the rates of asexuality on the full exact distributions of FIS, the probabilities of positive and negative FIS, the probabilities of fixation and the probabilities to observe changes in the sign of FIS over one generation. After an infinite number of generations, we distinguished three main patterns of effects of the rates of asexuality on genetic diversity that also varied according to the interactions of mutation and genetic drift. Even rare asexual events in mainly sexual populations impacted the balance between negative and positive FIS and the occurrence of extreme values. It also drastically modified the probability to change the sign of FIS value at one locus over one generation. When mutation prevailed over genetic drift, increasing rates of asexuality continuously increased the variance of FIS that reached its highest value in fully asexual populations. In consequence, even ancient asexual populations showed the entire FIS spectrum, including strong positive FIS. The prevalence of heterozygous loci only occurred in full asexual populations when genetic drift dominated. PMID:24465510
Holographic conformal partial waves as gravitational open Wilson networks
NASA Astrophysics Data System (ADS)
Bhatta, Atanu; Raman, Prashanth; Suryanarayana, Nemani V.
2016-06-01
We propose a method to holographically compute the conformal partial waves in any decomposition of correlation functions of primary operators in conformal field theories using open Wilson network operators in the holographic gravitational dual. The Wilson operators are the gravitational ones where gravity is written as a gauge theory in the first order Hilbert-Palatini formalism. We apply this method to compute the global conformal blocks and partial waves in 2d CFTs reproducing many of the known results.
Bifurcations and Exact Traveling Wave Solutions of a Modified Nonlinear Schrödinger Equation
NASA Astrophysics Data System (ADS)
Kou, Kitian; Li, Jibin
2016-06-01
In this paper, we consider two singular nonlinear planar dynamical systems created from the studies of one-dimensional bright and dark spatial solitons for one-dimensional beams in a nonlocal Kerr-like media. On the basis of the investigation of the dynamical behavior and bifurcations of solutions of the planar dynamical systems, we obtain all possible explicit exact parametric representations of solutions (including solitary wave solutions, periodic wave solutions, peakon and periodic peakons, compacton solutions, etc.) under different parameter conditions.
Exact solution for a photoacoustic wave from a finite-length cylindrical source.
Zalev, Jason; Kolios, Michael C
2015-04-01
In wide-field pulsed photoacoustics, a nearly instantaneous source of electromagnetic energy is applied uniformly to an absorbing medium to create an acoustic wave. In this work, an exact solution is derived for the photoacoustic wave originating from a finite-length solid cylindrical source in terms of known analytic functions involving elliptic integrals of canonical form. The solution is compared with the output of a finite-element simulation. PMID:25920820
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.
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.
NASA Astrophysics Data System (ADS)
Harko, T.; Mak, M. K.
2015-11-01
We consider quasi-stationary (travelling wave type) solutions to a general nonlinear reaction-convection-diffusion equation with arbitrary, autonomous coefficients. The second order nonlinear equation describing one dimensional travelling waves can be reduced to a first kind first order Abel equation. By using two integrability conditions for the Abel equation (the Chiellini lemma and the Lemke transformation), several classes of exact travelling wave solutions of the general reaction-convection-diffusion equation are obtained, corresponding to different functional relations imposed between the diffusion, convection and reaction functions. In particular, we obtain travelling wave solutions for two non-linear second order partial differential equations, representing generalizations of the standard diffusion equation and of the classical Fisher-Kolmogorov equation, to which they reduce for some limiting values of the model parameters. The models correspond to some specific, power law type choices of the reaction and convection functions, respectively. The travelling wave solutions of these two classes of differential equation are investigated in detail by using both numerical and semi-analytical methods.
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.
Exactness of wave functions from two-body exponential transformations in many-body quantum theory
Mazziotti, David A.
2004-01-01
Recent studies have considered the possibility that the exact ground-state wavefunction from any Hamiltonian with two-particle interactions may be generated from a single finite two-body exponential transformation acting on an arbitrary Slater determinant [Piecuch et al., Phys. Rev. Lett. 90, 113001 (2003)]. Using the Campbell-Baker-Hausdorff relation, we show that it is difficult for the variational minimum of this trial wave function to satisfy the contracted Schroedinger equation which is a necessary and sufficient condition for the wave function to satisfy the Schroedinger equation. A counterexample is presented through the Lipkin quasispin model with 4-50 fermions. When the number of fermions exceeds four, the wave function from a finite two-body exponential transformation is shown to be inexact. If the trial wave function ansatz is extended to include products of finite two-body exponential transformations acting on an arbitrary Slater-determinant reference, then we show that the ansatz includes the exact ground-state wave function from any Hamiltonian with only two-particle interactions. Connections between the two-body exponential transformation of the wave function and recent research on two-body exponential similarity transformations of the Hamiltonian [S.R. White, J. Chem. Phys. 117, 7472 (2002)] are discussed.
Lee, Jong-In; Kim, Young-Taek; Shin, Sungwon
2014-01-01
This study presents wave height distribution in terms of stem wave evolution phenomena on partially perforated wall structures through three-dimensional laboratory experiments. The plain and partially perforated walls were tested to understand their effects on the stem wave evolution under the monochromatic and random wave cases with the various wave conditions, incident angle (from 10 to 40 degrees), and configurations of front and side walls. The partially perforated wall reduced the relative wave heights more effectively compared to the plain wall structure. Partially perforated walls with side walls showed a better performance in terms of wave height reduction compared to the structure without the side wall. Moreover, the relative wave heights along the wall were relatively small when the relative chamber width is large, within the range of the chamber width in this study. The wave spectra showed a frequency dependency of the wave energy dissipation. In most cases, the existence of side wall is a more important factor than the porosity of the front wall in terms of the wave height reduction even if the partially perforated wall was still effective compared to the plain wall. PMID:25254260
Lee, Jong-In; Kim, Young-Taek; Shin, Sungwon
2014-01-01
This study presents wave height distribution in terms of stem wave evolution phenomena on partially perforated wall structures through three-dimensional laboratory experiments. The plain and partially perforated walls were tested to understand their effects on the stem wave evolution under the monochromatic and random wave cases with the various wave conditions, incident angle (from 10 to 40 degrees), and configurations of front and side walls. The partially perforated wall reduced the relative wave heights more effectively compared to the plain wall structure. Partially perforated walls with side walls showed a better performance in terms of wave height reduction compared to the structure without the side wall. Moreover, the relative wave heights along the wall were relatively small when the relative chamber width is large, within the range of the chamber width in this study. The wave spectra showed a frequency dependency of the wave energy dissipation. In most cases, the existence of side wall is a more important factor than the porosity of the front wall in terms of the wave height reduction even if the partially perforated wall was still effective compared to the plain wall. PMID:25254260
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.; 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 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
Correlations of π N partial waves for multireaction analyses
NASA Astrophysics Data System (ADS)
Döring, M.; Revier, J.; Rönchen, D.; Workman, R. L.
2016-06-01
In the search for missing baryonic resonances, many analyses include data from a variety of pion- and photon-induced reactions. For elastic π N 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. The influence of systematic errors is also considered.
Exact solution to plane-wave scattering by an ideal "left-handed" wedge
NASA Astrophysics Data System (ADS)
Monzon, Cesar; Forester, Donald W.; Smith, Douglas; Loschialpo, Peter
2006-02-01
An exact analytical solution to the problem of plane-wave diffraction by a penetrable left-handed medium (LHM) epsilon=µ=-1 wedge of arbitrary angle (subject to valid physical constraints) is presented. Standard analysis involving discontinuous angular eigenfunctions and even/odd symmetry decomposition resulted in a discrete spectrum leading to a series solution resembling the traditional perfect electric conductor wedge solution but exhibiting the expected negative refraction phenomenology. Numerical results are presented, some of which seemed paradoxical but are explainable by classical means. A new type of illusory edge radiation is observed and explained. Also, a novel edge-launched interface standing wave is observed on the directly illuminated side. The exact analytical solution is verified by comparison with finite-difference time-domain simulation on causal LHM materials.
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. PMID:23679540
NASA Astrophysics Data System (ADS)
Chen, Li-Bing; Jin, Rui-Bo; Lu, Hong
Teleportation of quantum gates using partially entangled states is considered. Different from the known probability schemes, we propose and study a method for teleporting a prototypical single-qubit rotation on a remote receiver with unit fidelity and unit probability by using two partially entangled pairs. The method is applicable to any two partially entangled pairs satisfying the condition that their smaller Schmidt coefficients γ and η are (2γ+2η-2γη-1)≥0. In our scheme, the sender's local generalized measurement described by a positive operator-valued measurement (POVM) lies at the heart. We construct the required POVM. The fact that the controlled teleportation of single-qubit rotation could be realized exactly using two partially entangled pairs is also notable. A sender could teleport a rotation on a remote receiver, an arbitrary one of the two receivers, via the control of the other in a network.
Killing spinors and exact plane-wave solutions of extended supergravity
NASA Astrophysics Data System (ADS)
Hull, C. M.
1984-07-01
Urrutia's ansatz for exact plane-wave solutions of simple supergravity is generalized to N=2 extended supergravity and conditions are given for the solutions to be nontrivial. Conditions are also given for the plane-wave background to be invariant under a local supersymmetry transformation generated by a Killing spinor. It is seen that even though a bosonic background can admit a spin-32 solution when it does not possess a Killing spinor, if it is supersymmetric it admits a more general gravitino solution. Comparison is made with the solutions of Aichelburg and Dereli.
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.
Amplification of sound waves in an imploding plasma shell - Exact results
NASA Astrophysics Data System (ADS)
Han, S. J.
1988-01-01
The model of Book (1978) is extended to provide proof for sound-wave amplifications in an imploding plasma shell. In the absence of a massless free surface, the boundary conditions are found to give the exact eigenvalues which determine the asymptotic solution to the problem. It is shown that in an imploding spherical shell, sound-wave amplifications (SWAs) can occur in the long-wavelength regime provided that the external pressure matches with the prescribed time-dependent pressure profile given in the present model. The amplitudes of SWA in the long-wavelength regime are larger than those found in the short-wavelength regime.
SLAC three-body partial wave analysis system
Aston, D.; Lasinski, T.A.; Sinervo, P.K.
1985-10-01
We present a heuristic description of the SLAC-LBL three-meson partial wave model, and describe how we have implemented it at SLAC. The discussion details the assumptions of the model and the analysis, and emphasizes the methods we have used to prepare and fit the data. 28 refs., 12 figs., 1 tab.
Kullback relative entropy and characterization of partially polarized optical waves.
Réfrégier, Philippe; Goudail, François
2006-03-01
Different properties of partially polarized light are discussed using the Kullback relative entropy, which provides a physically meaningful measure of proximity between probability density functions (PDFs). For optical waves with a Gaussian PDF, the standard degree of polarization is a simple function of the Kullback relative entropy between the considered optical light and a totally depolarized light of the same intensity. It is shown that the Kullback relative entropies between different PDFs allow one to define other properties such as a degree of anisotropy and a degree of non-Gaussianity. It is also demonstrated that, in dimension three, the Kullback relative entropy between a partially polarized light and a totally depolarized light can lead to natural definitions of two degrees of polarization needed to characterize the polarization state. These analyses enlighten the physical meaning of partial polarization of light waves in terms of a measure of disorder provided by the Shannon entropy. PMID:16539066
McKenzie, J. F.; Doyle, T. B.; Rajah, S. S.
2012-11-15
The theory of fully nonlinear stationary electrostatic ion cyclotron waves is further developed. The existence of two fundamental constants of motion; namely, momentum flux density parallel to the background magnetic field and energy density, facilitates the reduction of the wave structure equation to a first order differential equation. For subsonic waves propagating sufficiently obliquely to the magnetic field, soliton solutions can be constructed. Importantly, analytic expressions for the amplitude of the soliton show that it increases with decreasing wave Mach number and with increasing obliquity to the magnetic field. In the subsonic, quasi-parallel case, periodic waves exist whose compressive and rarefactive amplitudes are asymmetric about the 'initial' point. A critical 'driver' field exists that gives rise to a soliton-like structure which corresponds to infinite wavelength. If the wave speed is supersonic, periodic waves may also be constructed. The aforementioned asymmetry in the waveform arises from the flow being driven towards the local sonic point in the compressive phase and away from it in the rarefactive phase. As the initial driver field approaches the critical value, the end point of the compressive phase becomes sonic and the waveform develops a wedge shape. This feature and the amplitudes of the compressive and rarefactive portions of the periodic waves are illustrated through new analytic expressions that follow from the equilibrium points of a wave structure equation which includes a driver field. These expressions are illustrated with figures that illuminate the nature of the solitons. The presently described wedge-shaped waveforms also occur in water waves, for similar 'transonic' reasons, when a Coriolis force is included.
NASA Astrophysics Data System (ADS)
Dong, Huan-He; Zhang, Yan-Feng
2015-04-01
With the aid of binary Bell polynomial and a general Riemann theta function, we introduce how to obtain the exact periodic wave solutions by applying the generalized Dp¯-operators in term of the Hirota direct method when the appropriate value of p¯ is determined. Furthermore, the resulting approach is applied to solve the extended (2+1)-dimensional Shallow Water Wave equation, and the periodic wave solution is obtained and reduced to soliton solution via asymptotic analysis. Supported by Shandong Provincial Key Laboratory of Marine Ecology and Environment & Disaster Prevention and Mitigation project under Grant No. 2012010, National Natural Science Foundation of China under Grant No. 11271007, Special Funds for Theoretical Physics of the National Natural Science Foundation of China under Grant No. 11447205, Shandong University of Science and Technology Research Fund under Grant No. 2012KYTD105
Numerical method for wave forces acting on partially perforated caisson
NASA Astrophysics Data System (ADS)
Jiang, Feng; Tang, Xiao-cheng; Jin, Zhao; Zhang, Li; Chen, Hong-zhou
2015-04-01
The perforated caisson is widely applied to practical engineering because of its great advantages in effectively wave energy consumption and cost reduction. The attentions of many scientists were paid to the fluid-structure interaction between wave and perforated caisson studies, but until now, most concerns have been put on theoretical analysis and experimental model set up. In this paper, interaction between the wave and the partial perforated caisson in a 2D numerical wave flume is investigated by means of the renewed SPH algorithm, and the mathematical equations are in the form of SPH numerical approximation based on Navier-Stokes equations. The validity of the SPH mathematical method is examined and the simulated results are compared with the results of theoretical models, meanwhile the complex hydrodynamic characteristics when the water particles flow in or out of a wave absorbing chamber are analyzed and the wave pressure distribution of the perforated caisson is also addressed here. The relationship between the ratio of total horizontal force acting on caisson under regular waves and its influence factors is examined. The data show that the numerical calculation of the ratio of total horizontal force meets the empirical regression equation very well. The simulations of SPH about the wave nonlinearity and breaking are briefly depicted in the paper, suggesting that the advantages and great potentiality of the SPH method is significant compared with traditional methods.
NASA Astrophysics Data System (ADS)
Cuperman, S.; Heristchi, D.
1992-08-01
The transcendental dispersion equation for electromagnetic waves propagating in the slow mode in sheared non-neutral relativistic cylindrical electron beams in strong applied magnetic fields is solved exactly. Thus, rather than truncated power series for the modified Bessel functions involved, use is made of modern algorithms able to compute such functions up to 18-digit accuracy. Consequently, new and significantly more important branches of the velocity shear instability are found. When the shear-factor and/or the geometrical parameter a/b (pipe-to-beam radius ratio) are increased, the unstable branches join, and the higher-frequency, larger-wavenumber modes are significantly enhanced. Since analytical solutions of the exact dispersion relation cannot be obtained, it is suggested that in all similar cases the methods proposed and demonstrated here should be used to carry out a rigorous stability analysis.
The adiabatic limit of the exact factorization of the electron-nuclear wave function
NASA Astrophysics Data System (ADS)
Eich, F. G.; Agostini, Federica
2016-08-01
We propose a procedure to analyze the relation between the exact factorization of the electron-nuclear wave function and the Born-Oppenheimer approximation. We define the adiabatic limit as the limit of infinite nuclear mass. To this end, we introduce a unit system that singles out the dependence on the electron-nuclear mass ratio of each term appearing in the equations of the exact factorization. We observe how non-adiabatic effects induced by the coupling to the nuclear motion affect electronic properties and we analyze the leading term, connecting it to the classical nuclear momentum. Its dependence on the mass ratio is tested numerically on a model of proton-coupled electron transfer in different non-adiabatic regimes.
Exact Reconstruction for Near-Field Three-Dimensional Planar Millimeter-Wave Holographic Imaging
NASA Astrophysics Data System (ADS)
Qiao, Lingbo; Wang, Yingxin; Zhao, Ziran; Chen, Zhiqiang
2015-12-01
In this paper, an exact reconstruction formula is presented for near-field three-dimensional (3D) planar millimeter-wave (MMW) holographic imaging. The proposed formula is derived based on scalar diffraction theory, and the round-trip imaging process is equivalent to a unidirectional optical field propagation. Because of compensating the propagation loss of the source for the near-field imaging configuration, the inconsistency in range domain of the reconstructed 3D images is avoided. The proposed reconstruction formula also gives a phase correction for the reconstructed complex-valued reflectivity of the target and the range coordinate can be exactly determined. Simulations and laboratory imaging experiments are performed to demonstrate the effectiveness of the proposed reconstruction formula.
The adiabatic limit of the exact factorization of the electron-nuclear wave function.
Eich, F G; Agostini, Federica
2016-08-01
We propose a procedure to analyze the relation between the exact factorization of the electron-nuclear wave function and the Born-Oppenheimer approximation. We define the adiabatic limit as the limit of infinite nuclear mass. To this end, we introduce a unit system that singles out the dependence on the electron-nuclear mass ratio of each term appearing in the equations of the exact factorization. We observe how non-adiabatic effects induced by the coupling to the nuclear motion affect electronic properties and we analyze the leading term, connecting it to the classical nuclear momentum. Its dependence on the mass ratio is tested numerically on a model of proton-coupled electron transfer in different non-adiabatic regimes. PMID:27497542
Lu, J Y; Greenleaf, J F
1992-01-01
The authors report families of generalized nondiffracting solutions of the free-space scalar wave equation, and specifically, a subset of these nondiffracting solutions, which are called X waves. These nondiffracting X waves can be almost exactly realized over a finite depth of field with finite apertures and by either broadband or bandlimited radiators. With a 25-mm diameter planar radiator, a zeroth-order broadband X wave will have about 2.5-mm lateral and 0.17-mm axial -6-dB beam widths with a -6-dB depth of field of about 171 mm. A zeroth-order bandlimited X wave was produced and measured in water by a 10 element, 50-mm diameter, 2.5-MHz PZT ceramic/polymer composite J (0) Bessel nondiffracting annular array transducer with -6-dB lateral and axial beam widths of about 4.7 mm and 0.65 mm, respectively, over a -6-dB depth of field of about 358 mm. Possible applications of X waves in acoustic imaging and electromagnetic energy transmission are discussed. PMID:18263114
Atomic partial charges in condensed phase from an exact sum rule for infrared absorption
NASA Astrophysics Data System (ADS)
Vuilleumier, Rodolphe
2014-05-01
A general sum rule for infrared intensities provides a definition of effective partial charges which can be experimentally obtained using isotopic substitutions and is valid in both gas and condensed phases. Of particular interest is the case of molecular liquids. We have, therefore, determined the hydrogen partial charges in liquid methanol and liquid water from the available literature. The resulting charges are 0.63 e and 0.14 e for hydrogen atoms bounded to the methanol oxygen and carbon atoms, respectively, and 0.55 e for hydrogen atoms in liquid water. The effective partial charges in liquid water were also computed from density functional based ab initio molecular dynamics simulations and found in good agreement with experiment.
Calculation of the Scattering Amplitude Without Partial Wave Expansion
NASA Technical Reports Server (NTRS)
Shertzer, J.; Temkin, Aaron; Fisher, Richard R. (Technical Monitor)
2001-01-01
Two developments in the direct calculation of the angular differential scattering amplitude have been implemented: (a) The integral expansion of the scattering amplitude is simplified by analytically integration over the azimuthal angle. (b) The resulting integral as a function of scattering angle is calculated by using the numerically generated wave function from a finite element method calculation. Results for electron-hydrogen scattering in the static approximation will be shown to be as accurate as a partial wave expansion with as many l's as is necessary for convergence at the incident energy being calculated.
Exact quantization of Einstein-Rosen waves coupled to massless scalar matter.
Barbero G, J Fernando; Garay, Iñaki; Villaseñor, Eduardo J S
2005-07-29
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. PMID:16090861
Entropy and Exact Matrix-Product Representation of the Laughlin Wave Function
Iblisdir, S.; Latorre, J. I.; Orus, R.
2007-02-09
An analytical expression for the von Neumann entropy of the Laughlin wave function is obtained for any possible bipartition between the particles described by this wave function, for a filling fraction {nu}=1. Also, for a filling fraction {nu}=1/m, where m is an odd integer, an upper bound on this entropy is exhibited. These results yield a bound on the smallest possible size of the matrices for an exact representation of the Laughlin ansatz in terms of a matrix-product state. An analytical matrix-product state representation of this state is proposed in terms of representations of the Clifford algebra. For {nu}=1, this representation is shown to be asymptotically optimal in the limit of a large number of particles.
Entropy and exact matrix-product representation of the Laughlin wave function.
Iblisdir, S; Latorre, J I; Orús, R
2007-02-01
An analytical expression for the von Neumann entropy of the Laughlin wave function is obtained for any possible bipartition between the particles described by this wave function, for a filling fraction nu=1. Also, for a filling fraction nu=1/m, where m is an odd integer, an upper bound on this entropy is exhibited. These results yield a bound on the smallest possible size of the matrices for an exact representation of the Laughlin ansatz in terms of a matrix-product state. An analytical matrix-product state representation of this state is proposed in terms of representations of the Clifford algebra. For nu=1, this representation is shown to be asymptotically optimal in the limit of a large number of particles. PMID:17358918
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. PMID:25810953
Exact scale-invariant background of gravitational waves from cosmic defects.
Figueroa, Daniel G; Hindmarsh, Mark; Urrestilla, Jon
2013-03-01
We demonstrate that any scaling source in the radiation era produces a background of gravitational waves with an exact scale-invariant power spectrum. Cosmic defects, created after a phase transition in the early universe, are such a scaling source. We emphasize that the result is independent of the topology of the cosmic defects, the order of phase transition, and the nature of the symmetry broken, global or gauged. As an example, using large-scale numerical simulations, we calculate the scale-invariant gravitational wave power spectrum generated by the dynamics of a global O(N) scalar theory. The result approaches the large N theoretical prediction as N(-2), albeit with a large coefficient. The signal from global cosmic strings is O(100) times larger than the large N prediction. PMID:23521248
Parallel Implementation of Gamma-Point Pseudopotential Plane-Wave DFT with Exact Exchange
Bylaska, Eric J.; Tsemekhman, Kiril L.; Baden, Scott B.; Weare, John H.; Jonsson, Hannes
2011-01-15
One of the more persistent failures of conventional density functional theory (DFT) methods has been their failure to yield localized charge states such as polarons, excitons and solitons in solid-state and extended systems. It has been suggested that conventional DFT functionals, which are not self-interaction free, tend to favor delocalized electronic states since self-interaction creates a Coulomb barrier to charge localization. Pragmatic approaches in which the exchange correlation functionals are augmented with small amount of exact exchange (hybrid-DFT, e.g. B3LYP and PBE0) have shown promise in localizing charge states and predicting accurate band gaps and reaction barriers. We have developed a parallel algorithm for implementing exact exchange into pseudopotential plane-wave density functional theory and we have implemented it in the NWChem program package. The technique developed can readily be employed in plane-wave DFT programs. Furthermore, atomic forces and stresses are straightforward to implement, making it applicable to both confined and extended systems, as well as to Car-Parrinello ab initio molecular dynamic simulations. This method has been applied to several systems for which conventional DFT methods do not work well, including calculations for band gaps in oxides and the electronic structure of a charge trapped state in the Fe(II) containing mica, annite.
Wave Dispersion and Attenuation in Partially Saturated Sandstones
NASA Astrophysics Data System (ADS)
Nie, Jian-Xin; Yang, Ding-Hui; Yang, Hui-Zhu
2004-03-01
We investigate the wave dispersion and attenuation in partially water-saturated sandstones based on the improved Biot/squirt (BISQ) model in which the saturation is introduced. Numerical experiments indicate that the phase velocity of the fast P-wave decreases as the saturation increases in the low-frequency range (102-104 Hz), and reaches the minimum at the full-saturation state. The behaviour of the phase velocity varying with the saturation in the high-frequency range (104-106 Hz), however, is opposite to that in the low-frequency range. The peak value of P-wave attenuation increases with increasing saturation, and is the maximum at the fully saturated state. Numerical models and experiments show that the improved BISQ model is better than the traditional Gassmann-Biot model.
NASA Astrophysics Data System (ADS)
Grabowski, Paul; Chernoff, David
2010-02-01
The pseudosprectral method can produce solutions to partial differential equations which converge exponentially fast towards the exact solution. We present how to use this method to solve the non-relativistic Schr"odinger equation for helium and the negative hydrogen ion. We show how to properly treat the two-particle coalescence cusps and examine the effect of logarithmic terms in the exact solution. The only evidence of non-exponential convergence was for derivatives taken near the triple coalescence point. As developed and applied here the PS method has many virtues: no explicit assumptions need be made about the asymptotic behavior of the wavefunction near cusps or at large distances, the local energy (Hψ/ψ) is exactly equal to the calculated global energy at all collocation points, local errors go down everywhere with increasing resolution, the effective basis using Chebyshev polynomials is complete and simple, and the method is easily extensible to other bound states. As the number of collocation points grows, the method achieves exponential convergence up to the resolution tested. )
Wave force on double cylindrical piles: a comparison between exact and finite difference solutions
NASA Astrophysics Data System (ADS)
Ali, Lotfollahi-Yaghin Mohammad; Mehdi, Moosavi Sayyid; Amin, Lotfollahi-Yaghin
2011-03-01
The wave force exerted on vertical piles of offshore structures is the main criterion in designing them. In structures with more than one large pile, the influence of piles on each other is one of the most important issues being concerned in past researches. An efficient method for determining the interaction of piles is introduced in present research. First the wave force is calculated by the exact method using the diffraction theory, then in the finite difference numerical method the force is calculated by adding the velocity potentials of each pile and integration of pressure on their surface. The results showed that the ratio of the wave force on each of the double piles to a single pile has a damped oscillation around unity in which the amplitude of oscillation decreases with the increase in the spacing parameter. Also different wave incident directions and diffraction parameters were used and the results showed that the numerical solution has acceptable accuracy when the diffraction parameter is larger than unity.
Seismoelectric wave propagation numerical modelling in partially saturated materials
NASA Astrophysics Data System (ADS)
Warden, S.; Garambois, S.; Jouniaux, L.; Brito, D.; Sailhac, P.; Bordes, C.
2013-09-01
To better understand and interpret seismoelectric measurements acquired over vadose environments, both the existing theory and the wave propagation modelling programmes, available for saturated materials, should be extended to partial saturation conditions. We propose here an extension of Pride's equations aiming to take into account partially saturated materials, in the case of a water-air mixture. This new set of equations was incorporated into an existing seismoelectric wave propagation modelling code, originally designed for stratified saturated media. This extension concerns both the mechanical part, using a generalization of the Biot-Gassmann theory, and the electromagnetic part, for which dielectric permittivity and electrical conductivity were expressed against water saturation. The dynamic seismoelectric coupling was written as a function of the streaming potential coefficient, which depends on saturation, using four different relations derived from recent laboratory or theoretical studies. In a second part, this extended programme was used to synthesize the seismoelectric response for a layered medium consisting of a partially saturated sand overburden on top of a saturated sandstone half-space. Subsequent analysis of the modelled amplitudes suggests that the typically very weak interface response (IR) may be best recovered when the shallow layer exhibits low saturation. We also use our programme to compute the seismoelectric response of a capillary fringe between a vadose sand overburden and a saturated sand half-space. Our first modelling results suggest that the study of the seismoelectric IR may help to detect a sharp saturation contrast better than a smooth saturation transition. In our example, a saturation contrast of 50 per cent between a fully saturated sand half-space and a partially saturated shallow sand layer yields a stronger IR than a stepwise decrease in saturation.
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).
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. PMID:24678276
A New Pion-Nucleon Partial Wave Analysis
NASA Astrophysics Data System (ADS)
Sadler, Michael; Watson, Shon; Stahov, Jugoslav
2006-10-01
Existing determinations of the masses, widths and decay modes of low-lying excited states of the nucleon, as compiled in the Review of Particle Physics, are determined from energy-independent partial wave analyses of pion-nucleon scattering data. For the N*(1440) and most other resonances under 2 GeV, the analyses cited are the Karlsruhe-Helsinki, Carnegie Mellon-Berkeley and Kent State analyses, the latter of which used the elastic amplitudes from the other two. The data included in these analyses were published before 1980. Other analyses, notably the recent ones from George Washington University and the Pittsburgh-Argonne group, are ``not used for averages, fits, limits, etc.'' Complete sets of measurements (differential cross sections, analyzing powers and spin rotation parameters) have been measured in the N*(1440) resonance region since 1980, culminating in the Crystal Ball program at BNL to measure all-neutral final states (charge exchange, multiple pi-zero final states, and inverse photoproduction). A new partial wave analysis of the Karlsruhe-Helsinki type has been started by Abilene Christian University, University of Tuzla, and Rudjer Boskovic Institute. The analysis is constrained by fixed-t and interior hyperbolic dispersion relations. Comparisons of the new analysis to modern experimental data and to previous analyses will be presented.
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.
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.
Scattering of acoustic evanescent waves by circular cylinders: Partial wave series solution
NASA Astrophysics Data System (ADS)
Marston, Philip L.
2002-05-01
Evanescent acoustical waves occur in a variety of situations such as when sound is incident on a fluid interface beyond the critical angle and when flexural waves on a plate are subsonic with respect to the surrounding fluid. The scattering by circular cylinders at normal incidence was calculated to give insight into the consequences on the scattering of the evanescence of the incident wave. To analyze the scattering, it is necessary to express the incident wave using a modified expansion involving cylindrical functions. For plane evanescent waves, the expansion becomes a double summation with products of modified and ordinary Bessel functions. The resulting modified series is found for the scattering by a fluid cylinder in an unbounded medium. The perfectly soft and rigid cases are also examined. Unlike the case of an ordinary incident wave, the counterpropagating partial waves of the same angular order have unequal magnitudes when the incident wave is evanescent. This is a consequence of the exponential dependence of the incident wave amplitude on the transverse coordinate. The associated exponential dependence of the scattering on the location of a scatterer was previously demonstrated [T. J. Matula and P. L. Marston, J. Acoust. Soc. Am. 93, 1192-1195 (1993)].
Exact solutions of regular approximate relativistic wave equations for hydrogen-like atoms
NASA Astrophysics Data System (ADS)
van Leeuwen, R.; van Lenthe, E.; Baerends, E. J.; Snijders, J. G.
1994-07-01
Apart from relativistic effects originating from high kinetic energy of an electron in a flat potential, which are treated in first order by the Pauli Hamiltonian, there are relativistic effects even for low-energy electrons if they move in a strong Coulomb potential. The latter effects can be accurately treated already in the zeroth order of an expansion of the Foldy-Wouthuysen transformation, if the expansion is carefully chosen to be nondivergent for r→0 even for Coulomb potentials, as shown by Van Lenthe et al. [J. Chem. Phys. 99, 4597 (1993)] (cf. also Heully et al. [J. Phys. B 19, 2799 (1986)] and Chang et al. [Phys. Scr. 34, 394 (1986)]). In the present paper, it is shown that the solutions of the zeroth order of this two-component regular approximate (ZORA) equation for hydrogen-like atoms are simply scaled solutions of the large component of the Dirac wave function for this problem. The eigenvalues are related in a similar way. As a consequence, it is proven that under some restrictions, the ZORA Hamiltonian is bounded from below for Coulomb-like potentials. Also, an exact result for the first order regular approximate Hamiltonian is given. The method can also be used to obtain exact results for regular approximations of scalar relativistic equations, like the Klein-Gordon equation. The balance between relativistic effects originating from the Coulombic singularity in the potential (typically core penetrating s and p valence electrons in atoms and molecules) and from high kinetic energy (important for high-energy electrons in a flat potential and also for core-avoiding high angular momentum (d, f, and g states in atoms) are discussed.
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…
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.
NASA Astrophysics Data System (ADS)
Latifi, A.
2016-07-01
A special case of coupled integrable nonlinear equations with a singular dispersion law is derived in the context of the small amplitude limit of general wave equations in a fluid-type warm electrons/cold ions plasma irradiated by a continuous laser beam. This model accounts for a nonlinear mode coupling of the electrostatic wave with the ion sound wave and is shown to be highly unstable. Its instability is understood as a continuous secular transfer of energy from the electrostatic wave to the ion sound wave through the ponderomotive force. The exact asymptotic solution of the system is constructed and shows that the dynamics of the energy transfer results in a singular asymptotic behavior of the ion sound wave, which explains the low penetration of the incident laser beam.
Applicability of Parallel Computing to Partial Wave Analysis
NASA Astrophysics Data System (ADS)
Ruger, Justin; Gilfoyle, Gerard; Weygand, Dennis; CLAS Collaboration
2013-10-01
Bound states of Quantum Chromodynamics (QCD) give insights into the nature of confinement, a key element of the strong interaction. States may be identified from weak signals extracted from the analysis of high statistics data from reactions with many final state particles. One of the best tools for the analysis of these reactions is Partial Wave Analysis (PWA). PWA transforms an ensemble of experimental data from a large acceptance detector from free particle eigenstates to angular momentum eigenstates. The PWA program must be fast enough to deal with the large amounts of data available currently, as processing time scales with the number of events. The scope of this research is to study the applicability and scalability of Intel's Xeon Phi using the Many Integrated Core (MIC) architecture when applied to the existing PWA code at Jefferson Laboratory. An algorithm was developed for the Xeon Phi and scaled across 240 available threads, giving parallel functionality to the PWA which was originally written serially. This scaling can make the fitting process fifteen times faster. Supported by the US Department of Energy.
NASA Astrophysics Data System (ADS)
Zhang, Lijun; Chen, Li-Qun; Zhang, Jianming
2013-10-01
Bifurcation and exact solutions of the modified nonlinearly dispersive mK (m,n,k) equation with nonlinear dispersion um-1ut+a(un)x+b(uk)xxx = 0,nk≠0 are investigated in this paper. As a result, under different parameter conditions, abundant compactons, peakons and solitary solutions including not only some known results but also some new ones are obtained. We also point out the original reason of the existence of the non-smooth traveling wave solutions. The approach we used here is also suitable for the study of traveling wave solutions of some other nonlinear equations.
Kurokawa, Yusaku I; Nakashima, Hiroyuki; Nakatsuji, Hiroshi
2014-06-01
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. PMID:24907986
Kurokawa, Yusaku I. E-mail: h.nakatsuji@qcri.or.jp; Nakashima, Hiroyuki; Nakatsuji, Hiroshi E-mail: h.nakatsuji@qcri.or.jp
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.
Guo Shimin; Wang Hongli; Mei Liquan
2012-06-15
By combining the effects of bounded cylindrical geometry, azimuthal and axial perturbations, the nonlinear dust acoustic waves (DAWs) in an unmagnetized plasma consisting of negatively charged dust grains, nonextensive ions, and nonextensive electrons are studied in this paper. Using the reductive perturbation method, a (3 + 1)-dimensional variable-coefficient cylindrical Korteweg-de Vries (KdV) equation describing the nonlinear propagation of DAWs is derived. Via the homogeneous balance principle, improved F-expansion technique and symbolic computation, the exact traveling and solitary wave solutions of the KdV equation are presented in terms of Jacobi elliptic functions. Moreover, the effects of the plasma parameters on the solitary wave structures are discussed in detail. The obtained results could help in providing a good fit between theoretical analysis and real applications in space physics and future laboratory plasma experiments where long-range interactions are present.
Partial Antisymmetry and Approximate Primitive Wave Functions for Interacting Electronic Groups.
NASA Astrophysics Data System (ADS)
Vergenz, Robert Allan
The partial antisymmetry (PA) theorem of W. H. Adams (Chem. Phys. Letters, 68, 511 (1979)) shows that if one can determine an N-electron eigenfunction of a certain non-linear operator, then one can use the eigenfunction, without using full antisymmetry (FA), to calculate an eigenvalue of the Schrodinger Hamiltonian for the system. The operator neither depends on nor commutes with the antisymmetrizer, but involves partial antisymmetrizers. This work provides an initial numerical test of a new approach to calculating approximate interatomic interaction energies based on the PA theorem. Interaction energies were calculated for X ^1Sigma^{+}_ {rm g} Ne_2, Li_2 and Na_2, X^1Sigma^{+} LiNa, X^2Sigma^{+} _{rm g} Li_2 ^{+}, x ^7Sigma ^{+}_{rm u} N_2, x ^3Sigma ^{+}_{rm u} Li_2 and Na_2, x ^3Sigma^{+} LiNa and ionic and covalent configurations of X ^1Sigma^{+} LiF, all at several internuclear distances. Spin-coupled products of single determinants approximated the atomic wave functions, and accurate HF atomic bases were used. Three methods were used: the conventional method based on FA, the PA approach, and a method based on a hybrid set of assumptions. Results were compared with accurate potential curves from the literature. In nine cases of the eleven, including both bonding and repulsive interactions, the PA approximation gave results that were better or roughly the same as those using FA. In these cases there is thus no penalty exacted for the use of PA, though it is shown to be easier to use.
Bottrill, K R H; Hesketh, G; Parmigiani, F; Richardson, D J; Petropoulos, P
2016-02-01
Adopting an exact solution to four-wave mixing (FWM), wherein harmonic evolution is described by the sum of two Bessel functions, we identify two causes of amplitude to phase noise conversion which impair FWM saturation based amplitude regenerators: self-phase modulation (SPM) and Bessel-order mixing (BOM). By increasing the pump to signal power ratio, we may arbitrarily reduce their impact, realising a phase preserving amplitude regenerator. We demonstrate the technique by applying it to the regeneration of a 10 GBaud QPSK signal, achieving a high level of amplitude squeezing with minimal amplitude to phase noise conversion. PMID:26906847
Heating of ions by low-frequency Alfven waves in partially ionized plasmas
Dong Chuanfei; Paty, Carol S.
2011-03-15
In the solar atmosphere, the chromospheric and coronal plasmas are much hotter than the visible photosphere. The heating of the solar atmosphere, including the partially ionized chromosphere and corona, remains largely unknown. In this letter, we demonstrate that the ions can be substantially heated by Alfven waves with very low frequencies in partially ionized low-beta plasmas. This differs from other Alfven wave related heating mechanisms such as ion-neutral collisional damping of Alfven waves and heating described by previous work on resonant Alfven wave heating. We find that the nonresonant Alfven wave heating is less efficient in partially ionized plasmas than when there are no ion-neutral collisions, and the heating efficiency depends on the ratio of the ion-neutral collision frequency to the ion gyrofrequency.
Kurokawa, Yusaku I.; Nakashima, Hiroyuki; Nakatsuji, Hiroshi
2013-07-28
We derived the necessary conditions that the non-relativistic time-independent exact wave functions for two-particle systems must satisfy at a coalescence (or cusp) point. Some of such necessary conditions are already known to be Kato's cusp condition (CC) and Rassolov and Chipman's CC. In the present study, we extended and generalized those conditions, calling them generalized coalescence conditions (GCCs). Kato's CC and Rassolov and Chipman's CC were shown to be specific cases included in the GCCs. The GCCs can be applied not only to Coulombic systems but also to any systems where the interaction between two particles is represented in a power series of the inter-particle distance. We confirmed the correctness of our derivation of these GCCs by applying the free complement wave functions of a hydrogen atom in ground and excited states, a harmonic oscillator, and a system with an interacting potential of V=r.
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.
NASA Astrophysics Data System (ADS)
Shepherd, James J.; Scuseria, Gustavo E.; Spencer, James S.
2014-10-01
We investigate the sign problem for full configuration interaction quantum Monte Carlo (FCIQMC), a stochastic algorithm for finding the ground-state solution of the Schrödinger equation with substantially reduced computational cost compared with exact diagonalization. We find k -space Hubbard models for which the solution is yielded with storage that grows sublinearly in the size of the many-body Hilbert space, in spite of using a wave function that is simply a linear combination of states. The FCIQMC algorithm is able to find this sublinear scaling regime without bias and with only a choice of the Hamiltonian basis. By means of a demonstration we solve for the energy of a 70-site half-filled system (with a space of 1038 determinants) in 250 core hours, substantially quicker than the ˜1036 core hours that would be required by exact diagonalization. This is the largest space that has been sampled in an unbiased fashion. The challenge for the recently developed FCIQMC method is made clear: Expand the sublinear scaling regime while retaining exact-on-average accuracy. We comment upon the relationship between this and the scaling law previously observed in the initiator adaptation (i-FCIQMC). We argue that our results change the landscape for the development of FCIQMC and related methods.
NASA Astrophysics Data System (ADS)
Balram, Ajit C.; Jain, J. K.
2016-02-01
The microscopic wave functions of the composite fermion theory can incorporate electron mass anisotropy by a trivial rescaling of the coordinates. These wave functions are very likely adiabatically connected to the actual wave functions of the anisotropic fractional quantum Hall states. We show in this paper that they possess the nice property that their energies can be analytically related to the previously calculated energies for the isotropic states through a universal scale factor, thus allowing an estimation of several observables in the thermodynamic limit for all fractional quantum Hall states as well as the composite fermion Fermi sea. The rather weak dependence of the scale factor on the anisotropy provides insight into why fractional quantum Hall effect and composite fermions are quite robust to electron mass anisotropy. We discuss how better, though still approximate, wave functions can be obtained by introducing a variational parameter, following Haldane [F. D. M. Haldane, Phys. Rev. Lett. 107, 116801 (2011), 10.1103/PhysRevLett.107.116801], but the resulting wave functions are not readily amenable to calculations. Our considerations are also applicable, with minimal modification, to the case where the dielectric function of the background material is anisotropic.
NASA Astrophysics Data System (ADS)
Studenikin, A. I.
2008-04-01
We present quite a powerful method in investigations of different phenomena that can appear when neutrinos and electrons propagate in background matter. This method implies use of exact solutions of modified Dirac equations that contain the correspondent effective potentials accounting for the matter influence on particles. For several particular cases the exact solutions of modified Dirac and Dirac-Pauli equations for a neutrino and an electron in the background environment of different composition are obtained (the case of magnetized matter is also considered). Neutrino reflection, trapping, neutrino pair creation and annihilation in matter and neutrino energy quantization in a rotating medium are discussed. The neutrino Green functions in matter are also derived. The two recently proposed mechanisms of electromagnetic radiation by a neutrino and an electron in matter (the spin light of neutrino and electron, SLν and SLe) are considered. A possibility to introduce an effective 'matter-induced Lorentz force' acting on a neutrino and an electron is discussed. A new mechanism of electromagnetic radiation that can be emitted by an electron moving in the neutrino background with nonzero gradient of density is predicted.
Study on the electromagnetic waves propagation characteristics in partially ionized plasma slabs
NASA Astrophysics Data System (ADS)
Wang, Zhi-Bin; Li, Bo-Wen; Nie, Qiu-Yue; Wang, Xiao-Gang; Kong, Fan-Rong
2016-05-01
Propagation characteristics of electromagnetic (EM) waves in partially ionized plasma slabs are studied in this paper. Such features are significant to applications in plasma antennas, blackout of re-entry flying vehicles, wave energy injection to plasmas, and etc. We in this paper developed a theoretical model of EM wave propagation perpendicular to a plasma slab with a one-dimensional density inhomogeneity along propagation direction to investigate essential characteristics of EM wave propagation in nonuniform plasmas. Particularly, the EM wave propagation in sub-wavelength plasma slabs, where the geometric optics approximation fails, is studied and in comparison with thicker slabs where the geometric optics approximation applies. The influences of both plasma and collisional frequencies, as well as the width of the plasma slab, on the EM wave propagation characteristics are discussed. The results can help the further understanding of propagation behaviours of EM waves in nonuniform plasma, and applications of the interactions between EM waves and plasmas.
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.
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. PMID:19026052
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.
An algorithm for the calculation of the partial wave expansion of the Coulomb-distorted plane wave
NASA Astrophysics Data System (ADS)
Hornyak, I.; Kruppa, A. T.
2015-12-01
The partial wave expansion of the Coulomb-distorted plane wave is determined by the help of the complex generalized hypergeometric function 2F2(a , a ; a + l + 1 , a - l ; z) . An algorithm for the calculation of 2F2(a , a ; a + l + 1 , a - l ; z) is created and it is implemented as a FORTRAN-90 code. The code is fast and its accuracy is 14 significant decimal digits.
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.
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 non-Born-Oppenheimer wave functions for three-particle Hookean systems with arbitrary masses
NASA Astrophysics Data System (ADS)
Lopez, Xabier; Ugalde, Jesus M.; Echevarría, Lorenzo; Ludeña, Eduardo V.
2006-10-01
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-(e+e-e-) , H-(p+e-e-) , D-(d+e-e-) , T-(p+e-e-) , He4(he+2e-e-) , and the following molecular ions: Ps2+(e-e+e+) , H2+(e-p+p+) , HD+(e-d+p+) , HT+(e-t+p+) , DT+(e-d+t+) , D2+(e-d+d+) , T2+(e-t+t+) . The muonic and antiprotonic families are similar to the electronic ones except that the species are formed replacing e- by μ- or p- . 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.
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
Shape Waves in 2D Josephson Junctions: Exact Solutions and Time Dilation
Gulevich, D. R.; Savel'ev, Sergey; Kusmartsev, F. V.; 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.
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. PMID:18851404
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.
Partial-wave analysis for elastic p{sup 13}C scattering at astrophysical energies
Dubovichenko, S. B.
2012-03-15
A standard partial-wave analysis was performed on the basis of known measurements of differential cross sections for elastic p{sup 13}C scattering at energies in the range 250-750 keV. This analysis revealed that, in the energy range being considered, it is sufficient to take into account the {sup 3}S{sub 1} wave alone. A potential for the triplet {sup 3}S{sub 1}-wave state of the p{sup 13}C system in the region of the J{sup p}T = 1{sup -1} resonance at 0.55 MeV was constructed on the basis of the phase shifts obtained from the aforementioned partial-wave analysis.
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.
NASA Astrophysics Data System (ADS)
Achilleos, V.; Diamantidis, S.; Frantzeskakis, D. J.; Karachalios, N. I.; Kevrekidis, P. G.
2015-08-01
We study various properties of solutions of an extended nonlinear Schrödinger (ENLS) equation, which arises in the context of geometric evolution problems—including vortex filament dynamics—and governs propagation of short pulses in optical fibers and nonlinear metamaterials. For the periodic initial-boundary value problem, we derive conservation laws satisfied by local in time, weak H2 (distributional) solutions, and establish global existence of such weak solutions. The derivation is obtained by a regularization scheme under a balance condition on the coefficients of the linear and nonlinear terms—namely, the Hirota limit of the considered ENLS model. Next, we investigate conditions for the existence of traveling wave solutions, focusing on the case of bright and dark solitons. The balance condition on the coefficients is found to be essential for the existence of exact analytical soliton solutions; furthermore, we obtain conditions which define parameter regimes for the existence of traveling solitons for various linear dispersion strengths. Finally, we study the modulational instability of plane waves of the ENLS equation, and identify important differences between the ENLS case and the corresponding NLS counterpart. The analytical results are corroborated by numerical simulations, which reveal notable differences between the bright and the dark soliton propagation dynamics, and are in excellent agreement with the analytical predictions of the modulation instability analysis.
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.
Wave interaction with a partially reflecting vertical wall protected by a submerged porous bar
NASA Astrophysics Data System (ADS)
Zhao, Yang; Liu, Yong; Li, Huajun
2016-08-01
This study gives an analytical solution for wave interaction with a partially reflecting vertical wall protected by a submerged porous bar based on linear potential theory. The whole study domain is divided into multiple sub-regions in relation to the structures. The velocity potential in each sub-region is written as a series solution by the separation of variables. A partially reflecting boundary condition is used to describe the partial reflection of a vertical wall. Unknown expansion coefficients in the series solutions are determined by matching velocity potentials among different sub-regions. The analytical solution is verified by an independently developed multi-domain boundary element method (BEM) solution and experimental data. The wave run-up and wave force on the partially reflecting vertical wall are estimated and examined, which can be effectively reduced by the submerged porous bar. The horizontal space between the vertical wall and the submerged porous bar is a key factor, which affects the sheltering function of the porous bar. The wave resonance between the porous bar and the vertical wall may disappear when the vertical wall has a low reflection coefficient. The present analytical solution may be used to determine the optimum parameters of structures at a preliminary engineering design stage.
NASA Astrophysics Data System (ADS)
Elboudali, F.; Joulakian, B.
2001-12-01
The (e, 2e) ionization of diatomic lithium Li2 by fast electrons is studied by applying, for the slow ejected electron, an asymptotically exact partial-wave description, which takes into account the diatomic nature of the problem. The ionization is considered as a vertical transition from the lowest vibrational and rotational level of the fundamental electronic state 1Σg+ of Li2 to the fundamental 2Σg+ state of Li2+. After verification of the procedure on the (e, 2e) ionization of diatomic hydrogen H2 for which experimental and theoretical results exist we present the particularities and favourable directions for Li2 targets.
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.
A poroelastic model for ultrasonic wave attenuation in partially frozen brines
NASA Astrophysics Data System (ADS)
Matsushima, Jun; Nibe, Takao; Suzuki, Makoto; Kato, Yoshibumi; Rokugawa, Shuichi
2011-02-01
Although there are many possible mechanisms for the intrinsic seismic attenuation in composite materials that include fluids, relative motion between solids and fluids during seismic wave propagation is one of the most important attenuation mechanisms. In our previous study, we conducted ultrasonic wave transmission measurements on an ice-brine coexisting system to examine the influence on ultrasonic waves of the unfrozen brine in the pore microstructure of ice. In order to elucidate the physical mechanism responsible for ultrasonic wave attenuation in the frequency range of 350-600kHz, measured at different temperatures in partially frozen brines, we employed a poroelastic model based on the Biot theory to describe the propagation of ultrasonic waves through partially frozen brines. By assuming that the solid phase is ice and the liquid phase is the unfrozen brine, fluid properties measured by a pulsed nuclear magnetic resonance technique were used to calculate porosities at different temperatures. The computed intrinsic attenuation at 500kHz cannot completely predict the measured attenuation results from the experimental study in an ice-brine coexisting system, which suggests that other attenuation mechanisms such as the squirt-flow mechanism and wave scattering effect should be taken into account.
Mixing of partial waves near B*B̄^{*} threshold in e⁺e⁻ annihilation
Li, Xin; Voloshin, M. B.
2013-05-31
We consider the production of B*B̄^{*} meson pairs in e⁺e⁻ annihilation near the threshold. The rescattering due to pion exchange between the mesons results in a mixing between three partial wave amplitudes: two P-wave amplitudes with the total spin of the meson pair S=0 and S=2 and an F-wave amplitude. The mixing due to pion exchange with a low momentum transfer is calculable up to c.m. energy E≈15–20 MeV above the threshold. We find that the P–F mixing is numerically quite small in this energy range, while the mixing of the two P-wave amplitudes is rapidly changing with energy and can reach of order one at such low energies.
Mixing of partial waves near B*B̄* threshold in e⁺e⁻ annihilation
Li, Xin; Voloshin, M. B.
2013-05-31
We consider the production of B*B̄* meson pairs in e⁺e⁻ annihilation near the threshold. The rescattering due to pion exchange between the mesons results in a mixing between three partial wave amplitudes: two P-wave amplitudes with the total spin of the meson pair S=0 and S=2 and an F-wave amplitude. The mixing due to pion exchange with a low momentum transfer is calculable up to c.m. energy E≈15–20 MeV above the threshold. We find that the P–F mixing is numerically quite small in this energy range, while the mixing of the two P-wave amplitudes is rapidly changing with energy andmore » can reach of order one at such low energies.« less
Simultaneous observations of gravity waves in auroras and partial reflection radar data
NASA Astrophysics Data System (ADS)
Roldugin, Valentin; Cherniakov, Sergey; Roldugin, Aleksey
2016-07-01
Some events of wave-like patterns of night sky intensity were revealed from the obtained data of the all-sky camera at the observatory "Lovozero" (67.97 N, 35.02 E). Their wave-lengths were about several tens kilometers and their time periods were about 15-30 minutes. We consider the wave-like structures as manifestation of acoustic-gravity waves. Two cases (28 January 2012 and 26 February 2012) were compared with the data of the partial reflection radar at the observatory "Tumanny" (69.0 N, 35.7 E). At these cases peaks of reflection intensity took place at 80-90 km, and the intensity on these altitudes oscillated with periods which were similar to the luminous ones.
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. PMID:24562136
Partial Reflection and Trapping of a Fast-mode Wave in Solar Coronal Arcade Loops
NASA Astrophysics Data System (ADS)
Kumar, Pankaj; Innes, D. E.
2015-04-01
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-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-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.
Trapped internal waves over undular topography in a partially mixed estuary
NASA Astrophysics Data System (ADS)
Pietrzak, J.; Labeur, R. J.
The flow of a stratified fluid over small-scale topographic features in an estuary may generate significant internal wave activity. Lee waves and upstream influence generated at isolated topographic features have received considerable attention during the past few decades. Field surveys of a partially mixed estuary, the Rotterdam Waterway, in 1987, also showed a plethora of internal wave activity generated by isolated topography, banks and groynes. Additionally it revealed a spectacular series of resonant internal waves trapped above low-amplitude bed waves. The internal waves reached amplitudes of 3-4 m in an estuary with a mean depth of 16 m. The waves were observed during the decreasing flood tide and are thought to make a significant contribution to turbulence production and mixing. However, while stationary linear and finite amplitude theories can be used to explain the presence of these waves, it is important to further investigate their time-dependent and non-linear behaviour. With the development of advanced non-hydrostatic models it now becomes possible to further investigate these waves through numerical experimentation. This is the focus of the work presented here. The non-hydrostatic finite element numerical model FINEL3D developed by Labeur was used in the experiments presented here. The model has been shown to work well in a number of stratified flow investigations. Here, we first show that the model reproduces the field data and for idealised stationary flow scenarios that the results are in agreement with the resonant response predicted by linear theory. Then we explore the effects of non-linearity and time dependence and consider the importance of resonant internal waves for turbulence production in stratified coastal environments.
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.
O (p6) extension of the large-NC partial wave dispersion relations
NASA Astrophysics Data System (ADS)
Guo, Z. H.; Sanz-Cillero, J. J.; Zheng, H. Q.
2008-04-01
Continuing our previous work [Z.H. Guo, J.J. Sanz-Cillero, H.Q. Zheng, JHEP 0706 (2007) 030], large-NC techniques and partial wave dispersion relations are used to discuss ππ scattering amplitudes. We get a set of predictions for O (p6) low-energy chiral perturbation theory couplings. They are provided in terms of the masses and decay widths of scalar and vector mesons.
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 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.
Plateau Waves of Intracranial Pressure and Partial Pressure of Cerebral Oxygen.
Lang, Erhard W; Kasprowicz, Magdalena; Smielewski, Peter; Pickard, John; Czosnyka, Marek
2016-01-01
This study investigates 55 intracranial pressure (ICP) plateau waves recorded in 20 patients after severe traumatic brain injury (TBI) with a focus on a moving correlation coefficient between mean arterial pressure (ABP) and ICP, called PRx, which serves as a marker of cerebrovascular reactivity, and a moving correlation coefficient between ABP and cerebral partial pressure of oxygen (pbtO2), called ORx, which serves as a marker for cerebral oxygen reactivity. ICP and ICPamplitude increased significantly during the plateau waves, whereas CPP and pbtO2 decreased significantly. ABP, ABP amplitude, and heart rate remained unchanged. In 73 % of plateau waves PRx increased during the wave. ORx showed an increase during and a decrease after the plateau waves, which was not statistically significant. Our data show profound cerebral vasoparalysis on top of the wave and, to a lesser extent, impairment of cerebral oxygen reactivity. The different behavior of the indices may be due to the different latencies of the cerebral blood flow and oxygen level control mechanisms. While cerebrovascular reactivity is a rapidly reacting mechanism, cerebral oxygen reactivity is slower. PMID:27165902
Using a partial-wave method for sound-mean-flow scattering problems.
Berthet, R; Coste, C
2003-03-01
We present a semianalytical method, based on a partial-wave expansion and valid in the short wavelength limit for small Mach number flows, to analyze sound-vortical-flow interactions. It is more powerful than ray-tracing methods because it gives both amplitude and phase of the sound wave, and because it is less restrictive on the smallness of the wavelength. In contrast with the Born approximation approach, this method allows the computation of the sound field in the whole interaction domain (including the near field), and preserves energy conservation. Vortical flows with finite circulation are amenable to our analysis, which gives a satisfactory description of wave front dislocation by vorticity, in good agreement with direct numerical simulations. We extend previous versions of this method to the case of smooth vorticity profiles which are observed in aeroacoustics experiments. PMID:12689176
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.
NASA Astrophysics Data System (ADS)
Mehdipoor, M.; Neirameh, A.
2012-01-01
The nonlinear propagation of ion acoustic waves in an ideal plasmas containing degenerate electrons is investigated. The Korteweg-de-Vries (K-dV) equation is derived for ion acoustic waves by using reductive perturbation method. The analytical traveling wave solutions of the K-dV equation investigated, through the ( G'/ G)-expansion method. These traveling wave solutions are expressed by hyperbolic function, trigonometric functions are rational functions. When the parameters are taken special values, the solitary waves are derived from the traveling waves. Also, numerically the effect different parameters on these solitary waves investigated and it is seen that exist only the compressive solitary waves in Thomas-Fermi plasmas.
Partial-wave analysis of all nucleon-nucleon scattering data below 350 MeV
Stoks, V.G.J.; Klomp, R.A.M.; Rentmeester, M.C.M.; de Swart, J.J. )
1993-08-01
We present a multienergy partial-wave analysis of all [ital NN] scattering data below [ital T][sub lab]=350 MeV, published in a regular physics journal between 1955 and 1992. After careful examination, our final database consists of 1787 [ital pp] and 2514 [ital np] scattering data. Our fit to these data results in [chi][sup 2]/[ital N][sub df]=1.08, with [ital N][sub df]=3945 the total number of degrees of freedom. All phase shifts and mixing parameters can be determined accurately.
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.
NASA Astrophysics Data System (ADS)
Manakov, S. V.; Santini, P. M.
2011-10-01
We study the (n + 1)-dimensional generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation, a universal equation describing the propagation of weakly nonlinear, quasi-one-dimensional waves in n + 1 dimensions, and arising in several physical contexts, such as acoustics, plasma physics and hydrodynamics. For n = 2, this equation is integrable, and has been recently shown to be a prototype model equation in the description of the two-dimensional wave breaking of localized initial data. We construct an exact solution of the (n + 1)-dimensional model containing an arbitrary function of one variable, corresponding to its parabolic invariance, describing waves, constant on their paraboloidal wave front, breaking simultaneously in all points of it. Then, we use such a solution to build a uniform approximation of the solution of the Cauchy problem, for small and localized initial data, showing that such a small and localized initial data evolving according to the (n + 1)-dimensional dKP equation break, in the long time regime, if and only if 1 ⩽ n ⩽ 3, i.e., in physical space. Such a wave breaking takes place, generically, in a point of the paraboloidal wave front, and the analytic aspects of it are given explicitly in terms of the small initial data.
On certain new exact solutions of a diffusive predator-prey system
NASA Astrophysics Data System (ADS)
Kraenkel, R. A.; Manikandan, K.; Senthilvelan, M.
2013-05-01
We construct exact solutions for a system of two coupled nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the {G'}/{G} expansion method, we derive exact solutions to this model for two different wave speeds. For each wave velocity we report three different forms of solutions. We also discuss the biological relevance of the solutions obtained.
Solution of the Bethe-Goldstone equation without partial wave decomposition
NASA Astrophysics Data System (ADS)
White, Larz
Nucleon-nucleon scattering is a most fundamental process in nuclear physics. From the theoretical standpoint, its description in momentum space involves the solution of an integral equation in three dimensions, which is typically accomplished with the help of a partial wave expansion of the scattering amplitude. It is the purpose of this work to present a method for solving the nucleon-nucleon scattering equation without the use of such expansion. After verifying the accuracy of our numerical tools by comparing with existing solutions of the nucleon-nucleon scattering amplitude in free space, we proceed to apply the method to the equation describing scattering of two nucleons in the nuclear medium, known as the Bethe-Goldstone equation. An important feature of this equation is the presence of the so-called "Pauli blocking operator", which prevents scattering of two fermions into occupied states, as required by the Pauli principle. In standard solution methods based on partial wave expansions, it is necessary to apply an approximation to this operator, which involves averaging over angular variables and is therefore known as the "spherical approximation". In our method, this approximation can be avoided. Thus, a focal point of this study is a comparison of Pauli blocking effects calculated in the (angle-dependent) three-dimensional formalism as compared to the usual spherical approximation. We present results for nucleon-nucleon amplitudes and observables and discuss their implications.
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-atom energy spectrum in a harmonic trap near a Feshbach resonance at higher partial waves
NASA Astrophysics Data System (ADS)
Suzuki, Akira; Liang, Yi; Bhaduri, Rajat K.
2009-09-01
Two atoms in an optical lattice may be made to interact strongly at higher partial waves near a Feshbach resonance. These atoms, under appropriate constraints, could be bosonic or fermionic. The universal l=2 energy spectrum for such a system, with a caveat, is presented in this paper and checked with the spectrum obtained by direct numerical integration of the Schrödinger equation. The results reported here extend those of Yip for p -wave resonance [S.-K. Yip, Phys. Rev. A 78, 013612 (2008)], while exploring the limitations of a universal expression for the spectrum for the higher partial waves.
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.
NASA Astrophysics Data System (ADS)
Zhu, Shangguo; Tan, Shina
2014-03-01
It is well-known that cold atoms near s-wave Feshbach resonances have universal properties that are insensitive to the short-range details of the interaction. What is less known is that atoms near higher partial wave Feshbach resonances also have remarkable universal properties. We will illustrate this with a single atom interacting resonantly with two fixed static centers. At a Feshbach resonance point with orbital angular momentum L >= 1 , we find 2 L + 1 shallow bound states whose energies behave like 1 /R 2 L + 1 when the distance R between the two centers is large. This sheds additional light on the fundamental question whether Efimov effect exists for higher partial wave resonances. The effects of nonresonant partial-wave channels and the shape parameters in the effective range expansions enter as correction terms. Near p-wave and higher partial wave resonances, the energies can be described by a simple universal formula in terms of a parameter called ``proximity parameter.'' We will also discuss modifications of the low energy physics due to the long range Van der Waals potential. We gratefully acknowledge support by the National Science Foundation under Grant No. PHY-1068511 and by the Alfred P. Sloan Foundation.
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.
2011-11-15
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)
Sivan, Y.; Rozenberg, S.; Halstuch, A.
2016-04-01
We present an extension of the canonical coupled-mode theory of electromagnetic waves to the case of pulses and spatiotemporal perturbations in complex media. Unlike previous attempts to derive such a model, our approach involves no approximation, and it does not impose any restriction on the spatiotemporal profile. Moreover, the effect of modal dispersion on mode evolution and on the coupling to other modes is fully taken into account. Thus, our approach can yield any required accuracy by retaining as many terms in the expansion as needed. It also avoids various artifacts of previous derivations by introducing the correct form of the solution. We then validate the coupled-mode equations with exact numerical simulations, and we demonstrate the wide range of possibilities enabled by spatiotemporal perturbations of pulses, including pulse shortening or broadening or more complex shaping. Our formulation is valid across the electromagnetic spectrum, and it can be applied directly also to other wave systems.
Partial-wave decomposition of the finite-range effective tensor interaction
NASA Astrophysics Data System (ADS)
Davesne, D.; Becker, P.; Pastore, A.; Navarro, J.
2016-06-01
We perform a detailed analysis of the properties of the finite-range tensor term associated with the Gogny and M3Y effective interactions. In particular, by using a partial-wave decomposition of the equation of state of symmetric nuclear matter, we show how we can extract their tensor parameters directly from microscopic results based on bare nucleon-nucleon interactions. Furthermore, we show that the zero-range limit of both finite-range interactions has the form of the next-to-next-to-next-leading-order (N3LO) Skyrme pseudopotential, which thus constitutes a reliable approximation in the density range relevant for finite nuclei. Finally, we use Brueckner-Hartree-Fock results to fix the tensor parameters for the three effective interactions.
PyPWA: A partial-wave/amplitude analysis software framework
NASA Astrophysics Data System (ADS)
Salgado, Carlos
2016-05-01
The PyPWA project aims to develop a software framework for Partial Wave and Amplitude Analysis of data; providing the user with software tools to identify resonances from multi-particle final states in photoproduction. Most of the code is written in Python. The software is divided into two main branches: one general-shell where amplitude's parameters (or any parametric model) are to be estimated from the data. This branch also includes software to produce simulated data-sets using the fitted amplitudes. A second branch contains a specific realization of the isobar model (with room to include Deck-type and other isobar model extensions) to perform PWA with an interface into the computer resources at Jefferson Lab. We are currently implementing parallelism and vectorization using the Intel's Xeon Phi family of coprocessors.
Partial wave analysis of the reaction gamma p -> p omega$ and the search for nucleon resonances
M. Williams, D. Applegate, M. Bellis, C.A. Meyer
2009-12-01
An event-based partial wave analysis (PWA) of the reaction gamma p -> 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-> pi+ pi - pi0. The data confirm the dominance of the t-channel pi0 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.
The s-wave SU(5) monopole-fermion system reduces to a coupled set of exactly solvable QFTs
NASA Astrophysics Data System (ADS)
Craigie, N. S.; Nahm, W.
1984-11-01
By establishing that the SU(2) colour sector of fermions in the SU(5) 't Hooft-Polyakov monopole system has an underlying SU(2) Kac-Moody algebra with central charge unity, we show for massless fermions that the whole system can be reduced to a coupled set of exactly integrable two-dimensional QFT's in radial space. Consequently all the non-perturbative effects in the Green functions governing baryon number non-conservation can be explicitly computed up to the effect of the ordinary QCD confining vacuum, which is relevant only at long distances from the monopole's core.
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.
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. PMID:26986436
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.
Are seismic wave velocities and anisotropies reliable proxies for partial melts?
NASA Astrophysics Data System (ADS)
Lee, Amicia; Torvela, Taija; Lloyd, Geoffrey; Walker, Andrew
2015-04-01
Partial melts and their segregation weaken mineral crystallographic alignment, resulting in a decrease in seismic anisotropy (AV). Furthermore, introduction of melt induces a drop in seismic wave velocities, especially for shear (Vs) but also compressional (Vp) waves, although some solid-state processes can also lead to velocity drops. Thus, decreases in AV and/or V are often used to infer the presence and even the amount of melt in both the crust and mantle, for example via the Vp/Vs ratio. However, evidence is accumulating that the relationship between melt fraction and seismic properties is not straight-forward. We consider how varying melt fraction (f) might affect crustal seismic properties. Our modelling approach is based on electron backscattered diffraction (EBSD) analysis of crystallographic preferred orientation (CPO) patterns from granulite facies sheared migmatites. The CPO data are used to model the seismic properties of rocks with different solid/melt proportions. Subsequently, melt was simulated via an isotropic elastic stiffness matrix and combined mathematically with the CPO-derived seismic properties, and seismic properties then recalculated to take into account the presence of melt. These melt models, therefore, predict changes in seismic properties at different f. The models show that low (c. f < 0.15) and high (0.7 < f < 1) values affect seismic properties much more than the 'crystal mush' part (0.1 < f < 0.7): velocities (V) and anisotropies (AV) for both low and high f drop rapidly but 'plateau' at intermediate f. Our results imply that V and, especially, AV may not be reliable proxies for the amount of crustal melt present. Seismic wave behaviour in crystal-supported (0.1 < f < 0.7) material may be controlled by the solid rather than the melt phase.
Blankleider, B.; Afnan, I.R.
1985-04-01
The polarization observables of the reactions parrow parrow ..-->.. ..pi../sup +/d, parrowp ..-->.. darrow..pi../sup +/, and ..pi..darrow ..-->.. ..pi..darrow are investigated. Expressions relating these observables directly to (LSJ) partial wave amplitudes are derived and tabulations of the partial wave contributions are given for some of the observables. Examples are given of how such tabulations can be useful for optimizing the connection between theory and experiment and in suggesting possible new experiments. All observables are also calculated numerically using a unitary few-body model of the NN-..pi..NN system to generate the amplitudes. Sensitivity to the choice of P/sub 11/ interaction is investigated.
Boriskin, Artem V; Sauleau, Ronan; Nosich, Alexander I
2009-02-01
The near fields of small-size extended hemielliptic lenses made of rexolite and isotropic quartz and illuminated by E- and H-polarized plane waves are studied. Variations in the focal domain size, shape, and location are reported versus the angle of incidence of the incoming wave. The problem is solved numerically in a two-dimensional formulation. The accuracy of results is guaranteed by using a highly efficient numerical algorithm based on the combination of the Muller boundary integral equations, the method of analytical regularization, and the trigonometric Galerkin discretization scheme. The analysis fully accounts for the finite size of the lens as well as its curvature and thus can be considered as a reference solution for other electromagnetic solvers. Moreover, the trusted description of the focusing ability of a finite-size hemielliptic lens can be useful in the design of antenna receivers. PMID:19183675
Fully and partially coherent pathways in multiply enhanced odd-order wave-mixing spectroscopy.
Mathew, Nathan A; Yurs, Lena A; Block, Stephen B; Pakoulev, Andrei V; Kornau, Kathryn M; Sibert, Edwin L; Wright, John C
2010-01-21
Nuclear magnetic resonance spectroscopy relies on using multiple excitation pulses to create multiple quantum coherences that provide great specificity for chemical measurements. Coherent multidimensional spectroscopy (CMDS) is the optical analogue of NMR. Current CMDS methods use three excitation pulses and phase matching to create zero, single, and double quantum coherences. In order to create higher order multiple quantum coherences, the number of interactions must be increased by raising the excitation intensities high enough to create Rabi frequencies that are comparable to the dephasing rates of vibrational coherences. The higher Rabi frequencies create multiple, odd-order coherence pathways. The coherence pathways that involve intermediate populations are partially coherent and are sensitive to population relaxation effects. Pathways that are fully coherent involve only coherences and measure the direct coupling between excited quantum states. The fully coherent pathways are related to the multiple quantum coherences created in multiple pulse NMR methods such as heteronuclear multiple quantum coherence (HMQC) spectroscopy with the important difference that HMQC NMR methods have a defined number of interactions and avoid dynamic Stark effects whereas the multiply enhanced odd-order wave-mixing pathways do not. The difference arises because CMDS methods use phase matching to define the interactions and at high intensities, multiple pathways obey the same phase matching conditions. The multiple pathways correspond to the pathways created by dynamic Stark effects. This paper uses rhodium dicarbonyl chelate (RDC) as a model to demonstrate the characteristics of multiply enhanced odd-order wave-mixing (MEOW) methods. Dynamic Stark effects excite vibrational ladders on the symmetric and asymmetric CO stretch modes and create a series of multiple quantum coherences and populations using partially and fully coherent pathways. Vibrational quantum states up to v = 6
Mughab, S.F.
1985-01-01
A long standing discrepancy between measurements and calculations of the sign of the incoherent scattering length is attributed to two sources: (1) spin dependence of the potential scattering radius and (2) identification of additional s-wave resonances at higher neutron energies. Detailed examination of the reaction /sup 27/Al (n vector,..gamma..) /sup 28/Al induced by thermal neutrons revealed that R/sub +/ - R/sub -/ = 0.32 +- 0.10 fm. Also shape fit analysis of the total cross section showed the presence of s-wave resonances at neutron energies 280, 386, 422, 491, 523, and 615 keV. One interesting outcome is the demonstration of the admixture of s- and d-wave partial waves in these resonances and the presence of a large d-wave neutron strength in the above energy region.
NASA Astrophysics Data System (ADS)
Jackson, I.; Faul, U. H.; Fitz Gerald, J. D.
2001-12-01
The frequency-dependent mechanical behaviour expected of Earth materials at high temperature places a special premium on laboratory measurements of wave speeds and attenuation at seismic frequencies. The symposium in honour of Mervyn Paterson provides a welcome opportunity to acknowledge his vital role in the design of the specialised equipment for this purpose described by Jackson and Paterson (PEPI 45: 349-367, 1987; Pageoph 141: 445-466, 1993). This instrument allows the study of low-strain high-temperature viscoelastic behaviour through the application of torsional forced oscillation/ microcreep techniques within the P-T environment (200 MPa, 1600 K) provided by an internally heated gas apparatus. Application of these techniques to fine-grained synthetic olivine polycrystals is beginning to provide a robust basis for the understanding of seismic wave attenuation (and dispersion) in the upper mantle under sub-solidus conditions. More recently, we have begun to explore the effects of partial melting through the fabrication, characterisation and mechanical testing of a suite of fine-grained olivine polycrystals containing up to 4% basaltic melt. The most striking effect of the added melt is the appearance of a melt-related dissipation peak superimposed upon the dissipation background characteristic of melt-free materials - which varies monotonically with period and temperature. The melt-related dissipation peak is adequately modelled as a Gaussian in log X, where X = To exp(E/RT). The melt-related dissipation peak sweeps across the seismic band from period To > 100 s to To < 1 s as temperature increases across the range 1300 - 1600 K producing pronounced systematic changes in the frequency dependence of 1/Q, that may be seismologically observable. >http://rses.anu.adu.au/petrophysics/PetroHome.html
Bello-Rivas, Juan M.; Elber, Ron
2015-01-01
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. PMID:25747056
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.
Bello-Rivas, Juan M; Elber, Ron
2015-03-01
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. PMID:25747056
NASA Astrophysics Data System (ADS)
Kvasha, Oleg V.; Boström, Anders; Glushkova, Natalia V.; Glushkov, Evgeny V.
2011-08-01
The propagation of in-plane (P-SV) waves in a symmetrically three-layered thick plate with a periodic array of interface cracks is investigated. The exact dispersion relation is derived based on an integral equation approach and Floquet's theorem. The interface cracks can be a model for interface damage, but a much simpler model is a recently developed spring boundary condition. This boundary condition is used for the thick plate and also in the derivation of plate equations with the help of power series expansions in the thickness coordinate. For low frequencies (cracks small compared to the wavelength) the three approaches give more or less coinciding dispersion curves, and this is a confirmation that the spring boundary condition is a reasonable approximation at low frequencies.
Vallisneri, Michele
2011-11-01
Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise realizations, as well as the leading-order width of the posterior probability, but it is limited to high signal strengths often not realized in practice. By contrast, Monte Carlo Bayesian inference provides the full posterior for any signal strength, but it is too expensive to repeat for a representative set of noises. Here I describe an efficient semianalytical technique to map the exact sampling distribution of the maximum-likelihood estimator across noise realizations, for any signal strength. This technique can be applied to any estimation problem for signals in additive Gaussian noise. PMID:22181593
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. PMID:27437479
NASA Astrophysics Data System (ADS)
Kuruoğlu, Zeki C.
2014-01-01
Recently there has been a growing interest in computational methods for quantum scattering equations that avoid the traditional decomposition of wave functions and scattering amplitudes into partial waves. The aim of the present work is to show that the weighted-residual approach in combination with local basis functions give rise to convenient computational schemes for the solution of the multi-variable integral equations without the partial wave expansion. The weighted-residual approach provides a unifying framework for various variational and degenerate-kernel methods for integral equations of scattering theory. Using a direct-product basis of localized quadratic interpolation polynomials, Galerkin, collocation and Schwinger variational realizations of the weighted-residual approach have been implemented for a model potential. It is demonstrated that, for a given expansion basis, Schwinger variational method exhibits better convergence with basis size than Galerkin and collocation methods. A novel hybrid-collocation method is implemented with promising results as well.
Gulevich, D. R.; Savel'ev, Sergey; Kusmartsev, F. V.; 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.
Partial wave analysis of the Dirac fermions scattered from Schwarzschild black holes
NASA Astrophysics Data System (ADS)
Cotăescu, Ion I.; Crucean, Cosmin; Sporea, Ciprian A.
2016-03-01
Asymptotic analytic solutions of the Dirac equation, giving the scattering modes (of the continuous energy spectrum, E>mc^2) in Schwarzschild's chart and Cartesian gauge, are used for building the partial wave analysis of Dirac fermions scattered by black holes. In this framework, the analytic expressions of the differential cross section and induced polarization degree are derived in terms of scattering angle, mass of the black hole, and energy and mass of the fermion. Moreover, the closed form of the absorption cross section due to the scattering modes is derived showing that in the high-energy limit this tends to the event horizon area regardless of the fermion mass (including zero). A graphical study presents the differential cross section analyzing the forward/backward scattering (known also as glory scattering) and the polarization degree as functions of scattering angle. The graphical analysis shows the presence of oscillations in scattering intensity around forward/backward directions, phenomena known as spiral scattering. The energy dependence of the differential cross section is also established by using analytical and graphical methods.
Hadzimehmedovic, M.; Osmanovic, H.; Stahov, J.; Ceci, S.; Svarc, A.
2011-09-15
Each and every energy-dependent partial-wave analysis is parametrizing the pole positions in a procedure defined by the way the continuous energy dependence is implemented. These pole positions are, henceforth, inherently model dependent. To reduce this model dependence, we use only one, coupled-channel, unitary, fully analytic method based on the isobar approximation to extract the pole positions from each available member of the worldwide collection of partial-wave amplitudes, which are understood as nothing more but a good energy-dependent representation of genuine experimental numbers assembled in a form of partial-wave data. In that way, the model dependence related to the different assumptions on the analytic form of the partial-wave amplitudes is avoided, and the true confidence limit for the existence of a particular resonant state, at least in one model, is established. The way the method works and first results are demonstrated for the S{sub 11} partial wave.
NASA Astrophysics Data System (ADS)
Zhu, Shangguo; Tan, Shina
2013-06-01
It is well-known that cold atoms near s-wave Feshbach resonances have universal properties that are insensitive to the short-range details of the interaction. What is less known is that atoms near higher partial-wave Feshbach resonances also have remarkable universal properties. We illustrate this with a single atom interacting resonantly with two fixed static centers. At a Feshbach resonance point with orbital angular momentum L≥1, we find 2L+1 shallow bound states whose energies behave like 1/R2L+1 when the distance R between the two centers is large. We then compute corrections to the binding energies due to other parameters in the effective range expansions. For completeness we also compute the binding energies near s-wave Feshbach resonances, taking into account the corrections. Afterwards we turn to the bound states at large but finite scattering volumes. For p-wave and higher partial-wave resonances we derive a simple formula for the energies in terms of a parameter called “proximity parameter.” These results are applicable to a free atom interacting resonantly with two atoms that are localized to two lattice sites of an optical lattice, and to one light atom interacting with two heavy ones in free space. Modifications of the low energy physics due to the long range van der Waals potential are also discussed.
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.
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.
NASA Astrophysics Data System (ADS)
Albers, Bettina
2016-06-01
It is well known that the capillary pressure curve of partially saturated soils exhibits a hysteresis. For the same degree of saturation it has different values depending on the initial state of the soil, thus for drying of a wet soil or wetting of a dry soil. The influence of these different values of the capillary pressure on the propagation of sound waves is studied by use of a linear hyperbolic model. Even if the model does not contain a hysteresis operator, the effect of hysteresis in the capillary pressure curve is accounted for. In order to obtain the limits of phase speeds and attenuations for the two processes the correspondent values for main drying and main wetting are inserted into the model separately. This is done for two examples of soils, namely for Del Monte sand and for a silt loam both filled by an air-water mixture. The wave analysis reveals four waves: one transversal wave and three longitudinal waves. The waves which are driven by the immiscible pore fluids are influenced by the hysteresis in the capillary pressure curve while the waves which are mainly driven by the solid are not.
Das, J.N.; Paul, S.; Chakrabarti, K.
2003-04-01
Hyperspherical partial-wave theory has been applied here in a new way in the calculation of the triple differential cross sections for the ionization of hydrogen atoms by electron impact at low energies for various equal-energy-sharing kinematic conditions. The agreement of the cross section results with the recent absolute measurements of [J. Roeder, M. Baertschy, and I. Bray, Phys. Rev. A 45, 2951 (2002)] and with the latest theoretical results of the ECS and CCC calculations [J. Roeder, M. Baertschy, and I. Bray, Phys. Rev. A (to be published)] for different kinematic conditions at 17.6 eV is very encouraging. The other calculated results, for relatively higher energies, are also generally satisfactory, particularly for large {theta}{sub ab} geometries. In view of the present results, together with the fact that it is capable of describing unequal-energy-sharing kinematics [J. N. Das, J. Phys. B 35, 1165 (2002)], it may be said that the hyperspherical partial-wave theory is quite appropriate for the description of ionization events of electron-hydrogen-type systems. It is also clear that the present approach in the implementation of the hyperspherical partial-wave theory is very appropriate.
Shebloski, Barbara; Conger, Katherine J; Widaman, Keith F
2005-12-01
This study examined reciprocal links between parental differential treatment, siblings' perception of partiality, and self-worth with 3 waves of data from 384 adolescent sibling dyads. Results suggest that birth-order status was significantly associated with self-worth and perception of maternal and paternal differential treatment. There was a consistent across-time effect of self-worth on perception of parental partiality for later born siblings, but not earlier born siblings, and a consistent effect of differential treatment on perception of partiality for earlier born but not later born siblings. The results contribute new insight into the associations between perception of differential parenting and adolescents' adjustment and the role of birth order. PMID:16402879
Theory of wave propagation in partially saturated double-porosity rocks: a triple-layer patchy model
NASA Astrophysics Data System (ADS)
Sun, Weitao; Ba, Jing; Carcione, José M.
2016-04-01
Wave-induced local fluid flow is known as a key mechanism to explain the intrinsic wave dissipation in fluid-saturated rocks. Understanding the relationship between the acoustic properties of rocks and fluid patch distributions is important to interpret the observed seismic wave phenomena. A triple-layer patchy (TLP) model is proposed to describe the P-wave dissipation process in a double-porosity media saturated with two immiscible fluids. The double-porosity rock consists of a solid matrix with unique host porosity and inclusions which contain the second type of pores. Two immiscible fluids are considered in concentric spherical patches, where the inner pocket and the outer sphere are saturated with different fluids. The kinetic and dissipation energy functions of local fluid flow (LFF) in the inner pocket are formulated through oscillations in spherical coordinates. The wave propagation equations of the TLP model are based on Biot's theory and the corresponding Lagrangian equations. The P-wave dispersion and attenuation caused by the Biot friction mechanism and the local fluid flow (related to the pore structure and the fluid distribution) are obtained by a plane-wave analysis from the Christoffel equations. Numerical examples and laboratory measurements indicate that P-wave dispersion and attenuation are significantly influenced by the spatial distributions of both, the solid heterogeneity and the fluid saturation distribution. The TLP model is in reasonably good agreement with White's and Johnson's models. However, differences in phase velocity suggest that the heterogeneities associated with double-porosity and dual-fluid distribution should be taken into account when describing the P-wave dispersion and attenuation in partially saturated rocks.
NASA Astrophysics Data System (ADS)
Fontaine, Fabrice R.; Ildefonse, Benoit; Bagdassarov, Nickolai S.
2005-12-01
Torsion oscillatory deformation experiments have been performed at high temperatures (600-1170°C) and over a wide range of low frequencies (20-2.10-3 Hz) on fine-grained gabbronorite samples from the Oman ophiolite in order to determine the shear wave attenuation as a function of temperature and melt fraction. The specimens have a small and uniform grain size (0.25-0.3 mm) and do not contain secondary, hydrated minerals. Measurements of internal friction (Q-1) were performed using a forced oscillatory torsion apparatus at small strains (~10-7), and with increasing small temperature steps to reduce thermal microcracking. The general dependence of Q-1 to frequency is Q-1~ω-α, where ω is the angular velocity of forced oscillations and α is an empirical exponent. Below the melting temperature (~1050°C), α has average values of ~0.15 at low frequency (<=0.5 Hz) and 0.06 at higher frequency. Above the melting temperature, α has average values of ~0.22 at low frequency and -0.02 at higher frequency. This frequency dependence of Q-1 is attributed to a viscoelastic behaviour due to the diffusion controlled grain boundary sliding, and partially to the squirt flow of the melt-phase wetting grain boundaries. The onset of melting is associated with a markedly higher Q-1 and a stronger dependence of Q-1 on temperature. The melt-related mechanical dissipation process could be a melt squirt flow. The characteristic frequency for the melt squirt flow is ωm~ 0.15-300 Hz when the melt pocket aspect ratio is ~10-3-10-2. Around the melting temperature the internal friction can be approximated by an experimental power law Q-1=A.[ω-1.d-1. exp(-Ea/RT)]α with α~ 0.08, A= 34.72s-αμm-α and Ea~ 873 kJmol-1.
NASA Astrophysics Data System (ADS)
Rajabpour, M. A.
2016-06-01
We calculate analytically the Rényi bipartite entanglement entropy {{S}α} of the ground state of 1 + 1 dimensional conformal field theories (CFT) after performing a projective measurement in part of the system. We show that the entanglement entropy in this setup is dependent on the central charge and the operator content of the system. When the measurement region A separates the two parts B and \\bar{B} , the entanglement entropy between B and \\bar{B} decreases like a power-law with respect to the characteristic distance between the two regions with an exponent which is dependent on the rank α of the Rényi entanglement entropy and the smallest scaling dimension present in the system. We check our findings by making numerical calculations on the Klein–Gordon field theory (coupled harmonic oscillators) after fixing the position (partial measurement) of some of the oscillators. We also comment on the post-measurement entanglement entropy in the massive quantum field theories.
NASA Astrophysics Data System (ADS)
Yang, Wang; Li, Yi; Wu, Congjun
2016-08-01
We systematically generalize the exotic 3He -B phase, which not only exhibits unconventional symmetry but is also isotropic and topologically nontrivial, to arbitrary partial-wave channels with multicomponent fermions. The concrete example with four-component fermions is illustrated including the isotropic f -, p -, and d -wave pairings in the spin septet, triplet, and quintet channels, respectively. The odd partial-wave channel pairings are topologically nontrivial, while pairings in even partial-wave channels are topologically trivial. The topological index reaches the largest value of N2 in the p -wave channel (N is half of the fermion component number). The surface spectra exhibit multiple linear and even high order Dirac cones. Applications to multiorbital condensed matter systems and multicomponent ultracold large spin fermion systems are discussed.
Yang, Wang; Li, Yi; Wu, Congjun
2016-08-12
We systematically generalize the exotic ^{3}He-B phase, which not only exhibits unconventional symmetry but is also isotropic and topologically nontrivial, to arbitrary partial-wave channels with multicomponent fermions. The concrete example with four-component fermions is illustrated including the isotropic f-, p-, and d-wave pairings in the spin septet, triplet, and quintet channels, respectively. The odd partial-wave channel pairings are topologically nontrivial, while pairings in even partial-wave channels are topologically trivial. The topological index reaches the largest value of N^{2} in the p-wave channel (N is half of the fermion component number). The surface spectra exhibit multiple linear and even high order Dirac cones. Applications to multiorbital condensed matter systems and multicomponent ultracold large spin fermion systems are discussed. PMID:27563972
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.
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. PMID:26078134
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.
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)
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 broadens 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.
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.
NASA Astrophysics Data System (ADS)
Nakayama, M.; Kawakata, H.; Doi, I.; Takahashi, N.
2015-12-01
Recently, landslides due to heavy rain and/or earthquakes have been increasing and severe damage occurred in Japan in some cases (e.g., Chigira et al., 2013, Geomorph.). One of the principle factors activating landslides is groundwater. Continuous measurements of moisture in soil and/or pore pressure are performed to investigate the groundwater behavior. However, such measurements give information on only local behavior of the groundwater. To monitor the state of target slope, it is better to measure signals affected by the behavior of groundwater in a widely surrounding region. The elastic waves propagating through the medium under the target slope are one of candidates of such signals. In this study, we measure propagating waves through a sand soil made in laboratory, injecting water into it from the bottom. We investigate the characteristics of the propagating waves. We drop sand particles in a container (750 mm long, 300 mm wide and 400 mm high) freely and made a sand soil. The sand soil consists of two layers. One is made of larger sand particles (0.2-0.4 mm in diameter) and the other is made of smaller sand particles (0.05-0.2 mm in diameter). The dry density of these sand layers is about 1.45 g/cm3. We install a shaker for generating elastic waves, accelerometers and pore pressure gauges in the sand soil. We apply small voltage steps repeatedly, and we continuously measure elastic waves propagating through the sand soil at a sampling rate of 51.2 ksps for a period including the water injection period. We estimate the spatio-temporal variation in the maximum cross-correlation coefficients and the corresponding time lags, using template waveforms recorded in the initial period as references. The coefficient for the waveforms recorded at the accelerometer attached to the tip of the shaker is almost stable in high values with a slight decrease down to 0.94 in the period when the sand particles around the shaker are considered to become wet. On the other hand
Guide for the program EXACT-NL
NASA Astrophysics Data System (ADS)
Vanvledder, G. Ph.; Weber, S. L.
1987-02-01
A set of programs called EXACT-NL, which computes fetch or duration limited wave growth with an explicit expression for the resonant four-wave interactions is described. The manual is based on experience with EXACT-NL for the computation of shallow water growth curves and the investigation of the directional response of waves to variations in the wind field. Modifications necessary for these specific purposes are also described.
Partial wave analysis of J/ψ-->γ(K+K- π0)
NASA Astrophysics Data System (ADS)
BES Collaboration; Bai, J. Z.; Bian, J. G.; Chai, Z. W.; Chen, G. P.; Chen, H. F.; Chen, J. C.; Chen, Y.; Chen, Y. B.; Chen, Y. Q.; Cheng, B. S.; Cui, X. Z.; Ding, H. L.; Dong, L. Y.; Du, Z. Z.; Feng, S.; Gao, C. S.; Gao, M. L.; Gao, S. Q.; Gu, J. H.; Gu, S. D.; Gu, W. X.; Gu, Y. F.; Guo, Y. N.; Guo, Z. J.; Han, S. W.; Han, Y.; He, J.; He, J. T.; He, M.; Hu, G. Y.; Hu, H. M.; Hu, J. L.; Hu, Q. H.; Hu, T.; Hu, X. Q.; Huang, J. D.; Huang, Y. Z.; Jiang, C. H.; Jin, Y.; Ke, Z. J.; Lai, Y. F.; Lang, P. F.; Li, C. G.; Li, D.; Li, H. B.; Li, J.; Li, P. Q.; Li, R. B.; Li, W.; Li, W. D.; Li, W. G.; Li, X. H.; Li, X. N.; Liu, H. M.; Liu, J.; Liu, J. H.; Liu, R. G.; Liu, Y.; Lu, F.; Lu, J. G.; Lu, J. Y.; Lu, L. C.; Luo, C. H.; Ma, A. M.; Ma, E. C.; Ma, J. M.; Mao, H. S.; Mao, Z. P.; Meng, X. C.; Nie, J.; Qi, N. D.; Qi, X. R.; Qian, C. D.; Qiu, J. F.; Qu, Y. H.; Que, Y. K.; Rong, G.; Shao, Y. Y.; Shen, B. W.; Shen, D. L.; Shen, H.; Shen, X. Y.; Sheng, H. Y.; Shi, H. Z.; Song, X. F.; Sun, F.; Sun, H. S.; Tang, S. Q.; Tong, G. L.; Wang, F.; Wang, L. S.; Wang, L. Z.; Wang, M.; Wang, Meng; Wang, P.; Wang, P. L.; Wang, S. M.; Wang, T. J.; Wang, Y. Y.; Wei, C. L.; Wu, Y. G.; Xi, D. M.; Xia, X. M.; Xie, P. P.; Xie, Y.; Xie, Y. H.; Xiong, W. J.; Xu, C. C.; Xu, G. F.; Xue, S. T.; Yan, J.; Yan, W. G.; Yang, C. M.; Yang, C. Y.; Yang, J.; Yang, X. F.; Ye, M. H.; Ye, S. W.; Ye, Y. X.; Yi, K.; Yu, C. S.; Yu, C. X.; Yu, Y. H.; Yu, Z. Q.; Yu, Z. T.; Yuan, C. Z.; Yuan, Y.; Zhang, B. Y.; Zhang, C. C.; Zhang, D. H.; Zhang, Dehong; Zhang, H. L.; Zhang, J.; Zhang, J. L.; Zhang, J. W.; Zhang, L. S.; Zhang, Q. J.; Zhang, S. Q.; Zhang, X. Y.; Zhang, Y.; Zhang, Y. Y.; Zhao, D. X.; Zhao, H. W.; Zhao, J. W.; Zhao, M.; Zhao, W. R.; Zhao, Z. G.; Zheng, J. P.; Zheng, L. S.; Zheng, Z. P.; Zhou, G. P.; Zhou, H. S.; Zhou, L.; Zhu, Q. M.; Zhu, Y. C.; Zhu, Y. S.; Zhuang, B. A.; Bugg, D. V.; Sarantsev, A. V.; Zou, B. S.
1998-11-01
BES data on J/ψ-->γ(K+K-π0) display a strong peak in the K+K-π0 mass spectrum at 1450 MeV. This peak and a corresponding one in J/ψ-->γ(ηπ+π-) at ~1400 MeV may be fitted well by η(1440) with dominant decays to K*(890)K, using an s-dependent width in the Breit-Wigner amplitude. A broad background is also required in KK0 (where K0 stands for the Kπ S-wave) and also in ηππ, but is probably not resonant in this mass range.
On-shell coupled-channel approach to proton-hydrogen collisions without partial-wave expansion
Kadyrov, A. S.; Bray, I.; Stelbovics, A. T.
2006-01-15
A fully quantal approach to proton collisions with hydrogen based on the atomic-orbital close-coupling method is presented. The method leads to a system of coupled three-dimensional momentum-space integral equations for the scattering amplitudes. These equations are reduced to two-dimensional ones using an on-shell approximation. Furthermore, by considering the symmetry of the problem, we demonstrate that these can be reduced to just one dimension. The resulting equations are solved without partial-wave expansion. Cross sections for electron transfer in proton collisions with the ground state of atomic hydrogen are calculated and shown to agree well with experiment over a wide energy range.
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.
Effects of partial liquid/gas saturation on extensional wave attenuation in Berea sandstone
NASA Astrophysics Data System (ADS)
Yin, C.-S.; Batzle, M. L.; Smith, B. J.
1992-07-01
Extensional wave attenuation measurements on Berea sandstone were made during increasing (imbibition) and decreasing (drainage) brine saturations. Measurements on samples with both open-pore and closed-pore surfaces were made using the resonant-bar technique. The frequency dependence was examined using the forced-deformation method. The attenuation was found to be dependent on saturation history as well as degree of saturation and boundary flow conditions. The sample with open-pore surface had a larger attenuation which peaked at greater brine saturations than the sample with closed-pore surface. During drainage, the attenuation reached a maximum at about 90% brine saturation as opposed to about 97% brine saturation during imbibition. The variation of the size and number of air pockets within the rock can account for this discrepancy. The magnitude of the attenuation peak value decreases substantially with decreasing frequency to the extent that no attenuation peak with saturation was apparent at seismic frequencies, say, below 100 Hz.
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.
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 Astrophysics Data System (ADS)
Salvat, Francesc; Jablonski, Aleksander; Powell, Cedric J.
2005-01-01
The FORTRAN 77 code system ELSEPA for the calculation of elastic scattering of electrons and positrons by atoms, positive ions and molecules is presented. These codes perform relativistic (Dirac) partial-wave calculations for scattering by a local central interaction potential V(r). For atoms and ions, the static-field approximation is adopted, with the potential set equal to the electrostatic interaction energy between the projectile and the target, plus an approximate local exchange interaction when the projectile is an electron. For projectiles with kinetic energies up to 10 keV, the potential may optionally include a semiempirical correlation-polarization potential to describe the effect of the target charge polarizability. Also, for projectiles with energies less than 1 MeV, an imaginary absorptive potential can be introduced to account for the depletion of the projectile wave function caused by open inelastic channels. Molecular cross sections are calculated by means of a single-scattering independent-atom approximation in which the electron density of a bound atom is approximated by that of the free neutral atom. Elastic scattering by individual atoms in solids is described by means of a muffin-tin model potential. Partial-wave calculations are feasible on modest personal computers for energies up to about 5 MeV. The ELSEPA code also implements approximate factorization methods that allow the fast calculation of elastic cross sections for much higher energies. The interaction model adopted in the calculations is defined by the user by combining the different options offered by the code. The nuclear charge distribution can be selected among four analytical models (point nucleus, uniformly charged sphere, Fermi's distribution and Helm's uniform-uniform distribution). The atomic electron density is handled in numerical form. The distribution package includes data files with electronic densities of neutral atoms of the elements hydrogen to lawrencium ( Z=1
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)].
Symmetry analysis and exact solutions for a generalized Fisher equation in cylindrical coordinates
NASA Astrophysics Data System (ADS)
Rosa, M.; Bruzón, M. S.; Gandarias, M. L.
2015-08-01
In this paper, a generalized Fisher equation is studied from the point of view of the theory of symmetry reductions in partial differential equations. A group classification is obtained. All the reductions are derived from the optimal system of subalgebras. Some of the reduced equations admit Lie symmetries which yield to further reductions. By applying direct methods such as the simplest equation method we derive some exact wave solutions.
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.
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.
NASA Astrophysics Data System (ADS)
Dubrovsky, V. G.; Topovsky, A. V.
2013-03-01
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(n), n = 1, …, N are constructed via Zakharov and Manakov overline{partial }-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u(n) and calculated by overline{partial }-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schrödinger 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(n). It is shown that the sums u= u^{(k_1)}+ldots + u^{(k_m)}, 1 ⩽ k1 < k2 < … < km ⩽ 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 Schrödinger equation and can serve as model potentials for electrons in planar structures of modern electronics.
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.; Meyer, C. A.; Adhikari, K. P.; Anghinolfi, M.; Baghdasaryan, H.; Ball, J.; Battaglieri, M.; Bedlinskiy, I.; et al
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
Partial wave analysis of the reaction γp→pω and the search for nucleon resonances
NASA Astrophysics Data System (ADS)
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.
2009-12-01
An event-based partial wave analysis (PWA) of the reaction γp→pω 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 ω→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 F15(1680) and D13(1700) near threshold, as well as the G17(2190) at higher energies. Suggestive evidence for the presence of a JP=5/2+ state around 2 GeV, a “missing” state, has also been found. Evidence for other states is inconclusive.
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.
Physics of Partially Ionized Plasmas
NASA Astrophysics Data System (ADS)
Krishan, Vinod
2016-05-01
Figures; Preface; 1. Partially ionized plasmas here and everywhere; 2. Multifluid description of partially ionized plasmas; 3. Equilibrium of partially ionized plasmas; 4. Waves in partially ionized plasmas; 5. Advanced topics in partially ionized plasmas; 6. Research problems in partially ionized plasmas; Supplementary matter; Index.
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)
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.
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.
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.
Hammani, Kamal; Finot, Christophe; Millot, Guy
2009-04-15
We present experimental and theoretical results showing efficient emergence of rogue wavelike extreme intensity spikes during the fiber-based induced-modulational instability process driven by a partially incoherent pump. In particular, we show that the rogue event probability can be easily controlled by adjusting the pump-signal detuning. PMID:19370096
Chrysos, Michael
2016-03-21
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 12(1-x(2))(3)1+3x(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 12 for ν ≫ 0. For ΔJ = 0, analogous conclusions may be drawn from the expression (1+ln(1+x1-x)2arctanx)(-1). PMID:27004860
NASA Astrophysics Data System (ADS)
Brajanovski, Miroslav; Müller, Tobias M.; Parra, Jorge O.
2010-08-01
In this work we interpret the data showing unusually strong velocity dispersion of P-waves (up to 30%) and attenuation in a relatively narrow frequency range. The cross-hole and VSP data were measured in a reservoir, which is in the porous zone of the Silurian Kankakee Limestone Formation formed by vertical fractures within a porous matrix saturated by oil, and gas patches. Such a medium exhibits significant attenuation due to wave-induced fluid flow across the interfaces between different types of inclusions (fractures, fluid patches) and background. Other models of intrinsic attenuation (in particular squirt flow models) cannot explain the amount of observed dispersion when using realistic rock properties. In order to interpret data in a satisfactory way we develop a superposition model for fractured porous rocks accounting also for the patchy saturation effect.
NASA Astrophysics Data System (ADS)
Gabovich, A. M.; Li, Mai Suan; Pekala, M.; Szymczak, H.; Voitenko, A. I.
2005-03-01
We consider tunnelling between a metal partially gapped by charge density waves (CDWM) and an ordinary metal (M) or a ferromagnet (FM) separated by an insulator (I) in an external magnetic field H. Zeeman paramagnetic splitting is assumed to dominate in the CDWM over orbital magnetic effects. The quasiparticle tunnel current J and relevant differential conductance G are calculated as functions of the bias voltage V. The peaks of G(V), originating from the electron density of states singularities near the charge density wave gap edges, were shown to be split in the magnetic field, each peak having a predominant spin polarization. This effect is analogous to the H-induced splitting of G(V) peaks obtained by Tedrow and Meservey for junctions between normal metals and superconductors (S). Thus, it is possible to electrically measure the polarization of current carriers in such a set-up, although the behaviours of G(V) in the two cases are substantially different. The use of M-I-CDWM junctions instead of M-I-S ones has certain advantages. The absence of the Meissner effect, which weakens the constraints upon the junction geometry and electrode materials, comprises the main benefit. The other advantage is the larger energy range of the charge density wave gaps in comparison to that for superconductors' gaps, so that larger Hs may be applied.
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.
Local relativistic exact decoupling.
Peng, Daoling; Reiher, Markus
2012-06-28
We present a systematic hierarchy of approximations for local exact decoupling of four-component quantum chemical Hamiltonians based on the Dirac equation. Our ansatz reaches beyond the trivial local approximation that is based on a unitary transformation of only the atomic block-diagonal part of the Hamiltonian. Systematically, off-diagonal Hamiltonian matrix blocks can be subjected to a unitary transformation to yield relativistically corrected matrix elements. The full hierarchy is investigated with respect to the accuracy reached for the electronic energy and for selected molecular properties on a balanced test molecule set that comprises molecules with heavy elements in different bonding situations. Our atomic (local) assembly of the unitary exact-decoupling transformation--called local approximation to the unitary decoupling transformation (DLU)--provides an excellent local approximation for any relativistic exact-decoupling approach. Its order-N(2) scaling can be further reduced to linear scaling by employing a neighboring-atomic-blocks approximation. Therefore, DLU is an efficient relativistic method well suited for relativistic calculations on large molecules. If a large molecule contains many light atoms (typically hydrogen atoms), the computational costs can be further reduced by employing a well-defined nonrelativistic approximation for these light atoms without significant loss of accuracy. We also demonstrate that the standard and straightforward transformation of only the atomic block-diagonal entries in the Hamiltonian--denoted diagonal local approximation to the Hamiltonian (DLH) in this paper--introduces an error that is on the order of the error of second-order Douglas-Kroll-Hess (i.e., DKH2) when compared with exact-decoupling results. Hence, the local DLH approximation would be pointless in an exact-decoupling framework, but can be efficiently employed in combination with the fast to evaluate DKH2 Hamiltonian in order to speed up calculations
Exact models for trimerization and tetramerization in spin chains
NASA Astrophysics Data System (ADS)
Rachel, Stephan; Greiter, Martin
2008-10-01
We present exact models for an antiferromagnetic S=1 spin chain describing trimerization as well as for an antiferromagnetic S=3/2 spin chain describing tetramerization. These models can be seen as generalizations of the Majumdar-Ghosh model. For both models, we provide a local Hamiltonian and its exact threefold or fourfold degenerate ground state wave functions, respectively. We numerically confirm the validity of both models using exact diagonalization and discuss the low-lying excitations.
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. PMID:17677378
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.
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).
Linearly exact parallel closures for slab geometry
Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun
2013-08-15
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)
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.
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.
Exact quantization of a paraxial electromagnetic field
Aiello, A.; Woerdman, J. P.
2005-12-15
A nonperturbative quantization of a paraxial electromagnetic field is achieved via a generalized dispersion relation imposed on the longitudinal and the transverse components of the photon wave vector. This theoretical formalism yields a seamless transition between the paraxial- and the Maxwell-equation solutions. This obviates the need to introduce either ad hoc or perturbatively defined field operators. Moreover, our (exact) formalism remains valid beyond the quasimonochromatic paraxial limit.
Nonminimally coupled gravitational and electromagnetic fields: pp-wave solutions
Dereli, Tekin; Sert, Oezcan
2011-03-15
We give the Lagrangian formulation of a generic nonminimally extended Einstein-Maxwell theory with an action that is linear in the curvature and quadratic in the electromagnetic field. We derive the coupled field equations by a first-order variational principle using the method of Lagrange multipliers. We look for solutions describing plane-fronted Einstein-Maxwell waves with parallel rays. We give a family of exact pp-wave solutions associated with a partially massless spin-2 photon and a partially massive spin-2 graviton.
Efficient exact motif discovery
Marschall, Tobias; Rahmann, Sven
2009-01-01
Motivation: The motif discovery problem consists of finding over-represented patterns in a collection of biosequences. It is one of the classical sequence analysis problems, but still has not been satisfactorily solved in an exact and efficient manner. This is partly due to the large number of possibilities of defining the motif search space and the notion of over-representation. Even for well-defined formalizations, the problem is frequently solved in an ad hoc manner with heuristics that do not guarantee to find the best motif. Results: We show how to solve the motif discovery problem (almost) exactly on a practically relevant space of IUPAC generalized string patterns, using the p-value with respect to an i.i.d. model or a Markov model as the measure of over-representation. In particular, (i) we use a highly accurate compound Poisson approximation for the null distribution of the number of motif occurrences. We show how to compute the exact clump size distribution using a recently introduced device called probabilistic arithmetic automaton (PAA). (ii) We define two p-value scores for over-representation, the first one based on the total number of motif occurrences, the second one based on the number of sequences in a collection with at least one occurrence. (iii) We describe an algorithm to discover the optimal pattern with respect to either of the scores. The method exploits monotonicity properties of the compound Poisson approximation and is by orders of magnitude faster than exhaustive enumeration of IUPAC strings (11.8 h compared with an extrapolated runtime of 4.8 years). (iv) We justify the use of the proposed scores for motif discovery by showing our method to outperform other motif discovery algorithms (e.g. MEME, Weeder) on benchmark datasets. We also propose new motifs on Mycobacterium tuberculosis. Availability and Implementation: The method has been implemented in Java. It can be obtained from http://ls11-www
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
Agakishiev, G.; Arnold, O.; Belver, D.; Belyaev, A.; Berger-Chen, J. C.; Blanco, A.; Böhmer, M.; Boyard, J. L.; Cabanelas, P.; Chernenko, S.; et al
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
NASA Astrophysics Data System (ADS)
Valbuena, M. A.; Avila, J.; Pantin, V.; Drouard, S.; Guyot, H.; Asensio, M. C.
2006-05-01
Low dimensional (LD) metallic oxides have been a subject of continuous interest in the last two decades, mainly due to the electronic instabilities that they present at low temperatures. In particular, charge density waves (CDW) instabilities associated with a strong electron-phonon interaction have been found in Molybdenum metallic oxides such as KMo 6O 17 purple bronze. We report an angle resolved photoemission (ARPES) study from room temperature (RT) to T ˜40 K well below the Peierls transition temperature for this material, with CDW transition temperature TCDW ˜120 K. We have focused on photoemission spectra along ΓM high symmetry direction as well as photoemission measurements were taken as a function of temperature at one representative kF point in the Brillouin zone in order to look for the characteristic gap opening after the phase transition. We found out a pseudogap opening and a decrease in the density of states near the Fermi energy, EF, consistent with the partial removal of the nested portions of the Fermi surface (FS) at temperature below the CDW transition. In order to elucidate possible Fermi liquid (FL) or non-Fermi liquid (NFL) behaviour we have compared the ARPES data with that one reported on quasi-1D K 0.3MoO 3 blue bronze.
EXACT VECTORIAL LAW FOR AXISYMMETRIC MAGNETOHYDRODYNAMICS TURBULENCE
Galtier, S.
2009-10-20
Three-dimensional incompressible magnetohydrodynamics turbulence is investigated under the assumptions of homogeneity and axisymmetry. We demonstrate that previous works of Chandrasekhar may be improved significantly by using a different formalism for the representation of two-point correlation tensors. From this axisymmetric kinematics, the equations a la von Karman-Howarth are derived from which an exact relation is found in terms of measurable correlations. The relation is then analyzed in the particular case of a medium permeated by an imposed magnetic field B{sub 0} . We make the ansatz that the development of anisotropy implies an algebraic relation between the axial and the radial components of the separation vector r and we derive an exact vectorial law which is parameterized by the intensity of anisotropy. The critical balance proposed by Goldreich and Sridhar is used to fix this parameter and to obtain a unique exact expression; the particular limits of correlations transverse and parallel to B{sub 0} are given for which simple expressions are found. Predictions for the energy spectra are also proposed by a straightforward dimensional analysis of the exact law; it gives a stronger theoretical background to the heuristic spectra previously proposed in the context of the critical balance. We also discuss the wave turbulence limit of an asymptotically large external magnetic field which appears as a natural limit of the vectorial relation. A new interpretation of the anisotropic solar wind observations is eventually discussed.
NASA Astrophysics Data System (ADS)
Yaşar, Emrullah; Yıldırım, Yakup; Khalique, Chaudry Masood
In this paper Lie symmetry analysis of the seventh-order time fractional Sawada-Kotera-Ito (FSKI) equation with Riemann-Liouville derivative is performed. Using the Lie point symmetries of FSKI equation, it is shown that it can be transformed into a nonlinear ordinary differential equation of fractional order with a new dependent variable. In the reduced equation the derivative is in Erdelyi-Kober sense. Furthermore, adapting the Ibragimov's nonlocal conservation method to time fractional partial differential equations, we obtain conservation laws of the underlying equation. In addition, we construct some exact travelling wave solutions for the FSKI equation using the sub-equation method.
NASA Astrophysics Data System (ADS)
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 n0˜1027cm-3 and high-magnetic-field B0=1010 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.
Inhomogeneous mixmaster universes: Some exact solutions
Carmeli, M.; Charach, C.; Feinstein, A.
1983-10-15
Algorithms for generating new exact solutions of the Einstein-Klein-Gordon field equations, which describe inhomogeneous universes with S/sup 3/ topology of spatial sections, are developed. The known exact vacuum and still-fluid solutions with S/sup 3/ topology are used as an input. The methods developed are further applied to derive inhomogeneous generalizations of Bianchi type IX solutions and inhomogeneous S/sup 3/ Gowdy models with gravitational and scalar waves. It is shown that the new solutions, which are generalizations of the Bianchi type IX models, permit identification of the scalar field with the velocity potential of the stiff irrotational fluid. The latter result is further used to study the growth rate of density perturbations of the isotropic and anisotropic Bianchi type IX universes in a fully nonlinear relativistic regime. The role of anisotropy on the rate of growth of density perturbations is studied in detail.
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.
Partially wetting thin liquid films: structure and dynamics studied with coherent x rays.
Gutt, C; Sprung, M; Fendt, R; Madsen, A; Sinha, S K; Tolan, M
2007-08-31
We studied the surface structure of thin liquid films vapor deposited on solid substrates in a partial wetting situation by means of coherent x-ray scattering. No dynamics has been observed showing the absence of capillary waves on liquid films partially wetting a substrate. Instead an exponential form of the height-height correlation function has been found pointing toward a solidlike behavior of the thin liquid films at large length scales. The exact surface structure and degree of replication with the substrate depend on the deposition rate of the molecules. PMID:17931023
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. PMID:26783508
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)
Pandey, Manoj
2010-02-01
A group theoretic method is used to obtain an exact particular solution to the system of partial differential equations, describing one-dimensional unsteady planar, cylindrically and spherically symmetric motions in an ideal gas, involving shock waves. It is interesting to remark that the exact solution obtained here is precisely the blast wave solution obtained earlier using a different method of approach. Further, the evolution of a discontinuity wave and its interaction with the strong shock are studied within the state characterized by the exact particular solution. The properties of reflected and transmitted waves and the jump in the shock acceleration are completely characterized, and certain observations are noted in respect to their contrasting behavior.
Diffraction in time: An exactly solvable model
NASA Astrophysics Data System (ADS)
Goussev, Arseni
2014-03-01
In optics, diffraction is typically portrayed as deflection of light incident upon an obstacle with sharp boundaries, that can not be accounted for by reflection or refraction. Interestingly, quantum mechanics allows for an additional, intrinsically time-dependent manifestation of the phenomenon: Owing to the dispersive nature of quantum matter waves, sudden changes in boundary conditions may cause the particle wave function to develop interference fringes akin to those in stationary (optical) diffraction problems. This phenomenon, pioneered in 1952 by Moshinsky [Phys. Rev. 88, 625 (1952)] and presently referred to as ``diffraction in time,'' is at the heart of a vibrant area of experimental and theoretical research concerned with quantum transients. In my talk, I will introduce a new versatile exactly-solvable model of diffraction in time. The model describes dynamics of a quantum particle in the presence of an absorbing time-dependent barrier, and enables a quantitative description of diffraction and interference patterns in a large variety of setups.
NASA Astrophysics Data System (ADS)
Akter, Jesmin; Ali Akbar, M.
The modified simple equation (MSE) method is a competent and highly effective mathematical tool for extracting exact traveling wave solutions to nonlinear evolution equations (NLEEs) arising in science, engineering and mathematical physics. In this article, we implement the MSE method to find the exact solutions involving parameters to NLEEs via the Benney-Luke equation and the Phi-4 equations. The solitary wave solutions are derived from the exact traveling wave solutions when the parameters receive their special values.
Correlated Lloyd model: Exact solution
NASA Astrophysics Data System (ADS)
Kozlov, G. G.
2014-11-01
We describe an exactly solvable model of a disordered system that is a generalized Lloyd model; it differs from the classical model because the random potential is not a δ-correlated random process. We show that the exact average Green's function in this case is independent of the correlation radius of the random potential and, as in the classical Lloyd model, is a crystal Green's function whose energy argument acquires an imaginary part dependent on the disorder degree.
Exact treatment of the Jaynes-Cummings model under the action of an external classical field
NASA Astrophysics Data System (ADS)
Abdalla, M. Sebawe; Khalil, E. M.; Obada, A. S.-F.
2011-09-01
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 ω0 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.
Exact kink solitons in the presence of diffusion, dispersion, and polynomial nonlinearity
NASA Astrophysics Data System (ADS)
Raposo, E. P.; Bazeia, D.
1999-03-01
We describe exact travelling-wave kink soliton solutions in some classes of nonlinear partial differential equations, such as generalized Korteweg-de Vries-Burgers, Korteweg-de Vries-Huxley, and Korteweg-de Vries-Burgers-Huxley equations, as well as equations in the generic form ut + P( u) ux + vuxx - δuxxx = A( u), with polynomial functions P( u) and A( u) of u = u( x, t), whose generality allows the identification with a number of relevant equations in physics. We focus on the analysis of the role of diffusion, dispersion, nonlinear effects, and parity of the polynomials to the properties of the solutions, particularly their velocity of propagation. In addition, we show that, for some appropriate choices, these equations can be mapped onto equations of motion of relativistic (1 + 1)-dimensional φ4 and φ6 field theories of real scalar fields. Systems of two coupled nonlinear equations are also considered.
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. PMID:24116418
NASA Astrophysics Data System (ADS)
Polyanin, Andrei D.; Zhurov, Alexei I.
2014-03-01
We propose a new method for constructing exact solutions to nonlinear delay reaction-diffusion equations of the form ut=kuxx+F(u,w), where u=u(x,t),w=u(x,t-τ), and τ is the delay time. The method is based on searching for solutions in the form u=∑n=1Nξn(x)ηn(t), where the functions ξn(x) and ηn(t) are determined from additional functional constraints (which are difference or functional equations) and the original delay partial differential equation. All of the equations considered contain one or two arbitrary functions of a single argument. We describe a considerable number of new exact generalized separable solutions and a few more complex solutions representing a nonlinear superposition of generalized separable and traveling wave solutions. All solutions involve free parameters (in some cases, infinitely many parameters) and so can be suitable for solving certain problems and testing approximate analytical and numerical methods for nonlinear delay PDEs. The results are extended to a wide class of nonlinear partial differential-difference equations involving arbitrary linear differential operators of any order with respect to the independent variables x and t (in particular, this class includes the nonlinear delay Klein-Gordon equation) as well as to some partial functional differential equations with time-varying delay.
Exact solutions of the generalized Sinh-Gordon equation
NASA Astrophysics Data System (ADS)
Neirameh, A.
2016-07-01
In this paper, we successfully derive a new exact traveling wave solutions of the generalized Sinh-Gordon equation by new application of the homogeneous balance method. This method could be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in physics.
Novel quasi-exactly solvable models with anharmonic singular potentials
Agboola, Davids Zhang, Yao-Zhong
2013-03-15
We present new quasi-exactly solvable models with inverse quartic, sextic, octic and decatic power potentials, respectively. We solve these models exactly by means of the functional Bethe ansatz method. For each case, we give closed-form solutions for the energies and the wave functions as well as analytical expressions for the allowed potential parameters in terms of the roots of a set of algebraic equations. - Highlights: Black-Right-Pointing-Pointer The quasi-exactly solvable treatments of a class of singular anharmonic models. Black-Right-Pointing-Pointer Exact solutions to a class of integer power singular potential. Black-Right-Pointing-Pointer Solutions obtained in terms of the roots to the Bethe ansatz equations. Black-Right-Pointing-Pointer Results useful in describing diatomic molecules and elastic differential cross sections for high energy scattering.
NASA Astrophysics Data System (ADS)
Kouzakov, Konstantin A.; Popov, Yuri V.; Shablov, Vladimir L.
2010-01-01
The solutions analytically derived by W. Glöckle, J. Golak, R. Skibiński, and H. Witala [Phys. Rev. C 79, 044003 (2009)] for the three-dimensional wave function and on-shell t matrix in the case of scattering on a sharply cut-off Coulomb potential appear to be fallacious if finite values of a cut-off radius are concerned. And the analysis carried out for an infinite cut-off radius limit is incomplete.
Exact discretization by Fourier transforms
NASA Astrophysics Data System (ADS)
Tarasov, Vasily E.
2016-08-01
A discretization of differential and integral operators of integer and non-integer orders is suggested. New type of differences, which are represented by infinite series, is proposed. A characteristic feature of the suggested differences is an implementation of the same algebraic properties that have the operator of differentiation (property of algebraic correspondence). Therefore the suggested differences are considered as an exact discretization of derivatives. These differences have a property of universality, which means that these operators do not depend on the form of differential equations and the parameters of these equations. The suggested differences operators allows us to have difference equations whose solutions are equal to the solutions of corresponding differential equations. The exact discretization of the derivatives of integer orders is given by the suggested differences of the same integer orders. Similarly, the exact discretization of the Riesz derivatives and integrals of integer and non-integer order is given by the proposed fractional differences of the same order.